<description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>1A6BF5E0-52FA-4304-8084-B23D52EB0F6A</documentID> <versionID>FAD7FDC9-9A95-4B19-8E9D-5EA21EDF014C</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#000080"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="MS Sans Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="System" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Script" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 5" font-family="Roman" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Modern" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="56.63622" top="42.51969" bottom="42.51969"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.000001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="mks" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="3549" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="3512" left="54" top="17.25" width="360" height="15.75" align-x="54" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">PLL Design and Simulation by Dean Banerjee</c> </inlineAttr> </f> </text> </region> <region region-id="2578" left="6" top="78.75" width="192" height="14.25" align-x="6" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ENTER THESE (yellow)...</c> </inlineAttr> </f> </text> </region> <region region-id="2604" left="6" top="104.25" width="50.25" height="13.5" align-x="19.5" align-y="114" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ϕ</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="2605" left="114" top="102.75" width="205.5" height="13.5" align-x="114" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Phase margin.<sp count="5"/>Default is 50 degrees.</c> </f> </text> </region> <region region-id="2801" left="6" top="128.25" width="60" height="13.5" align-x="22.5" align-y="138" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fc</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">kHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="2802" left="114" top="126.75" width="87.75" height="13.5" align-x="114" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Loop Bandwidth</c> </f> <f family="Arial" charset="0"> <c val="#000080">.</c> </f> </text> </region> <region region-id="2803" left="6" top="152.25" width="75.75" height="13.5" align-x="39.75" align-y="162" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:apply> <ml:mult/> <ml:real>16</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="2804" left="114" top="150.75" width="122.25" height="13.5" align-x="114" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Comparison Frequency</c> </f> </text> </region> <region region-id="2805" left="6" top="174.75" width="73.5" height="29.25" align-x="34.5" align-y="192" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kvco</ml:id> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MHz</ml:id> <ml:id xml:space="preserve">volt</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="2806" left="114" top="180.75" width="113.25" height="13.5" align-x="114" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">VCO Tuning Constant</c> </f> </text> </region> <region region-id="2807" left="6" top="212.25" width="54" height="13.5" align-x="26.25" align-y="222" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:apply> <ml:mult/> <ml:real>30</ml:real> <ml:id xml:space="preserve">μA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="2808" left="114" top="210.75" width="213.75" height="14.25" align-x="114" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Phase Detector gain do not divide by 2*</c> </f> <f family="Symbol" charset="2"> <c val="#000080">p</c> </f> </text> </region> <region region-id="2809" left="6" top="236.25" width="75.75" height="13.5" align-x="30.75" align-y="246" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fout</ml:id> <ml:apply> <ml:mult/> <ml:real>1760</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="2810" left="114" top="234.75" width="291" height="13.5" align-x="114" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">RF output frequency.<sp count="2"/>Choose equal to sqrt(Fmax*Fmin) </c> </f> </text> </region> <region region-id="2811" left="6" top="260.25" width="46.5" height="13.5" align-x="35.25" align-y="270" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>29</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="2900" left="78" top="260.25" width="9.75" height="13.5" align-x="81.75" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">%</ml:id> </math> <rendering item-idref="9"/> </region> <region region-id="2814" left="114" top="258.75" width="302.25" height="27" align-x="114" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ratio of Poles T3/T1 expressed as a percentage.<sp count="2"/>Choose from 0 to 100.<sp count="2"/>0 = second order filter.<sp count="3"/>Default is 50% </text> </region> <region region-id="2863" left="114" top="294.75" width="336.75" height="40.5" align-x="114" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set method = 0 to use a more standard set of design equations.<sp count="2"/>Set method = 1 to use the Ultimate method, which is unorthodox, but does not use any approximations </text> </region> <region region-id="2860" left="6" top="302.25" width="49.5" height="13.5" align-x="42.75" align-y="312" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">method</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="2864" left="6" top="372.75" width="283.5" height="14.25" align-x="6" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATIONS USING THE ULTIMATE METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="2504" left="12" top="390.75" width="52.5" height="29.25" align-x="26.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fout</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="2865" left="198" top="404.25" width="54.75" height="13.5" align-x="216" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="2987" left="6" top="438.75" width="129.75" height="13.5" align-x="6" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SOLVE FOR T1 AND T2 </text> </region> <region region-id="2784" left="24" top="465" width="140.25" height="64.5" align-x="47.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="2815" left="264" top="486.75" width="107.25" height="35.25" align-x="289.5" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">g</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="2816" left="6" top="546.75" width="227.25" height="13.5" align-x="6" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This finds wcT2 as a function of wcT1 ( or x ) </text> </region> <region region-id="2988" left="6" top="568.5" width="48.75" height="17.25" align-x="18" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-5</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="2818" left="6" top="597" width="429" height="45" align-x="24" align-y="630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="2901" left="6" top="648.75" width="69" height="29.25" align-x="24" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="2902" left="180" top="648.75" width="66.75" height="29.25" align-x="198" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="3396" left="354" top="658.5" width="87.75" height="17.25" align-x="370.5" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.2766991189239115E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="19"/> </region> <region region-id="3402" left="354" top="688.5" width="87.75" height="17.25" align-x="370.5" align-y="702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.256042478845037E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="3401" left="354" top="718.5" width="83.25" height="17.25" align-x="370.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.2402427444879343E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="3000" left="6" top="768.75" width="305.25" height="13.5" align-x="6" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SET UP SYSTEM OF 4 EQUATIONS AND 4 UNKNOWNS </text> </region> <region region-id="2994" left="6" top="792.75" width="241.5" height="39" align-x="22.5" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k1</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="2997" left="372" top="806.25" width="57" height="13.5" align-x="387" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">nF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.075959571032407</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="2995" left="6" top="842.25" width="80.25" height="13.5" align-x="22.5" align-y="852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k2</ml:id> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="2998" left="348" top="850.5" width="105.75" height="17.25" align-x="363" align-y="864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k2</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">nF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.1906453735549191E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="2996" left="6" top="870.75" width="67.5" height="29.25" align-x="22.5" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k3</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="2999" left="348" top="886.5" width="109.5" height="17.25" align-x="363" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k3</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">nF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>9.46655454902197E-10</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="3001" left="6" top="918.75" width="359.25" height="13.5" align-x="6" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> USE THESE EQUATIONS TO FIND THE MAXIMUM VALUE FOR k4 </text> </region> <region region-id="3005" left="6" top="946.5" width="35.25" height="17.25" align-x="19.5" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">k3</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="3009" left="360" top="952.5" width="63" height="17.25" align-x="372" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>8.961565502960855E-19</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="29"/> </region> <region region-id="3015" left="6" top="980.25" width="111.75" height="13.5" align-x="19.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">k2</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="3010" left="360" top="976.5" width="119.25" height="17.25" align-x="372" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-1.1448242717507316E-15</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="31"/> </region> <region region-id="3014" left="6" top="1000.5" width="93.75" height="17.25" align-x="19.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">k2</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="3013" left="360" top="1000.5" width="63" height="17.25" align-x="372" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>5.3198464689026492E-16</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="33"/> </region> <region region-id="3023" left="6" top="1032.75" width="123" height="35.25" align-x="36.75" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4min</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="3017" left="360" top="1046.25" width="63.75" height="13.5" align-x="389.25" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4min</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.46485588345768269</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="3024" left="6" top="1074.75" width="125.25" height="35.25" align-x="39" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4max</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="3020" left="318" top="1084.5" width="90" height="17.25" align-x="349.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4max</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1277.0176011409178</ml:real> </result> </ml:eval> </math> <rendering item-idref="37"/> </region> <region region-id="3018" left="402" top="1088.25" width="48.75" height="13.5" align-x="418.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4</ml:id> <ml:id xml:space="preserve">k4min</ml:id> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="3022" left="6" top="1128.75" width="304.5" height="13.5" align-x="6" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NOW SOLVE FOR C1 AND THE OTHER COMPONENTS </text> </region> <region region-id="3025" left="6" top="1154.25" width="70.5" height="13.5" align-x="19.5" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T2</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k4</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="3032" left="336" top="1156.5" width="83.25" height="17.25" align-x="348" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.234488865381972E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="3026" left="6" top="1172.25" width="72" height="13.5" align-x="19.5" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">k2</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k3</ml:id> <ml:id xml:space="preserve">k4</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="3029" left="330" top="1180.5" width="108" height="17.25" align-x="342" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">pF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-4.2346512093367789E-05</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="3027" left="6" top="1190.25" width="45" height="13.5" align-x="19.5" align-y="1200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k3</ml:id> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="3033" left="330" top="1216.5" width="106.5" height="17.25" align-x="342" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">pF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.1907542269859009E-05</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad" power-numerator="2"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="44"/> </region> <region region-id="3034" left="6" top="1230.75" width="156" height="13.5" align-x="6" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SOLVE FOR COMPONENTS </text> </region> <region region-id="3035" left="6" top="1254.75" width="44.25" height="29.25" align-x="24" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="3040" left="126" top="1262.25" width="51" height="13.5" align-x="144" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k4</ml:id> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="3036" left="6" top="1292.25" width="82.5" height="13.5" align-x="24" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="3041" left="126" top="1290.75" width="55.5" height="29.25" align-x="144" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">k3</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="3038" left="6" top="1320.75" width="40.5" height="29.25" align-x="24" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="3043" left="78" top="1380.75" width="291" height="14.25" align-x="78" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATIONS USING THE STANDARD METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="3046" left="264" top="1416.75" width="97.5" height="33" align-x="282" align-y="1434" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="3048" left="6" top="1407" width="110.25" height="60.75" align-x="24" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="3045" left="156" top="1422.75" width="66.75" height="29.25" align-x="174" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="3047" left="6" top="1516.5" width="230.25" height="53.25" align-x="27.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1s</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T2</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T1</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T3</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="3052" left="270" top="1536.75" width="90" height="29.25" align-x="291.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2s</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1s</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="3054" left="390" top="1536.75" width="48" height="29.25" align-x="411.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">C1s</ml:id> <ml:real>10</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="3055" left="6" top="1596.75" width="48" height="29.25" align-x="27.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">C2s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="3056" left="90" top="1596.75" width="48" height="29.25" align-x="111.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">C3s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="3059" left="18" top="1650.75" width="438.75" height="28.5" align-x="18" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ASSIGN COMPONENT VALUES BASED ON USER'S SELECTION OF EITHER THE STANDARD OR ULTIMATE METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="3060" left="6" top="1700.25" width="131.25" height="13.5" align-x="24" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C1s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="3379" left="156" top="1700.25" width="131.25" height="13.5" align-x="174" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> <ml:id xml:space="preserve">C3s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="3382" left="312" top="1700.25" width="131.25" height="13.5" align-x="330" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> <ml:id xml:space="preserve">R3s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="3061" left="6" top="1724.25" width="131.25" height="13.5" align-x="24" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C2s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="3380" left="156" top="1724.25" width="131.25" height="13.5" align-x="174" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R2s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="3066" left="96" top="1764.75" width="289.5" height="14.25" align-x="96" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">THE CALCULATED VALUES ARE SHOWN BELOW</c> </inlineAttr> </f> </text> </region> <region region-id="3073" left="66" top="1790.25" width="76.5" height="13.5" align-x="82.5" align-y="1800" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.396149468523697</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="63"/> </region> <region region-id="3496" left="216" top="1790.25" width="63" height="13.5" align-x="232.5" align-y="1800" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>70.9847015023384</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="3075" left="348" top="1790.25" width="76.5" height="13.5" align-x="364.5" align-y="1800" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.5787200615449228</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="65"/> </region> <region region-id="3076" left="144" top="1814.25" width="83.25" height="13.5" align-x="160.5" align-y="1824" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kΩ</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>59.95717934666294</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kiloohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="66"/> </region> <region region-id="3077" left="276" top="1814.25" width="87.75" height="13.5" align-x="292.5" align-y="1824" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kΩ</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>176.56312961613122</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kiloohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="67"/> </region> <region region-id="3383" left="156" top="1848.75" width="167.25" height="14.25" align-x="156" align-y="1860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ENTER PARAMETERS HERE</c> </inlineAttr> </f> </text> </region> <region region-id="3413" left="36" top="1880.25" width="42" height="13.5" align-x="56.25" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kϕ</ml:id> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="3414" left="126" top="1880.25" width="69" height="13.5" align-x="159.75" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:define> </math> <rendering item-idref="69"/> </region> <region region-id="3415" left="258" top="1880.25" width="51" height="13.5" align-x="282.75" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fout</ml:id> <ml:id xml:space="preserve">Fout</ml:id> </ml:define> </math> <rendering item-idref="70"/> </region> <region region-id="3416" left="384" top="1880.25" width="58.5" height="13.5" align-x="412.5" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kvco</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:define> </math> <rendering item-idref="71"/> </region> <region region-id="3408" left="18" top="1904.25" width="37.5" height="13.5" align-x="36" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C1</ml:id> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="3409" left="108" top="1904.25" width="37.5" height="13.5" align-x="126" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:id xml:space="preserve">R3</ml:id> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="3410" left="210" top="1904.25" width="37.5" height="13.5" align-x="228" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="3411" left="306" top="1904.25" width="37.5" height="13.5" align-x="324" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="3412" left="384" top="1904.25" width="37.5" height="13.5" align-x="402" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R2</ml:id> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="3515" left="96" top="1938.75" width="147" height="13.5" align-x="96" align-y="1950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Changes to actual loop filter: </text> </region> <region region-id="3514" left="258" top="1940.25" width="41.25" height="13.5" align-x="276" align-y="1950" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>3</ml:real> <ml:id xml:space="preserve">pF</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="3378" left="48" top="1968" width="360" height="270" align-x="48" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{64818D10-4F9B-11CF-86EA-00AA00B929E8}" type="embedded" item-idref="78"/> <rendering item-idref="79"/> </region> <region region-id="3534" left="144" top="2280.75" width="162" height="14.25" align-x="144" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATE PARAMETERS</c> </inlineAttr> </f> </text> </region> <region region-id="2565" left="36" top="2316.75" width="52.5" height="29.25" align-x="50.25" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fout</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="3121" left="150" top="2314.5" width="141" height="31.5" align-x="161.25" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ζ</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="3120" left="324" top="2314.5" width="115.5" height="31.5" align-x="342.75" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωn</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="3123" left="138" top="2372.25" width="40.5" height="13.5" align-x="150.75" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>110</ml:real> </result> </ml:eval> </math> <rendering item-idref="83"/> </region> <region region-id="2826" left="210" top="2372.25" width="44.25" height="13.5" align-x="219.75" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ζ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79901234249949</ml:real> </result> </ml:eval> </math> <rendering item-idref="84"/> </region> <region region-id="3122" left="312" top="2364.75" width="77.25" height="29.25" align-x="335.25" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ωn</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>59.758221179567549</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="85"/> </region> <region region-id="3535" left="108" top="2412.75" width="248.25" height="14.25" align-x="108" align-y="2424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATE THE TRUE POLES AND ZERO</c> </inlineAttr> </f> </text> </region> <region region-id="3148" left="384" top="2442.75" width="70.5" height="13.5" align-x="384" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is T1+T3 </text> </region> <region region-id="3324" left="6" top="2450.25" width="52.5" height="13.5" align-x="24" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="3149" left="114" top="2442.75" width="224.25" height="29.25" align-x="126" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="3141" left="6" top="2490.75" width="94.5" height="29.25" align-x="18" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="3145" left="138" top="2496.75" width="68.25" height="13.5" align-x="138" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is T1*T3 </text> </region> <region region-id="3142" left="6" top="2532.75" width="90" height="35.25" align-x="24" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="3143" left="132" top="2532.75" width="90" height="35.25" align-x="150" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="90"/> </region> <region region-id="3144" left="270" top="2546.25" width="44.25" height="13.5" align-x="294.75" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">junk</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="3150" left="6" top="2592.75" width="219.75" height="13.5" align-x="6" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Make sure that T1 and T3 are not switched </text> </region> <region region-id="3151" left="6" top="2618.25" width="108.75" height="13.5" align-x="24" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="3153" left="162" top="2618.25" width="115.5" height="13.5" align-x="180" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">junk</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="3154" left="42" top="2658.75" width="341.25" height="13.5" align-x="42" align-y="2670" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Time Constant<tab/> <tab/>Filter Pole<tab/> <tab/> <tab/>Filter Zero</c> </inlineAttr> </f> </text> </region> <region region-id="3163" left="30" top="2692.5" width="87.75" height="17.25" align-x="46.5" align-y="2706" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.2435703018964589E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="94"/> </region> <region region-id="3155" left="180" top="2694.75" width="93" height="29.25" align-x="199.5" align-y="2712" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1380.534678787044</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="95"/> </region> <region region-id="3159" left="342" top="2700.75" width="15.75" height="13.5" align-x="342" align-y="2712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3164" left="30" top="2722.5" width="87.75" height="17.25" align-x="46.5" align-y="2736" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.256042478845037E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="96"/> </region> <region region-id="3160" left="318" top="2730.75" width="73.5" height="29.25" align-x="337.5" align-y="2748" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>234.96006089473295</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="97"/> </region> <region region-id="3169" left="198" top="2742.75" width="15.75" height="13.5" align-x="198" align-y="2754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3165" left="30" top="2752.5" width="87.75" height="17.25" align-x="46.5" align-y="2766" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.3659281070761467E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="98"/> </region> <region region-id="3166" left="48" top="2784.75" width="64.5" height="29.25" align-x="67.5" align-y="2802" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>18.857111205485634</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="99"/> </region> <region region-id="3491" left="180" top="2784.75" width="93" height="29.25" align-x="199.5" align-y="2802" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7321.0295243178034</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="100"/> </region> <region region-id="3492" left="342" top="2790.75" width="15.75" height="13.5" align-x="342" align-y="2802" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3167" left="132" top="2850.75" width="169.5" height="14.25" align-x="132" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">DEFINE LOOP PARAMETERS</c> </inlineAttr> </f> </text> </region> <region region-id="3171" left="6" top="2880.75" width="231.75" height="29.25" align-x="33.75" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T2</ml:id> <ml:imag font="0" symbol="i">1</ml:imag> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="3174" left="288" top="2886.75" width="117" height="13.5" align-x="288" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Loop Filter Impedance </text> </region> <region region-id="3172" left="6" top="2928.75" width="104.25" height="29.25" align-x="35.25" align-y="2946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="102"/> </region> <region region-id="3175" left="144" top="2934.75" width="104.25" height="13.5" align-x="144" align-y="2946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Forward Loop Gain </f> </text> </region> <region region-id="3173" left="6" top="2970.75" width="87.75" height="45" align-x="40.5" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">CL</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="103"/> </region> <region region-id="3176" left="144" top="2976.75" width="95.25" height="13.5" align-x="144" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Closed Loop Gain</f> </text> </region> <region region-id="3528" left="330" top="2970.75" width="130.5" height="29.25" align-x="342" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:sequence> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="3543" left="18" top="3042" width="430.5" height="186.75" align-x="18" align-y="3042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="105"/> <rendering item-idref="106"/> </region> <region region-id="3177" left="120" top="3240.75" width="200.25" height="14.25" align-x="120" align-y="3252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">BANDWIDTH AND PHASE MARGIN</c> </inlineAttr> </f> </text> </region> <region region-id="3191" left="6" top="3278.25" width="63.75" height="13.5" align-x="19.5" align-y="3288" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ω</ml:id> <ml:apply> <ml:mult/> <ml:real>600.0</ml:real> <ml:id xml:space="preserve">kHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="107"/> </region> <region region-id="3193" left="294" top="3276.75" width="167.25" height="13.5" align-x="294" align-y="3288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Initial Guess for Loop Bandwidth </text> </region> <region region-id="3189" left="6" top="3302.25" width="114.75" height="13.5" align-x="24" align-y="3312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="108"/> </region> <region region-id="2649" left="168" top="3300.75" width="77.25" height="29.25" align-x="191.25" align-y="3318" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>94.141856690516818</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="2745" left="294" top="3306.75" width="84.75" height="13.5" align-x="294" align-y="3318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Loop Bandwidth </text> </region> <region region-id="3188" left="6" top="3344.25" width="33" height="13.5" align-x="19.5" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">ωc</ml:id> </ml:define> </math> <rendering item-idref="110"/> </region> <region region-id="3181" left="78" top="3342.75" width="160.5" height="29.25" align-x="180" align-y="3360" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">CL</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>135.09744358124655</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="111"/> </region> <region region-id="3185" left="294" top="3348.75" width="81" height="13.5" align-x="294" align-y="3360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 0 db Bandwidth </text> </region> <region region-id="3187" left="6" top="3378.75" width="172.5" height="47.25" align-x="120" align-y="3414" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">CL</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>166.63838148302654</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="2746" left="294" top="3414.75" width="81" height="13.5" align-x="294" align-y="3426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 3 db Bandwidth </text> </region> <region region-id="3201" left="6" top="3438.75" width="138.75" height="29.25" align-x="105.75" align-y="3456" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">arg</ml:id> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>180</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:real>180</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>40.523341458010151</ml:real> </result> </ml:eval> </math> <rendering item-idref="113"/> </region> <region region-id="2875" left="294" top="3444.75" width="72.75" height="13.5" align-x="294" align-y="3456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Phase Margin </text> </region> <region region-id="2836" left="30" top="3504.75" width="390.75" height="14.25" align-x="30" align-y="3516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ADDED SPURIOUS ATTENUATION ( THIRD ORDER FILTERS ONLY )</c> </inlineAttr> </f> </text> </region> <region region-id="3203" left="66" top="3525" width="291" height="36.75" align-x="105.75" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">spur</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="114"/> </region> <region region-id="2680" left="42" top="3578.25" width="116.25" height="13.5" align-x="119.25" align-y="3588" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">spur</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>21.518471236644288</ml:real> </result> </ml:eval> </math> <rendering item-idref="115"/> </region> <region region-id="3336" left="210" top="3576.75" width="235.5" height="13.5" align-x="210" align-y="3588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Additional Reference freq (Fc) Atteunation </text> </region> <region region-id="2686" left="42" top="3606.75" width="126" height="29.25" align-x="133.5" align-y="3624" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">spur</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>9.8115863742663763</ml:real> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="3334" left="210" top="3612.75" width="97.5" height="13.5" align-x="210" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Attenuation at Fc/4 </text> </region> <region region-id="3215" left="84" top="3666.75" width="274.5" height="14.25" align-x="84" align-y="3678" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">OPTIMIZATION INDEX ( 100% = Most Optimized )</c> </inlineAttr> </f> </text> </region> <region region-id="3206" left="12" top="3687" width="173.25" height="64.5" align-x="43.5" align-y="3720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="3207" left="246" top="3702.75" width="162" height="29.25" align-x="277.5" align-y="3720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">Index</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Index</ml:id> </ml:apply> <ml:id xml:space="preserve">Index</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="118"/> </region> <region region-id="3208" left="150" top="3764.25" width="75" height="13.5" align-x="180" align-y="3774" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>77.572458349370081</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="119"/> </region> <region region-id="2712" left="240" top="3762.75" width="206.25" height="13.5" align-x="240" align-y="3774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is the Optimization Index in Percent </text> </region> <region region-id="3526" left="168" top="3798.75" width="125.25" height="14.25" align-x="168" align-y="3810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">DISPLAY BODE PLOT</c> </inlineAttr> </f> </text> </region> <region region-id="3213" left="12" top="3822" width="432" height="215.25" align-x="12" align-y="3822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="120"/> <rendering item-idref="121"/> </region> <region region-id="3219" left="102" top="4050.75" width="279.75" height="14.25" align-x="102" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">PHASE NOISE PROFILE FOR A NOISELESS VCO</c> </inlineAttr> </f> </text> </region> <region region-id="3222" left="282" top="4080.75" width="173.25" height="27" align-x="282" align-y="4092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 1 Hz Normalized Phase Detector Phase Noise, max typically -207 </text> </region> <region region-id="3226" left="6" top="4088.25" width="75" height="13.5" align-x="54" align-y="4098" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Noise1Hz</ml:id> <ml:real>-202</ml:real> </ml:define> </math> <rendering item-idref="122"/> </region> <region region-id="3230" left="120" top="4086.75" width="36" height="13.5" align-x="120" align-y="4098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dbc/Hz </text> </region> <region region-id="3225" left="6" top="4116.75" width="180.75" height="29.25" align-x="58.5" align-y="4134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">NoiseFloor</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">Noise1Hz</ml:id> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="3227" left="6" top="4160.25" width="99.75" height="13.5" align-x="57" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">NoiseFloor</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-129.95880017344075</ml:real> </result> </ml:eval> </math> <rendering item-idref="124"/> </region> <region region-id="3228" left="120" top="4158.75" width="36" height="13.5" align-x="120" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dbc/Hz </text> </region> <region region-id="3233" left="282" top="4158.75" width="143.25" height="13.5" align-x="282" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Noise Floor of PLL (in loop) </text> </region> <region region-id="3231" left="6" top="4190.25" width="148.5" height="13.5" align-x="110.25" align-y="4200" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">NoiseFloor</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-89.130946470276257</ml:real> </result> </ml:eval> </math> <rendering item-idref="125"/> </region> <region region-id="3232" left="168" top="4188.75" width="36" height="13.5" align-x="168" align-y="4200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dbc/Hz </text> </region> <region region-id="3234" left="282" top="4188.75" width="104.25" height="13.5" align-x="282" align-y="4200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> In loop Phase Noise </text> </region> <region region-id="3236" left="282" top="4242.75" width="92.25" height="13.5" align-x="282" align-y="4254" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> RMS Phase Error </text> </region> <region region-id="3235" left="12" top="4223.25" width="233.25" height="51.75" align-x="198" align-y="4260" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real font="0">2</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id 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Mathcad Professional 14.0 <description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>1A6BF5E0-52FA-4304-8084-B23D52EB0F6A</documentID> <versionID>FAD7FDC9-9A95-4B19-8E9D-5EA21EDF014C</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#000080"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" 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font-style="normal" underline="false"/> <mathStyle name="User 5" font-family="Roman" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Modern" font-charset="255" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="MS Serif" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="9" orientation="portrait" print-single-page-width="false" page-width="595.5" page-height="842.25"> <margins left="56.63622" right="56.63622" top="42.51969" bottom="42.51969"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.000001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false" zero-over-zero="0"> <compatibility multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="mks" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="3549" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="3512" left="54" top="17.25" width="360" height="15.75" align-x="54" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">PLL Design and Simulation by Dean Banerjee</c> </inlineAttr> </f> </text> </region> <region region-id="2578" left="6" top="78.75" width="192" height="14.25" align-x="6" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ENTER THESE (yellow)...</c> </inlineAttr> </f> </text> </region> <region region-id="2604" left="6" top="104.25" width="50.25" height="13.5" align-x="19.5" align-y="114" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ϕ</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="2605" left="114" top="102.75" width="205.5" height="13.5" align-x="114" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Phase margin.<sp count="5"/>Default is 50 degrees.</c> </f> </text> </region> <region region-id="2801" left="6" top="128.25" width="60" height="13.5" align-x="22.5" align-y="138" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fc</ml:id> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">kHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="2802" left="114" top="126.75" width="87.75" height="13.5" align-x="114" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Loop Bandwidth</c> </f> <f family="Arial" charset="0"> <c val="#000080">.</c> </f> </text> </region> <region region-id="2803" left="6" top="152.25" width="75.75" height="13.5" align-x="39.75" align-y="162" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:apply> <ml:mult/> <ml:real>16</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="2804" left="114" top="150.75" width="122.25" height="13.5" align-x="114" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Comparison Frequency</c> </f> </text> </region> <region region-id="2805" left="6" top="174.75" width="73.5" height="29.25" align-x="34.5" align-y="192" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kvco</ml:id> <ml:apply> <ml:mult/> <ml:real>40</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">MHz</ml:id> <ml:id xml:space="preserve">volt</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="2806" left="114" top="180.75" width="113.25" height="13.5" align-x="114" align-y="192" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">VCO Tuning Constant</c> </f> </text> </region> <region region-id="2807" left="6" top="212.25" width="54" height="13.5" align-x="26.25" align-y="222" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:apply> <ml:mult/> <ml:real>30</ml:real> <ml:id xml:space="preserve">μA</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="2808" left="114" top="210.75" width="213.75" height="14.25" align-x="114" align-y="222" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">Phase Detector gain do not divide by 2*</c> </f> <f family="Symbol" charset="2"> <c val="#000080">p</c> </f> </text> </region> <region region-id="2809" left="6" top="236.25" width="75.75" height="13.5" align-x="30.75" align-y="246" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fout</ml:id> <ml:apply> <ml:mult/> <ml:real>1760</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="2810" left="114" top="234.75" width="291" height="13.5" align-x="114" align-y="246" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <c val="#000080">RF output frequency.<sp count="2"/>Choose equal to sqrt(Fmax*Fmin) </c> </f> </text> </region> <region region-id="2811" left="6" top="260.25" width="46.5" height="13.5" align-x="35.25" align-y="270" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>29</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="2900" left="78" top="260.25" width="9.75" height="13.5" align-x="81.75" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math30">%</ml:id> </math> <rendering item-idref="9"/> </region> <region region-id="2814" left="114" top="258.75" width="302.25" height="27" align-x="114" align-y="270" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Ratio of Poles T3/T1 expressed as a percentage.<sp count="2"/>Choose from 0 to 100.<sp count="2"/>0 = second order filter.<sp count="3"/>Default is 50% </text> </region> <region region-id="2863" left="114" top="294.75" width="336.75" height="40.5" align-x="114" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Set method = 0 to use a more standard set of design equations.<sp count="2"/>Set method = 1 to use the Ultimate method, which is unorthodox, but does not use any approximations </text> </region> <region region-id="2860" left="6" top="302.25" width="49.5" height="13.5" align-x="42.75" align-y="312" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">method</ml:id> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="2864" left="6" top="372.75" width="283.5" height="14.25" align-x="6" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATIONS USING THE ULTIMATE METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="2504" left="12" top="390.75" width="52.5" height="29.25" align-x="26.25" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fout</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="2865" left="198" top="404.25" width="54.75" height="13.5" align-x="216" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="2987" left="6" top="438.75" width="129.75" height="13.5" align-x="6" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SOLVE FOR T1 AND T2 </text> </region> <region region-id="2784" left="24" top="465" width="140.25" height="64.5" align-x="47.25" align-y="498" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="2815" left="264" top="486.75" width="107.25" height="35.25" align-x="289.5" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">g</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:pow/> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="2816" left="6" top="546.75" width="227.25" height="13.5" align-x="6" align-y="558" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This finds wcT2 as a function of wcT1 ( or x ) </text> </region> <region region-id="2988" left="6" top="568.5" width="48.75" height="17.25" align-x="18" align-y="582" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-5</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="2818" left="6" top="597" width="429" height="45" align-x="24" align-y="630" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:id xml:space="preserve">x</ml:id> </ml:sequence> </ml:apply> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="2901" left="6" top="648.75" width="69" height="29.25" align-x="24" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="2902" left="180" top="648.75" width="66.75" height="29.25" align-x="198" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="3396" left="354" top="658.5" width="87.75" height="17.25" align-x="370.5" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.2766991189239115E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="19"/> </region> <region region-id="3402" left="354" top="688.5" width="87.75" height="17.25" align-x="370.5" align-y="702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.256042478845037E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="3401" left="354" top="718.5" width="83.25" height="17.25" align-x="370.5" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.2402427444879343E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="3000" left="6" top="768.75" width="305.25" height="13.5" align-x="6" align-y="780" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SET UP SYSTEM OF 4 EQUATIONS AND 4 UNKNOWNS </text> </region> <region region-id="2994" left="6" top="792.75" width="241.5" height="39" align-x="22.5" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k1</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="2997" left="372" top="806.25" width="57" height="13.5" align-x="387" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">nF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>0.075959571032407</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="23"/> </region> <region region-id="2995" left="6" top="842.25" width="80.25" height="13.5" align-x="22.5" align-y="852" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k2</ml:id> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="2998" left="348" top="850.5" width="105.75" height="17.25" align-x="363" align-y="864" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k2</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">nF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.1906453735549191E-08</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="2996" left="6" top="870.75" width="67.5" height="29.25" align-x="22.5" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k3</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="2999" left="348" top="886.5" width="109.5" height="17.25" align-x="363" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k3</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">nF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>9.46655454902197E-10</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="27"/> </region> <region region-id="3001" left="6" top="918.75" width="359.25" height="13.5" align-x="6" align-y="930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> USE THESE EQUATIONS TO FIND THE MAXIMUM VALUE FOR k4 </text> </region> <region region-id="3005" left="6" top="946.5" width="35.25" height="17.25" align-x="19.5" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">k3</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="3009" left="360" top="952.5" width="63" height="17.25" align-x="372" align-y="966" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>8.961565502960855E-19</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="29"/> </region> <region region-id="3015" left="6" top="980.25" width="111.75" height="13.5" align-x="19.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">k2</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="3010" left="360" top="976.5" width="119.25" height="17.25" align-x="372" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-1.1448242717507316E-15</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="31"/> </region> <region region-id="3014" left="6" top="1000.5" width="93.75" height="17.25" align-x="19.5" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">k2</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:id xml:space="preserve">k3</ml:id> </ml:apply> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="3013" left="360" top="1000.5" width="63" height="17.25" align-x="372" align-y="1014" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">nF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>5.3198464689026492E-16</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="nanofarad" power-numerator="2"/> <unitReference unit="second" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="33"/> </region> <region region-id="3023" left="6" top="1032.75" width="123" height="35.25" align-x="36.75" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4min</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="3017" left="360" top="1046.25" width="63.75" height="13.5" align-x="389.25" align-y="1056" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4min</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.46485588345768269</ml:real> </result> </ml:eval> </math> <rendering item-idref="35"/> </region> <region region-id="3024" left="6" top="1074.75" width="125.25" height="35.25" align-x="39" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4max</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">B</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:id xml:space="preserve">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="3020" left="318" top="1084.5" width="90" height="17.25" align-x="349.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4max</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1277.0176011409178</ml:real> </result> </ml:eval> </math> <rendering item-idref="37"/> </region> <region region-id="3018" left="402" top="1088.25" width="48.75" height="13.5" align-x="418.5" align-y="1098" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k4</ml:id> <ml:id xml:space="preserve">k4min</ml:id> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="3022" left="6" top="1128.75" width="304.5" height="13.5" align-x="6" align-y="1140" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NOW SOLVE FOR C1 AND THE OTHER COMPONENTS </text> </region> <region region-id="3025" left="6" top="1154.25" width="70.5" height="13.5" align-x="19.5" align-y="1164" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T2</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">k4</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="3032" left="336" top="1156.5" width="83.25" height="17.25" align-x="348" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>6.234488865381972E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="3026" left="6" top="1172.25" width="72" height="13.5" align-x="19.5" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">k2</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k3</ml:id> <ml:id xml:space="preserve">k4</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="3029" left="330" top="1180.5" width="108" height="17.25" align-x="342" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">B</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:id xml:space="preserve">pF</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>-4.2346512093367789E-05</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="3027" left="6" top="1190.25" width="45" height="13.5" align-x="19.5" align-y="1200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k3</ml:id> <ml:id xml:space="preserve">k1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="3033" left="330" top="1216.5" width="106.5" height="17.25" align-x="342" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C</ml:id> <ml:unitOverride> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">sec</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">pF</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.1907542269859009E-05</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad" power-numerator="2"/> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="44"/> </region> <region region-id="3034" left="6" top="1230.75" width="156" height="13.5" align-x="6" align-y="1242" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> SOLVE FOR COMPONENTS </text> </region> <region region-id="3035" left="6" top="1254.75" width="44.25" height="29.25" align-x="24" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve">B</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">A</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="3040" left="126" top="1262.25" width="51" height="13.5" align-x="144" align-y="1272" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">k4</ml:id> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="46"/> </region> <region region-id="3036" left="6" top="1292.25" width="82.5" height="13.5" align-x="24" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="3041" left="126" top="1290.75" width="55.5" height="29.25" align-x="144" align-y="1308" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">k3</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="3038" left="6" top="1320.75" width="40.5" height="29.25" align-x="24" align-y="1338" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="3043" left="78" top="1380.75" width="291" height="14.25" align-x="78" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATIONS USING THE STANDARD METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="3046" left="264" top="1416.75" width="97.5" height="33" align-x="282" align-y="1434" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="3048" left="6" top="1407" width="110.25" height="60.75" align-x="24" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:id xml:space="preserve">tan</ml:id> <ml:id xml:space="preserve">ϕ</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="3045" left="156" top="1422.75" width="66.75" height="29.25" align-x="174" align-y="1440" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3T1</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="52"/> </region> <region region-id="3047" left="6" top="1516.5" width="230.25" height="53.25" align-x="27.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1s</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T2</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T1</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ωc</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">T3</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="3052" left="270" top="1536.75" width="90" height="29.25" align-x="291.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2s</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1s</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="54"/> </region> <region region-id="3054" left="390" top="1536.75" width="48" height="29.25" align-x="411.75" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">C1s</ml:id> <ml:real>10</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="55"/> </region> <region region-id="3055" left="6" top="1596.75" width="48" height="29.25" align-x="27.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:id xml:space="preserve">C2s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="3056" left="90" top="1596.75" width="48" height="29.25" align-x="111.75" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3s</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">C3s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="3059" left="18" top="1650.75" width="438.75" height="28.5" align-x="18" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ASSIGN COMPONENT VALUES BASED ON USER'S SELECTION OF EITHER THE STANDARD OR ULTIMATE METHOD</c> </inlineAttr> </f> </text> </region> <region region-id="3060" left="6" top="1700.25" width="131.25" height="13.5" align-x="24" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C1s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="3379" left="156" top="1700.25" width="131.25" height="13.5" align-x="174" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> <ml:id xml:space="preserve">C3s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="3382" left="312" top="1700.25" width="131.25" height="13.5" align-x="330" align-y="1710" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> <ml:id xml:space="preserve">R3s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="3061" left="6" top="1724.25" width="131.25" height="13.5" align-x="24" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C2s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="61"/> </region> <region region-id="3380" left="156" top="1724.25" width="131.25" height="13.5" align-x="174" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">method</ml:id> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R2s</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="3066" left="96" top="1764.75" width="289.5" height="14.25" align-x="96" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">THE CALCULATED VALUES ARE SHOWN BELOW</c> </inlineAttr> </f> </text> </region> <region region-id="3073" left="66" top="1790.25" width="76.5" height="13.5" align-x="82.5" align-y="1800" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>3.396149468523697</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference 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<unitedValue> <ml:real>70.9847015023384</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="64"/> </region> <region region-id="3075" left="348" top="1790.25" width="76.5" height="13.5" align-x="364.5" align-y="1800" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">pF</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.5787200615449228</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="picofarad"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="65"/> </region> <region region-id="3076" left="144" top="1814.25" width="83.25" height="13.5" align-x="160.5" align-y="1824" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kΩ</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>59.95717934666294</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kiloohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="66"/> </region> <region region-id="3077" left="276" top="1814.25" width="87.75" height="13.5" align-x="292.5" align-y="1824" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">kΩ</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>176.56312961613122</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kiloohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="7" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="67"/> </region> <region region-id="3383" left="156" top="1848.75" width="167.25" height="14.25" align-x="156" align-y="1860" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ENTER PARAMETERS HERE</c> </inlineAttr> </f> </text> </region> <region region-id="3413" left="36" top="1880.25" width="42" height="13.5" align-x="56.25" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kϕ</ml:id> </ml:define> </math> <rendering item-idref="68"/> </region> <region region-id="3414" left="126" top="1880.25" width="69" height="13.5" align-x="159.75" align-y="1890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:define> </math> <rendering item-idref="69"/> </region> 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align-x="36" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C1</ml:id> </ml:define> </math> <rendering item-idref="72"/> </region> <region region-id="3409" left="108" top="1904.25" width="37.5" height="13.5" align-x="126" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R3</ml:id> <ml:id xml:space="preserve">R3</ml:id> </ml:define> </math> <rendering item-idref="73"/> </region> <region region-id="3410" left="210" top="1904.25" width="37.5" height="13.5" align-x="228" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="3411" left="306" top="1904.25" width="37.5" height="13.5" align-x="324" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="3412" left="384" top="1904.25" width="37.5" height="13.5" align-x="402" align-y="1914" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R2</ml:id> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="3515" left="96" top="1938.75" width="147" height="13.5" align-x="96" align-y="1950" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Changes to actual loop filter: </text> </region> <region region-id="3514" left="258" top="1940.25" width="41.25" height="13.5" align-x="276" align-y="1950" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">C3</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>3</ml:real> <ml:id xml:space="preserve">pF</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="3378" left="48" top="1968" width="360" height="270" align-x="48" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{64818D10-4F9B-11CF-86EA-00AA00B929E8}" type="embedded" item-idref="78"/> <rendering item-idref="79"/> </region> <region region-id="3534" left="144" top="2280.75" width="162" height="14.25" align-x="144" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATE PARAMETERS</c> </inlineAttr> </f> </text> </region> <region region-id="2565" left="36" top="2316.75" width="52.5" height="29.25" align-x="50.25" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fout</ml:id> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="80"/> </region> <region region-id="3121" left="150" top="2314.5" width="141" height="31.5" align-x="161.25" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ζ</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="81"/> </region> <region region-id="3120" left="324" top="2314.5" width="115.5" height="31.5" align-x="342.75" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωn</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="82"/> </region> <region region-id="3123" left="138" top="2372.25" width="40.5" height="13.5" align-x="150.75" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>110</ml:real> </result> </ml:eval> </math> <rendering item-idref="83"/> </region> <region region-id="2826" left="210" top="2372.25" width="44.25" height="13.5" align-x="219.75" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ζ</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.79901234249949</ml:real> </result> </ml:eval> </math> <rendering item-idref="84"/> </region> <region region-id="3122" left="312" top="2364.75" width="77.25" height="29.25" align-x="335.25" align-y="2382" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ωn</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>59.758221179567549</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="85"/> </region> <region region-id="3535" left="108" top="2412.75" width="248.25" height="14.25" align-x="108" align-y="2424" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">CALCULATE THE TRUE POLES AND ZERO</c> </inlineAttr> </f> </text> </region> <region region-id="3148" left="384" top="2442.75" width="70.5" height="13.5" align-x="384" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is T1+T3 </text> </region> <region region-id="3324" left="6" top="2450.25" width="52.5" height="13.5" align-x="24" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="86"/> </region> <region region-id="3149" left="114" top="2442.75" width="224.25" height="29.25" align-x="126" align-y="2460" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">R2</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">C2</ml:id> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="87"/> </region> <region region-id="3141" left="6" top="2490.75" width="94.5" height="29.25" align-x="18" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">y</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">R3</ml:id> </ml:apply> <ml:id xml:space="preserve">C1</ml:id> </ml:apply> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="88"/> </region> <region region-id="3145" left="138" top="2496.75" width="68.25" height="13.5" align-x="138" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is T1*T3 </text> </region> <region region-id="3142" left="6" top="2532.75" width="90" height="35.25" align-x="24" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="89"/> </region> <region region-id="3143" left="132" top="2532.75" width="90" height="35.25" align-x="150" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:id xml:space="preserve">y</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="90"/> </region> <region region-id="3144" left="270" top="2546.25" width="44.25" height="13.5" align-x="294.75" align-y="2556" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">junk</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:define> </math> <rendering item-idref="91"/> </region> <region region-id="3150" left="6" top="2592.75" width="219.75" height="13.5" align-x="6" align-y="2604" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Make sure that T1 and T3 are not switched </text> </region> <region region-id="3151" left="6" top="2618.25" width="108.75" height="13.5" align-x="24" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="92"/> </region> <region region-id="3153" left="162" top="2618.25" width="115.5" height="13.5" align-x="180" align-y="2628" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:id xml:space="preserve">junk</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="93"/> </region> <region region-id="3154" left="42" top="2658.75" width="341.25" height="13.5" align-x="42" align-y="2670" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Time Constant<tab/> <tab/>Filter Pole<tab/> <tab/> <tab/>Filter Zero</c> </inlineAttr> </f> </text> </region> <region region-id="3163" left="30" top="2692.5" width="87.75" height="17.25" align-x="46.5" align-y="2706" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T1</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7.2435703018964589E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="94"/> </region> <region region-id="3155" left="180" top="2694.75" width="93" height="29.25" align-x="199.5" align-y="2712" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1380.534678787044</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="95"/> </region> <region region-id="3159" left="342" top="2700.75" width="15.75" height="13.5" align-x="342" align-y="2712" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3164" left="30" top="2722.5" width="87.75" height="17.25" align-x="46.5" align-y="2736" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T2</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>4.256042478845037E-06</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="96"/> </region> <region region-id="3160" left="318" top="2730.75" width="73.5" height="29.25" align-x="337.5" align-y="2748" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>234.96006089473295</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="97"/> </region> <region region-id="3169" left="198" top="2742.75" width="15.75" height="13.5" align-x="198" align-y="2754" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3165" left="30" top="2752.5" width="87.75" height="17.25" align-x="46.5" align-y="2766" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">T3</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>1.3659281070761467E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="98"/> </region> <region region-id="3166" left="48" top="2784.75" width="64.5" height="29.25" align-x="67.5" align-y="2802" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>18.857111205485634</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="99"/> </region> <region region-id="3491" left="180" top="2784.75" width="93" height="29.25" align-x="199.5" align-y="2802" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>7321.0295243178034</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="100"/> </region> <region region-id="3492" left="342" top="2790.75" width="15.75" height="13.5" align-x="342" align-y="2802" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> n/a </text> </region> <region region-id="3167" left="132" top="2850.75" width="169.5" height="14.25" align-x="132" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">DEFINE LOOP PARAMETERS</c> </inlineAttr> </f> </text> </region> <region region-id="3171" left="6" top="2880.75" width="231.75" height="29.25" align-x="33.75" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">Z</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">T2</ml:id> <ml:imag font="0" symbol="i">1</ml:imag> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">C1</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> <ml:id xml:space="preserve">C3</ml:id> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="101"/> </region> <region region-id="3174" left="288" top="2886.75" width="117" height="13.5" align-x="288" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Loop Filter Impedance </text> </region> <region region-id="3172" left="6" top="2928.75" width="104.25" height="29.25" align-x="35.25" align-y="2946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">G</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">Kϕ</ml:id> <ml:id xml:space="preserve">Kvco</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">Z</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:imag symbol="i">1</ml:imag> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="102"/> </region> <region region-id="3175" left="144" top="2934.75" width="104.25" height="13.5" align-x="144" align-y="2946" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Forward Loop Gain </f> </text> </region> <region region-id="3173" left="6" top="2970.75" width="87.75" height="45" align-x="40.5" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">CL</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="103"/> </region> <region region-id="3176" left="144" top="2976.75" width="95.25" height="13.5" align-x="144" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Closed Loop Gain</f> </text> </region> <region region-id="3528" left="330" top="2970.75" width="130.5" height="29.25" align-x="342" align-y="2988" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:sequence> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>100</ml:real> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="104"/> </region> <region region-id="3543" left="18" top="3042" width="430.5" height="186.75" align-x="18" align-y="3042" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="105"/> <rendering item-idref="106"/> </region> <region region-id="3177" left="120" top="3240.75" width="200.25" height="14.25" align-x="120" align-y="3252" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">BANDWIDTH AND PHASE MARGIN</c> </inlineAttr> </f> </text> </region> <region region-id="3191" left="6" top="3278.25" width="63.75" height="13.5" align-x="19.5" align-y="3288" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ω</ml:id> <ml:apply> <ml:mult/> <ml:real>600.0</ml:real> <ml:id xml:space="preserve">kHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="107"/> </region> <region region-id="3193" left="294" top="3276.75" width="167.25" height="13.5" align-x="294" align-y="3288" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Initial Guess for Loop Bandwidth </text> </region> <region region-id="3189" left="6" top="3302.25" width="114.75" height="13.5" align-x="24" align-y="3312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="108"/> </region> <region region-id="2649" left="168" top="3300.75" width="77.25" height="29.25" align-x="191.25" align-y="3318" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ωc</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>94.141856690516818</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="109"/> </region> <region region-id="2745" left="294" top="3306.75" width="84.75" height="13.5" align-x="294" align-y="3318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Loop Bandwidth </text> </region> <region region-id="3188" left="6" top="3344.25" width="33" height="13.5" align-x="19.5" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">ωc</ml:id> </ml:define> </math> <rendering item-idref="110"/> </region> <region region-id="3181" left="78" top="3342.75" width="160.5" height="29.25" align-x="180" align-y="3360" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">CL</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>135.09744358124655</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="111"/> </region> <region region-id="3185" left="294" top="3348.75" width="81" height="13.5" align-x="294" align-y="3360" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 0 db Bandwidth </text> </region> <region region-id="3187" left="6" top="3378.75" width="172.5" height="47.25" align-x="120" align-y="3414" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:apply> <ml:id xml:space="preserve">root</ml:id> <ml:sequence> <ml:apply> <ml:minus/> <ml:apply> <ml:absval/> <ml:apply> <ml:id xml:space="preserve">CL</ml:id> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:sqrt/> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ω</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">kHz</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>166.63838148302654</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="kilohertz"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="112"/> </region> <region region-id="2746" left="294" top="3414.75" width="81" height="13.5" align-x="294" align-y="3426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 3 db Bandwidth </text> </region> <region region-id="3201" left="6" top="3438.75" width="138.75" height="29.25" align-x="105.75" align-y="3456" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:id xml:space="preserve">arg</ml:id> <ml:apply> <ml:id xml:space="preserve">G</ml:id> <ml:id xml:space="preserve">ωc</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>180</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:real>180</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>40.523341458010151</ml:real> </result> </ml:eval> </math> <rendering item-idref="113"/> </region> <region region-id="2875" left="294" top="3444.75" width="72.75" height="13.5" align-x="294" align-y="3456" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Phase Margin </text> </region> <region region-id="2836" left="30" top="3504.75" width="390.75" height="14.25" align-x="30" align-y="3516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">ADDED SPURIOUS ATTENUATION ( THIRD ORDER FILTERS ONLY )</c> </inlineAttr> </f> </text> </region> <region region-id="3203" left="66" top="3525" width="291" height="36.75" align-x="105.75" align-y="3546" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">spur</ml:id> <ml:boundVars> <ml:id xml:space="preserve">ω</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">T1</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ω</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="114"/> </region> <region region-id="2680" left="42" top="3578.25" width="116.25" height="13.5" align-x="119.25" align-y="3588" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">spur</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>21.518471236644288</ml:real> </result> </ml:eval> </math> <rendering item-idref="115"/> </region> <region region-id="3336" left="210" top="3576.75" width="235.5" height="13.5" align-x="210" align-y="3588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Additional Reference freq (Fc) Atteunation </text> </region> <region region-id="2686" left="42" top="3606.75" width="126" height="29.25" align-x="133.5" align-y="3624" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">spur</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>4</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">Fcomp</ml:id> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>9.8115863742663763</ml:real> </result> </ml:eval> </math> <rendering item-idref="116"/> </region> <region region-id="3334" left="210" top="3612.75" width="97.5" height="13.5" align-x="210" align-y="3624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Attenuation at Fc/4 </text> </region> <region region-id="3215" left="84" top="3666.75" width="274.5" height="14.25" align-x="84" align-y="3678" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">OPTIMIZATION INDEX ( 100% = Most Optimized )</c> </inlineAttr> </f> </text> </region> <region region-id="3206" left="12" top="3687" width="173.25" height="64.5" align-x="43.5" align-y="3720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T2</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T2</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T1</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T1</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">T3</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ωc</ml:id> <ml:id xml:space="preserve">T3</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="117"/> </region> <region region-id="3207" left="246" top="3702.75" width="162" height="29.25" align-x="277.5" align-y="3720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:apply> <ml:id xml:space="preserve">if</ml:id> <ml:sequence> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">Index</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Index</ml:id> </ml:apply> <ml:id xml:space="preserve">Index</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="118"/> </region> <region region-id="3208" left="150" top="3764.25" width="75" height="13.5" align-x="180" align-y="3774" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">Index</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">%</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>77.572458349370081</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="119"/> </region> <region region-id="2712" left="240" top="3762.75" width="206.25" height="13.5" align-x="240" align-y="3774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> This is the Optimization Index in Percent </text> </region> <region region-id="3526" left="168" top="3798.75" width="125.25" height="14.25" align-x="168" align-y="3810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">DISPLAY BODE PLOT</c> </inlineAttr> </f> </text> </region> <region region-id="3213" left="12" top="3822" width="432" height="215.25" align-x="12" align-y="3822" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="120"/> <rendering item-idref="121"/> </region> <region region-id="3219" left="102" top="4050.75" width="279.75" height="14.25" align-x="102" align-y="4062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">PHASE NOISE PROFILE FOR A NOISELESS VCO</c> </inlineAttr> </f> </text> </region> <region region-id="3222" left="282" top="4080.75" width="173.25" height="27" align-x="282" align-y="4092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> 1 Hz Normalized Phase Detector Phase Noise, max typically -207 </text> </region> <region region-id="3226" left="6" top="4088.25" width="75" height="13.5" align-x="54" align-y="4098" show-border="false" 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<ml:apply> <ml:plus/> <ml:id xml:space="preserve">Noise1Hz</ml:id> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Fcomp</ml:id> <ml:id xml:space="preserve">Hz</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="123"/> </region> <region region-id="3227" left="6" top="4160.25" width="99.75" height="13.5" align-x="57" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">NoiseFloor</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-129.95880017344075</ml:real> </result> </ml:eval> </math> <rendering item-idref="124"/> </region> <region region-id="3228" left="120" top="4158.75" width="36" height="13.5" align-x="120" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dbc/Hz </text> </region> <region region-id="3233" left="282" top="4158.75" width="143.25" height="13.5" align-x="282" align-y="4170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Noise Floor of PLL (in loop) </text> </region> <region region-id="3231" left="6" top="4190.25" width="148.5" height="13.5" align-x="110.25" align-y="4200" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">NoiseFloor</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-89.130946470276257</ml:real> </result> </ml:eval> </math> <rendering item-idref="125"/> </region> <region region-id="3232" left="168" top="4188.75" width="36" height="13.5" align-x="168" align-y="4200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> dbc/Hz </text> </region> <region region-id="3234" left="282" top="4188.75" width="104.25" height="13.5" align-x="282" align-y="4200" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> In loop Phase Noise </text> </region> 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is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">f2</ml:id> <ml:apply> <ml:mult/> <ml:real>1760</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="129"/> </region> <region region-id="3255" left="90" top="4578.75" width="83.25" height="13.5" align-x="90" align-y="4590" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Final Frequency</f> </text> </region> <region region-id="3254" left="270" top="4580.25" width="65.25" height="13.5" align-x="284.25" align-y="4590" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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xml:space="preserve">sec</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">den3</ml:id> <ml:id xml:space="preserve">den4</ml:id> </ml:apply> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="141"/> </region> <region region-id="3270" left="186" top="4836.75" width="86.25" height="100.5" align-x="196.5" align-y="4890" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="5" cols="1"> <ml:real>1.4248676888550065E+24</ml:real> <ml:real>6.0642974105006623E+18</ml:real> <ml:real>10106935142744.547</ml:real> <ml:real>8701564.20310485</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="142"/> </region> <region region-id="3271" left="6" top="4990.5" width="100.5" height="17.25" align-x="18" align-y="5004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:polyroots method="laguerre"/> <ml:id xml:space="preserve">v</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">sec</ml:id> <ml:real>-1</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="143"/> </region> <region region-id="3273" left="348" top="4992.75" width="102.75" height="13.5" align-x="348" align-y="5004" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">These are the poles</f> </text> </region> <region region-id="3272" left="156" top="4971.75" width="162.75" height="82.5" align-x="166.5" align-y="5016" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">p</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="4" cols="1"> <ml:real>-7450880.0340222511</ml:real> <ml:real>-445054.84857578727</ml:real> <ml:complex> <ml:real>-402814.66025384195</ml:real> <ml:imag>-517134.94631275767</ml:imag> </ml:complex> <ml:complex> <ml:real>-402814.66025296907</ml:real> <ml:imag>517134.94631269376</ml:imag> </ml:complex> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="144"/> </region> <region region-id="3276" left="6" top="5066.25" width="153" height="41.25" align-x="23.25" align-y="5094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">num0</ml:id> <ml:id xml:space="preserve">den4</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="145"/> </region> <region region-id="3277" left="198" top="5080.5" width="94.5" height="18.75" align-x="213.75" align-y="5094" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>0</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:complex> <ml:real>407233619146.89514</ml:real> <ml:imag>0.0073559468684679516</ml:imag> </ml:complex> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second" power-numerator="-2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="146"/> </region> <region region-id="3275" left="6" top="5120.25" width="153" height="41.25" align-x="23.25" align-y="5148" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">num0</ml:id> <ml:id 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tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">num0</ml:id> <ml:id xml:space="preserve">den4</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="149"/> </region> <region region-id="3281" left="198" top="5188.5" width="164.25" height="18.75" align-x="213.75" align-y="5202" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>2</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:complex> <ml:real>37570086385336.57</ml:real> <ml:imag>-310293768823.61566</ml:imag> </ml:complex> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second" power-numerator="-2"/> </unitMonomial> 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xml:space="preserve">p</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="151"/> </region> <region region-id="3283" left="198" top="5242.5" width="164.25" height="18.75" align-x="213.75" align-y="5256" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>3</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:complex> <ml:real>37570086385330.383</ml:real> <ml:imag>310293768951.03882</ml:imag> </ml:complex> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second" power-numerator="-2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="152"/> </region> <region region-id="3284" left="6" top="5304.75" width="80.25" height="13.5" align-x="6" align-y="5316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">4 Pole Analysis</f> </text> </region> <region region-id="3290" left="6" top="5330.25" width="51" height="13.5" align-x="18" align-y="5340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>4000</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="153"/> </region> <region region-id="3320" left="90" top="5330.25" width="34.5" height="13.5" align-x="99" align-y="5340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>3</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="154"/> </region> <region region-id="3291" left="6" top="5358.75" width="77.25" height="29.25" align-x="18.75" align-y="5376" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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<ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">i</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">e</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">t</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">R2</ml:id> <ml:id xml:space="preserve">C2</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> 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push-down="false" lock-width="true"> <f size="12">Maximum Range of the X axis</f> </text> </region> <region region-id="3309" left="6" top="5456.25" width="70.5" height="13.5" align-x="22.5" align-y="5466" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">tol</ml:id> <ml:apply> <ml:mult/> <ml:real>-0.01</ml:real> <ml:id xml:space="preserve">MHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="158"/> </region> <region region-id="3310" left="162" top="5454.75" width="239.25" height="13.5" align-x="162" align-y="5466" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="12">Tolerance Marker for Lock Time Measurments</f> </text> </region> <region 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