Mathcad Professional 14.0 <description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>8</revision> <documentID>3C1DF988-9844-415A-B6F4-13E092916ADB</documentID> <versionID>F6F9A6AF-F6B8-4611-A784-B1C298AD3793</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="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="dot" derivative="derivative" literal-subscript="small" 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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="1" orientation="portrait" print-single-page-width="false" page-width="612" page-height="792"> <margins left="65.19685" right="65.19685" 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="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="false" 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="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <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="1378" 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="1140" left="54" top="5.25" width="335.25" height="31.5" align-x="54" align-y="18" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="14"> <b> <inlineAttr line-through="false"> <c val="#000080">Microwave Stepped Impedance Filter Design Sheet</c> </inlineAttr> </b> </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="14"> <b> <inlineAttr line-through="false"> <c val="#000080">Type-2</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="1139" left="12" top="54" width="277.5" height="79.5" align-x="12" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{00021A13-0000-0000-C000-000000000046}" type="static" item-idref="1"/> <rendering item-idref="2"/> </region> <region region-id="1138" left="300" top="56.25" width="169.5" height="24" align-x="300" align-y="66" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#000080">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="663" left="12" top="152.25" width="444.75" height="216" align-x="12" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">This sheet is used to design microwave stepped impedance filters where each section is of the same length.<sp count="2"/>The maths for this are from "Theory & Design of Microwave Filters", Ian Hunter, IEE Press. </c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">There are three steps to this filter design:</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#000080">Step 1</c> </inlineAttr> </b> </f> <c val="#000080">, Get the filter g-values.<sp count="2"/>This sheet calculated these values according to the Chebychev polynomial.<sp count="2"/>Other sources of g cannot be used here as the g-values are modified by the length of the transmission line.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <b> <c val="#000080">Step 2</c> </b> </inlineAttr> </f> <c val="#000080">, Calculate Zo and wavelength depending on the type of filter.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">This MathCAD sheet stops at this point.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <b> <inlineAttr line-through="false"> <f family="Arial" charset="0"> <c val="#000080">Step 3</c> </f> </inlineAttr> </b> <c val="#000080">, Calculate length and width.<sp count="2"/>One method is to use Linecalc which is part of ADS.<sp count="2"/>For microstrip designs I have written a MathCAD sheet which is available from my wepage that works well for thin tracks, less well for thicker tracks. Also you can try </c> <inlineAttr line-through="false"> <c val="#000080"> <b> <f family="Arial" charset="0">transcalc.sourceforge.net</f> </b> </c> </inlineAttr> <c val="#000080"> for a Linecalc equivalent.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">Yellow is user input, Green is output</c> </p> </text> </region> <region region-id="480" left="6" top="402.75" width="195.75" height="14.25" align-x="6" align-y="414" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Main user input area:</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="146" left="354" top="411" width="77.25" height="18.75" align-x="372" align-y="426" 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">nH</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-9</ml:real> </ml:apply> <ml:id xml:space="preserve">henry</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="1039" left="12" top="429" width="46.5" height="15" align-x="39.75" align-y="438" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="1042" left="90" top="428.25" width="95.25" height="12" align-x="90" align-y="438" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">Passband ripple in dB</c> </p> </text> </region> <region region-id="149" left="12" top="453" width="30" height="12.75" align-x="25.5" align-y="462" 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="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">N</ml:id> <ml:real>17</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="150" left="90" top="452.25" width="230.25" height="12" align-x="90" align-y="462" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">Order of the filter, this needs to be between 3 and 18.</c> </p> </text> </region> <region region-id="792" left="12" top="477" width="48" height="15" align-x="24" align-y="486" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:apply> <ml:mult/> <ml:real>1</ml:real> <ml:id xml:space="preserve">GHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="682" left="90" top="476.25" width="93" height="12" align-x="90" align-y="486" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <c val="#000080">Cutoff frequency.</c> </p> </text> </region> <region region-id="711" left="12" top="501" width="47.25" height="15" align-x="27.75" align-y="510" 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" subscript="o">Z</ml:id> <ml:apply> <ml:mult/> <ml:real>50</ml:real> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="1070" left="12" top="525" width="48" height="12.75" align-x="28.5" align-y="534" 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">EL</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">20</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="1074" left="90" top="524.25" width="192.75" height="12" align-x="90" align-y="534" 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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <c val="#000080">Electrical Length of each section</c> </p> </text> </region> <region region-id="158" left="6" top="582.75" width="315.75" height="14.25" align-x="6" align-y="594" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">LPF Frequency Response, for Chebychev Polynomials</c> </inlineAttr> </b> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1058" left="12" top="602.25" width="449.25" height="12" align-x="12" align-y="612" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"> <c val="#000080">This section plots the frequency response for the Chebychev LPF</c> </p> </text> </region> <region region-id="1077" left="12" top="638.25" width="36" height="30" align-x="27.75" align-y="654" 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" subscript="o">Y</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="o">Z</ml:id> </ml:apply> </ml:define> </math> 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</ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1359" left="336" top="825" width="94.5" height="12.75" align-x="387" align-y="834" 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">Max_Atten</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>-231.95952831578822</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="1158" left="444" top="824.25" width="30.75" height="12" align-x="444" align-y="834" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">dB</p> </text> </region> <region region-id="1155" left="294" top="852" width="156" height="30" align-x="360" align-y="870" 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" subscript="lp_hp_sweep_wide">f</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>500</ml:real> </ml:apply> </ml:apply> </ml:sequence> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>5</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="1153" left="276" top="888" width="177.75" height="30" align-x="348" align-y="906" 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" subscript="lp_hp_sweep_narrow">f</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>1000</ml:real> </ml:apply> </ml:apply> </ml:sequence> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="c">f</ml:id> <ml:real>1.15</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="1099" left="12" top="885.75" width="171" height="38.25" align-x="60" align-y="918" 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" subscript="A">S11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</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:minus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve" subscript="A">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="895" left="6" top="942" width="434.25" height="231.75" align-x="6" align-y="942" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="20"/> <rendering item-idref="21"/> </region> <region region-id="1100" left="12" top="1170" width="427.5" height="243.75" align-x="12" align-y="1170" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="22"/> <rendering item-idref="23"/> </region> <region region-id="1217" left="6" top="1426.5" width="237.75" height="17.25" align-x="6" align-y="1440" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Calculate the Chebychev (g) Polynomials</c> </inlineAttr> </b> </f> <f family="Comic Sans MS" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </p> </text> </region> <region region-id="1105" left="18" top="1460.25" width="108.75" height="27.75" align-x="30" align-y="1476" 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">η</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">asinh</ml:id> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">ε</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1106" left="426" top="1467" width="45.75" height="12.75" align-x="438" align-y="1476" 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">η</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.16547732203736371</ml:real> </result> </ml:eval> </math> <rendering item-idref="25"/> </region> <region region-id="1167" left="12" top="1508.25" width="34.5" height="27.75" align-x="30" align-y="1524" 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:apply> <ml:indexer/> <ml:id xml:space="preserve">A</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="1172" left="114" top="1508.25" width="102" height="48.75" align-x="132" align-y="1524" 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>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">η</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">η</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="1171" left="258" top="1487.25" width="126.75" height="69.75" align-x="276" align-y="1524" 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>3</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">η</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> 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<text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="853" left="12" top="2852.25" width="449.25" height="108" align-x="12" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"> <c val="#000080">To test these values I have run a simulation on ADS for N=17, L=0.5dB, 20-degree EL, Zo=50R.<sp count="2"/>You can see the results are in good agreement. 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