<description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>14</revision> <documentID>CE077DE3-BA86-416E-957D-CEBD96C1601D</documentID> <versionID>6FAF283D-BC20-4BDD-88E3-53DF128DA8D6</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" definition="colon-equal" 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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="1079" 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="1038" left="84" top="11.25" width="407.25" height="15.75" align-x="84" align-y="24" 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">Microwave Stepped Impedance Filter Design Sheet</c> </inlineAttr> </f> </text> </region> <region region-id="1036" left="372" top="44.25" width="169.5" height="24" align-x="372" align-y="54" 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">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </f> </text> </region> <region region-id="1039" left="126" top="84" width="312" height="41.25" align-x="126" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="1" display-width="310.5" display-height="39.75"/> </picture> <rendering item-idref="2"/> </region> <region region-id="1017" left="24" top="140.25" width="523.5" height="204" align-x="24" align-y="150" 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"> <c val="#000080">T</c> <c val="#000080">The maths for this can be found at www.acusd.edu/~ekim/e194rfs01/iec19aek.pdf.<sp count="2"/> </c> <c val="#000080">I have also added some simulation results at the end.</c> <c val="#000080">There are three steps to this filter design:</c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Step 1</c> </inlineAttr> </f> <c val="#000080">, Get the filter g-values, this sheet calculated the g values according to the Chebychev polynomial, but these can be obtained in a variety of ways from books or from a program freely available from my web page.<sp count="2"/>You will be pleased to know that these g-values agree with my program!!</c> <inlineAttr line-through="false"> <c val="#000080"> <f family="Arial" charset="0">Step 2</f> </c> </inlineAttr> <c val="#000080">, Calculate Zo and wavelength depending on the type of filter.</c> <c val="#000080">This MathCAD sheet stops at this point.</c> <f family="Arial" charset="0"> <c val="#000080"> <inlineAttr line-through="false">Step 3</inlineAttr> </c> </f> <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"> <f family="Arial" charset="0"> transcalc.sourceforge.net </f> </c> </inlineAttr> <c val="#000080"> for a Linecalc equivalent.</c> <c val="#000080">Yellow is user input, Green is output</c> </text> </region> <region region-id="480" left="6" top="359.25" width="195.75" height="15.75" align-x="6" align-y="372" 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">Main user input area:</c> </inlineAttr> </f> </text> </region> <region region-id="373" left="270" top="369" width="64.5" height="18.75" align-x="289.5" align-y="384" 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">μm</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="146" left="354" top="369" width="80.25" height="18.75" align-x="372.75" align-y="384" 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="4"/> </region> <region region-id="922" left="12" top="381" width="48" height="15" align-x="40.5" align-y="390" 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>0.2</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="374" left="90" top="386.25" width="93.75" height="12" align-x="90" align-y="396" 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"> <c val="#000080">passband ripple in dB</c> </text> </region> <region region-id="149" left="12" top="411" width="27" height="12.75" align-x="26.25" align-y="420" 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>7</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="150" left="90" top="410.25" width="69.75" height="12" align-x="90" align-y="420" 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"> <c val="#000080">order of the filter</c> </text> </region> <region region-id="792" left="12" top="435" width="56.25" height="15" align-x="25.5" align-y="444" 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>10</ml:real> <ml:id xml:space="preserve">GHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="682" left="90" top="434.25" width="150.75" height="12" align-x="90" align-y="444" 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"> <c val="#000080">Cutoff frequency.</c> </text> </region> <region region-id="1042" left="240" top="435" width="50.25" height="15" align-x="256.5" align-y="444" 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="8"/> </region> <region region-id="158" left="6" top="480.75" width="315.75" height="14.25" align-x="6" align-y="492" 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="12"> <inlineAttr line-through="false"> <c val="#000080">LPF Frequency Response, for Chebychev Polynomials</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="406" left="12" top="506.25" width="529.5" height="24" align-x="12" align-y="516" 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"> <c val="#000080">This section plots the frequency response assuming the Chebychev polynomial values calculated later. The frequency response is for the coupled BPF, the LPF response is later.</c> </text> </region> <region region-id="888" left="12" top="548.25" width="36" height="30" align-x="27.75" align-y="564" 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> <rendering item-idref="9"/> </region> <region region-id="890" left="84" top="537.75" width="68.25" height="36" align-x="95.25" align-y="570" 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="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ε</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>10</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1057" left="498" top="573" width="45" height="12.75" align-x="509.25" align-y="582" 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">ε</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.04712854805089961</ml:real> </result> </ml:eval> </math> <rendering item-idref="11"/> </region> <region region-id="951" left="12" top="590.25" width="291" height="75.75" align-x="51" align-y="612" show-border="false" 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<ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1043" left="342" top="609.75" width="171" height="38.25" align-x="390" align-y="642" 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="13"/> </region> <region region-id="1044" left="12" top="690" width="151.5" height="30" align-x="78" align-y="708" 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" 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<ml:real>100</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="15"/> </region> <region region-id="1046" left="42" top="756" width="434.25" height="273.75" align-x="42" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="16"/> <rendering item-idref="17"/> </region> <region region-id="1047" left="48" top="1044" width="420" height="273.75" align-x="48" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="18"/> <rendering item-idref="19"/> </region> <region region-id="840" left="6" top="1342.5" width="237.75" height="17.25" align-x="6" align-y="1356" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Calculate the Chebychev (g) Polynomials</c> </inlineAttr> </f> <f family="Comic Sans MS" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="841" left="12" top="1389" width="37.5" height="12.75" align-x="22.5" align-y="1398" 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>1</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="842" left="84" top="1380" width="93.75" height="30" align-x="96" align-y="1398" 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">β</ml:id> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:id xml:space="preserve">coth</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>17.37</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="843" left="216" top="1382.25" width="71.25" height="27.75" align-x="228" align-y="1398" 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">γ</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">β</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="844" left="312" top="1382.25" width="99" height="27.75" align-x="327" align-y="1398" 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:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="845" left="12" top="1478.25" width="108" height="33.75" align-x="27.75" align-y="1500" 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">b</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">γ</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:apply> <ml:mult/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="846" left="156" top="1491" width="27.75" height="18" align-x="171.75" align-y="1500" 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">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="847" left="222" top="1496.25" width="227.25" height="36" align-x="222" align-y="1506" 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"> <c val="#000080">g(0) and g(N+1) represent the input/output coupling</c> <c val="#000080">for odd order filters, these are 1 representing the generator (and equal) load resistance</c> </text> </region> <region region-id="848" left="156" top="1515" width="27.75" height="18" align-x="171.75" 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">g</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="849" left="144" top="1539" width="41.25" height="18" align-x="173.25" align-y="1548" 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">g</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="850" left="12" top="1563" width="134.25" height="75" align-x="27.75" align-y="1584" 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">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">γ</ml:id> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1048" left="480" top="1551" width="57" height="144.75" align-x="490.5" align-y="1626" 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">g</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="9" cols="1"> <ml:real>1</ml:real> <ml:real>1.3722953545331131</ml:real> <ml:real>1.3781932078355106</ml:real> <ml:real>2.2756885464235208</ml:real> <ml:real>1.500146640085483</ml:real> <ml:real>2.2756885464235208</ml:real> <ml:real>1.378193207835511</ml:real> <ml:real>1.3722953545331114</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="1061" left="6" top="1674.75" width="178.5" height="14.25" align-x="6" align-y="1686" 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="12"> <inlineAttr line-through="false"> <c val="#000080">The next step is to calculate Zo.</c> </inlineAttr> </f> </text> </region> <region region-id="1062" left="12" top="1694.25" width="406.5" height="60" align-x="12" align-y="1704" 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"> <c val="#000080">This next section converts the g-values to Zo-values.<sp count="2"/>If you wish to use your own g-values, i.e not from the Chebychev polynomial then this is ok and you need to put them here as shown on the right. </c> <c val="#000080">User sets Zlow and Zhigh based on what is reasonable for the substrate.</c> <c val="#000080"> <sp/> </c> <c val="#000080">This filter alternates between these impedances</c> </text> </region> <region region-id="1063" left="498" top="1767" width="36.75" height="18" align-x="522.75" align-y="1776" 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">g</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="1064" left="12" top="1773" width="39.75" height="15" align-x="35.25" align-y="1782" 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="low">Z</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1065" left="66" top="1773" width="46.5" height="15" align-x="91.5" align-y="1782" 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="high">Z</ml:id> <ml:real>120</ml:real> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="1066" left="6" top="1797" width="139.5" height="47.25" align-x="76.5" align-y="1830" 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">angle_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">asin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">Z</ml:id> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="high">Z</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="1067" left="162" top="1812" width="135" height="63.75" align-x="233.25" align-y="1830" 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">angle_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">asin</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="low">Z</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">Z</ml:id> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="1068" left="390" top="1827" width="74.25" height="136.5" align-x="422.25" align-y="1836" 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:indexer/> <ml:id xml:space="preserve">angle_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>34.875123672428</ml:real> <ml:real>35.04692807765359</ml:real> <ml:real>71.478326812072993</ml:real> <ml:real>38.686672174056319</ml:real> <ml:real>71.478326812072993</ml:real> <ml:real>35.046928077653604</ml:real> <ml:real>34.875123672427947</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="35"/> </resultFormat> </math> <rendering item-idref="36"/> </region> <region region-id="1069" left="468" top="1827" width="74.25" height="136.5" align-x="500.25" align-y="1836" 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:indexer/> <ml:id xml:space="preserve">angle_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>33.292824594249531</ml:real> <ml:real>33.454684127578389</ml:real> <ml:real>65.543440118292054</ml:real> <ml:real>36.874098690361556</ml:real> <ml:real>65.543440118292054</ml:real> <ml:real>33.4546841275784</ml:real> <ml:real>33.292824594249488</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="37"/> </resultFormat> </math> <rendering item-idref="38"/> </region> <region region-id="1071" left="12" top="1928.25" width="361.5" height="84" align-x="12" align-y="1938" 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"> <c val="#000080">There are a number of points to note:</c> <c val="#000080">1. The user needs to choose Zhigh/Zlow depending on the substrate.<sp count="2"/> </c> <c val="#000080">2. If the angle exceeds 90 degrees then the ripple and N should be changed.<sp count="2"/> </c> <c val="#000080">3. For max repeat frequency then the smaller the maximum angle is better.</c> <c val="#000080">4. The filter is designed by switching between the inductance/capacitance values in turn, hence two filters are possible from any given results.</c> </text> </region> <region region-id="978" left="6" top="2028.75" width="123" height="14.25" align-x="6" align-y="2040" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Calculate dimensions</c> </inlineAttr> </f> </text> </region> <region region-id="979" left="18" top="2048.25" width="432" height="12" align-x="18" align-y="2058" 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"> <c val="#000080">Now we can calculate the length of each section.</c> </text> </region> <region region-id="996" left="18" top="2097" width="32.25" height="15" align-x="31.5" align-y="2106" 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="r">ε</ml:id> <ml:real>4.5</ml:real> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="995" left="78" top="2075.25" width="69" height="45" align-x="93.75" align-y="2106" 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="0">λ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>8</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="c">f</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="994" left="192" top="2088" width="36.75" height="33.75" align-x="204" align-y="2106" 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">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="0">λ</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="r">ε</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1054" left="426" top="2097" width="66" height="12.75" align-x="437.25" align-y="2106" 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">λ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>14.142135623730951</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="998" left="60" top="2151" width="162.75" height="33" align-x="134.25" align-y="2172" 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">length_L_equiv</ml:id> <ml:id 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xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>1.3078656686360062</ml:real> <ml:real>1.314224111614702</ml:real> <ml:real>2.5747894983299284</ml:real> <ml:real>1.4485514018942582</ml:real> <ml:real>2.5747894983299284</ml:real> <ml:real>1.3142241116147029</ml:real> <ml:real>1.3078656686360042</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="47"/> </resultFormat> </math> <rendering item-idref="48"/> </region> <region region-id="852" left="6" top="2370.75" width="107.25" height="14.25" align-x="6" align-y="2382" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </f> </text> </region> <region region-id="853" left="12" top="2390.25" width="534" height="36" align-x="12" align-y="2400" 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"> <c val="#000080">To test these values I have run a simulation on ADS and as you can see the results are in good agreement. Both the ripple and return loss (S11) agree, but the cutoff frequency is out and I am not sure why this is.<sp count="2"/>Both types of filter agree with each other.</c> </text> </region> <region region-id="1079" left="84" top="2454" width="427.5" height="390" align-x="84" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="49"/> <rendering item-idref="50"/> </region> <region region-id="1056" left="36" top="2964" width="477" height="294.75" align-x="36" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="51"/> <rendering item-idref="52"/> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAZ4AAAA1CAIAAAD+shrBAAAAAXNSR0IArs4c6QAAAARnQU1B 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align-y="24" 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">Microwave Stepped Impedance Filter Design Sheet</c> </inlineAttr> </f> </text> </region> <region region-id="1036" left="372" top="44.25" width="169.5" height="24" align-x="372" align-y="54" 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">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </f> </text> </region> <region region-id="1039" left="126" top="84" width="312" height="41.25" align-x="126" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="1" display-width="310.5" display-height="39.75"/> </picture> <rendering item-idref="2"/> </region> <region region-id="1017" left="24" top="140.25" width="523.5" height="204" align-x="24" align-y="150" 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"> <c val="#000080">T</c> <c val="#000080">The maths for this can be found at www.acusd.edu/~ekim/e194rfs01/iec19aek.pdf.<sp count="2"/> </c> <c val="#000080">I have also added some simulation results at the end.</c> <c val="#000080">There are three steps to this filter design:</c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Step 1</c> </inlineAttr> </f> <c val="#000080">, Get the filter g-values, this sheet calculated the g values according to the Chebychev polynomial, but these can be obtained in a variety of ways from books or from a program freely available from my web page.<sp count="2"/>You will be pleased to know that these g-values agree with my program!!</c> <inlineAttr line-through="false"> <c val="#000080"> <f family="Arial" charset="0">Step 2</f> </c> </inlineAttr> <c val="#000080">, Calculate Zo and wavelength depending on the type of filter.</c> <c val="#000080">This MathCAD sheet stops at this point.</c> <f family="Arial" charset="0"> <c val="#000080"> <inlineAttr line-through="false">Step 3</inlineAttr> </c> </f> <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"> <f family="Arial" charset="0"> transcalc.sourceforge.net </f> </c> </inlineAttr> <c val="#000080"> for a Linecalc equivalent.</c> <c val="#000080">Yellow is user input, Green is output</c> </text> </region> <region region-id="480" left="6" top="359.25" width="195.75" height="15.75" align-x="6" align-y="372" 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">Main user input area:</c> </inlineAttr> </f> </text> </region> <region region-id="373" left="270" top="369" width="64.5" height="18.75" align-x="289.5" align-y="384" 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">μm</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="146" left="354" top="369" width="80.25" height="18.75" align-x="372.75" align-y="384" 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="4"/> </region> <region region-id="922" left="12" top="381" width="48" height="15" align-x="40.5" align-y="390" 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>0.2</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="374" left="90" top="386.25" width="93.75" height="12" align-x="90" align-y="396" 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"> <c val="#000080">passband ripple in dB</c> </text> </region> <region region-id="149" left="12" top="411" width="27" height="12.75" align-x="26.25" align-y="420" 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>7</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="150" left="90" top="410.25" width="69.75" height="12" align-x="90" align-y="420" 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"> <c val="#000080">order of the filter</c> </text> </region> <region region-id="792" left="12" top="435" width="56.25" height="15" align-x="25.5" align-y="444" 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>10</ml:real> <ml:id xml:space="preserve">GHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="682" left="90" top="434.25" width="150.75" height="12" align-x="90" align-y="444" 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"> <c val="#000080">Cutoff frequency.</c> </text> </region> <region region-id="1042" left="240" top="435" width="50.25" height="15" align-x="256.5" align-y="444" 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="8"/> </region> <region region-id="158" left="6" top="480.75" width="315.75" height="14.25" align-x="6" align-y="492" 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="12"> <inlineAttr line-through="false"> <c val="#000080">LPF Frequency Response, for Chebychev Polynomials</c> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="406" left="12" top="506.25" width="529.5" height="24" align-x="12" align-y="516" 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"> <c val="#000080">This section plots the frequency response assuming the Chebychev polynomial values calculated later. The frequency response is for the coupled BPF, the LPF response is later.</c> </text> </region> <region region-id="888" left="12" top="548.25" width="36" height="30" align-x="27.75" align-y="564" 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> <rendering item-idref="9"/> </region> <region region-id="890" left="84" top="537.75" width="68.25" height="36" align-x="95.25" align-y="570" 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="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ε</ml:id> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>10</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1057" left="498" top="573" width="45" height="12.75" align-x="509.25" align-y="582" 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">ε</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.04712854805089961</ml:real> </result> </ml:eval> </math> <rendering item-idref="11"/> </region> <region region-id="951" left="12" top="590.25" width="291" height="75.75" align-x="51" align-y="612" 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">L</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:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ε</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:id xml:space="preserve">acos</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:ifThen> <ml:ifThen> <ml:apply> <ml:greaterThan/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">ε</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:id xml:space="preserve">cosh</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">N</ml:id> <ml:apply> <ml:id xml:space="preserve">acosh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:ifThen> </ml:program> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="1043" left="342" top="609.75" width="171" height="38.25" align-x="390" align-y="642" 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="13"/> </region> <region region-id="1044" left="12" top="690" width="151.5" height="30" align-x="78" align-y="708" 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>50</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="14"/> </region> <region region-id="1045" left="234" top="690" width="173.25" height="30" align-x="306" align-y="708" 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>100</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="15"/> </region> <region region-id="1046" left="42" top="756" width="434.25" height="273.75" align-x="42" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="16"/> <rendering item-idref="17"/> </region> <region region-id="1047" left="48" top="1044" width="420" height="273.75" align-x="48" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="18"/> <rendering item-idref="19"/> </region> <region region-id="840" left="6" top="1342.5" width="237.75" height="17.25" align-x="6" align-y="1356" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Calculate the Chebychev (g) Polynomials</c> </inlineAttr> </f> <f family="Comic Sans MS" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </text> </region> <region region-id="841" left="12" top="1389" width="37.5" height="12.75" align-x="22.5" align-y="1398" 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>1</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="842" left="84" top="1380" width="93.75" height="30" align-x="96" align-y="1398" 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">β</ml:id> <ml:apply> <ml:id xml:space="preserve">ln</ml:id> <ml:apply> <ml:id xml:space="preserve">coth</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>17.37</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="843" left="216" top="1382.25" width="71.25" height="27.75" align-x="228" align-y="1398" 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">γ</ml:id> <ml:apply> <ml:id xml:space="preserve">sinh</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">β</ml:id> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="844" left="312" top="1382.25" width="99" height="27.75" align-x="327" align-y="1398" 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:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="845" left="12" top="1478.25" width="108" height="33.75" align-x="27.75" align-y="1500" 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">b</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">γ</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:apply> <ml:mult/> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">N</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="846" left="156" top="1491" width="27.75" height="18" align-x="171.75" align-y="1500" 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">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="847" left="222" top="1496.25" width="227.25" height="36" align-x="222" align-y="1506" 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"> <c val="#000080">g(0) and g(N+1) represent the input/output coupling</c> <c val="#000080">for odd order filters, these are 1 representing the generator (and equal) load resistance</c> </text> </region> <region region-id="848" left="156" top="1515" width="27.75" height="18" align-x="171.75" 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">g</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="849" left="144" top="1539" width="41.25" height="18" align-x="173.25" align-y="1548" 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">g</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="850" left="12" top="1563" width="134.25" height="75" align-x="27.75" align-y="1584" 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">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve">γ</ml:id> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>4</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">a</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">b</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="1048" left="480" top="1551" width="57" height="144.75" align-x="490.5" align-y="1626" 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">g</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="9" cols="1"> <ml:real>1</ml:real> <ml:real>1.3722953545331131</ml:real> <ml:real>1.3781932078355106</ml:real> <ml:real>2.2756885464235208</ml:real> <ml:real>1.500146640085483</ml:real> <ml:real>2.2756885464235208</ml:real> <ml:real>1.378193207835511</ml:real> <ml:real>1.3722953545331114</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="29"/> </region> <region region-id="1061" left="6" top="1674.75" width="178.5" height="14.25" align-x="6" align-y="1686" 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="12"> <inlineAttr line-through="false"> <c val="#000080">The next step is to calculate Zo.</c> </inlineAttr> </f> </text> </region> <region region-id="1062" left="12" top="1694.25" width="406.5" height="60" align-x="12" align-y="1704" 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"> <c val="#000080">This next section converts the g-values to Zo-values.<sp count="2"/>If you wish to use your own g-values, i.e not from the Chebychev polynomial then this is ok and you need to put them here as shown on the right. </c> <c val="#000080">User sets Zlow and Zhigh based on what is reasonable for the substrate.</c> <c val="#000080"> <sp/> </c> <c val="#000080">This filter alternates between these impedances</c> </text> </region> <region region-id="1063" left="498" top="1767" width="36.75" height="18" align-x="522.75" align-y="1776" 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">g</ml:id> <ml:real>100</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="1064" left="12" top="1773" width="39.75" height="15" align-x="35.25" align-y="1782" 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="low">Z</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1065" left="66" top="1773" width="46.5" height="15" align-x="91.5" align-y="1782" 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="high">Z</ml:id> <ml:real>120</ml:real> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="1066" left="6" top="1797" width="139.5" height="47.25" align-x="76.5" align-y="1830" 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">angle_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">asin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">Z</ml:id> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="high">Z</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="1067" left="162" top="1812" width="135" height="63.75" align-x="233.25" align-y="1830" 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">angle_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">asin</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="low">Z</ml:id> <ml:apply> <ml:div/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="o">Z</ml:id> <ml:id xml:space="preserve">Ω</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="1068" left="390" top="1827" width="74.25" height="136.5" align-x="422.25" align-y="1836" 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:indexer/> <ml:id xml:space="preserve">angle_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>34.875123672428</ml:real> <ml:real>35.04692807765359</ml:real> <ml:real>71.478326812072993</ml:real> <ml:real>38.686672174056319</ml:real> <ml:real>71.478326812072993</ml:real> <ml:real>35.046928077653604</ml:real> <ml:real>34.875123672427947</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="35"/> </resultFormat> </math> <rendering item-idref="36"/> </region> <region region-id="1069" left="468" top="1827" width="74.25" height="136.5" align-x="500.25" align-y="1836" 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:indexer/> <ml:id xml:space="preserve">angle_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">deg</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>33.292824594249531</ml:real> <ml:real>33.454684127578389</ml:real> <ml:real>65.543440118292054</ml:real> <ml:real>36.874098690361556</ml:real> <ml:real>65.543440118292054</ml:real> <ml:real>33.4546841275784</ml:real> <ml:real>33.292824594249488</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="degree"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="37"/> </resultFormat> </math> <rendering item-idref="38"/> </region> <region region-id="1071" left="12" top="1928.25" width="361.5" height="84" align-x="12" align-y="1938" 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"> <c val="#000080">There are a number of points to note:</c> <c val="#000080">1. The user needs to choose Zhigh/Zlow depending on the substrate.<sp count="2"/> </c> <c val="#000080">2. If the angle exceeds 90 degrees then the ripple and N should be changed.<sp count="2"/> </c> <c val="#000080">3. For max repeat frequency then the smaller the maximum angle is better.</c> <c val="#000080">4. The filter is designed by switching between the inductance/capacitance values in turn, hence two filters are possible from any given results.</c> </text> </region> <region region-id="978" left="6" top="2028.75" width="123" height="14.25" align-x="6" align-y="2040" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Calculate dimensions</c> </inlineAttr> </f> </text> </region> <region region-id="979" left="18" top="2048.25" width="432" height="12" align-x="18" align-y="2058" 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"> <c val="#000080">Now we can calculate the length of each section.</c> </text> </region> <region region-id="996" left="18" top="2097" width="32.25" height="15" align-x="31.5" align-y="2106" 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="r">ε</ml:id> <ml:real>4.5</ml:real> </ml:define> </math> <rendering item-idref="39"/> </region> <region region-id="995" left="78" top="2075.25" width="69" height="45" align-x="93.75" align-y="2106" 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="0">λ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>8</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">m</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="c">f</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="40"/> </region> <region region-id="994" left="192" top="2088" width="36.75" height="33.75" align-x="204" align-y="2106" 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">λ</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="0">λ</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve" subscript="r">ε</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="1054" left="426" top="2097" width="66" height="12.75" align-x="437.25" align-y="2106" 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">λ</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>14.142135623730951</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="998" left="60" top="2151" width="162.75" height="33" align-x="134.25" align-y="2172" 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">length_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">angle_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="43"/> </region> <region region-id="999" left="246" top="2151" width="164.25" height="33" align-x="321" align-y="2172" 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">length_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">λ</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">angle_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:real>360</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="44"/> </region> <region region-id="1076" left="378" top="2217" width="69.75" height="136.5" align-x="411.75" align-y="2226" 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:indexer/> <ml:id xml:space="preserve">length_L_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>1.3700242468607404</ml:real> <ml:real>1.3767733613036703</ml:real> <ml:real>2.8079338664825015</ml:real> <ml:real>1.5197560131008965</ml:real> <ml:real>2.8079338664825015</ml:real> <ml:real>1.376773361303671</ml:real> <ml:real>1.3700242468607384</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="45"/> </resultFormat> </math> <rendering item-idref="46"/> </region> <region region-id="1077" left="462" top="2217" width="70.5" height="136.5" align-x="496.5" align-y="2226" 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:indexer/> <ml:id xml:space="preserve">length_C_equiv</ml:id> <ml:id xml:space="preserve">k</ml:id> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="7" cols="1"> <ml:real>1.3078656686360062</ml:real> <ml:real>1.314224111614702</ml:real> <ml:real>2.5747894983299284</ml:real> <ml:real>1.4485514018942582</ml:real> <ml:real>2.5747894983299284</ml:real> <ml:real>1.3142241116147029</ml:real> <ml:real>1.3078656686360042</ml:real> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat> <table item-idref="47"/> </resultFormat> </math> <rendering item-idref="48"/> </region> <region region-id="852" left="6" top="2370.75" width="107.25" height="14.25" align-x="6" align-y="2382" 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="12"> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </f> </text> </region> <region region-id="853" left="12" top="2390.25" width="534" height="36" align-x="12" align-y="2400" 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"> <c val="#000080">To test these values I have run a simulation on ADS and as you can see the results are in good agreement. Both the ripple and return loss (S11) agree, but the cutoff frequency is out and I am not sure why this is.<sp count="2"/>Both types of filter agree with each other.</c> </text> </region> <region region-id="1079" left="84" top="2454" width="427.5" height="390" align-x="84" align-y="2454" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="49"/> <rendering item-idref="50"/> </region> <region region-id="1056" left="36" top="2964" width="477" height="294.75" align-x="36" align-y="2964" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="51"/> <rendering item-idref="52"/> </region> </regions> <binaryContent> <item item-id="1">iVBORw0KGgoAAAANSUhEUgAAAZ4AAAA1CAIAAAD+shrBAAAAAXNSR0IArs4c6QAAAARnQU1B 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