<description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>4</revision> <documentID>1EAE18D4-B2A8-4138-93B3-1BBF16F5FCEB</documentID> <versionID>06DE2C6B-3622-458B-B913-C271A86DD7A4</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="1936" 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="1912" left="60" top="5.25" width="348.75" height="15.75" align-x="60" 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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Magnetically Coupled Chebychev BPF</c> </inlineAttr> </f> </text> </region> <region region-id="1917" left="324" top="26.25" width="169.5" height="24" align-x="324" align-y="36" 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="1914" left="60" top="72" width="350.25" height="217.5" align-x="60" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{11943940-36DE-11CF-953E-00C0A84029E9}" type="static" item-idref="1"/> <rendering item-idref="2"/> </region> <region region-id="1918" left="12" top="308.25" width="485.25" height="24" align-x="12" align-y="318" 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 sheet is used to design a </c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">microwave magnetically coupled BPF</c> </inlineAttr> </f> <c val="#000080">.<sp count="2"/>The maths for this filter is derived from equations in "Theory & Design of Microwave Filters", Ian Hunter, IEE Press. </c> </text> </region> <region region-id="1698" left="6" top="366.75" width="195.75" height="14.25" align-x="6" align-y="378" 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">Main user input area:</c> </inlineAttr> </f> </text> </region> <region region-id="1919" left="330" top="375" width="64.5" height="18.75" align-x="349.5" align-y="390" 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="1920" left="414" top="375" width="80.25" height="18.75" align-x="432.75" align-y="390" show-border="false" show-highlight="false" 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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 return loss in dB</c> </text> </region> <region region-id="1703" left="12" top="417" width="27" height="12.75" align-x="26.25" align-y="426" 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>3</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="1704" left="90" top="416.25" width="183.75" height="12" align-x="90" align-y="426" 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, this needs to be above 2</c> </text> </region> <region region-id="1705" left="12" top="441" width="58.5" height="15" align-x="32.25" align-y="450" 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="gm">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="7"/> </region> <region region-id="1902" left="96" top="441" width="96.75" height="12.75" align-x="147" align-y="450" 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">bandwidth</ml:id> <ml:apply> <ml:mult/> <ml:real>20</ml:real> <ml:id 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Calculating...</c> </inlineAttr> </f> </text> </region> <region region-id="1709" left="6" top="512.25" width="102.75" height="27.75" align-x="27.75" align-y="528" 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="low">f</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">bandwidth</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="1710" left="132" top="512.25" width="105" height="27.75" align-x="156" align-y="528" 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"> 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</ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1921" left="426" top="567" width="66" height="12.75" align-x="474" align-y="576" 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">bwpercent</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="1923" left="444" top="585" width="34.5" height="12.75" align-x="456" align-y="594" 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">α</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>50</ml:real> </result> </ml:eval> </math> <rendering item-idref="17"/> </region> <region region-id="1717" left="6" top="648.75" width="315.75" height="14.25" align-x="6" align-y="660" 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="1718" left="12" top="668.25" width="488.25" height="12" align-x="12" align-y="678" 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 for the Chebychev BPF</c> </text> </region> <region region-id="1719" left="12" top="704.25" width="37.5" height="30" align-x="28.5" align-y="720" 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="18"/> </region> <region region-id="1720" left="78" top="693.75" width="108" height="42" align-x="90.75" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" 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xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>0.024869896870943452</ml:real> <ml:real>0.024869896870943459</ml:real> </ml:matrix> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="5" show-trailing-zeros="true" 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"/> <table item-idref="46"/> </resultFormat> </math> <rendering item-idref="47"/> </region> <region region-id="1934" left="90" top="1944" width="350.25" height="217.5" align-x="90" align-y="1944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{11943940-36DE-11CF-953E-00C0A84029E9}" type="static" item-idref="48"/> <rendering item-idref="49"/> </region> <region region-id="1744" left="6" top="2280.75" width="107.25" height="14.25" align-x="6" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </f> </text> </region> <region region-id="1745" left="12" top="2300.25" width="480.75" height="60" align-x="12" align-y="2310" 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 for N=3, Return Loss 10dB, BW=20MHz, Zo=50R.<sp count="2"/>You can see the results are in good agreement. Both the ripple and return loss (S11) agree.<sp count="2"/> </c> <c val="#000080">You can see the downside of these filters that the frequency response repeats and the out of band attenuation is not a good we would like and not as good as expected from the ideal chebychev response.</c> </text> </region> <region region-id="1936" left="120" top="2382" width="299.25" height="347.25" align-x="120" align-y="2382" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{11943940-36DE-11CF-953E-00C0A84029E9}" type="static" item-idref="50"/> <rendering item-idref="51"/> </region> </regions> <binaryContent> <item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/+xdC4AdVXn+52bvnfBQIAaMirAIvg1CEJGASkx4iYEgiAFXybK7ya4mu2Gz YcFqtVZLaltLW6yVWou1tdTSVsVqq33YlgpaLbYNrbWVQsUSaoFARREL22/e58zMnTuPc+ae uff/dr9753Hnu+fxzT9zzrkzczARWeBF4IHu9AheD1p/wfapDXMT5y5M7SAXTwVtaclB4AGT 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Mathcad Professional 14.0 <description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>4</revision> <documentID>1EAE18D4-B2A8-4138-93B3-1BBF16F5FCEB</documentID> <versionID>06DE2C6B-3622-458B-B913-C271A86DD7A4</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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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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Magnetically Coupled Chebychev BPF</c> </inlineAttr> </f> </text> </region> <region region-id="1917" left="324" top="26.25" width="169.5" height="24" align-x="324" align-y="36" 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="1914" left="60" top="72" width="350.25" height="217.5" align-x="60" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{11943940-36DE-11CF-953E-00C0A84029E9}" type="static" item-idref="1"/> <rendering item-idref="2"/> </region> <region region-id="1918" left="12" top="308.25" width="485.25" height="24" align-x="12" align-y="318" 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 sheet is used to design a </c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">microwave magnetically coupled BPF</c> </inlineAttr> </f> <c val="#000080">.<sp count="2"/>The maths for this filter is derived from equations in "Theory & Design of Microwave Filters", Ian Hunter, IEE Press. </c> </text> </region> <region region-id="1698" left="6" top="366.75" width="195.75" height="14.25" align-x="6" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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</ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="1921" left="426" top="567" width="66" height="12.75" align-x="474" align-y="576" 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">bwpercent</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>2</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="1923" left="444" top="585" width="34.5" height="12.75" align-x="456" align-y="594" 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">α</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>50</ml:real> </result> </ml:eval> </math> <rendering item-idref="17"/> </region> <region region-id="1717" left="6" top="648.75" width="315.75" height="14.25" align-x="6" align-y="660" 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="1718" left="12" top="668.25" width="488.25" height="12" align-x="12" align-y="678" 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 for the Chebychev BPF</c> </text> </region> <region region-id="1719" left="12" top="704.25" width="37.5" height="30" align-x="28.5" align-y="720" 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="18"/> </region> <region region-id="1720" left="78" top="693.75" width="108" height="42" align-x="90.75" align-y="732" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ε</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:apply> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>-0.5</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="1925" left="438" top="729" width="49.5" height="12.75" align-x="449.25" align-y="738" 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>0.10050378152592121</ml:real> </result> </ml:eval> <resultFormat numeric-only="true"> <general precision="5" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="false" simplify-units="false" fractional-unit-exponent="false"/> </resultFormat> </math> <rendering item-idref="20"/> </region> <region region-id="1722" left="6" top="770.25" width="281.25" height="75.75" align-x="44.25" align-y="792" 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="c">f</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessOrEqual/> <ml:id 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<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: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="c">f</ml:id> </ml:apply> </ml:apply> </ml:apply> </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="21"/> </region> <region region-id="1723" left="6" top="861.75" width="171" height="38.25" align-x="54" align-y="894" 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="22"/> </region> <region region-id="1724" left="6" top="918" width="249" height="30" align-x="63.75" align-y="936" 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">f_bp_narrow</ml:id> <ml:range> <ml:sequence> <ml:apply> <ml:mult/> <ml:real>0.99</ml:real> <ml:id xml:space="preserve" subscript="low">f</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="high">f</ml:id> <ml:id xml:space="preserve" subscript="low">f</ml:id> </ml:apply> <ml:real>100</ml:real> </ml:apply> <ml:apply> <ml:mult/> <ml:real>0.99</ml:real> <ml:id xml:space="preserve" subscript="low">f</ml:id> </ml:apply> </ml:apply> </ml:sequence> <ml:apply> <ml:mult/> <ml:real>1.01</ml:real> <ml:id xml:space="preserve" subscript="high">f</ml:id> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="1725" left="6" top="960" width="343.5" height="30" align-x="54.75" align-y="978" 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">f_bp_wide</ml:id> <ml:range> <ml:sequence> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> <ml:real>100</ml:real> </ml:apply> </ml:apply> </ml:sequence> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>3</ml:real> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="1763" left="12" top="1002" width="414.75" height="225.75" align-x="12" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="25"/> <rendering item-idref="26"/> </region> <region region-id="1926" left="18" top="1230" width="414" height="237.75" align-x="18" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="27"/> <rendering item-idref="28"/> </region> <region region-id="1728" left="6" top="1528.5" width="171.75" height="17.25" align-x="6" align-y="1542" 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 circuit values.....</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="1729" left="180" top="1575" width="47.25" height="12.75" align-x="191.25" 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:id xml:space="preserve">n</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:sequence> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="1730" left="12" top="1574.25" width="108.75" height="27.75" align-x="24" align-y="1590" 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="30"/> </region> <region region-id="1731" left="180" top="1593" width="68.25" height="12.75" align-x="196.5" align-y="1602" 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">nn</ml:id> <ml:range> <ml:sequence> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:sequence> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">N</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> </ml:define> </math> <rendering item-idref="31"/> </region> <region region-id="1732" left="282" top="1559.25" width="165.75" height="54.75" align-x="327.75" align-y="1602" 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">K</ml:id> <ml:sequence> <ml:id xml:space="preserve">nn</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">nn</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:sequence> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <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> <ml:apply> <ml:id xml:space="preserve">sin</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">nn</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:parens> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">η</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="1733" left="12" top="1622.25" width="111.75" height="27.75" align-x="28.5" align-y="1638" 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">C</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:real font="0">2</ml:real> <ml:id xml:space="preserve">η</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">n</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:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="1734" left="12" top="1658.25" width="157.5" height="36" align-x="47.25" align-y="1674" 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">Cap</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:real>1</ml:real> </ml:sequence> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:parens> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real font="0">2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">α</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="o">Z</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering 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width="107.25" height="14.25" align-x="6" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </f> </text> </region> <region region-id="1745" left="12" top="2300.25" width="480.75" height="60" align-x="12" align-y="2310" 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 for N=3, Return Loss 10dB, BW=20MHz, Zo=50R.<sp count="2"/>You can see the results are in good agreement. 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