Mathcad Professional 14.0 <description/> <author>chris</author> <company/> <keywords/> <revisedBy>chris</revisedBy> </userData> <identityInfo> <revision>4</revision> <documentID>915B067A-C040-40A2-AFDF-EB33164ED948</documentID> <versionID>60719F10-599A-468D-9172-F2526AA59F70</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="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"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="14"> <b> <inlineAttr line-through="false"> <c val="#000080">Microwave Coupled Filter Design Sheet</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="633" left="36" top="36" width="181.5" height="102" align-x="36" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="1" display-width="180" display-height="100.5"/> </picture> <rendering item-idref="2"/> </region> <region region-id="631" left="288" top="56.25" width="169.5" height="24" align-x="288" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#000080">Chris Haji-Michael www.sunshadow.co.uk/chris.htm</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="663" left="12" top="146.25" width="444.75" height="216" align-x="12" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">This sheet is used to design microwave Coupled filters.<sp count="2"/> </c> <c val="#000080">The maths for this can be found at www.acusd.edu/~ekim/e194rfs01/iec19aek.pdf.<sp count="2"/>I have also added some simulation results at the end.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">There are three steps to this filter design:</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"> <c val="#000080">Step 1</c> </inlineAttr> </b> </f> <c val="#000080">, Get the filter g-values, 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> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false">Step 2</inlineAttr> </b> </f> </c> <c val="#000080">, Calculate Zoo/Zoe and wavelength depending on the type of filter.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">This MathCAD sheet stops at this point.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <b> <f family="Arial" charset="0"> <c val="#000080"> <inlineAttr line-through="false">Step 3</inlineAttr> </c> </f> </b> <c val="#000080">, Calculate length and width.<sp count="2"/>One method is to use Linecalc which is part of ADS.<sp count="2"/>For microstrip designs I have written a MathCAD sheet which is available from my wepage that works well for thin tracks, less well for thicker tracks. Also you can try </c> <inlineAttr line-through="false"> <c val="#000080"> <f family="Arial" charset="0"> <b>transcalc.sourceforge.net</b> </f> </c> </inlineAttr> <c val="#000080"> for a Linecalc equivalent.</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">Yellow is user input, Green is output</c> </p> </text> </region> <region region-id="480" left="6" top="414.75" width="195.75" height="14.25" align-x="6" 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"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Main user input area:</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="373" left="270" top="423" width="64.5" height="18.75" align-x="289.5" align-y="438" 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="423" width="80.25" height="18.75" align-x="372.75" align-y="438" 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="285" left="12" top="441" width="48" height="15" align-x="40.5" align-y="450" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="ar_db">L</ml:id> <ml:real>0.5</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="374" left="90" top="440.25" width="93.75" height="12" align-x="90" align-y="450" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">passband ripple in dB</c> </p> </text> </region> <region region-id="149" left="12" top="465" width="27" height="12.75" align-x="26.25" align-y="474" 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>5</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="150" left="90" top="464.25" width="257.25" height="12" align-x="90" align-y="474" 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="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">order of the filter (this sheet is only valid for odd values of N)</c> </p> </text> </region> <region region-id="151" left="12" top="489" width="64.5" height="15" align-x="33.75" align-y="498" 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">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="582" left="90" top="494.25" width="366" height="24" align-x="90" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <c val="#000080">bandpass cutoff frequencies, these are the equiripple band edge frequencies, not necessarily the 3 dB cutoff frequencies.</c> </p> </text> </region> <region region-id="378" left="12" top="513" width="66.75" height="15" align-x="36" align-y="522" 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">f</ml:id> <ml:apply> <ml:mult/> <ml:real>15</ml:real> <ml:id xml:space="preserve">GHz</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="287" left="12" top="537" width="50.25" height="15" align-x="28.5" align-y="546" 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="9"/> </region> <region region-id="158" left="6" top="594.75" width="317.25" height="14.25" align-x="6" align-y="606" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">BPF Frequency Response, for Chebychev Polynomials</c> </inlineAttr> </b> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </p> </text> </region> <region region-id="666" left="12" top="614.25" width="449.25" height="24" align-x="12" align-y="624" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"> <c val="#000080">This section plots the frequency response for the Chebychev polynomial values calculated later. The frequency response is for the coupled BPF.</c> </p> </text> </region> <region region-id="584" left="12" top="656.25" width="37.5" height="30" align-x="28.5" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml: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="10"/> </region> <region region-id="585" left="90" top="661.5" width="76.5" height="16.5" align-x="110.25" align-y="672" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:apply> <ml:sqrt/> 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left="12" top="764.25" width="300.75" height="75.75" align-x="54" align-y="786" 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="18"/> </region> <region region-id="672" left="288" top="848.25" width="164.25" height="12" align-x="288" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">f1 = fc for lowpass, f_gm for bandpass</c> </p> </text> </region> <region region-id="667" left="12" top="867.75" width="177.75" height="38.25" align-x="63" align-y="900" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="A">S11</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:real>10</ml:real> <ml:apply> <ml:id xml:space="preserve">log</ml:id> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:neg/> <ml:apply> <ml:id xml:space="preserve" subscript="A">L</ml:id> <ml:sequence> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="1">f</ml:id> </ml:sequence> </ml:apply> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="668" left="12" top="930" width="141.75" height="32.25" align-x="42.75" align-y="948" 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="bp">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">f</ml:id> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="gm">f</ml:id> <ml:id xml:space="preserve">f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> <ml:id xml:space="preserve" subscript="gm">f</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="669" left="12" top="972" width="260.25" height="30" align-x="71.25" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">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="21"/> </region> <region region-id="670" left="12" top="1008" width="343.5" height="30" align-x="60.75" align-y="1026" 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>2</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>2</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>2</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="22"/> </region> <region region-id="414" left="18" top="1062" width="434.25" height="357.75" align-x="18" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="23"/> <rendering item-idref="24"/> </region> <region region-id="599" left="12" top="1434" width="438" height="333.75" align-x="12" align-y="1434" 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="418" left="6" top="1798.5" width="237.75" height="17.25" align-x="6" align-y="1812" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Calculate the Chebychev (g) Polynomials</c> </inlineAttr> </b> </f> <f family="Comic Sans MS" charset="0" size="12"> <inlineAttr line-through="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </f> </p> </text> </region> <region region-id="419" left="12" top="1839" width="37.5" height="12.75" align-x="22.5" align-y="1848" 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="27"/> </region> <region region-id="420" left="84" top="1830" width="93.75" height="30" align-x="96" align-y="1848" 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="28"/> </region> <region region-id="307" left="216" top="1832.25" width="71.25" height="27.75" align-x="228" align-y="1848" 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="29"/> </region> <region region-id="308" left="312" top="1832.25" width="99" height="27.75" align-x="327" align-y="1848" 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="30"/> </region> <region region-id="421" left="12" top="1880.25" width="108" height="33.75" align-x="27.75" align-y="1902" 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="31"/> </region> <region region-id="422" left="156" top="1893" width="27.75" height="18" align-x="171.75" align-y="1902" 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="32"/> </region> <region region-id="314" left="222" top="1898.25" width="227.25" height="36" align-x="222" align-y="1908" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"> <c val="#000080">g(0) and g(N+1) represent the input/output coupling</c> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">for odd order filters, these are 1 representing the generator (and equal) load resistance</c> </p> </text> </region> <region region-id="423" left="156" top="1917" width="27.75" height="18" align-x="171.75" align-y="1926" 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="33"/> </region> <region region-id="424" left="144" top="1941" width="41.25" height="18" align-x="173.25" align-y="1950" 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="34"/> </region> <region region-id="426" left="12" top="1977" width="134.25" height="75" align-x="27.75" align-y="1998" 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="35"/> </region> <region region-id="689" left="384" top="1981.5" width="57" height="111.75" align-x="394.5" align-y="2040" 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="7" cols="1"> <ml:real>1</ml:real> <ml:real>1.7058213827945443</ml:real> <ml:real>1.2296101340704062</ml:real> <ml:real>2.5408809032568787</ml:real> <ml:real>1.229610134070406</ml:real> <ml:real>1.7058213827945448</ml:real> <ml:real>1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="36"/> </region> <region region-id="430" left="6" top="2130.75" width="210" height="14.25" align-x="6" align-y="2142" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">The next step is to calculate Zoo Zoe.</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="431" left="12" top="2156.25" width="432" height="36" align-x="12" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">This next section converts the g-values to J-values and in turn to Zoo and Zoe.<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</c> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="center" list-style-type="none" tabs="inherit"> <c val="#000080">here as follows.<sp count="2"/> </c> </p> </text> </region> <region region-id="440" left="12" top="2211" width="47.25" height="12.75" align-x="23.25" align-y="2220" 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>0</ml:real> <ml:real>1</ml:real> </ml:sequence> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="642" left="402" top="2211" width="36.75" height="18" align-x="426.75" align-y="2220" 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="38"/> </region> <region region-id="441" left="12" top="2238.75" width="155.25" height="111" align-x="35.25" align-y="2256" 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">JJ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">i</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:equal/> <ml:id xml:space="preserve">i</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve">bw</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:real>2</ml:real> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">g</ml:id> <ml:real>0</ml:real> </ml:apply> </ml:apply> <ml:apply> 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margin-right="inherit" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <inlineAttr underline="false"> <c val="#000080">Now calculate the coupling between sections of the filter.<sp count="2"/>The first and last represent the input and output couplings.<sp count="2"/> </c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr underline="false" line-through="false"> <c val="#000080">If the filter is a tapped filter, the input and output coupling is not achieved using a coupler, and these values are ignored (these are the first and last in the list, and generally represent the smallest coupling value in the filter, which is why it is often desirable to avoid such coupler designs)</c> </inlineAttr> </f> <f family="Arial" charset="0"> <inlineAttr underline="false"> <c val="#000080">. </c> </inlineAttr> </f> <inlineAttr underline="false"> <c val="#000080"> <sp/> </c> </inlineAttr> </p> </text> </region> <region 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is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="guide">λ</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">mm</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:real>2.8867513459481291</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="millimeter"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> <region region-id="622" left="270" top="2780.25" width="189" height="12" align-x="270" align-y="2790" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <c val="#000080">length of each quarter wave coupled section</c> </p> </text> </region> <region region-id="659" left="6" top="2832.75" width="107.25" height="14.25" align-x="6" align-y="2844" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <c val="#000080">Simulation Results</c> </inlineAttr> </b> </f> </p> </text> </region> <region region-id="660" left="12" top="2852.25" width="449.25" height="24" align-x="12" align-y="2862" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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