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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">Impedance Transformer</c> </inlineAttr> </f> </text> </region> <region region-id="1034" left="312" top="38.25" width="169.5" height="24" align-x="312" align-y="48" 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="1032" left="12" top="74.25" width="474" height="60" align-x="12" align-y="84" 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 an impedance transformer that is very small for its performance.<sp count="2"/>The equations are from </c> <f family="Arial" charset="0"> <inlineAttr line-through="false"> <c val="#000080">Ang, Lee, Leong, "Broadband Quarter-Wavelength Impedance Transformer, IEEE MTT Dec 2004</c> </inlineAttr> </f> <c val="#000080">.<sp count="2"/> </c> <c val="#000080">Yellow is user input, Green is output</c> </text> </region> <region region-id="1235" left="42" top="162" width="396.75" height="192.75" align-x="42" align-y="162" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="1" display-width="395.25" display-height="191.25"/> </picture> <rendering item-idref="2"/> </region> <region region-id="828" left="6" top="392.25" width="423" height="39.75" align-x="96.75" align-y="414" show-border="false" 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xml:space="preserve">θ</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">Z2</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="1232" left="6" top="785.25" width="481.5" height="75.75" align-x="15" align-y="798" 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">Calculations</c> </inlineAttr> </f> <c val="#000080">The calculations are done using the Find command where convergences is helped by setting CTOL=0.05.<sp count="2"/>After convergence, put the the output results back to the guess values and repeat the convergence until the two are the same, then change CTOL to 0.0005 and converge again.<sp count="2"/> </c> <f 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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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Simulations</c> </inlineAttr> </f> <c val="#000080">50 Ohms to 100 Ohms, Zo=154.3, Zoe=153.9, Zo=39.8</c> <c val="#000080">50 Ohms to 200 Ohms, Zo=205.2, Zoe=233.4, Zo=54.0</c> <c val="#000080">Please refer to other MathCAD sheets on this site to convert from Zo and Zoo/Zoe to microstrip widths and spacings.</c> </text> </region> <region region-id="1248" left="90" top="1650" width="312.75" height="236.25" align-x="90" align-y="1650" 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="38"/> <rendering item-idref="39"/> </region> <region region-id="1242" left="96" top="1944" width="286.5" height="350.25" 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<ml:Find auto-method="true" method="levenberg" derivative-estimation="central" variable-estimation="tangent" linear-check="false" multistart="false" evolutionary="false"/> <ml:sequence> <ml:id xml:space="preserve">Zo</ml:id> <ml:id xml:space="preserve">Zoe</ml:id> <ml:id xml:space="preserve">Zoo</ml:id> </ml:sequence> </ml:apply> <ml:unitOverride> <ml:id xml:space="preserve">Ω</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math30"> <unitedValue> <ml:matrix rows="3" cols="1"> <ml:complex> <ml:real>258.34408347588175</ml:real> <ml:imag>8.2709118491033516E-10</ml:imag> </ml:complex> <ml:complex> <ml:real>233.47448126609999</ml:real> <ml:imag>4.2754937720429555E-10</ml:imag> </ml:complex> <ml:complex> <ml:real>75.514420986188185</ml:real> <ml:imag>-3.1777701146772124E-10</ml:imag> </ml:complex> </ml:matrix> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="ohm"/> </unitMonomial> </unitedValue> </result> </ml:eval> <resultFormat 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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"> <f family="Arial" charset="0" size="14"> <inlineAttr line-through="false"> <c val="#000080">Simulations</c> </inlineAttr> </f> <c val="#000080">50 Ohms to 100 Ohms, Zo=154.3, Zoe=153.9, Zo=39.8</c> <c val="#000080">50 Ohms to 200 Ohms, Zo=205.2, Zoe=233.4, Zo=54.0</c> <c val="#000080">Please refer to other MathCAD sheets on this site to convert from Zo and Zoo/Zoe to microstrip widths and spacings.</c> </text> </region> <region region-id="1248" left="90" top="1650" width="312.75" height="236.25" align-x="90" align-y="1650" 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="38"/> <rendering item-idref="39"/> </region> <region region-id="1242" left="96" top="1944" width="286.5" height="350.25" 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