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<title>Multiconductor Microstrip Circuits</title>
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<h1 align="center" class="style1">Open Source Mathematica ® Code Multiconductor Modeling and Analysis</h1>
<h1 align="center" class="style1">Microstrip Circuits</h1>
<p><strong>See <a href="#notes111">Notes (Scroll Down)</a></strong>.</p>
<table width="800" border="1">
<tbody>
<tr>
<th width="43" scope="col"><div align="center">Case</div></th>
<th width="852" scope="col">Description</th>
<th width="96" scope="col">Code</th>
<th width="67" scope="col">WEB View</th>
<th width="408" scope="col">Result Plots</th>
</tr>
<tr>
<td><div align="center">1</div></td>
<td>Near End Cross Talk. Mathematica® Code for Multiconductor Microstrip Based on Riddle, Ardalan, Suh<em> </em>Report <a href="Multiconductor_Derivation_Ardalan_Riddle_1988_CCSP.pdf"><img src="../pdf.gif" width="22" height="21" alt=""/></a>. Two Conductor Microstrip Parameters Based on [Hill,1994]. See <a href="#notes">Notes</a>. Code is for arbitrary number of conductors. Use the <a href="#tools">Tool</a> to generate Per Unit Parameters for Microstrip Circuit.</td>
<td><a href="Microstrip/Multiconductor_PerUnitLengthMicrostripAboveGround_2_Conductor_Comparison_Published_Results.nb">Notebook</a></td>
<td><a href="Microstrip/WEBViews/Multiconductor_PerUnitLengthMicrostripAboveGround_2_Conductor_Comparison_Published_Results/Multiconductor_PerUnitLengthMicrostripAboveGround_2_Conductor_Comparison_Published_Results.htm">HTML</a></td>
<td><p><a href="Microstrip/Near_End_Cross_Talk_Mathematica_Code_Based_On_Ardalan_et_al_1988.png">Near End Cross Talk S13</a></p></td>
</tr>
<tr>
<td><div align="center">2</div></td>
<td>Near End Cross Talk. Mathematica® Code for Multiconductor Microstrip Based on Theory [Hill, 1994] </td>
<td><a href="Microstrip/Multiconductor_Microstrip_Theory_2_Conductor.nb">Notebook</a></td>
<td><a href="Microstrip/WEBViews/Multiconductor_Microstrip_Theory_2_Conductor/Multiconductor_Microstrip_Theory_2_Conductor.htm">HTML</a></td>
<td><a href="Microstrip/Near_End_Cross_Talk_Mathematica_Code_Based_On_Theory_Hill_1994.png">Near End Cross Talk S13</a></td>
</tr>
<tr>
<td><div align="center">3</div></td>
<td>Far End Cross Talk. Mathematica® Code for Multiconductor Microstrip Based on Riddle, Ardalan, Suh<em> </em>Report <a href="Multiconductor_Derivation_Ardalan_Riddle_1988_CCSP.pdf"><img src="../pdf.gif" width="22" height="21" alt=""/></a>. Two Conductor Microstrip Parameters Based on [Hill,1994]. See <a href="#notes">Notes</a>. Code is for arbitrary number of conductors. Use the <a href="#tools">Tool</a> to generate Per Unit Parameters for Microstrip Circuit.</td>
<td> </td>
<td> </td>
<td><a href="Microstrip/Microstrip_Ardalan_Riddle_Theory_Far_End_ Hill_1994_Experiment.png">Far End Cross Talk S14</a> (Note Rs=0, Vs=1 Volt).</td>
</tr>
<tr>
<td><div align="center">4</div></td>
<td>Far End Cross Talk Measurements from [Hill,1994]. Ardalan <em>et al.</em> <a href="Multiconductor_Derivation_Ardalan_Riddle_1988_CCSP.pdf"><img src="../pdf.gif" width="22" height="21" alt=""/></a> predicts the measurement (using Mathematica® Code Case 3 ) very well especially at the higher frequencies. See Case 3. </td>
<td> </td>
<td> </td>
<td><a href="Microstrip/Far_End_Cross_Talk_S41_Measurements_Hill_1994.png">Far End Cross Talk S14 Measurements</a> from [Hill,1994]</td>
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<p> </p>
<h2 class="style1"><div id=”tools”> Tools</div></h2>
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<th width="81" scope="col">WEB View</th>
<th width="81" scope="col">Graphic</th>
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<tr>
<td><div align="center">1</div></td>
<td>Mathematica® Code for Computing the Per Unit Inductance and Capacitance Matrices for Multiconductor Microstrip Systems. Based on FORTRAN Code by Clayton Paul. See comments.</td>
<td><a href="Microstrip/PerUnitLengthCalcMultiConductorMicroStrip.nb">Notebook</a></td>
<td><a href="Microstrip/WEBViews/PerUnitLengthCalcMultiConductorMicroStrip/PerUnitLengthCalcMultiConductorMicroStrip.htm">HTML</a></td>
<td><a href="Microstrip/WEBViews/PerUnitLengthCalcMultiConductorMicroStrip/PerUnitLengthCalcMultiConductorMicroStrip.htm"><img src="Microstrip/Tool_PerUnitParameters_Microstrip.png" width="331" height="124" alt=""/></a></td>
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<td><div align="center"></div></td>
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<h2 class="style1">References:</h2>
<p style="margin-left:1em;">1- Mike Riddle, Sasan Ardalan, John Suh,<strong> Derivation of Voltage and Current Transfer Functions for Multiconductor Transmission Lines</strong>,CCSP, NC State University, 1988. Also published in the<span style="margin-left:1em;"> <em>IEEE International Conference on Circuits and Systems</em>, 1989</span>. For CCSP NC State Report see the <span style="margin-left:1em;"><a href="Multiconductor_Derivation_Ardalan_Riddle_1988_CCSP.pdf"><img src="../pdf.gif" width="22" height="21" alt=""/>PDF Report</a></span>.</p>
<p style="margin-left:1em;">2- David A.Hill, Kenneth H.Cavcey, Robert T.Johnk, <strong>Crosstalk Between Microstrip Transmission Lines,</strong><em> IEEE Transactions on Electromagnetic Compatibility,VOL.36,NO.4, November 1</em>994.</p>
<h2 align="center" class="style1"> Case 1</h2>
<p align="center"><img src="Microstrip/Near_End_Cross_Talk_Mathematica_Code_Based_On_Ardalan_et_al_1988.png" width="1023" height="842" alt=""/></p>
<p align="center"><span class="style1">Case 2</span></p>
<p align="center"><img src="Microstrip/Near_End_Cross_Talk_Mathematica_Code_Based_On_Theory_Hill_1994.png" width="1140" height="774" alt=""/></p>
<p align="center"><span class="style1">Case 3</span></p>
<p> </p>
<p align="center"><img src="Microstrip/Microstrip_Ardalan_Riddle_Theory_Far_End_ Hill_1994_Experiment.png" width="1096" height="862" alt=""/></p>
<p align="center"> </p>
<p align="center" class="style1">Case 4</p>
<p align="center"><img src="Microstrip/Far_End_Cross_Talk_S41_Measurements_Hill_1994.png" width="858" height="837" alt=""/></p>
<p align="center"> </p>
<p align="center"> </p>
<p align="center"> </p>
<div id=”notes111”></div>
<div id="notes"><strong>Notes</strong></div>
<p style="margin-left:1em;">The Mathematica Code is based on Riddle, Ardalan , Suh, 1988 <a href="Multiconductor_Derivation_Ardalan_Riddle_1988_CCSP.pdf"><img src="../pdf.gif" width="22" height="21" alt=""/></a> and has no approximations. Although the code provided is for a 2 Conductor Coupled Microstrip circuit it is written for an arbitrary number of conductors. The key is to generate the Per Unit Length Parameters using the Mathematica <a href="#tools1">Tool</a> and pasting them in ( for Matrices LL and Cap). Also set the number of conductors ( NN). Note that you must decide which result you want to examine. Look at the Vx vector which is the calculated voltage at each node at a distance x from the source To calculate S14 ( Far End Crosstalk) you need Vx for x=0 and Vx fo x=L. Two step process. Unless you set the source impedance to zero for the generator.</p>
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