Using coarse
and fine convergence on the Si8000 

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The Si8000 field solver "goal seeks" for parameter dimensions (core
thickness H1, trace widths W1, W2, etc.) on
controlled impedance structures using an iterative calculation process.
Goal seeking continues until the Si8000 convergence process brings the
parameter within acceptable limits.
Controlled impedance structure parameters Although any parameter can vary, many
parameters within a structure will be fixed and will not require goal
seeking. The substrate dielectric Er1 will be a function of the glass/resin mix (assuming FR4) and will be in the order of 3.8 to 5.0 (bulk values) though should only vary within small limits of the specified value between batches. The coating dielectric constant CEr will be a function of the coating ink; in this example we assume the same Er values for core material and coating. Other parameters will be determined by the manufacturing process: the coating thicknesses C1 and C2 will be a function of the method of application of LPI, curtain coat, spray, etc., the etch factor of the signal trace will be fixed by the etching process. Using coarse and fine convergence Some parameters will be variable but constrained within limits; for example, core thickness will vary but in discrete increments. For these parameters, it is appropriate to goal seek using coarse convergence, with its associated time savings, to arrive at a final value. Other parameters such as trace width W1, W2 can be regarded as infinitely variable. To arrive at the correct value within fine limits use fine convergence. Solving for parameter values In this note we consider the Coated Microstrip 1B structure, a coated microstrip with a single dielectric below the signal trace. The Coated Microstrip 1B model is shown below alongside the default Si8000 parameters for the structure. 

Coated Microstrip with single dielectric below the trace 

For this example we will derive the
parameter values to produce an impedance of 75Ohms.
Ensure the Interface Style is set to Standard. (This saves excessive time goal seeking on tolerances — only turn the extended interface on when you have found your nominal values) This is especially true on the more complex coplanar structures, which make extensive demands on your PC. Begin by entering the parameter values which are defined by the supplied materials and manufacturing processes. For this example leave all values as above. Click the Calculate button to calculate Zo. The resulting impedance should be 71.12Ohms. In this example we require a value as close to 75Ohms as practicable. Solving for Substrate height We first require a value for core thickness to match the thickness produced by the material supplier. Because the value of H1 is not infinitely variable we can choose coarse convergence. This will reduce the number of iterations before the value for core thickness (H1) is brought within acceptable limits. 

Use the Si8000 Configure
command to specify calculation parameters.
By default the number of Goal Seek Tries is set to 20, the value for fine convergence is set to 0.01Ohms and the value for coarse convergence is set to 2Ohms. Change these values to limits appropriate to the application. The etch factor (the difference between W1 and W2) is set by default to 1mil. Alter the value (the Si8000 will model positive or negative slopes) to match the finished process value. 
Si8000 configuration screen 
To goal seek for height enter a value of 75Ohms in the Impedance text box and click the Substrate 1 Height Calculate button to solve for H1. The resulting value of H1 should be 9.55 mils. In this application the nearest available finished material thickness is 9.3 mils. Calculating for Zo using this value for H1 yields an impedance value of 74.11Ohms, an error of just over 1%. For many applications this would be acceptable Solving for trace width With the dielectric height decided, we solve for trace width to produce a final impedance of exactly 75Ohms. Because the trace width is infinitely variable, we use fine convergence. Switch the Si8000 Convergence setting to Fine. Enter 9.3 mils in the Substrate 1 Height text box, reenter 75Ohms in the Impedance text box and click the Upper Trace Width Calculate button W2, the upper trace width resolves to 5.78 mils; with the lower trace width etch factor at 1 mil the lower trace width will therefore be 6.78 mil. The resulting impedance will resolve to 75 Ohms. At Polar, we are always interested in new suggestions and ideas for application notes. If you have an idea related to high speed board construction, or a suggestion for an application note please email ralph.bryce@polarinstruments.com 
Polar Instruments Ltd www.polarinstruments.com Tel: +44 1481 253081 Fax: +44 1481 252476 © Polar Instruments 2003 

© Polar Instruments 2003. Polar Instruments pursues a policy of continuous improvement. The specifications in this document may therefore be changed without notice. All trademarks recognised. 