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Statistical Simulations
Figure 1. Monte Carlo simulation (red) results using Gaussian distributions for the inductors and min/max/step (~bi-model) deviations for the capacitors (0.85/1.15/0.3) around the nominal value and measured data for 14 filter samples. The red curves are the statistical simulations and the other colors represent 14 measured filter samples.

Statistical Simulations

An advantage of the equivalent circuit model approach is in representing manufacturing tolerance. Results from a Monte Carlo simulation using Gaussian distributions about the nominal part values are shown in Figure 1.

In the simulator, the standard deviations for the inductors and capacitors were specified at +/- 1.66% and +/- 5%, respectively. Over 30 simulation trials, the extreme capacitance values obtained were 86% and 114% of the nominal value, or about three standard deviations. This is a typical result, and is the reason why the specified standard deviation in a simulator should be ~33% of the vendor-specified tolerance if the part value spread is assumed to be Gaussian.

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