RF Filter Monte Carlo Analysis
Analyse how component tolerances affect your filter's passband ripple and stopband rejection. Run thousands of Monte Carlo trials to get yield and worst-case statistics.
How It Works
Monte Carlo analysis evaluates how real-world component tolerances affect filter performance. Instead of assuming ideal values, each trial randomly perturbs every capacitor and inductor within its tolerance band, simulates the filter response, and records key metrics.
Over hundreds or thousands of trials, you get the spread of the frequency response and the yield — the percentage of builds meeting your spec — which directly predicts manufacturing success rate.
A build passes when its peak-to-peak |S21| variation across the passband stays within the passband limit and its rejection in the stopband (from 2× the cutoff upward for a low-pass filter, below half the cutoff for a high-pass one) reaches the stopband minimum. Enter your own limits, or leave them blank: the defaults allow 0.5 dB more passband variation and 3 dB less rejection than the design achieves when built from standard (E24) values. Either way the limits stay fixed as you change the tolerance, so yield can only fall as the parts get worse. The passband is evaluated on a dense grid, fine enough to resolve every ripple peak.
Two distribution models are supported: uniform (every value within the tolerance range is equally likely — worst-case analysis) and Gaussian (values cluster around nominal with 3σ equal to the stated tolerance — more realistic for precision components).
The tool synthesises Butterworth (maximally flat) or Chebyshev Type I (equiripple passband) LC ladder filters, then runs the Monte Carlo sweep using exact ABCD matrix chain multiplication for accuracy.
An even-order Chebyshev prototype cannot have equal source and load impedances: its last element value gn+1 is greater than 1, so the design needs a load of gn+1·Z₀. The tool designs and simulates with that load and reports it; into Z₀ the passband would not be equiripple. Odd orders, and every Butterworth, are equally terminated.
Related Calculators
Read the Guide
FAQ
How many Monte Carlo trials do I need?+
For a rough yield estimate, 200-500 trials suffice. For accurate tail statistics (e.g. worst-case at 99.7% confidence), use 2,000-10,000 trials. The free tier supports up to 500; upgrade to Pro for up to 10,000.
Uniform vs Gaussian distribution — which should I use?+
Use uniform for worst-case analysis (every value in the tolerance range is equally likely). Use Gaussian when your components are precision-graded — values cluster near nominal, with outliers rare. Gaussian typically yields higher pass rates for the same tolerance.
Is a Chebyshev filter more sensitive to tolerances than a Butterworth?+
Its ripple peaks and band edge move more for a given component spread, but whether that costs yield depends on the spec. Judged against its own design with the default limits, a 5th-order 0.5 dB Chebyshev yields 91 % with 10 % Gaussian parts and a 5th-order Butterworth 83 %, because the Butterworth passband includes the steep approach to its −3 dB point. Set the limits your system actually needs and compare the two there.
What does the result show?+
The yield with its 95 % confidence interval and the limits it was judged against; the ideal, standard-value and Monte Carlo mean responses with the 5th–95th percentile envelope; each component’s effect on the passband; a histogram of the passband variation across the trials; and the bill of materials in standard values.
Why does an even-order Chebyshev report a different load impedance?+
The Chebyshev prototype of even order ends in g(n+1) = coth²(β/4), which is above 1, so its passband is equiripple only when the load is g(n+1) × Z₀ — about 99 Ω for a 4th-order 0.5 dB design in a 50 Ω system. The tool designs into that load and states it. If both ends must be 50 Ω, use an odd order or add a matching section.