yield_examples

yield_examples — process/mismatch correlations + Monte Carlo yield (Enhancement-151)

Two related pieces that complete the statistical flow:

1. Native process/mismatch correlations — mccorr + mvnorm(), so random .params can be correlated (a shared process factor, a mismatch covariance, an arbitrary correlation matrix) instead of only independent.
2. A packaged yield command — montecarlo, which runs the Monte Carlo, applies pass/fail specs, and reports the yield with a confidence interval.

Correlations — mccorr + mvnorm

Plain ngspice Monte Carlo draws every agauss/gauss independently, so matched devices can't be modelled — yet whether two devices' variation is correlated is often what decides the yield. mccorr registers a k × k correlation matrix (Cholesky-factored once), and mvnorm(i) returns the i-th component of one correlated standard-normal draw per Monte Carlo sample:

mccorr 2  1 0.9  0.9 1                 ; 90% correlation between two factors
.param r1 = 1000 + 50*mvnorm(1)        ; r1, r2 now vary together
.param r2 = 1000 + 50*mvnorm(2)

mvnorm(i) inherits the active sampler: it composes with Latin-Hypercube (Enhancement-149) and scaled-sigma importance sampling (Enhancement-150) automatically, and with no matrix registered it simply draws independently. The common process + local mismatch model is the special case p = sigma_proc*mvnorm(shared) + sigma_mm*agauss(...).

Yield — montecarlo

montecarlo <N> [-lhs] [-seed <s>] [-analysis <cmd>]
           (-spec <metric> [-max <hi>] [-min <lo>])...

Runs N samples; a sample passes only if every spec's metric is within its -max/-min limits. Reports the yield (fraction passing) with a Wilson 95% confidence interval and a per-spec violation count, and leaves montecarlo_yield, montecarlo_npass, montecarlo_n for scripting. -lhs draws Latin-Hypercube samples for a much lower-variance yield estimate.

• Process corners are the ordinary .lib/.include corner selection — load a corner model set, then run montecarlo at that corner. Correlations and corners compose: run the yield MC at each corner.

Files

• yield_demo.cir — a matched resistor divider with a ±4% ratio spec; the same devices give ~100% yield when process-correlated (ρ=0.9) but only ~74% when independent (ρ=0) — the correlation model is what decides it. Run with ngspice -b yield_demo.cir.
• verify_yield.py — validation against analytic ground truth (Sparse-only — a heavy, thousands-of-re-sources deck):
  1. an mccorr ρ=+0.7 / −0.6 matrix reproduces the target correlation, means, and sigmas;
  2. mvnorm without a matrix draws independently;
  3. a non-positive-definite matrix is rejected;
  4. single two-sided spec yield matches P(|Z| < k);
  5. two independent specs' yields multiply;
  6. -lhs is unbiased and much lower-variance;
  7. positive parameter correlation raises the joint yield.

python3 verify_yield.py

Notes

• mvnorm(i) returns a unit-variance standard normal; scale it in the .param (nom + sigma*mvnorm(i)). The mccorr matrix is a correlation matrix (unit diagonal).
• Correlations and yield are front-end features (they change only which parameter values are drawn), so they are solver-independent; the verify is a heavy deck and runs under Sparse only.
• Every SPICE deck's first line is the title (ignored by the parser); the decks here start with a * title line accordingly.