complexpole_examples

complexpole_examples — complex poles/zeros in laplace/zi root forms (Enhancement-31)

Demonstrates complex conjugate poles and zeros in the root-based Laplace / z-domain filter forms (*_np, *_zd, *_zp), using version11's own openvaf-r and ngspice-46.

What was broken

The pole/zero vectors of laplace_np/laplace_zd/laplace_zp and the zi_* counterparts are, per the LRM, (real, imaginary) pairs. OpenVAF expanded them as a list of individual real roots, so complex conjugate poles/zeros — every resonant or underdamped section — couldn't be expressed. A Q=5 resonant low-pass via laplace_np with the correct complex pole pair produced −242 dB of garbage.

The fix

laplace_roots_to_poly (shared by all six root forms) now reads the vector as (re, im) pairs and expands Π_k (s − (re_k + j·im_k)) with complex arithmetic, returning the real polynomial coefficients (the imaginary parts cancel for physical, conjugate-paired inputs). See ../Enhancement-31.md.

Root vectors are now written as pairs:

• real root: '{r, 0} (a lone '{r} is also accepted)
• complex conjugate: '{re, +im, re, -im}

The demo

complexpole_demo.va builds two sections that require complex roots and compares the root form to the equivalent laplace_nd polynomial baseline:

• resonant low-pass — laplace_np with a complex conjugate pole pair -w0/(2Q) ± j·w0·√(1−1/4Q²);
• notch / band-stop — laplace_zd with imaginary-axis complex zeros ± j·w0.

Run

python3 verify_complexpole.py

Checks (ALL PASS): laplace_np (complex poles) and laplace_zd (complex zeros) match the laplace_nd baseline to 0.00 dB; the complex poles give a real resonant peak of +18.06 dB at 1 MHz (= 20·log₁₀(Q=8)); the complex zeros give a deep notch null at 1 MHz.