complexpole_demo.va

// complexpole_demo.va -- Enhancement-31: complex conjugate poles/zeros in the
// laplace/zi ROOT forms (`*_np`, `*_zd`, `*_zp`).
//
// Per the Verilog-AMS LRM the pole/zero vectors of the pole/zero forms hold
// (real, imaginary) PAIRS: element 2k is the real part and 2k+1 the imaginary part
// of root k. A complex conjugate pair is written `{re, +im, re, -im}`; a real root
// is `{re, 0}` (a lone trailing real element is also accepted). Previously OpenVAF
// read the vector as individual REAL roots, so complex poles/zeros -- i.e. every
// resonant / underdamped section -- were impossible.
//
// This model builds two classic 2nd-order sections that REQUIRE complex roots and
// cross-checks the root forms against the equivalent `laplace_nd` polynomial form:
//
//   * a resonant low-pass  H(s) = w0^2 / (s^2 + (w0/Q) s + w0^2)
//       poles = -w0/(2Q) +/- j*w0*sqrt(1 - 1/(4Q^2))   (complex conjugate pair)
//       -> laplace_np with a complex pole pair, vs laplace_nd baseline
//
//   * a notch / band-stop  H(s) = (s^2 + w0^2) / (s^2 + (w0/Q) s + w0^2)
//       zeros = +/- j*w0                                (imaginary-axis pair)
//       -> laplace_zd with a complex zero pair, vs laplace_nd baseline

`include "disciplines.vams"

module complexpole_demo(in, lp_nd, lp_np, notch_nd, notch_zd);
    input in;
    output lp_nd, lp_np, notch_nd, notch_zd;
    electrical in, lp_nd, lp_np, notch_nd, notch_zd;

    parameter real w0 = 6.283185307e6 from (0:inf);   // 2*pi*1e6  (f0 = 1 MHz)
    parameter real Q  = 8.0           from (0:inf);   // quality factor

    real w02, wnQ, sig, wd;

    analog begin
        w02 = w0 * w0;
        wnQ = w0 / Q;
        sig = -w0 / (2.0 * Q);                       // pole real part
        wd  = w0 * sqrt(1.0 - 1.0 / (4.0 * Q * Q));  // pole imaginary part

        // Resonant low-pass -- complex conjugate POLES
        V(lp_nd) <+ laplace_nd(V(in), '{w02},          '{w02, wnQ, 1.0});
        // Enhancement-395: the root forms are products of (1 - s/r), per LRM
        // 4.5.11, so the denominator built from the pole pair already carries
        // the 1/w02 normalisation and the numerator is a bare 1.0. It used to
        // be '{w02} here, compensating for an UNNORMALISED prod(s - r).
        V(lp_np) <+ laplace_np(V(in), '{1.0},           '{sig, wd, sig, -wd});

        // Notch -- complex ZEROS on the imaginary axis at +/- j*w0
        V(notch_nd) <+ laplace_nd(V(in), '{w02, 0.0, 1.0}, '{w02, wnQ, 1.0});
        // Same normalisation on the ZERO side: prod(1 - s/z) for zeros at
        // +/- j*w0 is (s^2 + w02)/w02, so the denominator coefficients are
        // scaled by 1/w02 to keep H(s) identical to the nd spelling.
        V(notch_zd) <+ laplace_zd(V(in), '{0.0, w0, 0.0, -w0},
                                  '{1.0, wnQ/w02, 1.0/w02});
    end
endmodule