Nonlinearity behavior of OTA all-pass unit

[jpcima]

Stumbled upon this paper, suggesting a digital model for OTA stages.

Huovilainen, Antti. "Enhanced digital models for analog modulation effects." Proc. Int. Conf. Digital Audio Effects (DAFx-05), Madrid, Spain. 2005.

I wrote faust code of the digital model section 3.2 (substitute the tanh later)

ota_allpass(f, x) =
  x + w
letrec {
  'w = w + (2 * R1 * Vt * g / R2) * ma.tanh(-R2 * (x + x' + w) / (2 * R1 * Vt));
}
with {
  g = 1 - exp(f * (-2 * ma.PI / ma.SR));
  // components
  R1 = 27e3;
  R2 = 10e3;
  C = 68e-9;
  // characteristics
  Vt = 25e-3;
};

Effect on phase response depending on signal level. (on the left is original, right is OTA)

[jpcima]

This is a tabulated tanh function.

copysign(x, y) = ba.if(y<0, -1, +1) * abs(x);

fastTanh(x) = copysign((tab(i1), tab(i2)) : si.interpolate(mu), x) with {
  xmax = 5.0;
  size = 128;
  tab = rdtable(size, (float(ba.time)/float(size-1)) : *(xmax) : ma.tanh);
  pos = (float(size-1)/xmax)*abs(x);
  mu = pos-int(pos);
  i1 = min(int(pos), size-1);
  i2 = min(int(pos)+1, size-1);
};