Microstrip Impedance Calculator

// src/lib/circuit-engine.ts — the module this page actually calls.
// Hammerstad & Jensen, "Accurate Models for Microstrip Computer-Aided Design",
// IEEE MTT-S Digest, June 1980. One model end to end: no piecewise u<=1 kernel,
// and no W/h <= 1/(2*pi) thickness branch (that split is Schneider 1969).
const ETA0 = 376.730313668;                      // CODATA 2018 sqrt(mu0/eps0)

function duThickness(u, th, Er) {                // th = t/h, BOTH normalised to h
  if (!(th > 0)) return 0;
  const k = Math.tanh(Math.sqrt(6.517 * u));
  const du1 = (th / Math.PI) * Math.log(1 + (4 * Math.E / th) * k * k);
  return 0.5 * du1 * (1 + 1 / Math.cosh(Math.sqrt(Er - 1)));   // Er = 1 -> factor 1
}
function z0Homogeneous(u) {                      // air-filled impedance, ohm
  const fu = 6 + (2 * Math.PI - 6) * Math.exp(-Math.pow(30.666 / u, 0.7528));
  return (ETA0 / (2 * Math.PI)) * Math.log(fu / u + Math.sqrt(1 + (2 / u) * (2 / u)));
}
function epsEffHammerstad(u, Er) {
  const a = 1 + Math.log((Math.pow(u, 4) + Math.pow(u / 52, 2)) / (Math.pow(u, 4) + 0.432)) / 49
              + Math.log(1 + Math.pow(u / 18.1, 3)) / 18.7;
  const b = 0.564 * Math.pow((Er - 0.9) / (Er + 3), 0.053);
  return (Er + 1) / 2 + ((Er - 1) / 2) * Math.pow(1 + 10 / u, -a * b);
}
function microstripZ0(W, H, Tmm, Er) {
  const u = W / H, th = Tmm / H;
  const u1 = u + duThickness(u, th, 1);          // air-filled corrected width
  const ur = u + duThickness(u, th, Er);         // dielectric-loaded corrected width
  const e0 = epsEffHammerstad(ur, Er), zr = z0Homogeneous(ur);
  const ratio = z0Homogeneous(u1) / zr;          // Tmm = 0 -> ratio = 1
  return { Z0: zr / Math.sqrt(e0), eff: e0 * ratio * ratio };
}
function gamma(ZL, Z0) { return (ZL - Z0) / (ZL + Z0); }