// -------------------------------------------------------------------
void COPLANAR::calc()
{
skindepth = skin_depth();
// other local variables (quasi-static constants)
double k1, kk1, kpk1, k2, k3, q1, q2, q3 = 0, qz, er0 = 0;
double zl_factor;
// compute the necessary quasi-static approx. (K1, K3, er(0) and Z(0))
k1 = w / (w + s + s);
kk1 = ellipk( k1 );
kpk1 = ellipk( sqrt( 1 - k1 * k1 ) );
q1 = kk1 / kpk1;
// backside is metal
if( backMetal )
{
k3 = tanh( (M_PI / 4) * (w / h) ) / tanh( (M_PI / 4) * (w + s + s) / h );
q3 = ellipk( k3 ) / ellipk( sqrt( 1 - k3 * k3 ) );
qz = 1 / (q1 + q3);
er0 = 1 + q3 * qz * (er - 1);
zl_factor = ZF0 / 2 * qz;
}
// backside is air
else
{
k2 = sinh( (M_PI / 4) * (w / h) ) / sinh( (M_PI / 4) * (w + s + s) / h );
q2 = ellipk( k2 ) / ellipk( sqrt( 1 - k2 * k2 ) );
er0 = 1 + (er - 1) / 2 * q2 / q1;
zl_factor = ZF0 / 4 / q1;
}
// adds effect of strip thickness
if( t > 0 )
{
double d, se, We, ke, qe;
d = (t * 1.25 / M_PI) * ( 1 + log( 4 * M_PI * w / t ) );
se = s - d;
We = w + d;
// modifies k1 accordingly (k1 = ke)
ke = We / (We + se + se); // ke = k1 + (1 - k1 * k1) * d / 2 / s;
qe = ellipk( ke ) / ellipk( sqrt( 1 - ke * ke ) );
// backside is metal
if( backMetal )
{
qz = 1 / (qe + q3);
er0 = 1 + q3 * qz * (er - 1);
zl_factor = ZF0 / 2 * qz;
}
// backside is air
else
{
zl_factor = ZF0 / 4 / qe;
}
// modifies er0 as well
er0 = er0 - (0.7 * (er0 - 1) * t / s) / ( q1 + (0.7 * t / s) );
}
// pre-compute square roots
double sr_er = sqrt( er );
double sr_er0 = sqrt( er0 );
// cut-off frequency of the TE0 mode
double fte = (C0 / 4) / ( h * sqrt( er - 1 ) );
// dispersion factor G
double p = log( w / h );
double u = 0.54 - (0.64 - 0.015 * p) * p;
double v = 0.43 - (0.86 - 0.54 * p) * p;
double G = exp( u * log( w / s ) + v );
// loss constant factors (computed only once for efficency sake)
double ac = 0;
if( t > 0 )
{
// equations by GHIONE
double n = (1 - k1) * 8 * M_PI / ( t * (1 + k1) );
double a = w / 2;
double b = a + s;
ac = ( M_PI + log( n * a ) ) / a + ( M_PI + log( n * b ) ) / b;
}
double ac_factor = ac / ( 4 * ZF0 * kk1 * kpk1 * (1 - k1 * k1) );
double ad_factor = ( er / (er - 1) ) * tand * M_PI / C0;
// ....................................................
double sr_er_f = sr_er0;
// add the dispersive effects to er0
sr_er_f += (sr_er - sr_er0) / ( 1 + G * pow( f / fte, -1.8 ) );
// for now, the loss are limited to strip losses (no radiation
// losses yet) losses in neper/length
atten_cond = 20.0 / log( 10.0 ) * len
* ac_factor * sr_er0 * sqrt( M_PI * MU0 * f / sigma );
atten_dielectric = 20.0 / log( 10.0 ) * len
* ad_factor * f * (sr_er_f * sr_er_f - 1) / sr_er_f;
ang_l = 2.0 * M_PI * len * sr_er_f * f / C0; /* in radians */
er_eff = sr_er_f * sr_er_f;
Z0 = zl_factor / sr_er_f;
}
double coplanar::KoverKp(double k) {
if ((k < 0.0) || (k >= 1.0))
return std::numeric_limits<double>::quiet_NaN();
return (ellipk(k) / ellipk(sqrt(1-k*k)));
}
