c_microstrip.cpp

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/*
 * c_microstrip.cpp - coupled microstrip class implementation
 * 
 * Copyright (C) 2002 Claudio Girardi <claudio.girardi@ieee.org>
 * Copyright (C) 2005, 2006 Stefan Jahn <stefan@lkcc.org>
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this package; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street - Fifth Floor,
 * Boston, MA 02110-1301, USA.  
 *
 */

/* c_microstrip.c - Puts up window for coupled microstrips and 
 * performs the associated calculations
 * Based on the original microstrip.c by Gopal Narayanan 
 */

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <math.h>

#include "units.h"
#include "transline.h"
#include "microstrip.h"
#include "c_microstrip.h"

c_microstrip::c_microstrip() : transline()
{
  aux_ms = NULL;
}

c_microstrip::~c_microstrip()
{
  if (aux_ms) delete aux_ms;
}

/*
 * delta_u_thickness_single() computes the thickness effect on
 * normalized width for a single microstrip line
 *
 * References: H. A. Atwater, "Simplified Design Equations for
 * Microstrip Line Parameters", Microwave Journal, pp. 109-115,
 * November 1989.
 */
double c_microstrip::delta_u_thickness_single(double u, double t_h)
{
  double delta_u;

  if (t_h > 0.0) {
    delta_u = (1.25 * t_h / M_PI) * (1.0 + log((2.0 + (4.0 * M_PI * u - 2.0) / (1.0 + exp(-100.0 * (u - 1.0 / (2.0 * M_PI))))) / t_h));
  } else {
    delta_u = 0.0;
  }
  return delta_u;
}

/*
 * delta_u_thickness() - compute the thickness effect on normalized
 * width for coupled microstrips
 *
 * References: Rolf Jansen, "High-Speed Cmputation of Single and
 * Coupled Microstrip Parameters Including Dispersion, High-Order
 * Modes, Loss and Finite Strip Thickness", IEEE Trans. MTT, vol. 26,
 * no. 2, pp. 75-82, Feb. 1978
 */
void c_microstrip::delta_u_thickness()
{
  double e_r, u, g, t_h;
  double delta_u, delta_t, delta_u_e, delta_u_o;

  e_r = er;
  u = w / h;            /* normalized line width */
  g = s / h;            /* normalized line spacing */
  t_h = t / h;          /* normalized strip thickness */

  if (t_h > 0.0) {
    /* single microstrip correction for finite strip thickness */
    delta_u = delta_u_thickness_single(u, t_h);
    delta_t = t_h / (g * e_r);
    /* thickness correction for the even- and odd-mode */
    delta_u_e = delta_u * (1.0 - 0.5 * exp(-0.69 * delta_u / delta_t));
    delta_u_o = delta_u_e + delta_t;
  } else {
    delta_u_e = delta_u_o = 0.0;
  }

  w_t_e = w + delta_u_e * h;
  w_t_o = w + delta_u_o * h;
}

/*
 * compute various parameters for a single line
 */
void c_microstrip::compute_single_line()
{
  double w_h, ht_h;
  double Z0_single, er_eff_single;

  ht_h = ht / h;
  w_h = w / h;

  if (aux_ms == NULL)
    aux_ms = new microstrip ();

  /* prepare parameters for single microstrip computations */
  aux_ms->er = er;
  aux_ms->w = w;
  aux_ms->h = h;
  aux_ms->t = 0.0;
  //aux_ms->t = t;
  aux_ms->ht = 1e12;        /* arbitrarily high */
  aux_ms->f = f;
  aux_ms->mur = mur;
  aux_ms->microstrip_Z0();
  aux_ms->dispersion();

  er_eff_single = aux_ms->er_eff_0;
  Z0_single = aux_ms->Z0_0;
}


/*
 * filling_factor_even() - compute the filling factor for the coupled
 * microstrips even-mode without cover and zero conductor thickness
 */
double c_microstrip::filling_factor_even(double u, double g, double e_r)
{
  double v, v3, v4, a_e, b_e, q_inf;

  v = u * (20.0 + g * g) / (10.0 + g * g) + g * exp(-g);
  v3 = v * v * v;
  v4 = v3 * v;
  a_e = 1.0 + log((v4 + v * v / 2704.0) / (v4 + 0.432)) / 49.0 + log(1.0 + v3 / 5929.741)
    / 18.7;
  b_e = 0.564 * pow(((e_r - 0.9) / (e_r + 3.0)), 0.053);

  /* filling factor, with width corrected for thickness */
  q_inf = pow((1.0 + 10.0 / v), -a_e * b_e);

  return q_inf;
}

double c_microstrip::filling_factor_odd(double u, double g, double e_r)
{
  double b_o, c_o, d_o, q_inf;

  b_o = 0.747 * e_r / (0.15 + e_r);
  c_o = b_o - (b_o - 0.207) * exp(-0.414 * u);
  d_o = 0.593 + 0.694 * exp(-0.562 * u);

  /* filling factor, with width corrected for thickness */
  q_inf = exp(-c_o * pow(g, d_o));

  return q_inf;
}


/*
 * delta_q_cover_even() - compute the cover effect on filling factor
 * for the even-mode
 */
double c_microstrip::delta_q_cover_even(double h2h)
{
  double q_c;

  if (h2h <= 39) {
    q_c = tanh(1.626 + 0.107 * h2h - 1.733 / sqrt(h2h));
  } else {
    q_c = 1.0;
  }

  return q_c;
}

/*
 * delta_q_cover_odd() - compute the cover effect on filling factor
 * for the odd-mode
 */
double c_microstrip::delta_q_cover_odd(double h2h)
{
  double q_c;

  if (h2h <= 7) {
    q_c = tanh(9.575 / (7.0 - h2h) - 2.965 + 1.68 * h2h - 0.311 * h2h * h2h);
  } else {
    q_c = 1.0;
  }

  return q_c;
}

void c_microstrip::er_eff_static()
{
  double u_t_e, u_t_o, g, h2, h2h;
  double a_o, t_h, q, q_c, q_t, q_inf;
  double er_eff_single;

  /* compute zero-thickness single line parameters */
  compute_single_line();
  er_eff_single = aux_ms->er_eff_0;

  h2 = ht;
  u_t_e = w_t_e / h;        /* normalized even_mode line width */
  u_t_o = w_t_o / h;        /* normalized odd_mode line width */
  g = s / h;            /* normalized line spacing */
  h2h = h2 / h;         /* normalized cover height */
  t_h = t / h;          /* normalized strip thickness */

  /* filling factor, computed with thickness corrected width */
  q_inf = filling_factor_even(u_t_e, g, er);
  /* cover effect */
  q_c = delta_q_cover_even(h2h);
  /* thickness effect */
  q_t = aux_ms->delta_q_thickness(u_t_e, t_h);
  /* resultant filling factor */
  q = (q_inf - q_t) * q_c;
  /* static even-mode effective dielectric constant */
  er_eff_e_0 = 0.5 * (er + 1.0) + 0.5 * (er - 1.0) * q;

  /* filling factor, with width corrected for thickness */
  q_inf = filling_factor_odd(u_t_o, g, er);
  /* cover effect */
  q_c = delta_q_cover_odd(h2h);
  /* thickness effect */
  q_t = aux_ms->delta_q_thickness(u_t_o, t_h);
  /* resultant filling factor */
  q = (q_inf - q_t) * q_c;

  a_o = 0.7287 * (er_eff_single - 0.5 * (er + 1.0)) * (1.0 - exp(-0.179 * u_t_o));

  /* static odd-mode effective dielectric constant */
  er_eff_o_0 = (0.5 * (er + 1.0) + a_o - er_eff_single) * q + er_eff_single;
}


double c_microstrip::delta_Z0_even_cover(double g, double u, double h2h)
{
  double f_e, g_e, delta_Z0_even;
  double x, y, A, B, C, D, E, F;

  A = -4.351 / pow(1.0 + h2h, 1.842);
  B = 6.639 / pow(1.0 + h2h, 1.861);
  C = -2.291 / pow(1.0 + h2h, 1.90);
  f_e = 1.0 - atanh(A + (B + C * u) * u);

  x = pow(10.0, 0.103 * g - 0.159);
  y = pow(10.0, 0.0492 * g - 0.073);
  D = 0.747 / sin(0.5 * M_PI * x);
  E = 0.725 * sin(0.5 * M_PI * y);
  F = pow(10.0, 0.11 - 0.0947 * g);
  g_e = 270.0 * (1.0 - tanh(D + E * sqrt(1.0 + h2h) - F / (1.0 + h2h)));

  delta_Z0_even = f_e * g_e;

  return delta_Z0_even;
}


double c_microstrip::delta_Z0_odd_cover(double g, double u, double h2h)
{
  double f_o, g_o, delta_Z0_odd;
  double G, J, K, L;

  J = tanh(pow(1.0 + h2h, 1.585) / 6.0);
  f_o = pow(u, J);

  G = 2.178 - 0.796 * g;
  if (g > 0.858) {
    K = log10(20.492 * pow(g, 0.174));
  } else {
    K = 1.30;
  }
  if (g > 0.873) {
    L = 2.51 * pow(g, -0.462);
  } else {
    L = 2.674;
  }
  g_o = 270.0 * (1.0 - tanh(G + K * sqrt(1.0 + h2h) - L / (1.0 + h2h)));

  delta_Z0_odd = f_o * g_o;

  return delta_Z0_odd;
}

void c_microstrip::Z0_even_odd()
{
  double er_eff, h2, u_t_e, u_t_o, g, h2h;
  double Q_1, Q_2, Q_3, Q_4, Q_5, Q_6, Q_7, Q_8, Q_9, Q_10;
  double delta_Z0_e_0, delta_Z0_o_0, Z0_single, er_eff_single;

  h2 = ht;
  u_t_e = w_t_e / h;        /* normalized even-mode line width */
  u_t_o = w_t_o / h;        /* normalized odd-mode line width */
  g = s / h;            /* normalized line spacing */
  h2h = h2 / h;         /* normalized cover height */

  Z0_single = aux_ms->Z0_0;
  er_eff_single = aux_ms->er_eff_0;

  /* even-mode */
  er_eff = er_eff_e_0;
  Q_1 = 0.8695 * pow(u_t_e, 0.194);
  Q_2 = 1.0 + 0.7519 * g + 0.189 * pow(g, 2.31);
  Q_3 = 0.1975 + pow((16.6 + pow((8.4 / g), 6.0)), -0.387) + log(pow(g, 10.0) / (1.0 + pow(g / 3.4, 10.0))) / 241.0;
  Q_4 = 2.0 * Q_1 / (Q_2 * (exp(-g) * pow(u_t_e, Q_3) + (2.0 - exp(-g)) * pow(u_t_e, -Q_3)));
  /* static even-mode impedance */
  Z0_e_0 = Z0_single * sqrt(er_eff_single / er_eff) / (1.0 - sqrt(er_eff_single) * Q_4 * Z0_single / ZF0);
  /* correction for cover */
  delta_Z0_e_0 = delta_Z0_even_cover(g, u_t_e, h2h) / sqrt(er_eff);

  Z0_e_0 = Z0_e_0 - delta_Z0_e_0;

  /* odd-mode */
  er_eff = er_eff_o_0;
  Q_5 = 1.794 + 1.14 * log(1.0 + 0.638 / (g + 0.517 * pow(g, 2.43)));
  Q_6 = 0.2305 + log(pow(g, 10.0) / (1.0 + pow(g / 5.8, 10.0))) / 281.3 + log(1.0 + 0.598 * pow(g, 1.154)) / 5.1;
  Q_7 = (10.0 + 190.0 * g * g) / (1.0 + 82.3 * g * g * g);
  Q_8 = exp(-6.5 - 0.95 * log(g) - pow(g / 0.15, 5.0));
  Q_9 = log(Q_7) * (Q_8 + 1.0 / 16.5);
  Q_10 = (Q_2 * Q_4 - Q_5 * exp(log(u_t_o) * Q_6 * pow(u_t_o, -Q_9))) / Q_2;

  /* static odd-mode impedance */
  Z0_o_0 = Z0_single * sqrt(er_eff_single / er_eff) / (1.0 - sqrt(er_eff_single) * Q_10 * Z0_single / ZF0);
  /* correction for cover */
  delta_Z0_o_0 = delta_Z0_odd_cover(g, u_t_o, h2h) / sqrt(er_eff);

  Z0_o_0 = Z0_o_0 - delta_Z0_o_0;
}


/*
 * mur_eff() - returns effective magnetic permeability 
 */
double c_microstrip::calc_mur_eff()
{
  double mureff;
  mureff = mur;     /* FIXME: ... */
  return mureff;
}


/*
 * er_eff_freq() - compute er_eff as a function of frequency
 */
void c_microstrip::er_eff_freq()
{
  double P_1, P_2, P_3, P_4, P_5, P_6, P_7;
  double P_8, P_9, P_10, P_11, P_12, P_13, P_14, P_15;
  double F_e, F_o;
  double er_eff, u, g, f_n;

  u = w / h;            /* normalize line width */
  g = s / h;            /* normalize line spacing */

  /* normalized frequency [GHz * mm] */
  f_n = f * h / 1e06;

  er_eff = er_eff_e_0;
  P_1 = 0.27488 + (0.6315 + 0.525 / pow(1.0 + 0.0157 * f_n, 20.0)) * u - 0.065683 * exp(-8.7513 * u);
  P_2 = 0.33622 * (1.0 - exp(-0.03442 * er));
  P_3 = 0.0363 * exp(-4.6 * u) * (1.0 - exp(-pow(f_n / 38.7, 4.97)));
  P_4 = 1.0 + 2.751 * (1.0 - exp(-pow(er / 15.916, 8.0)));
  P_5 = 0.334 * exp(-3.3 * pow(er / 15.0, 3.0)) + 0.746;
  P_6 = P_5 * exp(-pow(f_n / 18.0, 0.368));
  P_7 = 1.0 + 4.069 * P_6 * pow(g, 0.479) * exp(-1.347 * pow(g, 0.595) - 0.17 * pow(g, 2.5));

  F_e = P_1 * P_2 * pow((P_3 * P_4 + 0.1844 * P_7) * f_n, 1.5763);
  /* even-mode effective dielectric constant */
  er_eff_e = er - (er - er_eff) / (1.0 + F_e);

  er_eff = er_eff_o_0;
  P_8 = 0.7168 * (1.0 + 1.076 / (1.0 + 0.0576 * (er - 1.0)));
  P_9 = P_8 - 0.7913 * (1.0 - exp(-pow(f_n / 20.0, 1.424))) * atan(2.481 * pow(er / 8.0, 0.946));
  P_10 = 0.242 * pow(er - 1.0, 0.55);
  P_11 = 0.6366 * (exp(-0.3401 * f_n) - 1.0) * atan(1.263 * pow(u / 3.0, 1.629));
  P_12 = P_9 + (1.0 - P_9) / (1.0 + 1.183 * pow(u, 1.376));
  P_13 = 1.695 * P_10 / (0.414 + 1.605 * P_10);
  P_14 = 0.8928 + 0.1072 * (1.0 - exp(-0.42 * pow(f_n / 20.0, 3.215)));
  P_15 = fabs(1.0 - 0.8928 * (1.0 + P_11) * P_12 * exp(-P_13 * pow(g, 1.092)) / P_14);

  F_o = P_1 * P_2 * pow((P_3 * P_4 + 0.1844) * f_n * P_15, 1.5763);
  /* odd-mode effective dielectric constant */
  er_eff_o = er - (er - er_eff) / (1.0 + F_o);
}

/*
 * conductor_losses() - compute microstrips conductor losses per unit
 * length
 */
void c_microstrip::conductor_losses()
{
  double e_r_eff_e_0, e_r_eff_o_0, Z0_h_e, Z0_h_o, delta;
  double K, R_s, Q_c_e, Q_c_o, alpha_c_e, alpha_c_o;

  e_r_eff_e_0 = er_eff_e_0;
  e_r_eff_o_0 = er_eff_o_0;
  Z0_h_e = Z0_e_0 * sqrt(e_r_eff_e_0);  /* homogeneous stripline impedance */
  Z0_h_o = Z0_o_0 * sqrt(e_r_eff_o_0);  /* homogeneous stripline impedance */
  delta = skindepth;

  if (f > 0.0) {
    /* current distribution factor (same for the two modes) */
    K = exp(-1.2 * pow((Z0_h_e + Z0_h_o) / (2.0 * ZF0), 0.7));
    /* skin resistance */
    R_s = 1.0 / (sigma * delta);
    /* correction for surface roughness */
    R_s *= 1.0 + ((2.0 / M_PI) * atan(1.40 * pow((rough / delta), 2.0)));
    
    /* even-mode strip inductive quality factor */
    Q_c_e = (M_PI * Z0_h_e * w * f) / (R_s * C0 * K);
    /* even-mode losses per unith length */
    alpha_c_e = (20.0 * M_PI / log(10.0)) * f * sqrt(e_r_eff_e_0) / (C0 * Q_c_e);
    
  /* odd-mode strip inductive quality factor */
    Q_c_o = (M_PI * Z0_h_o * w * f) / (R_s * C0 * K);
    /* odd-mode losses per unith length */
    alpha_c_o = (20.0 * M_PI / log(10.0)) * f * sqrt(e_r_eff_o_0) / (C0 * Q_c_o);
  } else {
    alpha_c_e = alpha_c_o = 0.0;
  }
  
  atten_cond_e = alpha_c_e * l;
  atten_cond_o = alpha_c_o * l;
}


/*
 * dielectric_losses() - compute microstrips dielectric losses per
 * unit length
 */
void c_microstrip::dielectric_losses()
{
  double e_r, e_r_eff_e_0, e_r_eff_o_0;
  double alpha_d_e, alpha_d_o;

  e_r = er;
  e_r_eff_e_0 = er_eff_e_0;
  e_r_eff_o_0 = er_eff_o_0;

  alpha_d_e = (20.0 * M_PI / log(10.0)) * (f / C0) * (e_r / sqrt(e_r_eff_e_0)) * ((e_r_eff_e_0 - 1.0) / (e_r - 1.0)) * tand;
  alpha_d_o = (20.0 * M_PI / log(10.0)) * (f / C0) * (e_r / sqrt(e_r_eff_o_0)) * ((e_r_eff_o_0 - 1.0) / (e_r - 1.0)) * tand;

  atten_dielectric_e = alpha_d_e * l;
  atten_dielectric_o = alpha_d_o * l;
}


/*
 * c_microstrip_attenuation() - compute attenuation of coupled
 * microstrips
 */
void c_microstrip::attenuation()
{
  skindepth = skin_depth();
  conductor_losses();
  dielectric_losses();
}


/*
 * line_angle() - calculate strips electrical lengths in radians
 */
void c_microstrip::line_angle()
{
  double e_r_eff_e, e_r_eff_o;
  double v_e, v_o, lambda_g_e, lambda_g_o;

  e_r_eff_e = er_eff_e;
  e_r_eff_o = er_eff_o;

  /* even-mode velocity */
  v_e = C0 / sqrt(e_r_eff_e);
  /* odd-mode velocity */
  v_o = C0 / sqrt(e_r_eff_o);
  /* even-mode wavelength */
  lambda_g_e = v_e / f;
  /* odd-mode wavelength */
  lambda_g_o = v_o / f;
  /* electrical angles */
  ang_l_e = 2.0 * M_PI * l / lambda_g_e;    /* in radians */
  ang_l_o = 2.0 * M_PI * l / lambda_g_o;    /* in radians */
}


void c_microstrip::syn_err_fun(double *f1, double *f2, double s_h, double w_h, double e_r, double w_h_se, double w_h_so)
{

  double g, h;

  g = cosh(0.5 * M_PI * s_h);
  h = cosh(M_PI * w_h + 0.5 * M_PI * s_h);

  *f1 = (2.0 / M_PI) * acosh((2.0 * h - g + 1.0) / (g + 1.0));
  *f2 = (2.0 / M_PI) * acosh((2.0 * h - g - 1.0) / (g - 1.0));
  if (e_r <= 6.0) {
    *f2 += (4.0 / (M_PI * (1.0 + e_r / 2.0))) * acosh(1.0 + 2.0 * w_h / s_h);
  } else {
    *f2 += (1.0 / M_PI) * acosh(1.0 + 2.0 * w_h / s_h);
  }
  *f1 -= w_h_se;
  *f2 -= w_h_so;
}

/*
 * synth_width - calculate widths given Z0 and e_r
 * from Akhtarzad S. et al., "The design of coupled microstrip lines",
 * IEEE Trans. MTT-23, June 1975 and
 * Hinton, J.H., "On design of coupled microstrip lines", IEEE Trans.
 * MTT-28, March 1980
 */
void c_microstrip::synth_width()
{
  double Z0, e_r;
  double w_h_se, w_h_so, w_h, a, ce, co, s_h;
  double f1, f2, ft1, ft2, j11, j12, j21, j22, d_s_h, d_w_h, err;
  double eps = 1e-04;

  f1 = f2 = 0;
  e_r = er;

  Z0 = Z0e / 2.0;
  /* Wheeler formula for single microstrip synthesis */
  a = exp(Z0 * sqrt(e_r + 1.0) / 42.4) - 1.0;
  w_h_se = 8.0 * sqrt(a * ((7.0 + 4.0 / e_r) / 11.0) + ((1.0 + 1.0 / e_r) / 0.81)) / a;

  Z0 = Z0o / 2.0;
  /* Wheeler formula for single microstrip synthesis */
  a = exp(Z0 * sqrt(e_r + 1.0) / 42.4) - 1.0;
  w_h_so = 8.0 * sqrt(a * ((7.0 + 4.0 / e_r) / 11.0) + ((1.0 + 1.0 / e_r) / 0.81)) / a;

  ce = cosh(0.5 * M_PI * w_h_se);
  co = cosh(0.5 * M_PI * w_h_so);
  /* first guess at s/h */
  s_h = (2.0 / M_PI) * acosh((ce + co - 2.0) / (co - ce));
  /* first guess at w/h */
  w_h = acosh((ce * co - 1.0) / (co - ce)) / M_PI - s_h / 2.0;

  s = s_h * h;
  w = w_h * h;

  syn_err_fun(&f1, &f2, s_h, w_h, e_r, w_h_se, w_h_so);

  /* rather crude Newton-Rhapson; we need this beacuse the estimate of */
  /* w_h is often quite far from the true value (see Akhtarzad S. et al.) */
  do {
    /* compute Jacobian */
    syn_err_fun(&ft1, &ft2, s_h + eps, w_h, e_r, w_h_se, w_h_so);
    j11 = (ft1 - f1) / eps;
    j21 = (ft2 - f2) / eps;
    syn_err_fun(&ft1, &ft2, s_h, w_h + eps, e_r, w_h_se, w_h_so);
    j12 = (ft1 - f1) / eps;
    j22 = (ft2 - f2) / eps;

    /* compute next step */
    d_s_h = (-f1 * j22 + f2 * j12) / (j11 * j22 - j21 * j12);
    d_w_h = (-f2 * j11 + f1 * j21) / (j11 * j22 - j21 * j12);
    //g_print("j11 = %e\tj12 = %e\tj21 = %e\tj22 = %e\n", j11, j12, j21, j22);
    //g_print("det = %e\n", j11*j22 - j21*j22);
    //g_print("d_s_h = %e\td_w_h = %e\n", d_s_h, d_w_h);

    s_h += d_s_h;
    w_h += d_w_h;

    /* chech the error */
    syn_err_fun(&f1, &f2, s_h, w_h, e_r, w_h_se, w_h_so);

    err = sqrt(f1 * f1 + f2 * f2);
    /* converged ? */
  } while (err > 1e-04);


  s = s_h * h;
  w = w_h * h;
}


/*
 * Z0_dispersion() - calculate frequency dependency of characteristic
 * impedances
 */
void c_microstrip::Z0_dispersion()
{
  double Q_0;
  double Q_11, Q_12, Q_13, Q_14, Q_15, Q_16, Q_17, Q_18, Q_19, Q_20, Q_21;
  double Q_22, Q_23, Q_24, Q_25, Q_26, Q_27, Q_28, Q_29;
  double r_e, q_e, p_e, d_e, C_e;
  double e_r_eff_o_f, e_r_eff_o_0;
  double e_r_eff_single_f, e_r_eff_single_0, Z0_single_f;
  double f_n, g, u, e_r;
  double R_1, R_2, R_7, R_10, R_11, R_12, R_15, R_16, tmpf;

  e_r = er;

  u = w / h;            /* normalize line width */
  g = s / h;            /* normalize line spacing */

  /* normalized frequency [GHz * mm] */
  f_n = f * h / 1e06;

  e_r_eff_single_f = aux_ms->er_eff;
  e_r_eff_single_0 = aux_ms->er_eff_0;
  Z0_single_f = aux_ms->Z0;

  e_r_eff_o_f = er_eff_o;
  e_r_eff_o_0 = er_eff_o_0;

  Q_11 = 0.893 * (1.0 - 0.3 / (1.0 + 0.7 * (e_r - 1.0)));
  Q_12 = 2.121 * (pow(f_n / 20.0, 4.91) / (1.0 + Q_11 * pow(f_n / 20.0, 4.91))) * exp(-2.87 * g) * pow(g, 0.902);
  Q_13 = 1.0 + 0.038 * pow(e_r / 8.0, 5.1);
  Q_14 = 1.0 + 1.203 * pow(e_r / 15.0, 4.0) / (1.0 + pow(e_r / 15.0, 4.0));
  Q_15 = 1.887 * exp(-1.5 * pow(g, 0.84)) * pow(g, Q_14) / (1.0 + 0.41 * pow(f_n / 15.0, 3.0) * pow(u, 2.0 / Q_13) / (0.125 + pow(u, 1.626 / Q_13)));
  Q_16 = (1.0 + 9.0 / (1.0 + 0.403 * pow(e_r - 1.0, 2))) * Q_15;
  Q_17 = 0.394 * (1.0 - exp(-1.47 * pow(u / 7.0, 0.672))) * (1.0 - exp(-4.25 * pow(f_n / 20.0, 1.87)));
  Q_18 = 0.61 * (1.0 - exp(-2.13 * pow(u / 8.0, 1.593))) / (1.0 + 6.544 * pow(g, 4.17));
  Q_19 = 0.21 * g * g * g * g / ((1.0 + 0.18 * pow(g, 4.9)) * (1.0 + 0.1 * u * u) * (1.0 + pow(f_n / 24.0, 3.0)));
  Q_20 = (0.09 + 1.0 / (1.0 + 0.1 * pow(e_r - 1, 2.7))) * Q_19;
  Q_21 = fabs(1.0 - 42.54 * pow(g, 0.133) * exp(-0.812 * g) * pow(u, 2.5) / (1.0 + 0.033 * pow(u, 2.5)));

  r_e = pow(f_n / 28.843, 12);
  q_e = 0.016 + pow(0.0514 * e_r * Q_21, 4.524);
  p_e = 4.766 * exp(-3.228 * pow(u, 0.641));
  d_e = 5.086 * q_e * (r_e / (0.3838 + 0.386 * q_e)) * (exp(-22.2 * pow(u, 1.92)) / (1.0 + 1.2992 * r_e)) * (pow(e_r - 1.0, 6.0) / (1.0 + 10 * pow(e_r - 1.0, 6.0)));
  C_e = 1.0 + 1.275 * (1.0 - exp(-0.004625 * p_e * pow(e_r, 1.674) * pow(f_n / 18.365, 2.745))) - Q_12 + Q_16 - Q_17 + Q_18 + Q_20;


  R_1 = 0.03891 * pow(e_r, 1.4);
  R_2 = 0.267 * pow(u, 7.0);
  R_7 = 1.206 - 0.3144 * exp(-R_1) * (1.0 - exp(-R_2));
  R_10 = 0.00044 * pow(e_r, 2.136) + 0.0184;
  tmpf = pow(f_n / 19.47, 6.0);
  R_11 = tmpf / (1.0 + 0.0962 * tmpf);
  R_12 = 1.0 / (1.0 + 0.00245 * u * u);
  R_15 = 0.707 * R_10 * pow(f_n / 12.3, 1.097);
  R_16 = 1.0 + 0.0503 * e_r * e_r * R_11 * (1.0 - exp(-pow(u / 15.0, 6.0)));
  Q_0 = R_7 * (1.0 - 1.1241 * (R_12 / R_16) * exp(-0.026 * pow(f_n, 1.15656) - R_15));

  /* even-mode frequency-dependent characteristic impedances */
  Z0e = Z0_e_0 * pow(0.9408 * pow(e_r_eff_single_f, C_e) - 0.9603, Q_0) / pow((0.9408 - d_e) * pow(e_r_eff_single_0, C_e) - 0.9603, Q_0);

  Q_29 = 15.16 / (1.0 + 0.196 * pow(e_r - 1.0, 2.0));
  tmpf = pow(e_r - 1.0, 3.0);
  Q_28 = 0.149 * tmpf / (94.5 + 0.038 * tmpf);
  tmpf = pow(e_r - 1.0, 1.5);
  Q_27 = 0.4 * pow(g, 0.84) * (1.0 + 2.5 * tmpf / (5.0 + tmpf));
  tmpf = pow((e_r - 1.0) / 13.0, 12.0);
  Q_26 = 30.0 - 22.2 * (tmpf / (1.0 + 3.0 * tmpf)) - Q_29;
  tmpf = (e_r - 1.0) * (e_r - 1.0);
  Q_25 = (0.3 * f_n * f_n / (10.0 + f_n * f_n)) * (1.0 + 2.333 * tmpf / (5.0 + tmpf));
  Q_24 = 2.506 * Q_28 * pow(u, 0.894) * pow((1.0 + 1.3 * u) * f_n / 99.25, 4.29) / (3.575 + pow(u, 0.894));
  Q_23 = 1.0 + 0.005 * f_n * Q_27 / ((1.0 + 0.812 * pow(f_n / 15.0, 1.9)) * (1.0 + 0.025 * u * u));
  Q_22 = 0.925 * pow(f_n / Q_26, 1.536) / (1.0 + 0.3 * pow(f_n / 30.0, 1.536));

  /* odd-mode frequency-dependent characteristic impedances */
  Z0o = Z0_single_f + (Z0_o_0 * pow(e_r_eff_o_f / e_r_eff_o_0, Q_22) - Z0_single_f * Q_23) / (1.0 + Q_24 + pow(0.46 * g, 2.2) * Q_25);
}


void c_microstrip::calc()
{
  /* compute thickness corrections */
  delta_u_thickness();
  /* get effective dielectric constants */
  er_eff_static();
  /* impedances for even- and odd-mode */
  Z0_even_odd();
  /* calculate freq dependence of er_eff_e, er_eff_o */
  er_eff_freq();
  /* FIXME: (not used) Get effective magnetic permeability */
  mur_eff = calc_mur_eff();
  /* calculate frequency  dependence of Z0e, Z0o */
  Z0_dispersion();
  /* calculate losses */
  attenuation();
  /* calculate electrical lengths */
  line_angle();
}

/*
 * get_microstrip_sub
 * get and assign microstrip substrate parameters
 * into microstrip structure
 */
void c_microstrip::get_c_microstrip_sub()
{
  er = getProperty ("Er");
  mur = getProperty ("Mur");
  h = getProperty ("H", UNIT_LENGTH, LENGTH_M);
  ht = getProperty ("H_t", UNIT_LENGTH, LENGTH_M);
  t = getProperty ("T", UNIT_LENGTH, LENGTH_M);
  sigma = getProperty ("Cond");
  tand = getProperty ("Tand");
  rough = getProperty ("Rough", UNIT_LENGTH, LENGTH_M);
}

/*
 * get_c_microstrip_comp
 * get and assign microstrip component parameters
 * into microstrip structure
 */
void c_microstrip::get_c_microstrip_comp()
{
  f = getProperty ("Freq", UNIT_FREQ, FREQ_HZ);
}

/*
 * get_c_microstrip_elec
 * get and assign microstrip electrical parameters
 * into microstrip structure
 */
void c_microstrip::get_c_microstrip_elec()
{
  Z0e = getProperty ("Z0e", UNIT_RES, RES_OHM);
  Z0o = getProperty ("Z0o", UNIT_RES, RES_OHM);
  ang_l_e = getProperty ("Ang_l", UNIT_ANG, ANG_RAD);
  ang_l_o = getProperty ("Ang_l", UNIT_ANG, ANG_RAD);
}


/*
 * get_c_microstrip_phys
 * get and assign microstrip physical parameters
 * into microstrip structure
 */
void c_microstrip::get_c_microstrip_phys()
{
  w = getProperty ("W", UNIT_LENGTH, LENGTH_M);
  s = getProperty ("S", UNIT_LENGTH, LENGTH_M);
  l = getProperty ("L", UNIT_LENGTH, LENGTH_M);
}


void c_microstrip::show_results()
{
  setProperty ("Z0e", Z0e, UNIT_RES, RES_OHM);
  setProperty ("Z0o", Z0o, UNIT_RES, RES_OHM);
  setProperty ("Ang_l", sqrt (ang_l_e * ang_l_o), UNIT_ANG, ANG_RAD);

  setResult (0, er_eff_e, "");
  setResult (1, er_eff_o, "");
  setResult (2, atten_cond_e, "dB");
  setResult (3, atten_cond_o, "dB");
  setResult (4, atten_dielectric_e, "dB");
  setResult (5, atten_dielectric_o, "dB");

  double val = convertProperty ("T", skindepth, UNIT_LENGTH, LENGTH_M);
  setResult (6, val, getUnit ("T"));
}


/*
 * analysis function
 */
void c_microstrip::analyze()
{
  /* Get and assign substrate parameters */
  get_c_microstrip_sub();
  /* Get and assign component parameters */
  get_c_microstrip_comp();
  /* Get and assign physical parameters */
  get_c_microstrip_phys();

  /* compute coupled microstrip parameters */
  calc();
  /* print results in the subwindow */
  show_results();
}


void c_microstrip::syn_fun(double *f1, double *f2, double s_h, double w_h, double Z0_e, double Z0_o)
{
  s = s_h * h;
  w = w_h * h;

  /* compute coupled microstrip parameters */
  calc();

  *f1 = Z0e - Z0_e;
  *f2 = Z0o - Z0_o;
}

/*
 * synthesis function
 */
void c_microstrip::synthesize()
{
  double Z0_e, Z0_o;
  double f1, f2, ft1, ft2, j11, j12, j21, j22, d_s_h, d_w_h, err;
  double eps = 1e-04;
  double w_h, s_h, le, lo;

  /* Get and assign substrate parameters */
  get_c_microstrip_sub();

  /* Get and assign component parameters */
  get_c_microstrip_comp();

  /* Get and assign electrical parameters */
  get_c_microstrip_elec();

  /* Get and assign physical parameters */
  /* at present it is required only for getting strips length */
  get_c_microstrip_phys();


  /* required value of Z0_e and Z0_o */
  Z0_e = Z0e;
  Z0_o = Z0o;

  /* calculate width and use for initial value in Newton's method */
  synth_width();
  w_h = w / h;
  s_h = s / h;
  f1 = f2 = 0;

  /* rather crude Newton-Rhapson */
  do {
    /* compute Jacobian */
    syn_fun(&ft1, &ft2, s_h + eps, w_h, Z0_e, Z0_o);
    j11 = (ft1 - f1) / eps;
    j21 = (ft2 - f2) / eps;
    syn_fun(&ft1, &ft2, s_h, w_h + eps, Z0_e, Z0_o);
    j12 = (ft1 - f1) / eps;
    j22 = (ft2 - f2) / eps;

    /* compute next step; increments of s_h and w_h */
    d_s_h = (-f1 * j22 + f2 * j12) / (j11 * j22 - j21 * j12);
    d_w_h = (-f2 * j11 + f1 * j21) / (j11 * j22 - j21 * j12);

    s_h += d_s_h;
    w_h += d_w_h;

    /* compute the error with the new values of s_h and w_h */
    syn_fun(&f1, &f2, s_h, w_h, Z0_e, Z0_o);
    err = sqrt(f1 * f1 + f2 * f2);

    /* converged ? */
  } while (err > 1e-04);

  /* denormalize computed width and spacing */
  s = s_h * h;
  w = w_h * h;

  setProperty ("W", w, UNIT_LENGTH, LENGTH_M);
  setProperty ("S", s, UNIT_LENGTH, LENGTH_M);

  /* calculate physical length */
  ang_l_e = getProperty ("Ang_l", UNIT_ANG, ANG_RAD);
  ang_l_o = getProperty ("Ang_l", UNIT_ANG, ANG_RAD);
  le = C0 / f / sqrt(er_eff_e * mur_eff) * ang_l_e / 2.0 / M_PI;
  lo = C0 / f / sqrt(er_eff_o * mur_eff) * ang_l_o / 2.0 / M_PI;
  l = sqrt (le * lo);
  setProperty ("L", l, UNIT_LENGTH, LENGTH_M);

  calc();
  /* print results in the subwindow */
  show_results();
}