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kicad/pcb_calculator/transline/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 <cmath>
#include <units.h>
#include <transline.h>
#include <microstrip.h>
#include <c_microstrip.h>
C_MICROSTRIP::C_MICROSTRIP() : TRANSLINE()
{
m_Name = "Coupled_MicroStrip";
aux_ms = NULL;
// Initialize these variables mainly to avoid warnings from a static analyzer
h = 0.0; // height of substrate
ht = 0.0; // height to the top of box
t = 0.0; // thickness of top metal
rough = 0.0; // Roughness of top metal
w = 0.0; // width of lines
w_t_e = 0.0; // even-mode thickness-corrected line width
w_t_o = 0.0; // odd-mode thickness-corrected line width
l = 0.0; // length of lines
s = 0.0; // spacing of lines
Z0_e_0 = 0.0; // static even-mode impedance
Z0_o_0 = 0.0; // static odd-mode impedance
Z0e = 0.0; // even-mode impedance
Z0o = 0.0; // odd-mode impedance
c_e = 0.0; // even-mode capacitance
c_o = 0.0; // odd-mode capacitance
ang_l_e = 0.0; // even-mode electrical length in angle
ang_l_o = 0.0; // odd-mode electrical length in angle
er_eff_e = 0.0; // even-mode effective dielectric constant
er_eff_o = 0.0; // odd-mode effective dielectric constant
er_eff_e_0 = 0.0; // static even-mode effective dielectric constant
er_eff_o_0 = 0.0; // static odd-mode effective dielectric constant
w_eff = 0.0; // Effective width of line
atten_dielectric_e = 0.0; // even-mode dielectric losses (dB)
atten_cond_e = 0.0; // even-mode conductors losses (dB)
atten_dielectric_o = 0.0; // odd-mode conductors losses (dB)
atten_cond_o = 0.0; // odd-mode conductors losses (dB)
}
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 Computation 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()
{
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->m_freq = m_freq;
aux_ms->m_murC = m_murC;
aux_ms->microstrip_Z0();
aux_ms->dispersion();
}
/*
* 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;
}
/**
* filling_factor_odd() - compute the filling factor for the coupled
* microstrips odd-mode without cover and zero conductor thickness
*/
double C_MICROSTRIP::filling_factor_odd( double u, double g, double e_r )
{
double b_odd = 0.747 * e_r / (0.15 + e_r);
double c_odd = b_odd - (b_odd - 0.207) * exp( -0.414 * u );
double d_odd = 0.593 + 0.694 * exp( -0.562 * u );
/* filling factor, with width corrected for thickness */
double q_inf = exp( -c_odd * pow( g, d_odd ) );
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;
}
/**
* er_eff_static() - compute the static effective dielectric constants
*
* References: Manfred Kirschning and Rolf Jansen, "Accurate
* Wide-Range Design Equations for the Frequency-Dependent
* Characteristic of Parallel Coupled Microstrip Lines", IEEE
* Trans. MTT, vol. 32, no. 1, Jan. 1984
*/
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;
}
/**
* delta_Z0_even_cover() - compute the even-mode impedance correction
* for a homogeneous microstrip due to the cover
*
* References: S. March, "Microstrip Packaging: Watch the Last Step",
* Microwaves, vol. 20, no. 13, pp. 83.94, Dec. 1981.
*/
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;
}
/**
* delta_Z0_odd_cover() - compute the odd-mode impedance correction
* for a homogeneous microstrip due to the cover
*
* References: S. March, "Microstrip Packaging: Watch the Last Step",
* Microwaves, vol. 20, no. 13, pp. 83.94, Dec. 1981.
*/
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;
}
/**
* Z0_even_odd() - compute the static even- and odd-mode static
* impedances
*
* References: Manfred Kirschning and Rolf Jansen, "Accurate
* Wide-Range Design Equations for the Frequency-Dependent
* Characteristic of Parallel Coupled Microstrip Lines", IEEE
* Trans. MTT, vol. 32, no. 1, Jan. 1984
*/
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;
}
/*
* 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 = m_freq * 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 = m_skindepth;
if( m_freq > 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 / (m_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 * m_freq) / (R_s * C0 * K);
/* even-mode losses per unith length */
alpha_c_e = ( 20.0 * M_PI / log( 10.0 ) ) * m_freq * 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 * m_freq) / (R_s * C0 * K);
/* odd-mode losses per unith length */
alpha_c_o = ( 20.0 * M_PI / log( 10.0 ) ) * m_freq * 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 ) ) *
(m_freq / C0) * ( e_r / sqrt( e_r_eff_e_0 ) ) * ( (e_r_eff_e_0 - 1.0) / (e_r - 1.0) ) * m_tand;
alpha_d_o =
( 20.0 * M_PI /
log( 10.0 ) ) *
(m_freq / C0) * ( e_r / sqrt( e_r_eff_o_0 ) ) * ( (e_r_eff_o_0 - 1.0) / (e_r - 1.0) ) * m_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()
{
m_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 / m_freq;
/* odd-mode wavelength */
lambda_g_o = v_o / m_freq;
/* 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, he;
g = cosh( 0.5 * M_PI * s_h );
he = cosh( M_PI * w_h + 0.5 * M_PI * s_h );
*f1 = (2.0 / M_PI) * acosh( (2.0 * he - g + 1.0) / (g + 1.0) );
*f2 = (2.0 / M_PI) * acosh( (2.0 * he - 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 = m_freq * 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();
/* 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( EPSILONR_PRM );
m_murC = getProperty( MURC_PRM );
h = getProperty( H_PRM );
ht = getProperty( H_T_PRM );
t = getProperty( T_PRM );
m_sigma = 1.0/getProperty( RHO_PRM );
m_tand = getProperty( TAND_PRM );
rough = getProperty( ROUGH_PRM );
}
/*
* get_c_microstrip_comp
* get and assign microstrip component parameters
* into microstrip structure
*/
void C_MICROSTRIP::get_c_microstrip_comp()
{
m_freq = getProperty( FREQUENCY_PRM );
}
/*
* get_c_microstrip_elec
* get and assign microstrip electrical parameters
* into microstrip structure
*/
void C_MICROSTRIP::get_c_microstrip_elec()
{
Z0e = getProperty( Z0_E_PRM );
Z0o = getProperty( Z0_O_PRM );
ang_l_e = getProperty( ANG_L_PRM );
ang_l_o = getProperty( ANG_L_PRM );
}
/*
* get_c_microstrip_phys
* get and assign microstrip physical parameters
* into microstrip structure
*/
void C_MICROSTRIP::get_c_microstrip_phys()
{
w = getProperty( PHYS_WIDTH_PRM );
s = getProperty( PHYS_S_PRM );
l = getProperty( PHYS_LEN_PRM );
}
void C_MICROSTRIP::show_results()
{
setProperty( Z0_E_PRM, Z0e );
setProperty( Z0_O_PRM , Z0o );
setProperty( ANG_L_PRM, sqrt( ang_l_e * ang_l_o ) );
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" );
setResult( 6, m_skindepth / UNIT_MICRON, "µm" );
}
/*
* 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( PHYS_WIDTH_PRM, w );
setProperty( PHYS_S_PRM, s );
/* calculate physical length */
ang_l_e = getProperty( ANG_L_PRM );
ang_l_o = getProperty( ANG_L_PRM );
le = C0 / m_freq / sqrt( er_eff_e ) * ang_l_e / 2.0 / M_PI;
lo = C0 / m_freq / sqrt( er_eff_o ) * ang_l_o / 2.0 / M_PI;
l = sqrt( le * lo );
setProperty( PHYS_LEN_PRM, l );
calc();
/* print results in the subwindow */
show_results();
}
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