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kicad/pcb_calculator/transline/microstrip.cpp

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/*
* microstrip.cpp - microstrip class implementation
*
* Copyright (C) 2001 Gopal Narayanan <gopal@astro.umass.edu>
* Copyright (C) 2002 Claudio Girardi <claudio.girardi@ieee.org>
* Copyright (C) 2005, 2006 Stefan Jahn <stefan@lkcc.org>
* Modified for Kicad: 2011 jean-pierre.charras
*
* 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.
*
*/
/* microstrip.c - Puts up window for microstrip 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>
MICROSTRIP::MICROSTRIP() : TRANSLINE()
{
m_name = "MicroStrip";
}
/*
* Z0_homogeneous() - compute the impedance for a stripline in a
* homogeneous medium, without cover effects
*/
double MICROSTRIP::Z0_homogeneous( double u )
{
double f, Z0;
f = 6.0 + (2.0 * M_PI - 6.0) * exp( -pow( 30.666 / u, 0.7528 ) );
Z0 = ( ZF0 / (2.0 * M_PI) ) * log( f / u + sqrt( 1.0 + 4.0 / (u * u) ) );
return Z0;
}
/*
* delta_Z0_cover() - compute the cover effect on impedance for a
* stripline in a homogeneous medium
*/
double MICROSTRIP::delta_Z0_cover( double u, double h2h )
{
double P, Q;
double h2hp1;
h2hp1 = 1.0 + h2h;
P = 270.0 * ( 1.0 - tanh( 1.192 + 0.706 * sqrt( h2hp1 ) - 1.389 / h2hp1 ) );
Q = 1.0109 - atanh( (0.012 * u + 0.177 * u * u - 0.027 * u * u * u) / (h2hp1 * h2hp1) );
return P * Q;
}
/*
* filling_factor() - compute the filling factor for a microstrip
* without cover and zero conductor thickness
*/
double MICROSTRIP::filling_factor( double u, double e_r )
{
double a, b, q_inf;
double u2, u3, u4;
u2 = u * u;
u3 = u2 * u;
u4 = u3 * u;
a = 1.0 +
log( (u4 + u2 / 2704) / (u4 + 0.432) ) / 49.0 + log( 1.0 + u3 / 5929.741 ) / 18.7;
b = 0.564 * pow( (e_r - 0.9) / (e_r + 3.0), 0.053 );
q_inf = pow( 1.0 + 10.0 / u, -a * b );
return q_inf;
}
/*
* delta_q_cover() - compute the cover effect on filling factor
*/
double MICROSTRIP::delta_q_cover( double h2h )
{
double q_c;
q_c = tanh( 1.043 + 0.121 * h2h - 1.164 / h2h );
return q_c;
}
/*
* delta_q_thickness() - compute the thickness effect on filling factor
*/
double MICROSTRIP::delta_q_thickness( double u, double t_h )
{
double q_t;
q_t = (2.0 * log( 2.0 ) / M_PI) * ( t_h / sqrt( u ) );
return q_t;
}
/*
* e_r_effective() - compute effective dielectric constant from
* material e_r and filling factor
*/
double MICROSTRIP::e_r_effective( double e_r, double q )
{
double e_r_eff;
e_r_eff = 0.5 * (e_r + 1.0) + 0.5 * q * (e_r - 1.0);
return e_r_eff;
}
/*
* delta_u_thickness - compute the thickness effect on normalized width
*/
double MICROSTRIP::delta_u_thickness( double u, double t_h, double e_r )
{
double delta_u;
if( t_h > 0.0 )
{
/* correction for thickness for a homogeneous microstrip */
delta_u = (t_h / M_PI) * log( 1.0 + (4.0 * M_E) * pow( tanh( sqrt(
6.517 * u ) ), 2.0 ) / t_h );
/* correction for strip on a substrate with relative permettivity e_r */
delta_u = 0.5 * delta_u * ( 1.0 + 1.0 / cosh( sqrt( e_r - 1.0 ) ) );
}
else
{
delta_u = 0.0;
}
return delta_u;
}
/*
* microstrip_Z0() - compute microstrip static impedance
*/
void MICROSTRIP::microstrip_Z0()
{
double e_r, h2, h2h, u, t_h;
double Z0_h_r, Z0;
double delta_u_1, delta_u_r, q_inf, q_c, q_t, e_r_eff, e_r_eff_t, q;
e_r = er;
h2 = ht;
h2h = h2 / h;
u = w / h;
t_h = t / h;
/* compute normalized width correction for e_r = 1.0 */
delta_u_1 = delta_u_thickness( u, t_h, 1.0 );
/* compute homogeneous stripline impedance */
Z0_h_1 = Z0_homogeneous( u + delta_u_1 );
/* compute normalized width corection */
delta_u_r = delta_u_thickness( u, t_h, e_r );
u += delta_u_r;
/* compute homogeneous stripline impedance */
Z0_h_r = Z0_homogeneous( u );
/* filling factor, with width corrected for thickness */
q_inf = filling_factor( u, e_r );
/* cover effect */
q_c = delta_q_cover( h2h );
/* thickness effect */
q_t = delta_q_thickness( u, t_h );
/* resultant filling factor */
q = (q_inf - q_t) * q_c;
/* e_r corrected for thickness and non homogeneous material */
e_r_eff_t = e_r_effective( e_r, q );
/* effective dielectric constant */
e_r_eff = e_r_eff_t * pow( Z0_h_1 / Z0_h_r, 2.0 );
/* characteristic impedance, corrected for thickness, cover */
/* and non homogeneous material */
Z0 = Z0_h_r / sqrt( e_r_eff_t );
w_eff = u * h;
er_eff_0 = e_r_eff;
Z0_0 = Z0;
}
/*
* e_r_dispersion() - computes the dispersion correction factor for
* the effective permeability
*/
double MICROSTRIP::e_r_dispersion( double u, double e_r, double f_n )
{
double P_1, P_2, P_3, P_4, P;
P_1 = 0.27488 + u * ( 0.6315 + 0.525 / pow( 1.0 + 0.0157 * f_n, 20.0 ) ) - 0.065683 * exp(
-8.7513 * u );
P_2 = 0.33622 * ( 1.0 - exp( -0.03442 * e_r ) );
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( e_r / 15.916, 8.0 ) ) );
P = P_1 * P_2 * pow( (P_3 * P_4 + 0.1844) * f_n, 1.5763 );
return P;
}
/*
* Z0_dispersion() - computes the dispersion correction factor for the
* characteristic impedance
*/
double MICROSTRIP::Z0_dispersion( double u,
double e_r,
double e_r_eff_0,
double e_r_eff_f,
double f_n )
{
double R_1, R_2, R_3, R_4, R_5, R_6, R_7, R_8, R_9, R_10, R_11, R_12, R_13, R_14, R_15, R_16,
R_17, D, tmpf;
R_1 = 0.03891 * pow( e_r, 1.4 );
R_2 = 0.267 * pow( u, 7.0 );
R_3 = 4.766 * exp( -3.228 * pow( u, 0.641 ) );
R_4 = 0.016 + pow( 0.0514 * e_r, 4.524 );
R_5 = pow( f_n / 28.843, 12.0 );
R_6 = 22.2 * pow( u, 1.92 );
R_7 = 1.206 - 0.3144 * exp( -R_1 ) * ( 1.0 - exp( -R_2 ) );
R_8 = 1.0 + 1.275 *
( 1.0 - exp( -0.004625 * R_3 * pow( e_r, 1.674 ) * pow( f_n / 18.365, 2.745 ) ) );
tmpf = pow( e_r - 1.0, 6.0 );
R_9 = 5.086 * R_4 *
( R_5 /
(0.3838 + 0.386 *
R_4) ) * ( exp( -R_6 ) / (1.0 + 1.2992 * R_5) ) * ( tmpf / (1.0 + 10.0 * tmpf) );
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_13 = 0.9408 * pow( e_r_eff_f, R_8 ) - 0.9603;
R_14 = (0.9408 - R_9) * pow( e_r_eff_0, R_8 ) - 0.9603;
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 ) ) );
R_17 = R_7 * ( 1.0 - 1.1241 * (R_12 / R_16) * exp( -0.026 * pow( f_n, 1.15656 ) - R_15 ) );
D = pow( R_13 / R_14, R_17 );
return D;
}
/*
* dispersion() - compute frequency dependent parameters of
* microstrip
*/
void MICROSTRIP::dispersion()
{
double e_r, e_r_eff_0;
double u, f_n, P, e_r_eff_f, D, Z0_f;
e_r = er;
e_r_eff_0 = er_eff_0;
u = w / h;
/* normalized frequency [GHz * mm] */
f_n = f * h / 1e06;
P = e_r_dispersion( u, e_r, f_n );
/* effective dielectric constant corrected for dispersion */
e_r_eff_f = e_r - (e_r - e_r_eff_0) / (1.0 + P);
D = Z0_dispersion( u, e_r, e_r_eff_0, e_r_eff_f, f_n );
Z0_f = Z0_0 * D;
er_eff = e_r_eff_f;
Z0 = Z0_f;
}
/*
* conductor_losses() - compute microstrip conductor losses per unit
* length
*/
double MICROSTRIP::conductor_losses()
{
double e_r_eff_0, delta;
double K, R_s, Q_c, alpha_c;
e_r_eff_0 = er_eff_0;
delta = skindepth;
if( f > 0.0 )
{
/* current distribution factor */
K = exp( -1.2 * pow( Z0_h_1 / 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 ) ) );
/* strip inductive quality factor */
Q_c = (M_PI * Z0_h_1 * w * f) / (R_s * C0 * K);
alpha_c = ( 20.0 * M_PI / log( 10.0 ) ) * f * sqrt( e_r_eff_0 ) / (C0 * Q_c);
}
else
{
alpha_c = 0.0;
}
return alpha_c;
}
/*
* dielectric_losses() - compute microstrip dielectric losses per unit
* length
*/
double MICROSTRIP::dielectric_losses()
{
double e_r, e_r_eff_0;
double alpha_d;
e_r = er;
e_r_eff_0 = er_eff_0;
alpha_d =
( 20.0 * M_PI /
log( 10.0 ) ) *
(f / C0) * ( e_r / sqrt( e_r_eff_0 ) ) * ( (e_r_eff_0 - 1.0) / (e_r - 1.0) ) * tand;
return alpha_d;
}
/*
* attenuation() - compute attenuation of microstrip
*/
void MICROSTRIP::attenuation()
{
skindepth = skin_depth();
atten_cond = conductor_losses() * l;
atten_dielectric = dielectric_losses() * l;
}
/*
* mur_eff_ms() - returns effective magnetic permeability
*/
void MICROSTRIP::mur_eff_ms()
{
double mureff;
mureff = (2.0 * mur) / ( (1.0 + mur) + ( (1.0 - mur) * pow( ( 1.0 + (10.0 * h / w) ), -0.5 ) ) );
mur_eff = mureff;
}
/*
* synth_width - calculate width given Z0 and e_r
*/
double MICROSTRIP::synth_width()
{
double e_r, a, b;
double w_h, w;
e_r = er;
a =
( (Z0 / ZF0 / 2 /
M_PI) * sqrt( (e_r + 1) / 2. ) ) + ( (e_r - 1) / (e_r + 1) * ( 0.23 + (0.11 / e_r) ) );
b = ZF0 / 2 * M_PI / ( Z0 * sqrt( e_r ) );
if( a > 1.52 )
{
w_h = 8 * exp( a ) / (exp( 2. * a ) - 2);
}
else
{
w_h =
(2. /
M_PI) *
( b - 1. -
log( (2 * b) - 1. ) + ( (e_r - 1) / (2 * e_r) ) * (log( b - 1. ) + 0.39 - 0.61 / e_r) );
}
if( h > 0.0 )
{
w = w_h * h;
return w;
}
else
{
w = 0;
}
return w;
}
/*
* line_angle() - calculate microstrip length in radians
*/
void MICROSTRIP::line_angle()
{
double e_r_eff;
double v, lambda_g;
e_r_eff = er_eff;
/* velocity */
v = C0 / sqrt( e_r_eff * mur_eff );
/* wavelength */
lambda_g = v / f;
/* electrical angles */
ang_l = 2.0 * M_PI * l / lambda_g; /* in radians */
}
void MICROSTRIP::calc()
{
/* effective permeability */
mur_eff_ms();
/* static impedance */
microstrip_Z0();
/* calculate freq dependence of er and Z0 */
dispersion();
/* calculate electrical lengths */
line_angle();
/* calculate losses */
attenuation();
}
/*
* get_microstrip_sub () - get and assign microstrip substrate
* parameters into microstrip structure
*/
void MICROSTRIP::get_microstrip_sub()
{
er = getProperty( EPSILONR_PRM );
mur = getProperty( MUR_PRM );
h = getProperty( H_PRM );
ht = getProperty( H_T_PRM );
t = getProperty( T_PRM );
sigma = 1.0 / getProperty( RHO_PRM );
murC = getProperty( MURC_PRM );
tand = getProperty( TAND_PRM );
rough = getProperty( ROUGH_PRM );
}
/*
* get_microstrip_comp() - get and assign microstrip component
* parameters into microstrip structure
*/
void MICROSTRIP::get_microstrip_comp()
{
f = getProperty( FREQUENCY_PRM );
}
/*
* get_microstrip_elec() - get and assign microstrip electrical
* parameters into microstrip structure
*/
void MICROSTRIP::get_microstrip_elec()
{
Z0 = getProperty( Z0_PRM );
ang_l = getProperty( ANG_L_PRM );
}
/*
* get_microstrip_phys() - get and assign microstrip physical
* parameters into microstrip structure
*/
void MICROSTRIP::get_microstrip_phys()
{
w = getProperty( PHYS_WIDTH_PRM );
l = getProperty( PHYS_LEN_PRM );
}
void MICROSTRIP::show_results()
{
setProperty( Z0_PRM, Z0 );
setProperty( ANG_L_PRM, ang_l );
setResult( 0, er_eff, "" );
setResult( 1, atten_cond, "dB" );
setResult( 2, atten_dielectric, "dB" );
setResult( 3, skindepth/UNIT_MICRON, "<EFBFBD>m" );
}
/*
* analysis function
*/
void MICROSTRIP::analyze()
{
/* Get and assign substrate parameters */
get_microstrip_sub();
/* Get and assign component parameters */
get_microstrip_comp();
/* Get and assign physical parameters */
get_microstrip_phys();
/* compute microstrip parameters */
calc();
/* print results in the subwindow */
show_results();
}
#define MAX_ERROR 0.000001
/*
* synthesis function
*/
void MICROSTRIP::synthesize()
{
double Z0_dest, Z0_current, Z0_result, increment, slope, error;
int iteration;
/* Get and assign substrate parameters */
get_microstrip_sub();
/* Get and assign component parameters */
get_microstrip_comp();
/* Get and assign electrical parameters */
get_microstrip_elec();
/* Get and assign physical parameters */
/* at present it is required only for getting strips length */
get_microstrip_phys();
/* calculate width and use for initial value in Newton's method */
w = synth_width();
/* required value of Z0 */
Z0_dest = Z0;
/* Newton's method */
iteration = 0;
/* compute microstrip parameters */
calc();
Z0_current = Z0;
error = fabs( Z0_dest - Z0_current );
while( error > MAX_ERROR )
{
iteration++;
increment = (w / 100.0);
w += increment;
/* compute microstrip parameters */
calc();
Z0_result = Z0;
/* f(w(n)) = Z0 - Z0(w(n)) */
/* f'(w(n)) = -f'(Z0(w(n))) */
/* f'(Z0(w(n))) = (Z0(w(n)) - Z0(w(n+delw))/delw */
/* w(n+1) = w(n) - f(w(n))/f'(w(n)) */
slope = (Z0_result - Z0_current) / increment;
/* printf("%g\n",slope); */
w += (Z0_dest - Z0_current) / slope - increment;
/* printf("ms->w = %g\n", ms->w); */
/* find new error */
/* compute microstrip parameters */
calc();
Z0_current = Z0;
error = fabs( Z0_dest - Z0_current );
/* printf("Iteration = %d\n",iteration);
* printf("w = %g\t Z0 = %g\n",ms->w, Z0_current); */
if( iteration > 100 )
break;
}
setProperty( PHYS_WIDTH_PRM, w );
/* calculate physical length */
ang_l = getProperty( ANG_L_PRM );
l = C0 / f / sqrt( er_eff * mur_eff ) * ang_l / 2.0 / M_PI; /* in m */
setProperty( PHYS_LEN_PRM, l );
/* compute microstrip parameters */
calc();
/* print results in the subwindow */
show_results();
}
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