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kicad/pcb_calculator/transline/coplanar.cpp

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/*
* coplanar.cpp - coplanar class implementation
*
* Copyright (C) 2008 Michael Margraf <michael.margraf@alumni.tu-berlin.de>
* 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.
*
*/
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <units.h>
#include <transline.h>
#include <coplanar.h>
COPLANAR::COPLANAR() : TRANSLINE()
{
m_Name = "CoPlanar";
backMetal = false;
// Initialize these variables mainly to avoid warnings from a static analyzer
h = 0.0; // height of substrate
t = 0.0; // thickness of top metal
w = 0.0; // width of line
s = 0.0; // width of gap between line and ground
len = 0.0; // length of line
Z0 = 0.0; // characteristic impedance
ang_l = 0.0; // Electrical length in angle
atten_dielectric = 0.0; // Loss in dielectric (dB)
atten_cond = 0.0; // Loss in conductors (dB)
er_eff = 1.0; // Effective dielectric constant
}
GROUNDEDCOPLANAR::GROUNDEDCOPLANAR() : COPLANAR()
{
m_Name = "GrCoPlanar";
backMetal = true;
}
// -------------------------------------------------------------------
void COPLANAR::getProperties()
{
m_freq = getProperty( FREQUENCY_PRM );
w = getProperty( PHYS_WIDTH_PRM );
s = getProperty( PHYS_S_PRM );
len = getProperty( PHYS_LEN_PRM );
h = getProperty( H_PRM );
t = getProperty( T_PRM );
er = getProperty( EPSILONR_PRM );
m_murC = getProperty( MURC_PRM );
m_tand = getProperty( TAND_PRM );
m_sigma = 1.0 / getProperty( RHO_PRM );
Z0 = getProperty( Z0_PRM );
ang_l = getProperty( ANG_L_PRM );
}
// -------------------------------------------------------------------
void COPLANAR::calc()
{
m_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 efficiency's 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) ) * m_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( m_freq / 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 * m_freq / m_sigma );
atten_dielectric = 20.0 / log( 10.0 ) * len
* ad_factor * m_freq * (sr_er_f * sr_er_f - 1) / sr_er_f;
ang_l = 2.0 * M_PI * len * sr_er_f * m_freq / C0; /* in radians */
er_eff = sr_er_f * sr_er_f;
Z0 = zl_factor / sr_er_f;
}
// -------------------------------------------------------------------
void COPLANAR::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, m_skindepth / UNIT_MICRON, "µm" );
}
// -------------------------------------------------------------------
void COPLANAR::analyze()
{
getProperties();
/* compute coplanar parameters */
calc();
/* print results in the subwindow */
show_results();
}
#define MAX_ERROR 0.000001
// -------------------------------------------------------------------
void COPLANAR::synthesize()
{
double Z0_dest, Z0_current, Z0_result, increment, slope, error;
int iteration;
getProperties();
/* required value of Z0 */
Z0_dest = Z0;
double ang_l_tmp = getProperty( ANG_L_PRM );
// compute inital coplanar parameters. This function modify Z0 and ang_l
// (set to NaN in some cases)
calc();
if( std::isnan( Z0 ) ) // cannot be synthesized with current parameters
{
Z0 = Z0_dest;
ang_l= ang_l_tmp;
if( isSelected( PHYS_WIDTH_PRM ) )
{
setProperty( PHYS_WIDTH_PRM, NAN );
}
else
{
setProperty( PHYS_S_PRM, NAN );
}
setProperty( PHYS_LEN_PRM, NAN );
/* print results in the subwindow */
show_results();
return;
}
/* Newton's method */
iteration = 0;
Z0_current = Z0;
error = fabs( Z0_dest - Z0_current );
while( error > MAX_ERROR )
{
iteration++;
if( isSelected( PHYS_WIDTH_PRM ) )
{
increment = w / 100.0;
w += increment;
}
else
{
increment = s / 100.0;
s += increment;
}
/* compute coplanar 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;
slope = (Z0_dest - Z0_current) / slope - increment;
if( isSelected( PHYS_WIDTH_PRM ) )
w += slope;
else
s += slope;
if( w <= 0.0 )
w = increment;
if( s <= 0.0 )
s = increment;
/* find new error */
/* compute coplanar parameters */
calc();
Z0_current = Z0;
error = fabs( Z0_dest - Z0_current );
if( iteration > 100 )
break;
}
setProperty( PHYS_WIDTH_PRM, w );
setProperty( PHYS_S_PRM, s );
/* calculate physical length */
ang_l = getProperty( ANG_L_PRM );
len = C0 / m_freq / sqrt( er_eff ) * ang_l / 2.0 / M_PI; /* in m */
setProperty( PHYS_LEN_PRM, len );
/* compute coplanar parameters */
calc();
/* print results in the subwindow */
show_results();
}
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