kicad/pcb_calculator/transline/microstrip.cpp

/*
 * 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: 2018 Jean-Pierre Charras <jp.charras at wanadoo.fr>
 *
 * 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 <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>

#include <units.h>
#include <transline.h>
#include <microstrip.h>

MICROSTRIP::MICROSTRIP() : TRANSLINE()
{
    m_Name = "MicroStrip";

    // 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
    mur = 0.0;                  // magnetic permeability of substrate
    w = 0.0;                    // width of line
    l = 0.0;                    // length of line
    Z0_0 = 0.0;                 // static characteristic impedance
    Z0 = 0.0;                   // characteristic impedance
    ang_l = 0.0;                // Electrical length in angle
    er_eff_0 = 0.0;             // Static effective dielectric constant
    er_eff = 0.0;               // Effective dielectric constant
    mur_eff = 0.0;              // Effective mag. permeability
    w_eff = 0.0;                // Effective width of line
    atten_dielectric = 0.0;     // Loss in dielectric (dB)
    atten_cond = 0.0;           // Loss in conductors (dB)
    Z0_h_1 = 0.0;               // homogeneous stripline impedance
}


/*
 * Z0_homogeneous() - compute the impedance for a stripline in a
 * homogeneous medium, without cover effects
 */
double MICROSTRIP::Z0_homogeneous( double u )
{
    double freq, Z0_value;

    freq  = 6.0 + (2.0 * M_PI - 6.0) * exp( -pow( 30.666 / u, 0.7528 ) );
    Z0_value = ( ZF0 / (2.0 * M_PI) ) * log( freq / u + sqrt( 1.0 + 4.0 / (u * u) ) );
    return Z0_value;
}


/*
 * 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;
    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 = m_freq * 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     = m_skindepth;

    if( m_freq > 0.0 )
    {
        /* current distribution factor */
        K = exp( -1.2 * pow( Z0_h_1 / 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 ) ) );
        /* strip inductive quality factor */
        Q_c     = (M_PI * Z0_h_1 * w * m_freq) / (R_s * C0 * K);
        alpha_c = ( 20.0 * M_PI / log( 10.0 ) ) * m_freq * 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 ) ) *
        (m_freq / C0) * ( e_r / sqrt( e_r_eff_0 ) ) * ( (e_r_eff_0 - 1.0) / (e_r - 1.0) ) * m_tand;

    return alpha_d;
}


/*
 * attenuation() - compute attenuation of microstrip
 */
void MICROSTRIP::attenuation()
{
    m_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()
{
    mur_eff = (2.0 * mur) / ( (1.0 + mur) + ( (1.0 - mur) * pow( ( 1.0 + (10.0 * h / w) ), -0.5 ) ) );
}


// synth_width - calculate width given Z0 and e_r
double MICROSTRIP::synth_width()
{
    double e_r, a, b;
    double w_h, width;

    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 )
        width = w_h * h;
    else
        width = 0;

    return width;
}


/*
 * 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 / m_freq;
    /* 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 );
    m_sigma = 1.0 / getProperty( RHO_PRM );
    m_murC  = getProperty( MURC_PRM );
    m_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()
{
    m_freq = 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, m_skindepth/UNIT_MICRON, "µm" );
}


/*
 * 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 / m_freq / 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();
}