/* * microstrip.cpp - microstrip class implementation * * Copyright (C) 2001 Gopal Narayanan * Copyright (C) 2002 Claudio Girardi * Copyright (C) 2005, 2006 Stefan Jahn * Modified for Kicad: 2015 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 #include #include #include #include #include #include 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 = 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() { 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 / 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, "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 / 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(); }