KiCad PCB EDA Suite
c_microstrip.cpp
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1/*
2 * c_microstrip.cpp - coupled microstrip class implementation
3 *
4 * Copyright (C) 2002 Claudio Girardi <[email protected]>
5 * Copyright (C) 2005, 2006 Stefan Jahn <[email protected]>
6 *
7 * This program is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or (at
10 * your option) any later version.
11 *
12 * This program is distributed in the hope that it will be useful, but
13 * WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 * General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with this package; see the file COPYING. If not, write to
19 * the Free Software Foundation, Inc., 51 Franklin Street - Fifth Floor,
20 * Boston, MA 02110-1301, USA.
21 *
22 */
23
24/* c_microstrip.c - Puts up window for coupled microstrips and
25 * performs the associated calculations
26 * Based on the original microstrip.c by Gopal Narayanan
27 */
28
29#include <cmath>
30#include <cstdio>
31#include <cstdlib>
32#include <cstring>
33
34#include "c_microstrip.h"
35#include "microstrip.h"
36#include "transline.h"
37#include "units.h"
38
40 h( 0.0 ), // height of substrate
41 ht( 0.0 ), // height to the top of box
42 t( 0.0 ), // thickness of top metal
43 rough( 0.0 ), // Roughness of top metal
44 w( 0.0 ), // width of lines
45 w_t_e( 0.0 ), // even-mode thickness-corrected line width
46 w_t_o( 0.0 ), // odd-mode thickness-corrected line width
47 l( 0.0 ), // length of lines
48 s( 0.0 ), // spacing of lines
49 Z0_e_0( 0.0 ), // static even-mode impedance
50 Z0_o_0( 0.0 ), // static odd-mode impedance
51 Zdiff( 0.0), // differential impedance
52 Z0e( 0.0 ), // even-mode impedance
53 Z0o( 0.0 ), // odd-mode impedance
54 c_e( 0.0 ), // even-mode capacitance
55 c_o( 0.0 ), // odd-mode capacitance
56 ang_l_e( 0.0 ), // even-mode electrical length in angle
57 ang_l_o( 0.0 ), // odd-mode electrical length in angle
58 er_eff_e( 0.0 ), // even-mode effective dielectric constant
59 er_eff_o( 0.0 ), // odd-mode effective dielectric constant
60 er_eff_e_0( 0.0 ), // static even-mode effective dielectric constant
61 er_eff_o_0( 0.0 ), // static odd-mode effective dielectric constant
62 w_eff( 0.0 ), // Effective width of line
63 atten_dielectric_e( 0.0 ), // even-mode dielectric losses (dB)
64 atten_cond_e( 0.0 ), // even-mode conductors losses (dB)
65 atten_dielectric_o( 0.0 ), // odd-mode dielectric losses (dB)
66 atten_cond_o( 0.0 ), // odd-mode conductors losses (dB)
67 aux_ms( nullptr )
68{
69 m_Name = "Coupled_MicroStrip";
70 Init();
71}
72
73
75{
76 delete aux_ms;
77}
78
79
80/*
81 * delta_u_thickness_single() computes the thickness effect on
82 * normalized width for a single microstrip line
83 *
84 * References: H. A. Atwater, "Simplified Design Equations for
85 * Microstrip Line Parameters", Microwave Journal, pp. 109-115,
86 * November 1989.
87 */
88double C_MICROSTRIP::delta_u_thickness_single( double u, double t_h )
89{
90 double delta_u;
91
92 if( t_h > 0.0 )
93 {
94 delta_u =
95 (1.25 * t_h /
96 M_PI) *
97 ( 1.0 +
98 log( ( 2.0 +
99 (4.0 * M_PI * u -
100 2.0) / ( 1.0 + exp( -100.0 * ( u - 1.0 / (2.0 * M_PI) ) ) ) ) / t_h ) );
101
102 }
103 else
104 {
105 delta_u = 0.0;
106 }
107 return delta_u;
108}
109
110
111/*
112 * delta_u_thickness() - compute the thickness effect on normalized
113 * width for coupled microstrips
114 *
115 * References: Rolf Jansen, "High-Speed Computation of Single and
116 * Coupled Microstrip Parameters Including Dispersion, High-Order
117 * Modes, Loss and Finite Strip Thickness", IEEE Trans. MTT, vol. 26,
118 * no. 2, pp. 75-82, Feb. 1978
119 */
121{
122 double e_r, u, g, t_h;
123 double delta_u, delta_t, delta_u_e, delta_u_o;
124
126 u = m_parameters[PHYS_WIDTH_PRM] / m_parameters[H_PRM]; /* normalized line width */
127 g = m_parameters[PHYS_S_PRM] / m_parameters[H_PRM]; /* normalized line spacing */
128 t_h = m_parameters[T_PRM] / m_parameters[H_PRM]; /* normalized strip thickness */
129
130 if( t_h > 0.0 )
131 {
132 /* single microstrip correction for finite strip thickness */
133 delta_u = delta_u_thickness_single( u, t_h );
134 delta_t = t_h / ( g * e_r );
135 /* thickness correction for the even- and odd-mode */
136 delta_u_e = delta_u * ( 1.0 - 0.5 * exp( -0.69 * delta_u / delta_t ) );
137 delta_u_o = delta_u_e + delta_t;
138 }
139 else
140 {
141 delta_u_e = delta_u_o = 0.0;
142 }
143
146}
147
148
149/*
150 * compute various parameters for a single line
151 */
153{
154 if( aux_ms == NULL )
155 aux_ms = new MICROSTRIP();
156
157 /* prepare parameters for single microstrip computations */
161 aux_ms->m_parameters[T_PRM] = 0.0;
162
163 //aux_ms->m_parameters[H_T_PRM] = m_parameters[H_T_PRM];
164 aux_ms->m_parameters[H_T_PRM] = 1e12; /* arbitrarily high */
169}
170
171
172/*
173 * filling_factor_even() - compute the filling factor for the coupled
174 * microstrips even-mode without cover and zero conductor thickness
175 */
176double C_MICROSTRIP::filling_factor_even( double u, double g, double e_r )
177{
178 double v, v3, v4, a_e, b_e, q_inf;
179
180 v = u * ( 20.0 + g * g ) / ( 10.0 + g * g ) + g * exp( -g );
181 v3 = v * v * v;
182 v4 = v3 * v;
183 a_e = 1.0 + log( ( v4 + v * v / 2704.0 ) / ( v4 + 0.432 ) ) / 49.0
184 + log( 1.0 + v3 / 5929.741 ) / 18.7;
185 b_e = 0.564 * pow( ( ( e_r - 0.9 ) / ( e_r + 3.0 ) ), 0.053 );
186
187 /* filling factor, with width corrected for thickness */
188 q_inf = pow( ( 1.0 + 10.0 / v ), -a_e * b_e );
189
190 return q_inf;
191}
192
193
198double C_MICROSTRIP::filling_factor_odd( double u, double g, double e_r )
199{
200 double b_odd = 0.747 * e_r / ( 0.15 + e_r );
201 double c_odd = b_odd - ( b_odd - 0.207 ) * exp( -0.414 * u );
202 double d_odd = 0.593 + 0.694 * exp( -0.562 * u );
203
204 /* filling factor, with width corrected for thickness */
205 double q_inf = exp( -c_odd * pow( g, d_odd ) );
206
207 return q_inf;
208}
209
210
211/*
212 * delta_q_cover_even() - compute the cover effect on filling factor
213 * for the even-mode
214 */
216{
217 double q_c;
218
219 if( h2h <= 39 )
220 q_c = tanh( 1.626 + 0.107 * h2h - 1.733 / sqrt( h2h ) );
221 else
222 q_c = 1.0;
223
224 return q_c;
225}
226
227
228/*
229 * delta_q_cover_odd() - compute the cover effect on filling factor
230 * for the odd-mode
231 */
233{
234 double q_c;
235
236 if( h2h <= 7 )
237 q_c = tanh( 9.575 / ( 7.0 - h2h ) - 2.965 + 1.68 * h2h - 0.311 * h2h * h2h );
238 else
239 q_c = 1.0;
240
241 return q_c;
242}
243
244
254{
255 double u_t_e, u_t_o, g, h2, h2h;
256 double a_o, t_h, q, q_c, q_t, q_inf;
257 double er_eff_single;
258 double er;
259
261
262 /* compute zero-thickness single line parameters */
264 er_eff_single = aux_ms->er_eff_0;
265
266 h2 = m_parameters[H_T_PRM];
267 u_t_e = w_t_e / m_parameters[H_PRM]; /* normalized even_mode line width */
268 u_t_o = w_t_o / m_parameters[H_PRM]; /* normalized odd_mode line width */
269 g = m_parameters[PHYS_S_PRM] / m_parameters[H_PRM]; /* normalized line spacing */
270 h2h = h2 / m_parameters[H_PRM]; /* normalized cover height */
271 t_h = m_parameters[T_PRM] / m_parameters[H_PRM]; /* normalized strip thickness */
272
273 /* filling factor, computed with thickness corrected width */
274 q_inf = filling_factor_even( u_t_e, g, er );
275 /* cover effect */
276 q_c = delta_q_cover_even( h2h );
277 /* thickness effect */
278 q_t = aux_ms->delta_q_thickness( u_t_e, t_h );
279 /* resultant filling factor */
280 q = ( q_inf - q_t ) * q_c;
281 /* static even-mode effective dielectric constant */
282 er_eff_e_0 = 0.5 * ( er + 1.0 ) + 0.5 * ( er - 1.0 ) * q;
283
284 /* filling factor, with width corrected for thickness */
285 q_inf = filling_factor_odd( u_t_o, g, er );
286 /* cover effect */
287 q_c = delta_q_cover_odd( h2h );
288 /* thickness effect */
289 q_t = aux_ms->delta_q_thickness( u_t_o, t_h );
290 /* resultant filling factor */
291 q = ( q_inf - q_t ) * q_c;
292
293 a_o = 0.7287 * ( er_eff_single - 0.5 * ( er + 1.0 ) ) * ( 1.0 - exp( -0.179 * u_t_o ) );
294
295 /* static odd-mode effective dielectric constant */
296 er_eff_o_0 = ( 0.5 * ( er + 1.0 ) + a_o - er_eff_single ) * q + er_eff_single;
297}
298
299
307double C_MICROSTRIP::delta_Z0_even_cover( double g, double u, double h2h )
308{
309 double f_e, g_e, delta_Z0_even;
310 double x, y, A, B, C, D, E, F;
311
312 A = -4.351 / pow( 1.0 + h2h, 1.842 );
313 B = 6.639 / pow( 1.0 + h2h, 1.861 );
314 C = -2.291 / pow( 1.0 + h2h, 1.90 );
315 f_e = 1.0 - atanh( A + ( B + C * u ) * u );
316
317 x = pow( 10.0, 0.103 * g - 0.159 );
318 y = pow( 10.0, 0.0492 * g - 0.073 );
319 D = 0.747 / sin( 0.5 * M_PI * x );
320 E = 0.725 * sin( 0.5 * M_PI * y );
321 F = pow( 10.0, 0.11 - 0.0947 * g );
322 g_e = 270.0 * ( 1.0 - tanh( D + E * sqrt( 1.0 + h2h ) - F / ( 1.0 + h2h ) ) );
323
324 delta_Z0_even = f_e * g_e;
325
326 return delta_Z0_even;
327}
328
329
337double C_MICROSTRIP::delta_Z0_odd_cover( double g, double u, double h2h )
338{
339 double f_o, g_o, delta_Z0_odd;
340 double G, J, K, L;
341
342 J = tanh( pow( 1.0 + h2h, 1.585 ) / 6.0 );
343 f_o = pow( u, J );
344
345 G = 2.178 - 0.796 * g;
346
347 if( g > 0.858 )
348 K = log10( 20.492 * pow( g, 0.174 ) );
349 else
350 K = 1.30;
351
352 if( g > 0.873 )
353 L = 2.51 * pow( g, -0.462 );
354 else
355 L = 2.674;
356
357 g_o = 270.0 * ( 1.0 - tanh( G + K * sqrt( 1.0 + h2h ) - L / ( 1.0 + h2h ) ) );
358
359 delta_Z0_odd = f_o * g_o;
360
361 return delta_Z0_odd;
362}
363
364
375{
376 double er_eff, h2, u_t_e, u_t_o, g, h2h;
377 double Q_1, Q_2, Q_3, Q_4, Q_5, Q_6, Q_7, Q_8, Q_9, Q_10;
378 double delta_Z0_e_0, delta_Z0_o_0, Z0_single, er_eff_single;
379
380 h2 = m_parameters[H_T_PRM];
381 u_t_e = w_t_e / m_parameters[H_PRM]; /* normalized even-mode line width */
382 u_t_o = w_t_o / m_parameters[H_PRM]; /* normalized odd-mode line width */
383 g = m_parameters[PHYS_S_PRM] / m_parameters[H_PRM]; /* normalized line spacing */
384 h2h = h2 / m_parameters[H_PRM]; /* normalized cover height */
385
386 Z0_single = aux_ms->Z0_0;
387 er_eff_single = aux_ms->er_eff_0;
388
389 /* even-mode */
391 Q_1 = 0.8695 * pow( u_t_e, 0.194 );
392 Q_2 = 1.0 + 0.7519 * g + 0.189 * pow( g, 2.31 );
393 Q_3 = 0.1975 + pow( ( 16.6 + pow( ( 8.4 / g ), 6.0 ) ), -0.387 )
394 + log( pow( g, 10.0 ) / ( 1.0 + pow( g / 3.4, 10.0 ) ) ) / 241.0;
395 Q_4 = 2.0 * Q_1
396 / ( Q_2 * ( exp( -g ) * pow( u_t_e, Q_3 ) + ( 2.0 - exp( -g ) ) * pow( u_t_e, -Q_3 ) ) );
397 /* static even-mode impedance */
398 Z0_e_0 = Z0_single * sqrt( er_eff_single / er_eff )
399 / ( 1.0 - sqrt( er_eff_single ) * Q_4 * Z0_single / ZF0 );
400 /* correction for cover */
401 delta_Z0_e_0 = delta_Z0_even_cover( g, u_t_e, h2h ) / sqrt( er_eff );
402
403 Z0_e_0 = Z0_e_0 - delta_Z0_e_0;
404
405 /* odd-mode */
407 Q_5 = 1.794 + 1.14 * log( 1.0 + 0.638 / ( g + 0.517 * pow( g, 2.43 ) ) );
408 Q_6 = 0.2305 + log( pow( g, 10.0 ) / ( 1.0 + pow( g / 5.8, 10.0 ) ) ) / 281.3
409 + log( 1.0 + 0.598 * pow( g, 1.154 ) ) / 5.1;
410 Q_7 = ( 10.0 + 190.0 * g * g ) / ( 1.0 + 82.3 * g * g * g );
411 Q_8 = exp( -6.5 - 0.95 * log( g ) - pow( g / 0.15, 5.0 ) );
412 Q_9 = log( Q_7 ) * ( Q_8 + 1.0 / 16.5 );
413 Q_10 = ( Q_2 * Q_4 - Q_5 * exp( log( u_t_o ) * Q_6 * pow( u_t_o, -Q_9 ) ) ) / Q_2;
414
415 /* static odd-mode impedance */
416 Z0_o_0 = Z0_single * sqrt( er_eff_single / er_eff )
417 / ( 1.0 - sqrt( er_eff_single ) * Q_10 * Z0_single / ZF0 );
418 /* correction for cover */
419 delta_Z0_o_0 = delta_Z0_odd_cover( g, u_t_o, h2h ) / sqrt( er_eff );
420
421 Z0_o_0 = Z0_o_0 - delta_Z0_o_0;
422}
423
424
425/*
426 * er_eff_freq() - compute er_eff as a function of frequency
427 */
429{
430 double P_1, P_2, P_3, P_4, P_5, P_6, P_7;
431 double P_8, P_9, P_10, P_11, P_12, P_13, P_14, P_15;
432 double F_e, F_o;
433 double er_eff, u, g, f_n;
434
435 u = m_parameters[PHYS_WIDTH_PRM] / m_parameters[H_PRM]; /* normalize line width */
436 g = m_parameters[PHYS_S_PRM] / m_parameters[H_PRM]; /* normalize line spacing */
437
438 /* normalized frequency [GHz * mm] */
440
442 P_1 = 0.27488 + ( 0.6315 + 0.525 / pow( 1.0 + 0.0157 * f_n, 20.0 ) ) * u
443 - 0.065683 * exp( -8.7513 * u );
444 P_2 = 0.33622 * ( 1.0 - exp( -0.03442 * m_parameters[EPSILONR_PRM] ) );
445 P_3 = 0.0363 * exp( -4.6 * u ) * ( 1.0 - exp( -pow( f_n / 38.7, 4.97 ) ) );
446 P_4 = 1.0 + 2.751 * ( 1.0 - exp( -pow( m_parameters[EPSILONR_PRM] / 15.916, 8.0 ) ) );
447 P_5 = 0.334 * exp( -3.3 * pow( m_parameters[EPSILONR_PRM] / 15.0, 3.0 ) ) + 0.746;
448 P_6 = P_5 * exp( -pow( f_n / 18.0, 0.368 ) );
449 P_7 = 1.0
450 + 4.069 * P_6 * pow( g, 0.479 ) * exp( -1.347 * pow( g, 0.595 ) - 0.17 * pow( g, 2.5 ) );
451
452 F_e = P_1 * P_2 * pow( ( P_3 * P_4 + 0.1844 * P_7 ) * f_n, 1.5763 );
453 /* even-mode effective dielectric constant */
455
457 P_8 = 0.7168 * ( 1.0 + 1.076 / ( 1.0 + 0.0576 * ( m_parameters[EPSILONR_PRM] - 1.0 ) ) );
458 P_9 = P_8
459 - 0.7913 * ( 1.0 - exp( -pow( f_n / 20.0, 1.424 ) ) )
460 * atan( 2.481 * pow( m_parameters[EPSILONR_PRM] / 8.0, 0.946 ) );
461 P_10 = 0.242 * pow( m_parameters[EPSILONR_PRM] - 1.0, 0.55 );
462 P_11 = 0.6366 * ( exp( -0.3401 * f_n ) - 1.0 ) * atan( 1.263 * pow( u / 3.0, 1.629 ) );
463 P_12 = P_9 + ( 1.0 - P_9 ) / ( 1.0 + 1.183 * pow( u, 1.376 ) );
464 P_13 = 1.695 * P_10 / ( 0.414 + 1.605 * P_10 );
465 P_14 = 0.8928 + 0.1072 * ( 1.0 - exp( -0.42 * pow( f_n / 20.0, 3.215 ) ) );
466 P_15 = fabs( 1.0 - 0.8928 * ( 1.0 + P_11 ) * P_12 * exp( -P_13 * pow( g, 1.092 ) ) / P_14 );
467
468 F_o = P_1 * P_2 * pow( ( P_3 * P_4 + 0.1844 ) * f_n * P_15, 1.5763 );
469 /* odd-mode effective dielectric constant */
471}
472
473
474/*
475 * conductor_losses() - compute microstrips conductor losses per unit
476 * length
477 */
479{
480 double e_r_eff_e_0, e_r_eff_o_0, Z0_h_e, Z0_h_o, delta;
481 double K, R_s, Q_c_e, Q_c_o, alpha_c_e, alpha_c_o;
482
483 e_r_eff_e_0 = er_eff_e_0;
484 e_r_eff_o_0 = er_eff_o_0;
485 Z0_h_e = Z0_e_0 * sqrt( e_r_eff_e_0 ); /* homogeneous stripline impedance */
486 Z0_h_o = Z0_o_0 * sqrt( e_r_eff_o_0 ); /* homogeneous stripline impedance */
488
489 if( m_parameters[FREQUENCY_PRM] > 0.0 )
490 {
491 /* current distribution factor (same for the two modes) */
492 K = exp( -1.2 * pow( ( Z0_h_e + Z0_h_o ) / ( 2.0 * ZF0 ), 0.7 ) );
493 /* skin resistance */
494 R_s = 1.0 / ( m_parameters[SIGMA_PRM] * delta );
495 /* correction for surface roughness */
496 R_s *= 1.0
497 + ( ( 2.0 / M_PI )
498 * atan( 1.40 * pow( ( m_parameters[ROUGH_PRM] / delta ), 2.0 ) ) );
499
500 /* even-mode strip inductive quality factor */
501 Q_c_e = ( M_PI * Z0_h_e * m_parameters[PHYS_WIDTH_PRM] * m_parameters[FREQUENCY_PRM] )
502 / ( R_s * C0 * K );
503 /* even-mode losses per unit length */
504 alpha_c_e = ( 20.0 * M_PI / log( 10.0 ) ) * m_parameters[FREQUENCY_PRM]
505 * sqrt( e_r_eff_e_0 ) / ( C0 * Q_c_e );
506
507 /* odd-mode strip inductive quality factor */
508 Q_c_o = ( M_PI * Z0_h_o * m_parameters[PHYS_WIDTH_PRM] * m_parameters[FREQUENCY_PRM] )
509 / ( R_s * C0 * K );
510 /* odd-mode losses per unit length */
511 alpha_c_o = ( 20.0 * M_PI / log( 10.0 ) ) * m_parameters[FREQUENCY_PRM]
512 * sqrt( e_r_eff_o_0 ) / ( C0 * Q_c_o );
513 }
514 else
515 {
516 alpha_c_e = alpha_c_o = 0.0;
517 }
518
521}
522
523
524/*
525 * dielectric_losses() - compute microstrips dielectric losses per
526 * unit length
527 */
529{
530 double e_r, e_r_eff_e_0, e_r_eff_o_0;
531 double alpha_d_e, alpha_d_o;
532
534 e_r_eff_e_0 = er_eff_e_0;
535 e_r_eff_o_0 = er_eff_o_0;
536
537 alpha_d_e = ( 20.0 * M_PI / log( 10.0 ) ) * ( m_parameters[FREQUENCY_PRM] / C0 )
538 * ( e_r / sqrt( e_r_eff_e_0 ) ) * ( ( e_r_eff_e_0 - 1.0 ) / ( e_r - 1.0 ) )
540 alpha_d_o = ( 20.0 * M_PI / log( 10.0 ) ) * ( m_parameters[FREQUENCY_PRM] / C0 )
541 * ( e_r / sqrt( e_r_eff_o_0 ) ) * ( ( e_r_eff_o_0 - 1.0 ) / ( e_r - 1.0 ) )
543
546}
547
548
549/*
550 * c_microstrip_attenuation() - compute attenuation of coupled
551 * microstrips
552 */
554{
558}
559
560
561/*
562 * line_angle() - calculate strips electrical lengths in radians
563 */
565{
566 double e_r_eff_e, e_r_eff_o;
567 double v_e, v_o, lambda_g_e, lambda_g_o;
568
569 e_r_eff_e = er_eff_e;
570 e_r_eff_o = er_eff_o;
571
572 /* even-mode velocity */
573 v_e = C0 / sqrt( e_r_eff_e );
574 /* odd-mode velocity */
575 v_o = C0 / sqrt( e_r_eff_o );
576 /* even-mode wavelength */
577 lambda_g_e = v_e / m_parameters[FREQUENCY_PRM];
578 /* odd-mode wavelength */
579 lambda_g_o = v_o / m_parameters[FREQUENCY_PRM];
580 /* electrical angles */
581 ang_l_e = 2.0 * M_PI * m_parameters[PHYS_LEN_PRM] / lambda_g_e; /* in radians */
582 ang_l_o = 2.0 * M_PI * m_parameters[PHYS_LEN_PRM] / lambda_g_o; /* in radians */
583}
584
585
592{
593 Zdiff = 2 * Z0_o_0;
594}
595
596
597void C_MICROSTRIP::syn_err_fun( double* f1, double* f2, double s_h, double w_h, double e_r,
598 double w_h_se, double w_h_so )
599{
600 double g, he;
601
602 g = cosh( 0.5 * M_PI * s_h );
603 he = cosh( M_PI * w_h + 0.5 * M_PI * s_h );
604
605 *f1 = ( 2.0 / M_PI ) * acosh( ( 2.0 * he - g + 1.0 ) / ( g + 1.0 ) );
606 *f2 = ( 2.0 / M_PI ) * acosh( ( 2.0 * he - g - 1.0 ) / ( g - 1.0 ) );
607
608 if( e_r <= 6.0 )
609 *f2 += ( 4.0 / ( M_PI * ( 1.0 + e_r / 2.0 ) ) ) * acosh( 1.0 + 2.0 * w_h / s_h );
610 else
611 *f2 += ( 1.0 / M_PI ) * acosh( 1.0 + 2.0 * w_h / s_h );
612
613 *f1 -= w_h_se;
614 *f2 -= w_h_so;
615}
616
617
618/*
619 * synth_width - calculate widths given Z0 and e_r
620 * from Akhtarzad S. et al., "The design of coupled microstrip lines",
621 * IEEE Trans. MTT-23, June 1975 and
622 * Hinton, J.H., "On design of coupled microstrip lines", IEEE Trans.
623 * MTT-28, March 1980
624 */
626{
627 double Z0, e_r;
628 double w_h_se, w_h_so, w_h, a, ce, co, s_h;
629 double f1, f2, ft1, ft2, j11, j12, j21, j22, d_s_h, d_w_h, err;
630 double eps = 1e-04;
631
632 f1 = f2 = 0;
634
635 Z0 = m_parameters[Z0_E_PRM] / 2.0;
636 /* Wheeler formula for single microstrip synthesis */
637 a = exp( Z0 * sqrt( e_r + 1.0 ) / 42.4 ) - 1.0;
638 w_h_se = 8.0 * sqrt( a * ( ( 7.0 + 4.0 / e_r ) / 11.0 ) + ( ( 1.0 + 1.0 / e_r ) / 0.81 ) ) / a;
639
640 Z0 = m_parameters[Z0_O_PRM] / 2.0;
641 /* Wheeler formula for single microstrip synthesis */
642 a = exp( Z0 * sqrt( e_r + 1.0 ) / 42.4 ) - 1.0;
643 w_h_so = 8.0 * sqrt( a * ( ( 7.0 + 4.0 / e_r ) / 11.0 ) + ( ( 1.0 + 1.0 / e_r ) / 0.81 ) ) / a;
644
645 ce = cosh( 0.5 * M_PI * w_h_se );
646 co = cosh( 0.5 * M_PI * w_h_so );
647 /* first guess at m_parameters[PHYS_S_PRM]/h */
648 s_h = ( 2.0 / M_PI ) * acosh( ( ce + co - 2.0 ) / ( co - ce ) );
649 /* first guess at w/h */
650 w_h = acosh( ( ce * co - 1.0 ) / ( co - ce ) ) / M_PI - s_h / 2.0;
651
654
655 syn_err_fun( &f1, &f2, s_h, w_h, e_r, w_h_se, w_h_so );
656
657 /* rather crude Newton-Rhapson; we need this because the estimate of */
658 /* w_h is often quite far from the true value (see Akhtarzad S. et al.) */
659 do
660 {
661 /* compute Jacobian */
662 syn_err_fun( &ft1, &ft2, s_h + eps, w_h, e_r, w_h_se, w_h_so );
663 j11 = ( ft1 - f1 ) / eps;
664 j21 = ( ft2 - f2 ) / eps;
665 syn_err_fun( &ft1, &ft2, s_h, w_h + eps, e_r, w_h_se, w_h_so );
666 j12 = ( ft1 - f1 ) / eps;
667 j22 = ( ft2 - f2 ) / eps;
668
669 /* compute next step */
670 d_s_h = ( -f1 * j22 + f2 * j12 ) / ( j11 * j22 - j21 * j12 );
671 d_w_h = ( -f2 * j11 + f1 * j21 ) / ( j11 * j22 - j21 * j12 );
672
673 //g_print("j11 = %e\tj12 = %e\tj21 = %e\tj22 = %e\n", j11, j12, j21, j22);
674 //g_print("det = %e\n", j11*j22 - j21*j22);
675 //g_print("d_s_h = %e\td_w_h = %e\n", d_s_h, d_w_h);
676
677 s_h += d_s_h;
678 w_h += d_w_h;
679
680 /* check the error */
681 syn_err_fun( &f1, &f2, s_h, w_h, e_r, w_h_se, w_h_so );
682
683 err = sqrt( f1 * f1 + f2 * f2 );
684 /* converged ? */
685 } while( err > 1e-04 );
686
687
690}
691
692
693/*
694 * Z0_dispersion() - calculate frequency dependency of characteristic
695 * impedances
696 */
698{
699 double Q_0;
700 double Q_11, Q_12, Q_13, Q_14, Q_15, Q_16, Q_17, Q_18, Q_19, Q_20, Q_21;
701 double Q_22, Q_23, Q_24, Q_25, Q_26, Q_27, Q_28, Q_29;
702 double r_e, q_e, p_e, d_e, C_e;
703 double e_r_eff_o_f, e_r_eff_o_0;
704 double e_r_eff_single_f, e_r_eff_single_0, Z0_single_f;
705 double f_n, g, u, e_r;
706 double R_1, R_2, R_7, R_10, R_11, R_12, R_15, R_16, tmpf;
707
709
710 u = m_parameters[PHYS_WIDTH_PRM] / m_parameters[H_PRM]; /* normalize line width */
711 g = m_parameters[PHYS_S_PRM] / m_parameters[H_PRM]; /* normalize line spacing */
712
713 /* normalized frequency [GHz * mm] */
715
716 e_r_eff_single_f = aux_ms->er_eff;
717 e_r_eff_single_0 = aux_ms->er_eff_0;
718 Z0_single_f = aux_ms->m_parameters[Z0_PRM];
719
720 e_r_eff_o_f = er_eff_o;
721 e_r_eff_o_0 = er_eff_o_0;
722
723 Q_11 = 0.893 * ( 1.0 - 0.3 / ( 1.0 + 0.7 * ( e_r - 1.0 ) ) );
724 Q_12 = 2.121 * ( pow( f_n / 20.0, 4.91 ) / ( 1.0 + Q_11 * pow( f_n / 20.0, 4.91 ) ) )
725 * exp( -2.87 * g ) * pow( g, 0.902 );
726 Q_13 = 1.0 + 0.038 * pow( e_r / 8.0, 5.1 );
727 Q_14 = 1.0 + 1.203 * pow( e_r / 15.0, 4.0 ) / ( 1.0 + pow( e_r / 15.0, 4.0 ) );
728 Q_15 = 1.887 * exp( -1.5 * pow( g, 0.84 ) ) * pow( g, Q_14 )
729 / ( 1.0
730 + 0.41 * pow( f_n / 15.0, 3.0 ) * pow( u, 2.0 / Q_13 )
731 / ( 0.125 + pow( u, 1.626 / Q_13 ) ) );
732 Q_16 = ( 1.0 + 9.0 / ( 1.0 + 0.403 * pow( e_r - 1.0, 2 ) ) ) * Q_15;
733 Q_17 = 0.394 * ( 1.0 - exp( -1.47 * pow( u / 7.0, 0.672 ) ) )
734 * ( 1.0 - exp( -4.25 * pow( f_n / 20.0, 1.87 ) ) );
735 Q_18 = 0.61 * ( 1.0 - exp( -2.13 * pow( u / 8.0, 1.593 ) ) ) / ( 1.0 + 6.544 * pow( g, 4.17 ) );
736 Q_19 = 0.21 * g * g * g * g
737 / ( ( 1.0 + 0.18 * pow( g, 4.9 ) ) * ( 1.0 + 0.1 * u * u )
738 * ( 1.0 + pow( f_n / 24.0, 3.0 ) ) );
739 Q_20 = ( 0.09 + 1.0 / ( 1.0 + 0.1 * pow( e_r - 1, 2.7 ) ) ) * Q_19;
740 Q_21 = fabs( 1.0
741 - 42.54 * pow( g, 0.133 ) * exp( -0.812 * g ) * pow( u, 2.5 )
742 / ( 1.0 + 0.033 * pow( u, 2.5 ) ) );
743
744 r_e = pow( f_n / 28.843, 12 );
745 q_e = 0.016 + pow( 0.0514 * e_r * Q_21, 4.524 );
746 p_e = 4.766 * exp( -3.228 * pow( u, 0.641 ) );
747 d_e = 5.086 * q_e * ( r_e / ( 0.3838 + 0.386 * q_e ) )
748 * ( exp( -22.2 * pow( u, 1.92 ) ) / ( 1.0 + 1.2992 * r_e ) )
749 * ( pow( e_r - 1.0, 6.0 ) / ( 1.0 + 10 * pow( e_r - 1.0, 6.0 ) ) );
750 C_e = 1.0
751 + 1.275
752 * ( 1.0
753 - exp( -0.004625 * p_e * pow( e_r, 1.674 )
754 * pow( f_n / 18.365, 2.745 ) ) )
755 - Q_12 + Q_16 - Q_17 + Q_18 + Q_20;
756
757
758 R_1 = 0.03891 * pow( e_r, 1.4 );
759 R_2 = 0.267 * pow( u, 7.0 );
760 R_7 = 1.206 - 0.3144 * exp( -R_1 ) * ( 1.0 - exp( -R_2 ) );
761 R_10 = 0.00044 * pow( e_r, 2.136 ) + 0.0184;
762 tmpf = pow( f_n / 19.47, 6.0 );
763 R_11 = tmpf / ( 1.0 + 0.0962 * tmpf );
764 R_12 = 1.0 / ( 1.0 + 0.00245 * u * u );
765 R_15 = 0.707 * R_10 * pow( f_n / 12.3, 1.097 );
766 R_16 = 1.0 + 0.0503 * e_r * e_r * R_11 * ( 1.0 - exp( -pow( u / 15.0, 6.0 ) ) );
767 Q_0 = R_7 * ( 1.0 - 1.1241 * ( R_12 / R_16 ) * exp( -0.026 * pow( f_n, 1.15656 ) - R_15 ) );
768
769 /* even-mode frequency-dependent characteristic impedances */
770 m_parameters[Z0_E_PRM] = Z0_e_0 * pow( 0.9408 * pow( e_r_eff_single_f, C_e ) - 0.9603, Q_0 )
771 / pow( ( 0.9408 - d_e ) * pow( e_r_eff_single_0, C_e ) - 0.9603, Q_0 );
772
773 Q_29 = 15.16 / ( 1.0 + 0.196 * pow( e_r - 1.0, 2.0 ) );
774 tmpf = pow( e_r - 1.0, 3.0 );
775 Q_28 = 0.149 * tmpf / ( 94.5 + 0.038 * tmpf );
776 tmpf = pow( e_r - 1.0, 1.5 );
777 Q_27 = 0.4 * pow( g, 0.84 ) * ( 1.0 + 2.5 * tmpf / ( 5.0 + tmpf ) );
778 tmpf = pow( ( e_r - 1.0 ) / 13.0, 12.0 );
779 Q_26 = 30.0 - 22.2 * ( tmpf / ( 1.0 + 3.0 * tmpf ) ) - Q_29;
780 tmpf = ( e_r - 1.0 ) * ( e_r - 1.0 );
781 Q_25 = ( 0.3 * f_n * f_n / ( 10.0 + f_n * f_n ) ) * ( 1.0 + 2.333 * tmpf / ( 5.0 + tmpf ) );
782 Q_24 = 2.506 * Q_28 * pow( u, 0.894 ) * pow( ( 1.0 + 1.3 * u ) * f_n / 99.25, 4.29 )
783 / ( 3.575 + pow( u, 0.894 ) );
784 Q_23 = 1.0
785 + 0.005 * f_n * Q_27
786 / ( ( 1.0 + 0.812 * pow( f_n / 15.0, 1.9 ) ) * ( 1.0 + 0.025 * u * u ) );
787 Q_22 = 0.925 * pow( f_n / Q_26, 1.536 ) / ( 1.0 + 0.3 * pow( f_n / 30.0, 1.536 ) );
788
789 /* odd-mode frequency-dependent characteristic impedances */
791 Z0_single_f
792 + ( Z0_o_0 * pow( e_r_eff_o_f / e_r_eff_o_0, Q_22 ) - Z0_single_f * Q_23 )
793 / ( 1.0 + Q_24 + pow( 0.46 * g, 2.2 ) * Q_25 );
794}
795
796
798{
799 /* compute thickness corrections */
801 /* get effective dielectric constants */
803 /* impedances for even- and odd-mode */
804 Z0_even_odd();
805 /* calculate freq dependence of er_eff_e, er_eff_o */
806 er_eff_freq();
807 /* calculate frequency dependence of Z0e, Z0o */
809 /* calculate losses */
810 attenuation();
811 /* calculate electrical lengths */
812 line_angle();
813 /* calculate diff impedance */
815}
816
817
819{
822 setProperty( ANG_L_PRM, sqrt( ang_l_e * ang_l_o ) );
823
824 //Check for errors
825 if( !std::isfinite( m_parameters[Z0_O_PRM] ) || m_parameters[Z0_O_PRM] <= 0.0 )
827
828 if( !std::isfinite( m_parameters[Z0_E_PRM] ) || m_parameters[Z0_E_PRM] <= 0.0 )
830
831 if( !std::isfinite( m_parameters[ANG_L_PRM] ) || m_parameters[ANG_L_PRM] <= 0.0 )
833
834 // Check for warnings
835 if( !std::isfinite( m_parameters[PHYS_WIDTH_PRM] ) || m_parameters[PHYS_WIDTH_PRM] <= 0.0 )
837
838 if( !std::isfinite( m_parameters[PHYS_S_PRM] ) || m_parameters[PHYS_S_PRM] <= 0.0 )
840
841 if( !std::isfinite( m_parameters[PHYS_LEN_PRM] ) || m_parameters[PHYS_LEN_PRM] <= 0.0 )
843}
844
846{
850
851 //Check for errors
852 if( !std::isfinite( m_parameters[PHYS_WIDTH_PRM] ) || m_parameters[PHYS_WIDTH_PRM] <= 0.0 )
854
855 if( !std::isfinite( m_parameters[PHYS_S_PRM] ) || m_parameters[PHYS_S_PRM] <= 0.0 )
857
858 if( !std::isfinite( m_parameters[PHYS_LEN_PRM] ) || m_parameters[PHYS_LEN_PRM] <= 0.0 )
860
861 // Check for warnings
862 if( !std::isfinite( m_parameters[Z0_O_PRM] ) || m_parameters[Z0_O_PRM] <= 0.0 )
864
865 if( !std::isfinite( m_parameters[Z0_E_PRM] ) || m_parameters[Z0_E_PRM] <= 0.0 )
867
868 if( !std::isfinite( m_parameters[ANG_L_PRM] ) || m_parameters[ANG_L_PRM] <= 0.0 )
870}
871
873{
874
875 setResult( 0, er_eff_e, "" );
876 setResult( 1, er_eff_o, "" );
877 setResult( 2, atten_cond_e, "dB" );
878 setResult( 3, atten_cond_o, "dB" );
879 setResult( 4, atten_dielectric_e, "dB" );
880 setResult( 5, atten_dielectric_o, "dB" );
881
883 setResult( 7, Zdiff, "Ω" );
884}
885
886
888 double* f1, double* f2, double s_h, double w_h, double Z0_e, double Z0_o )
889{
892
893 /* compute coupled microstrip parameters */
894 calcAnalyze();
895
896 *f1 = m_parameters[Z0_E_PRM] - Z0_e;
897 *f2 = m_parameters[Z0_O_PRM] - Z0_o;
898}
899
900
901/*
902 * synthesis function
903 */
905{
906 double Z0_e, Z0_o, ang_l_dest;
907 double f1, f2, ft1, ft2, j11, j12, j21, j22, d_s_h, d_w_h, err;
908 double eps = 1e-04;
909 double w_h, s_h, le, lo;
910
911
912 /* required value of Z0_e and Z0_o */
913 Z0_e = m_parameters[Z0_E_PRM];
914 Z0_o = m_parameters[Z0_O_PRM];
915
916
919 ang_l_dest = m_parameters[ANG_L_PRM];
920
921
922 /* calculate width and use for initial value in Newton's method */
923 synth_width();
926 f1 = f2 = 0;
927
928 /* rather crude Newton-Rhapson */
929 do
930 {
931 /* compute Jacobian */
932 syn_fun( &ft1, &ft2, s_h + eps, w_h, Z0_e, Z0_o );
933 j11 = ( ft1 - f1 ) / eps;
934 j21 = ( ft2 - f2 ) / eps;
935 syn_fun( &ft1, &ft2, s_h, w_h + eps, Z0_e, Z0_o );
936 j12 = ( ft1 - f1 ) / eps;
937 j22 = ( ft2 - f2 ) / eps;
938
939 /* compute next step; increments of s_h and w_h */
940 d_s_h = ( -f1 * j22 + f2 * j12 ) / ( j11 * j22 - j21 * j12 );
941 d_w_h = ( -f2 * j11 + f1 * j21 ) / ( j11 * j22 - j21 * j12 );
942
943 s_h += d_s_h;
944 w_h += d_w_h;
945
946 /* compute the error with the new values of s_h and w_h */
947 syn_fun( &f1, &f2, s_h, w_h, Z0_e, Z0_o );
948 err = sqrt( f1 * f1 + f2 * f2 );
949
950 /* converged ? */
951 } while( err > 1e-04 );
952
953 /* denormalize computed width and spacing */
956
957
958 /* calculate physical length */
959 le = C0 / m_parameters[FREQUENCY_PRM] / sqrt( er_eff_e ) * ang_l_dest / 2.0 / M_PI;
960 lo = C0 / m_parameters[FREQUENCY_PRM] / sqrt( er_eff_o ) * ang_l_dest / 2.0 / M_PI;
961 m_parameters[PHYS_LEN_PRM] = sqrt( le * lo );
962
963 calcAnalyze();
964
965 m_parameters[ANG_L_PRM] = ang_l_dest;
966 m_parameters[Z0_E_PRM] = Z0_e;
967 m_parameters[Z0_O_PRM] = Z0_o;
968}
double delta_Z0_odd_cover(double, double, double)
delta_Z0_odd_cover() - compute the odd-mode impedance correction for a homogeneous microstrip due to ...
double delta_Z0_even_cover(double, double, double)
delta_Z0_even_cover() - compute the even-mode impedance correction for a homogeneous microstrip due t...
void show_results() override
Shows results.
double w_t_e
Definition: c_microstrip.h:43
double er_eff_o_0
Definition: c_microstrip.h:59
void er_eff_freq()
double ang_l_e
Definition: c_microstrip.h:54
double er_eff_e
Definition: c_microstrip.h:56
void conductor_losses()
void calcAnalyze() override
Computation for analysis.
double ang_l_o
Definition: c_microstrip.h:55
void synth_width()
void Z0_even_odd()
Z0_even_odd() - compute the static even- and odd-mode static impedances.
void dielectric_losses()
void Z0_dispersion()
MICROSTRIP * aux_ms
Definition: c_microstrip.h:96
void delta_u_thickness()
double er_eff_o
Definition: c_microstrip.h:57
double atten_cond_o
Definition: c_microstrip.h:64
double filling_factor_even(double, double, double)
void showAnalyze() override
Shows synthesis results and checks for errors / warnings.
void showSynthesize() override
Shows analysis results and checks for errors / warnings.
void syn_fun(double *, double *, double, double, double, double)
void attenuation()
void er_eff_static()
er_eff_static() - compute the static effective dielectric constants
double atten_dielectric_o
Definition: c_microstrip.h:63
double Zdiff
Definition: c_microstrip.h:49
double atten_cond_e
Definition: c_microstrip.h:62
double delta_q_cover_odd(double)
double Z0_e_0
Definition: c_microstrip.h:47
void compute_single_line()
void syn_err_fun(double *, double *, double, double, double, double, double)
double w_t_o
Definition: c_microstrip.h:44
double atten_dielectric_e
Definition: c_microstrip.h:61
double filling_factor_odd(double, double, double)
filling_factor_odd() - compute the filling factor for the coupled microstrips odd-mode without cover ...
void calcSynthesize() override
Computation for synthesis.
double Z0_o_0
Definition: c_microstrip.h:48
double delta_u_thickness_single(double, double)
void diff_impedance()
Note that differential impedance is exactly twice the odd mode impedance.
double er_eff_e_0
Definition: c_microstrip.h:58
double delta_q_cover_even(double)
void microstrip_Z0()
Definition: microstrip.cpp:176
double Z0_0
Definition: microstrip.h:45
void dispersion()
Definition: microstrip.cpp:288
double delta_q_thickness(double, double)
Definition: microstrip.cpp:128
double er_eff_0
Definition: microstrip.h:48
void Init()
Definition: transline.cpp:90
void setResult(int, double, const char *)
Definition: transline.cpp:133
double m_parameters[EXTRA_PRMS_COUNT]
Definition: transline.h:131
const char * m_Name
Definition: transline.h:84
void setProperty(enum PRMS_ID aPrmId, double aValue)
Definition: transline.cpp:109
double skin_depth()
@function skin_depth calculate skin depth
Definition: transline.cpp:237
double er_eff
Definition: transline.h:133
void setErrorLevel(PRMS_ID, char)
@function setErrorLevel
Definition: transline.cpp:435
#define F(x, y, z)
Definition: md5_hash.cpp:15
#define G(x, y, z)
Definition: md5_hash.cpp:16
constexpr int delta
@ SIGMA_PRM
Definition: transline.h:69
@ SKIN_DEPTH_PRM
Definition: transline.h:70
@ Z0_O_PRM
Definition: transline.h:54
@ FREQUENCY_PRM
Definition: transline.h:51
@ T_PRM
Definition: transline.h:46
@ Z0_E_PRM
Definition: transline.h:53
@ MURC_PRM
Definition: transline.h:50
@ Z0_PRM
Definition: transline.h:52
@ TAND_PRM
Definition: transline.h:40
@ PHYS_LEN_PRM
Definition: transline.h:60
@ ANG_L_PRM
Definition: transline.h:55
@ H_T_PRM
Definition: transline.h:44
@ ROUGH_PRM
Definition: transline.h:47
@ EPSILONR_PRM
Definition: transline.h:39
@ PHYS_S_PRM
Definition: transline.h:58
@ H_PRM
Definition: transline.h:42
@ PHYS_WIDTH_PRM
Definition: transline.h:56
#define TRANSLINE_WARNING
Definition: transline.h:30
#define TRANSLINE_ERROR
Definition: transline.h:31
#define ZF0
Definition: units.h:62
double atanh(double x)
Definition: units.h:51
#define C0
Definition: units.h:61
double acosh(double x)
Definition: units.h:40
#define UNIT_MICRON
Definition: units_scales.h:35