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resolve_q.cpp
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/* resolve_q.cpp - source text to Coil64 - Radio frequency inductor and choke calculator
Copyright (C) 2019 Kustarev V.
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 3 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 program. If not, see <https://www.gnu.org/licenses
*/
#include "resolve_q.h"
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// LINEAR INTERPOLATION FUNCTION FROM ARNOLD'S TABLES///
/// https://ieeexplore.ieee.org/document/5240803
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table7_Phi(double z){
double za[] = {0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9,
3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0};
double Fi[] = {0.001, 0.003, 0.005, 0.008, 0.013, 0.02, 0.029, 0.041, 0.055, 0.072, 0.092, 0.114, 0.139, 0.167, 0.196, 0.226, 0.257,
0.288, 0.319, 0.349, 0.378, 0.406, 0.432, 0.457, 0.48, 0.501, 0.539, 0.571, 0.599, 0.622, 0.643, 0.661, 0.677, 0.691,
0.704, 0.716, 0.727, 0.737, 0.746, 0.755, 0.763, 0.782, 0.797, 0.811, 0.823, 0.833, 0.843, 0.851, 0.858};
unsigned int zi;
double result = 0;
if (z > 10) {
result = 1 - (M_SQRT2 / z);
} else {
zi = 0;
while ((z >= za[zi]) && (zi < sizeof(za)/sizeof(za[0]) - 1)) {
zi++;
if (zi > 0) {
result = ((Fi[zi] - Fi[zi - 1]) / (za[zi] - za[zi - 1])) * (z - za[zi - 1]) + Fi[zi - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table7_Chi(double z){
double za[] = {0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9,
3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, 4.6, 4.8, 5.0, 5.2, 5.4, 5.6, 5.8, 6.0, 6.5, 7.0, 7.5, 8.0, 8.5, 9.0, 9.5, 10.0};
double Ci[] = {0.001, 0.002, 0.004, 0.006, 0.010, 0.015, 0.022, 0.03, 0.041, 0.053, 0.067, 0.083, 0.101, 0.12, 0.14, 0.16, 0.18, 0.199,
0.218, 0.235, 0.251, 0.265, 0.278, 0.289, 0.299, 0.307, 0.32, 0.33, 0.337, 0.343, 0.348, 0.353, 0.357, 0.361, 0.365, 0.37,
0.374, 0.378, 0.382, 0.386, 0.389, 0.397, 0.404, 0.41, 0.416, 0.42, 0.425, 0.428, 0.432};
unsigned int zi;
double result = 0;
if (z > 10) {
result = 0.5 - (1 / (z * M_SQRT2));
} else {
zi = 0;
while ((z >= za[zi]) && (zi < sizeof(za)/sizeof(za[0]) - 1)) {
zi++;
if (zi > 0) {
result = ((Ci[zi] - Ci[zi - 1]) / (za[zi] - za[zi - 1])) * (z - za[zi - 1]) + Ci[zi - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table8_v(double N){
double Na[] = {2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 67, 100, 125, 167, 250, 500};
double v[] ={-1, -0.25, 0.21, 0.52, 0.76, 0.94, 1.09, 1.22, 1.33, 1.5, 1.63, 1.73, 1.82, 1.91, 2.06, 2.17, 2.26, 2.33, 2.39, 2.44,
2.56, 2.71, 2.77, 2.85, 2.94, 3.05};
unsigned int ni;
double result = 0;
if (N > 500) {
result = 3.29;
} else {
ni = 0;
while ((N >= Na[ni]) && (ni < sizeof(Na)/sizeof(Na[0]) - 1)) {
ni++;
if (ni > 0) {
result = ((v[ni] - v[ni - 1]) / (Na[ni] - Na[ni - 1])) * (N - Na[ni - 1]) + v[ni - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table8_w(double N){
double Na[] = {2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 67, 100, 125, 167, 250, 500};
double w[] = {1, 2.4, 3.5, 4.3, 4.9, 5.4, 5.9, 6.3, 6.6, 7.0, 7.4, 7.8, 8.0, 8.2, 8.6, 8.9, 9.1, 9.3, 9.4, 9.5, 9.7, 10.0, 10.2, 10.3, 10.4, 10.6};
unsigned int ni;
double result = 0;
if (N > 500) {
result = 10.8;
} else {
ni = 0;
while ((N >= Na[ni]) && (ni < sizeof(Na)/sizeof(Na[0]) - 1)) {
ni++;
if (ni > 0) {
result = ((w[ni] - w[ni - 1]) / (Na[ni] - Na[ni - 1])) * (N - Na[ni - 1]) + w[ni - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table3(double N){
double Na[] = {2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 34, 50, 100};
double p[] = {2.29, 1.79, 1.48, 1.28, 1.12, 1.01, 0.91, 0.84, 0.78, 0.68, 0.60, 0.54, 0.50, 0.46, 0.39, 0.31, 0.22, 0.12};
unsigned int ni;
double result = 0;
if (N > 100) {
result = 1e-6;
} else {
ni = 0;
while ((N >= Na[ni]) && (ni < sizeof(Na)/sizeof(Na[0]) - 1)) {
ni++;
if (ni > 0) {
result = ((p[ni] - p[ni - 1]) / (Na[ni] - Na[ni - 1])) * (N - Na[ni - 1]) + p[ni - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table5(double ro){
double roa[] = {0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2, 4.4, 4.6, 4.8, 5.0,
5.6, 6.25, 7.14, 7.7, 8.33, 9.1, 10, 11.1, 12.5, 14.28, 16.66, 20, 25, 33.33, 50, 100};
double g[] = {0.06, 0.18, 0.32, 0.49, 0.85, 1.23, 1.61, 1.99, 2.36, 2.71, 3.04, 3.35, 3.63, 3.90, 4.16, 4.39, 4.61, 4.82, 5.01, 5.19,
5.36, 5.51, 5.66, 5.80, 5.93, 6.06, 6.18, 6.46, 6.76, 7.09, 7.26, 7.43, 7.61, 7.79, 7.98, 8.17, 8.37, 8.57, 8.78, 9.00, 9.21, 9.43, 9.65};
unsigned int ni;
double result = 0;
if (ro > 100) {
result = 9.87;
} else {
ni = 0;
while ((ro >= roa[ni]) && (ni < sizeof(roa)/sizeof(roa[0]) - 1)) {
ni++;
if (ni > 0) {
result = ((g[ni] - g[ni - 1]) / (roa[ni] - roa[ni - 1])) * (ro - roa[ni - 1]) + g[ni - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table4_a(double r){
double ra[] = {0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0};
double a[] = {3.29, 3.24, 3.13, 2.99, 2.83, 2.67, 2.51, 2.36, 2.21, 2.07, 1.95, 1.83, 1.72, 1.63, 1.54, 1.46, 1.28, 1.14, 1.02, 0.93,
0.85, 0.78, 0.72, 0.67, 0.63, 0.59};
unsigned int ri;
double result = 0;
if (r > 8.0) {
result = 19 / (4 * r);
} else {
ri = 0;
while ((r >= ra[ri]) && (ri < sizeof(ra)/sizeof(ra[0]) - 1)) {
ri++;
if (ri > 0) {
result = ((a[ri] - a[ri - 1]) / (ra[ri] - ra[ri - 1])) * (r - ra[ri - 1]) + a[ri - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double LinearInterpolation_Table4_b(double r){
double ra[] = {0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 6.0, 6.5, 7.0, 7.5, 8.0};
double b[] = {0, -0.03, -0.04, -0.04, -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03, 0.04, 0.04, 0.05, 0.06, 0.06, 0.08, 0.09, 0.1, 0.11, 0.12,
0.12, 0.13, 0.13, 0.13, 0.14};
unsigned int ri;
double result = 0;
if (r > 8.0) {
result = 4 / 19 - 3 / (5 * r);
} else {
ri = 0;
while ((r >= ra[ri]) && (ri < sizeof(ra)/sizeof(ra[0]) - 1)) {
ri++;
if (ri > 0) {
result = ((b[ri] - b[ri - 1]) / (ra[ri] - ra[ri - 1])) * (r - ra[ri - 1]) + b[ri - 1];
}
}
}
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///CALCULATING PROXIMITY EFFECT FACTOR BY ARNOLD RESEARCH
///https://ieeexplore.ieee.org/document/5240803
/// ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double lookup_Psi(double Df, double dw, double pt, double N, double fm, Material mt){
//el->winding length [mm], Df->coilformer diameter [mm], pt->winding pitch [mm], Dw->wire diameter [mm], fm -> frequency [kHz]
double d, P, rc, f, si, zeta, eta, ro, z, Phi, Chi, v, w, alpha, betta, gamma, pm, a, b, u1, u2, g;
d = dw / 10;
P = pt / 10;
rc = Df / 20;
f = fm * 1e3;
si = 1e-11 / mtrl[mt][Rho];
eta = d / P;
zeta = P / rc;
ro = (N - 1) * zeta;
z = M_PI * d * sqrt(2 * f * si);
Phi = LinearInterpolation_Table7_Phi(z);
Chi = LinearInterpolation_Table7_Chi(z);
v = LinearInterpolation_Table8_v(N);
w = LinearInterpolation_Table8_w(N);
alpha = (1 + 0.209 * w * pow(Phi, 2) * pow(eta, 4)) / (1 + 0.084 * w * pow(Phi, 2) * pow(eta, 4));
betta = 1 / (pow((1 - 0.278 * v * Phi * eta * eta), 1.8));
gamma = 1 / (pow((1 + 0.385 * v * Phi * eta * eta), 1.3));
pm = LinearInterpolation_Table3(N);
a = LinearInterpolation_Table4_a(ro);
b = LinearInterpolation_Table4_b(ro);
u1 = a - (1 / (1 / pm + ro * b));
g = LinearInterpolation_Table5(ro);
u2 = g / (1 + (0.42 + (0.3 / ro)) * sqrt(zeta) + (1.35 + (2.8 / sqrt(ro))) * pow(zeta, 1.5));
double result = alpha + eta * eta * Chi * (betta * u1 + gamma * u2);
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// CALCULATING SKIN-EFFECT FACTOR FOR ROUND WIRE BY D.KNIGHT RESEARCH
///http://www.g3ynh.info/zdocs/comps/Zint.pdf
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double get_Xir(Material mt, double fm, double dw){
//AC resistance factor. TED-MLD formula (skin effect factor)
double y, z, f, r, delta_i, delta_i_prim;
f = fm * 1e3;
r = dw / 2000;
delta_i = sqrt(mtrl[mt][Rho] / (f * M_PI * mu0 * (1 + mtrl[mt][Chi])));
delta_i_prim = delta_i * (1 - exp(-r / delta_i));
z = 0.62006 * r / delta_i;
y = 0.189774 / pow((1 + 0.272481 * pow((pow(z, 1.82938) - pow(z, -0.99457)), 2)), 1.0941);
double result = (r * r) / ((2 * r * delta_i_prim - delta_i_prim * delta_i_prim) * (1 + y));
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// CALCULATING SKIN-EFFECT FACTOR FOR RECTANGULAR CONDUCTOR BY ALAN PAYNE RESEARCH
/// http://g3rbj.co.uk/wp-content/uploads/2017/06/The-ac-Resistance-of-Rectangular-Conductors-Payne-Issue-3.pdf
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double get_Xic(Material mt, double f, double w, double t){
//AC resistance factor formula 4.8.1
double delta = sqrt(mtrl[mt][Rho] / (f * M_PI * mu0 * (1 + mtrl[mt][Chi])));
double p = sqrt(w * t)/(1.26 * delta);
double Ff = 1 - exp(-0.026 * p);
double x = ((2 * delta / t) * (1 + t / w) + 8 * pow(delta / t, 3)/(w / t)) / (pow(w / t, 0.33)*exp(-3.5*(t / delta)) + 1);
double Kc = 1 + Ff * (1.2 / exp(2.1 * (t / w)) + 1.2 / exp(2.1 * (w / t)));
double result = Kc / (1 - exp(-x));
return result;
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// PUBLIC FUNCTIONS REALIZATION
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// Q-FACTOR OF THE ONE-LAYER COIL WITH ROUND WIRE (WITH PROXIMITY EFFECT)
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
unsigned long int solve_Qr(double I, double Df, double pm, double dw, double fa, double fsr, double N, double Cs, Material mt, _CoilResult *result){
//I->inductance µH
//l->winding length mm, Df->coilwinding diameter mm, pm->winding pitch mm, dw->wire diameter mm
//fm->frequency MHz, N->number of turns, mt->material of wire
double Induct, fm, f, D, r, p, WireLength, Rdc, Rac0, Rac, Xi, Psi, kQ, R_ind, Rl, Rc;
Induct = I * 1.0e-6;
fm = fa * 1e3;
f = fm * 1e3;
D = Df / 1000;
r = dw / 2000;
p = pm / 1000;
WireLength = M_PI * N * sqrt(D * D + p * p / 4);
Rdc = mtrl[mt][Rho] * WireLength / (M_PI * r * r);
Xi = get_Xir(mt, fm, dw);
Psi = lookup_Psi(Df, dw, pm, N, fm, mt);
Rac0 = Rdc * (1 + ((Xi - 1) * Psi * (N - 1 + 1 / Psi)) / N);
kQ = pow((1 - (fm * I * Cs) / 2.53e7), 2);
Rac = Rac0 / kQ;
Rl = 2 * M_PI * f * Induct;
Rc = 1 / (2 * M_PI * f * Cs * 1e-12);
R_ind = 1 / (1 / Rl + 1 / Rc);
double Q = (R_ind / Rac) * (1 - fa / fsr);
double ESR = R_ind / Q;
result->seven = ESR;
return round(Q);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// Q-FACTOR OF THE ONE-LAYER COIL WITH RECTANGULAR WIRE
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
unsigned long int solve_Qc(double I, double Df, double pm, double _w, double _t, double fa, double fsr, double N, double Cs, Material mt, _CoilResult *result){
//I->inductance µH
//l->winding length mm, Df->coilwinding diameter mm, pm->winding pitch mm, _w->wire width mm, _t->wire thickness mm
//fm->frequency MHz, N->number of turns, mt->material of wire
double Induct, fm, f, D, w, t, p, WireLength, Rdc, Rac0, Rac, Xi, kQ, R_ind, Rl, Rc, Psi;
Induct = I * 1e-6;
fm = fa * 1e3;
f = fm * 1e3;
D = Df / 1000;
w = _w / 1000;
t = _t / 1000;
p = pm / 1000;
WireLength = M_PI * N * sqrt(D * D + p * p / 4);
Rdc = mtrl[mt][Rho] * WireLength / (w * t);
Xi = get_Xic(mt, f, w, t);
Psi = lookup_Psi(Df, _w, pm, N, fm, mt);
Rac0 = Rdc * (1 + ((Xi - 1) * Psi * (N - 1 + 1 / Psi)) / N);
kQ = pow((1 - (fm * I * Cs) / 2.53e7), 2);
Rac = Rac0 / kQ;
Rl = 2 * M_PI * f * Induct;
Rc = 1 / (2 * M_PI * f * Cs * 1e-12);
R_ind = 1 / (1 / Rl + 1 / Rc);
double Q = (R_ind / Rac) * (1 - fa / fsr);
double ESR = R_ind / Q;
result->seven = ESR;
return round(Q);
}
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// Q-FACTOR OF THE PCB SPIRAL COIL
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double solve_Qpcb(long N, double _I, double _D, double _d, double _W, double _t, double _s, double _f, double tand, int layout){
//_I->inductance µH, N->number of turns, _D->outer winding diameter mm, _d->inner winding diameter mm
// _f->frequency MHz, _t-> thickness of the trace, _W->width of the trace, _s->winding pitch
double f = _f * 1e6;
double I = _I * 1e-6;
double D = _D * 1e-3;
double d = _d * 1e-3;
double W = _W * 1e-3;
double t = _t * 1e-3;
double s = _s * 1e-3;
double StripLength = 0;
switch (layout) {
case 0:{
StripLength += d / 2;
for (int i = 0; i < N; i++){
StripLength += 2 * (2 * d + (4 * i + 1) * s);
}
StripLength -= D / 2;
break;
}
case 1:{
StripLength = find_actual_spiral_length(N, d, s);
break;
}
case 2:{
for (int i = 0; i < N; i++){
StripLength += d - i * s + D - i * s + (d - (i + 1) * s) + (D - (i + 1) * s);
}
break;
}
default:
break;
}
double Qs = 1 / tand;
double Rdc = mtrl[1][Rho] * StripLength / (W * t);
double delta = sqrt(mtrl[1][Rho] / (f * M_PI * mu0 * (1 + mtrl[1][Chi])));
double Xi = t / (delta*(1 - exp(-t/delta)));
double Psi = (Xi / 3) * pow(3 * W / (2 * s), 4);
double Rac = Rdc * (Xi + Psi);
double Xl = 2 * M_PI * f * I;
double Qm = Xl / Rac;
double Q = 1 / (1 / Qs + 1 / Qm);
return (Q);
}