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resolves.cpp
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/* resolves.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 "resolves.h"
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
///ROUTINE FUNCTIONS
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
#pragma pack(push,1)
struct _Elliptic{
double Fk;
double Ek;
};
#pragma pack(pop)
#pragma pack(push,1)
struct _MagCoreConst{
double C1;
double C2;
};
#pragma pack(pop)
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double odCalc(double id){
//Calculating the outer diameter (od) of the wire with insulation from the internal diameter (id) without insulation
const double M = 0.96344;
const double b = -0.19861;
double od1 = exp(M * log(id) + b);
double od2 = 1.09 * id;
double od = qMax(od1, od2);
return od;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double convertfromAWG(QString AWG, bool *isOK){
QRegularExpression awgrule(AWG_REG_EX);
double result = 0;
if (awgrule.match(AWG).hasMatch()){
QStringList captured = awgrule.match(AWG).capturedTexts();
QString cap = captured[0];
if (AWG == cap){
if (AWG == "0000") result = 11.684;
else if (AWG == "000") result = 10.40384;
else if (AWG == "00") result = 9.26592;
else {
double awg = AWG.toDouble();
result = 0.127 * pow(92, (36 - awg) / 39);
}
if (isOK != NULL) *isOK = true;
} else if (isOK != NULL) *isOK = false;
} else if (isOK != NULL) *isOK = false;
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
QString converttoAWG(double d, bool *isOK){
QString result ="";
if (!(d > 12)){
if ((d <= 12) && (d >= 11)) result = "0000";
else if ((d < 11) && (d >= 10)) result = "000";
else if ((d < 10) && (d >= 8.6)) result = "00";
else if ((d < 8.6) && (d >= 0.00785)){
double AWG = round(-39 * log(d / 0.127) / log(92) + 36);
result = QString::number(AWG);
}
if (isOK != NULL) *isOK = true;
} else if (isOK != NULL) *isOK = false;
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double find_Archimedean_spiral_length(int n, double a) {
//function to calculate the Archimedean spiral length
double phi = 2 * n * M_PI;
double l = (a / (4 * M_PI)) * (phi * sqrt(1 + phi * phi) + log(phi + sqrt(1 + phi * phi)));
return l;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double find_actual_spiral_length(int N, double Din, double k) {
//Find the spiral length
int ni = ceil(Din / (2 * k));
double Lin = find_Archimedean_spiral_length(ni, k);
int n = ni + N;
double Lt = find_Archimedean_spiral_length(n, k);
return (Lt - Lin);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getToroidEqMagLength(double OD, double ID){
return M_PI * log(OD / ID) / (1.0 / ID - 1.0 / OD);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getToroidEqCrossSec(double OD, double ID, double he){
return 0.5 * he * pow(log(OD / ID), 2) / (1.0 / ID - 1.0 / OD);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getSaturationCurrent(double Bs, double le, double mu, double N){
return 1e-4 * Bs * le / (mu0 * mu * N); // le [mm], Bs [Gs], return value in [mA]
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double find_Helix_turn_length(double r, double p){
return sqrt(pow(2 * M_PI * r, 2) + p * p);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double rosaKm(double n){
//Rosa's round wire mutual inductance correction
double n2 = n * n;
double n3 = n2 * n;
double n5 = n3 * n2;
double n7 = n5 * n2;
double n9 = n7 * n2;
return (log(2 * M_PI) - 1.5 - log(n) / (6 * n) - 0.33084236 / n - 1 / (120 * n3) + 1 / (504 * n5) - 0.0011923 / n7 + 0.0005068 / n9);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double rosaKs(double x){
//Rosa's round wire self inductance correction
return (1.25 - log(2 * x));
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void EF(double c, _Elliptic *result){
//the complete elliptic integrals of the first and second kind
double a = 1;
double b = sqrt(1 - pow(c, 2));
double E = 1 - pow(c, 2) / 2;
double i = 1;
while (fabs(a - b) > 1e-15) {
double a1 = (a + b) / 2;
double b1 = sqrt(a * b);
E = E - i * pow((a - b) / 2, 2);
i = 2 * i;
a = a1;
b = b1;
}
double Fk = M_PI / (2 * a);
double Ek = E * Fk;
result->Ek = Ek;
result->Fk = Fk;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double Mut(double r1, double r2, double x, double g){
//Mutual inductance of two coaxial circular filaments
//r1,r2 - radii of the two circular filaments
//x - distance between the centres of the circular filaments
//g - Geometric Mean Distance
double l = sqrt(pow(r2 - r1, 2) + pow(x, 2));
double c = 2 * sqrt(r1 * r2) / sqrt(pow(r1 + r2, 2) + pow(l - g, 2));
_Elliptic Ec;
EF(c, &Ec);
double result = -0.004 * M_PI * sqrt(r1 * r2) * ((c - 2 / c) * Ec.Fk + (2 / c) * Ec.Ek);
return (result);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double SelfInductanceStraightWire(double l, double dw){
double r = 0.5 * dw * exp(0.25);
double result = 0.002 * (l * log((l + sqrt(l * l + r * r)) / r) - sqrt(l * l + r * r) + l / 4 + r);
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double MutInductanceStraightWire(double L1, double l2, double D){
double tmpLength = 0;
L1 = L1 / 2;
l2 = l2 / 2;
if (L1 < l2){
tmpLength = L1;
L1 = l2;
l2 = tmpLength;
}
double result = 0.002 * (2 * L1 * log((L1 + l2 + sqrt((L1 + l2) * (L1 + l2) + D * D)) / D) + (L1 - l2) *
log((L1 + l2 + sqrt((L1 + l2) * (L1 + l2) + D * D)) / (L1 - l2 + sqrt((L1 - l2) * (L1 - l2) + D * D))) +
sqrt((L1 - l2) * (L1 - l2) + D * D) - sqrt((L1 + l2) * (L1 + l2) + D * D));
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double Ingrnd(double phi, double kphitheta, double sinpsi, double cos2psi, double rr, double y){
// by Robert Weaver from http://electronbunker.ca/eb/CalcMethods2d.html
//Integrand function called by HeliCoilS()
double result = (1 + cos2psi * (cos(kphitheta) - 1)) / sqrt(2 * rr * (1 - cos(kphitheta)) + (sinpsi * phi - y) *
(sinpsi * phi - y));
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double HeliCoilS(double Lw, double psi, double r, double dw, double w, double t, bool isRoundWire, unsigned int accuracy){
// by Robert Weaver from http://electronbunker.ca/eb/CalcMethods2d.html (Version 1.0, 2011-03-25)
// edited by Valery Kustarev 2018-12-16
// Uses helical filament mutual inductance formula
// evaluated using Simpson's rule, and conductor gmd
// Lw = total length of wire
// psi = pitch angle of winding
// r = radius of winding
// dw = wire diameter
// MaxErr = max allowable error (set to 10000)
//
//px = p/(2pi) = lCOIL/(2piN)
//psi = Arctan(px/(piD)) = Arctan(p/(2pi^2*D))
//lW = piND/cos psi
//where:
//D is coil diameter = 2r;
//p is centre to centre turns spacing;
//lCOIL is length of coil.
// If Lw>2*pi*r, check that pitch angle >= psi-c (close wound pitch)
double sinpsic, psic, g, rr, psio, ThetaO, Y0, cosThetaO, k1, k2, t1, t0, c2s, ss, k, a, b, grandtotal;
double dx, MaxErr, CurrentErr, kat, kbt, Sum2, LastIntg, Sum, phi, kpt, Integral, aaa, bbb, ccc, ddd;
int m;
int err = ceil((float)accuracy / 2);
MaxErr = pow(10,-err);
Integral = 0;
// grandtotal = 0;
if (Lw > 2 * M_PI * r) {
if (isRoundWire){
sinpsic = dw / (2 * M_PI * r);
} else {
sinpsic = w / (2 * M_PI * r);
}
psic = atan(sinpsic / sqrt(1 - sinpsic * sinpsic));
if (psi < psic) {
// pitch angle is too small, // so set value of function to an illegal value and exit
return -1;
}
}
// gmd of solid round conductor. Other values may be substituted
// for different conductor geometries
if (isRoundWire){
g = exp(-0.25) * dw / 2;
} else {
g = 0.2235*(w + t);
}
rr = r * r;
psio = 0.5 * M_PI - psi;
// Calculate Filament 2 offset angle
// Trap for psi=0 condition in which case ThetaO=0 and Y0=g
// Trap for psio=0 condition in which case use simplified formula for ThetaO and Y0=0
// which happens with circular (non-helical) filament
if (psi == 0) {
ThetaO = 0;
Y0 = g;
} else if (psio == 0) {
cosThetaO = 1 - (g * g / (2 * rr));
ThetaO = -fabs(atan(sqrt(1 - cosThetaO * cosThetaO) / cosThetaO));
Y0 = 0;
} else {
// Use Newton-Raphson method
k1 = (g * g) / (2 * r * r) - 1;
k2 = tan(psio);
k2 = 0.5 * k2 * k2;
t1 = g / r * sin(psi);
do {
t0 = t1;
t1 = t0 - (k1 + cos(t0) - k2 * t0 * t0) / (-sin(t0) - 2 * k2 * t0);
} while (fabs(t1 - t0) > 1e-12);
ThetaO = -fabs(t1);
// Calculate Filament 2 Y-offset, using formula (29)
Y0 = sqrt(g * g - 2 * rr * (1 - cos(ThetaO)));
}
// Psi constants
c2s = cos(psi) * cos(psi);
ss = sin(psi);
k = cos(psi) / r;
// Start of Simpson's rule code
a = 0;
b = Lw / 32768;
if (b > Lw) {
b = Lw;
}
grandtotal = 0;
while (a < Lw) {
dx = b - a;
m = 1;
CurrentErr = 2 * MaxErr;
kat = k * a;
kbt = k * b;
aaa = (Lw - a) * (Ingrnd(-a, -kat - ThetaO, ss, c2s, rr, Y0));
bbb = Ingrnd(a, kat - ThetaO, ss, c2s, rr, Y0);
ccc = (Lw - b) * (Ingrnd(-b, -kbt - ThetaO, ss, c2s, rr, Y0));
ddd = Ingrnd(b, kbt - ThetaO, ss, c2s, rr, Y0);
Sum2 = aaa + bbb + ccc + ddd;
// Initialize LastResult to trapezoidal area for test purposes
LastIntg = Sum2 / 2 * dx;
while ((CurrentErr > MaxErr) || (m < 1024)) {
m = 2 * m;
dx = dx / 2;
Sum = 0;
int max= round((float)m/2);
for (int i = 1; i <= max; i++){
phi = 2 * i * dx + a;
kpt = k * phi;
Sum = Sum + (Lw - phi) * (Ingrnd(-phi, -kpt - ThetaO, ss, c2s, rr, Y0) + Ingrnd(phi, kpt - ThetaO, ss, c2s, rr, Y0));
}
Integral = (4 * (Sum) + Sum2) * dx / 3;
CurrentErr = fabs((Integral) / (LastIntg) - 1);
LastIntg = Integral;
Sum2 = Sum2 + Sum * 2;
}
grandtotal += Integral;
a = b;
b = b * 2;
if (b > Lw) {
b = Lw;
}
}
double result = 1e-1 * grandtotal;
return result;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double solveHelicalInductance(double N, double _p, double _Dk, double _dw, double _w, double _t, double *lw, bool isRoundWire, unsigned int accuracy){
double lW, dw = 0, w = 0, t = 0;
double psi;
double sinpsi;
double p = _p / 1000;
double Dk = _Dk / 1000;
double Result;
if (isRoundWire){
dw = _dw / 1000;
} else {
w = _w / 1000;
t = _t / 1000;
}
//psi= atan(p/(2*pi*pi*Dk));
sinpsi = p / (M_PI * Dk);
psi = atan(sinpsi / sqrt(1 - sinpsi * sinpsi));
lW = M_PI * N * Dk / cos(psi);
if (isRoundWire){
Result = HeliCoilS(lW, psi, Dk / 2, dw, 0, 0, isRoundWire, accuracy);
} else {
Result = HeliCoilS(lW, psi, Dk / 2, 0, w, t, isRoundWire, accuracy);
}
*lw = lW;
return (Result);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double deriveOneLayerPoligonalN(double Dk, double dw, double p, double n, double I, double *lw, double *iDk, unsigned int accuracy){
double Ind, N_max, N_min, N, k, Kw, rA, rP;
k = 2;
N_min = 0;
rA = sqrt((1 / M_PI) * (0.5 * n * pow(0.5 * Dk,2) * sin(2 * M_PI / n)));
rP = (0.5 / M_PI) * (Dk * n * sin(M_PI / n));
Kw = sqrt(1 / 369.0);
*iDk = 2 * (((Kw * pow(rP,2)) + ((2 - Kw) * pow(rA,2))) / (2 * rA));
N = sqrt(I / (0.0002 * M_PI * *iDk * (log(1 + M_PI / (2 * k)) + 1 / (2.3004 + 3.437 * k + 1.763 * k * k - 0.47 /
pow((0.755 + 1 / k), 1.44)))));
_CoilResult res;
getOneLayerI_Poligonal(Dk, dw, p, N, n, &res, accuracy);
Ind = res.sec;
while (Ind < I){
N_min = N;
N_max = 2 * N;
N = (N_max + N_min) / 2;
getOneLayerI_Poligonal(Dk, dw, p, N, n, &res, accuracy);
Ind = res.sec;
}
N_max = N;
while (fabs(1 - (Ind / I)) > 0.001){
N = (N_min + N_max) / 2;
getOneLayerI_Poligonal(Dk, dw, p, N, n, &res, accuracy);
Ind = res.sec;
if (Ind > I)
N_max = N;
else
N_min = N;
}
*lw = res.thd;
return N;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerN_Poligonal(double I, double Dk, double dw, double p, double n, _CoilResult *result, unsigned int accuracy){
double N, lw, iDk;
N = deriveOneLayerPoligonalN(Dk, dw, p, n, I, &lw, &iDk, accuracy);
result->sec = p * N;
result->thd = lw;
result->seven = iDk;
return N;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getOneLayerI_Poligonal(double Dk, double dw, double p, double N, double n, _CoilResult *result, unsigned int accuracy){
double Kw, rA, rP, lk, iDk, lw;
lk = N * p;
rA = sqrt((1 / M_PI) * (0.5 * n * pow(0.5 * Dk,2) * sin(2.0 * M_PI / n)));
rP = (0.5 / M_PI) * (Dk * n * sin(M_PI / n));
Kw = sqrt(1 / (1 + 368.0 * (lk / Dk)));
iDk = 2.0 * (((Kw * pow(rP, 2)) + ((2.0 - Kw) * pow(rA, 2))) / (2.0 * rA));
result->sec = solveHelicalInductance(N, p, iDk, dw, 0, 0, &lw, true, accuracy);
result->thd = lw;
result->seven = iDk;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getFerriteCoreMagConst(double l1, double l2, double l3, double l4, double l5,
double A1, double A2, double A3, double A4, double A5, _MagCoreConst *c)
{
//auxiliary function to get the constants C1 & C2 of a ferrite core with the close magnetic circuit
double sum11 = l1 / A1;
double sum21 = l1 / (A1 * A1);
double sum12 = l2 / A2;
double sum22 = l2 / (A2 * A2);
double sum13 = l3 / A3;
double sum23 = l3 / (A3 * A3);
double sum14 = l4 / A4;
double sum24 = l4 / (A4 * A4);
double sum15 = l5 / A5;
double sum25 = l5 / (A5 * A5);
c->C1 = sum11 + sum12 + sum13 + sum14 + sum15;
c->C2 = sum21 + sum22 + sum23 + sum24 + sum25;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// PUBLIC FUNCTIONS REALIZATION
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerN_withRoundWire(double Dk, double dw, double p, double I, double *lw, unsigned int accuracy){
double ind, N_max, N_min, N, k;
k = 2;
N_min = 0;
N = sqrt(I / (0.0002 * M_PI * Dk * (log(1 + M_PI / (2 * k)) + 1 / (2.3004 + 3.437 * k + 1.763 * k * k - 0.47 / pow((0.755 + 1 / k), 1.44)))));
ind = solveHelicalInductance(N, p, Dk, dw, 0, 0, lw, true, accuracy);
while (ind < I) {
N_min = N;
N_max = 2 * N;
N = (N_max + N_min) / 2;
ind = solveHelicalInductance(N, p, Dk, dw, 0, 0, lw, true, accuracy);
}
N_max = N;
while (fabs(1 - (ind / I)) > 0.001) {
N = (N_min + N_max) / 2;
ind = solveHelicalInductance(N, p, Dk, dw, 0, 0, lw, true, accuracy);
if (ind > I) {
N_max = N;
} else {
N_min = N;
}
}
return N;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerN_byWindingLength( double D, double L, double I, _CoilResult *result, unsigned int accuracy){
double dw = 0, lTmp = 0, N = 0, k, lw, dw_max = 0.25 * D, dw_min = 0, Dk;
int i = 0;
while (fabs(1 - lTmp/L) > 0.05){
dw = (dw_min + dw_max) / 2;
k = odCalc(dw);
Dk = D + k;
N = getOneLayerN_withRoundWire(Dk, dw, k, I, &lw, accuracy);
lTmp = N * k + k;
if (lTmp > L){
dw_max = dw;
} else {
dw_min = dw;
}
i++;
if (i > 500)
return 0;
}
result->sec = lw;
result->five = dw;
return N;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerI_withRoundWire(double Dk, double dw, double p, double N, double *lw, unsigned int accuracy){
return solveHelicalInductance(N, p, Dk, dw, 0, 0, lw, true, accuracy);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerN_withRectWire(double Dk, double w, double t, double p, double I, double *lw, unsigned int accuracy){
double ind, N_max, N_min, N, k;
k = 2;
N_min = 0;
N = sqrt(I / (0.0002 * M_PI * Dk * (log(1 + M_PI / (2 * k)) + 1 / (2.3004 + 3.437 * k + 1.763 * k * k - 0.47 / pow((0.755 + 1 / k), 1.44)))));
ind = solveHelicalInductance(N, p, Dk, 0, w, t, lw, false, accuracy);
while (ind < I) {
N_min = N;
N_max = 2 * N;
N = (N_max + N_min) / 2;
ind = solveHelicalInductance(N, p, Dk, 0, w, t, lw, false, accuracy);
}
N_max = N;
while (fabs(1 - (ind / I)) > 0.001) {
N = (N_min + N_max) / 2;
ind = solveHelicalInductance(N, p, Dk, 0, w, t, lw, false, accuracy);
if (ind > I) {
N_max = N;
} else {
N_min = N;
}
}
return N;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
double getOneLayerI_withRectWire(double Dk, double w, double t, double p, double N, double *lw, unsigned int accuracy){
return solveHelicalInductance(N, p, Dk, 0, w, t, lw, false, accuracy);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerN(double I, double D, double dw, double k, double lk, double gap, long Ng, _CoilResult *result, bool isOrthocyclic){
double n_g = 0;
double jg = 0;
D = D / 10;
lk = lk / 10;
dw = dw / 10;
k = k / 10;
gap = gap / 10;
if (Ng == -1) {
gap = 0;
}
double Ltotal = 0; // initialize variable of total self-inductance
int nLayer = 0;
double lw = 0;
double r0 = (D + k) / 2;
unsigned long int N = 0;
int Nl = (int) floor(lk / k); // number of turns in layer
if (isOrthocyclic)
Nl = (int) floor((lk - 0.5 * k) / k);
double g = exp(-0.25) * dw / 2;
while (Ltotal < I) // start calculation loop increasing N-turns to reach requiring inductance (I)
{
N++;
int Nc = (N - 1) % Nl; // position of N-turn in layer
nLayer = (int) floor((N - 1) / Nl); // current layer for N-turn
if (((nLayer % Ng) == 0) && (nLayer > 0)) {
n_g = gap;
} else {
n_g = 0;
}
double nx; // x-offset of turn
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
nx = Nc * k + 0.5 * k;
} else
nx = Nc * k;
double ny; // y-offset of turn
if (isOrthocyclic){
ny = r0 + dens * k * nLayer + n_g;
} else
ny = r0 + k * nLayer + n_g;
double Lns = Mut(ny, ny, g, 0); // self inductance of current turn
lw = lw + find_Helix_turn_length(ny, k); // length of wire with the current turn
double M = 0; // start calculation loop of the mutual inductance - current turn (N) + all another turns (j)
if (N > 1) {
int j;
for (j = N; j >= 2; j--) {
double Jc = (j - 2) % Nl;
double jx; // x-offset of turn
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
jx = Jc * k + 0.5 * k;
} else
jx = Jc * k;
int jLayer = (int) floor((j - 2) / Nl);
if (((jLayer % Ng) == 0) && (jLayer > 0)) {
jg = gap;
} else {
jg = 0;
}
double jy;
if (isOrthocyclic){
jy = r0 + dens * k * jLayer + jg;
} else
jy = r0 + k * jLayer + jg;
M = M + 2 * Mut(ny, jy, nx - jx, g); // mutual inductance
// between current
// N-turn and j-turn
}
}
Ltotal += Lns + M; // total summary inductance (adding self-inductance and mutual inductance of current N-turn)
}
double Resistivity = mtrl[Cu][Rho]*1e2;
double R = (Resistivity * lw * 4) / (M_PI * dw * dw); // resistance of the wire
double lw0 = lw / 100;
double NumberInterLayer = (double) floor(nLayer / Ng);
double c;
if (isOrthocyclic)
c = (nLayer * dens * k + k + NumberInterLayer * gap) *10;
else
c = (nLayer * k + NumberInterLayer * gap) * 10;
result->N = R;
result->sec = lw0;
result->thd = nLayer + 1;
result->fourth = c;
result->five = NumberInterLayer;
result->six = N;
// return: N(turns); R(resistance) Ohm; lw0(length of wire) m;
// NLayer (Number of layer); c (Winding thickness) mm
// NumberInterLayer (Number of inter-layers);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerI_byN(double D, double lk, double dw, double k, double N, _CoilResult *result, bool isOrthocyclic)
{
D = D / 10;
lk = lk / 10;
dw = dw / 10;
k = k / 10;
int Nl, Nc, Jc, nLayer = 0, jLayer;
double nx, ny, jx, jy, Lns, M;
double Ltotal = 0; // initialize variable of total self-inductance
double lw = 0;
double r0 = (D + k) / 2;
Nl = (int) floor(lk / k);
if (isOrthocyclic)
Nl = (int) floor((lk - 0.5 * k) / k);
double g = exp(-0.25) * dw / 2;
for (int w = 1; w < N + 1; w++){
Nc = (w - 1) % Nl;
nLayer = (int) floor((w - 1) / Nl);
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
nx = Nc * k + 0.5 * k;
} else
nx = Nc * k;
if (isOrthocyclic){
ny = r0 + dens * k * nLayer;
} else
ny = r0 + k * nLayer;
Lns = Mut(ny, ny, g, 0);
// self inductance of current turn
lw = lw + find_Helix_turn_length(ny, k);
M = 0;
if (w > 1) {
for (int j = w; j >= 2; j--) {
Jc = (j - 2) % Nl;
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
jx = Jc * k + 0.5 * k;
} else
jx = Jc * k;
jLayer = (int) floor((j - 2) / Nl);
if (isOrthocyclic){
jy = r0 + dens * k * jLayer;
} else
jy = r0 + k * jLayer;
M = M + 2 * Mut(ny, jy, nx - jx, g);
}
}
Ltotal += Lns + M;
}
double Resistivity = mtrl[Cu][Rho]*1e2;
double Rdc = (Resistivity * lw * 4) / (M_PI * dw * dw);
double thickness = 0.0;
if (isOrthocyclic)
thickness = (nLayer * dens * k + k) * 10;
else
thickness = (nLayer + 1) * k * 10;
result->N = Ltotal; //inductance value
result->sec = nLayer + 1; //number of layers
result->thd = lw * 0.01; //length of wire
result->fourth = Rdc; //resistance to DC
result->five = thickness; //coil thickness
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerI(double D, double lk, double dw, double k, double c, double gap, long Ng, _CoilResult *result, bool isOrthocyclic){
double bTmp, nTmp, lw, Lns, Ltotal, r0, M, g, nx, ny, jx, jy, n_g = 0, jg = 0, ind1, ind2, N1, N2;
int n, Nl, j, Nc, Jc, nLayer, jLayer;
ind1 = 0;
D = D / 10;
lk = lk / 10;
c = c / 10;
nTmp = 0;
bTmp = 0;
dw = dw / 10;
k = k / 10;
gap = gap / 10;
if (Ng == -1) {
gap = 0;
}
Ltotal = 0; // initialize variable of total self-inductance
lw = 0;
r0 = (D + k) / 2;
n = 0;
Nl = (int) floor(lk / k);
if (isOrthocyclic)
Nl = (int) floor((lk - 0.5 * k) / k);
g = exp(-0.25) * dw / 2;
while (bTmp < c) {
n++;
Nc = (n - 1) % Nl;
nLayer = (int) floor((n - 1) / Nl);
if (((nLayer % Ng) == 0) && (nLayer > 0)) {
n_g = gap;
} else {
n_g = 0;
}
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
nx = Nc * k + 0.5 * k;
} else
nx = Nc * k;
if (isOrthocyclic){
ny = r0 + dens * k * nLayer + n_g;
} else
ny = r0 + k * nLayer + n_g;
Lns = Mut(ny, ny, g, 0);
// self inductance of current turn
lw = lw + find_Helix_turn_length(ny, k);
M = 0;
if (n > 1) {
for (j = n; j >= 2; j--) {
Jc = (j - 2) % Nl;
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
jx = Jc * k + 0.5 * k;
} else
jx = Jc * k;
jLayer = (int) floor((j - 2) / Nl);
if (((jLayer % Ng) == 0) && (jLayer > 0)) {
jg = gap;
} else {
jg = 0;
}
if (isOrthocyclic){
jy = r0 + dens * k * jLayer + jg;
} else
jy = r0 + k * jLayer + jg;
M = M + 2 * Mut(ny, jy, nx - jx, g);
}
}
Ltotal += Lns + M;
if (nTmp < c - k) {
if (isOrthocyclic)
nTmp = (nLayer * dens * k + k);
else
nTmp = (nLayer + 1) * k;
ind1 = Ltotal;
}
if (isOrthocyclic)
bTmp = ((nLayer + 1) * dens * k);
else
bTmp = nLayer * k;
}
N1 = n - Nl;
N2 = n + Nl;
ind2 = Ltotal;
result->N = ind1;
result->sec = ind2;
result->thd = N1;
result->fourth = N2;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerI_fromResistance (double D, double lk, double c, double k, double Rm, _CoilResult *result, bool isOrthocyclic){
double dw, bTmp, tmpR, lw, Lns, Ltotal, r0, M, g, nx, ny, jx, jy, N1, N2;
int n, Nl, j, Nc, Jc, nLayer = 0, jLayer;
double aWire[67][5] = {{0.06, 0.075, 0.09, 0.085, 0.09},
{0.063, 0.078, 0.09, 0.085, 0.09}, {0.07, 0.084, 0.092, 0.092, 0.1}, {0.071, 0.088, 0.095, 0.095, 0.1},
{0.08, 0.095, 0.105, 0.105, 0.11}, {0.09, 0.105, 0.12, 0.115, 0.12}, {0.1, 0.122, 0.13, 0.125, 0.13},
{0.112, 0.134, 0.14, 0.125, 0.14}, {0.12, 0.144, 0.15, 0.145, 0.15}, {0.125, 0.149, 0.155, 0.15, 0.155},
{0.13, 0.155, 0.16, 0.155, 0.16}, {0.14, 0.165, 0.17, 0.165, 0.17}, {0.15, 0.176, 0.19, 0.18, 0.19},
{0.16, 0.187, 0.2, 0.19, 0.2}, {0.17, 0.197, 0.21, 0.2, 0.21}, {0.18, 0.21, 0.22, 0.21, 0.22},
{0.19, 0.22, 0.23, 0.22, 0.23}, {0.2, 0.23, 0.24, 0.23, 0.24}, {0.21, 0.24, 0.25, 0.25, 0.25},
{0.224, 0.256, 0.27, 0.26, 0.27}, {0.236, 0.26, 0.285, 0.27, 0.28}, {0.25, 0.284, 0.3, 0.275, 0.3},
{0.265, 0.305, 0.315, 0.305, 0.31}, {0.28, 0.315, 0.33, 0.315, 0.33}, {0.3, 0.34, 0.35, 0.34, 0.34},
{0.315, 0.35, 0.365, 0.352, 0.36}, {0.335, 0.375, 0.385, 0.375, 0.38}, {0.355, 0.395, 0.414, 0.395, 0.41},
{0.38, 0.42, 0.44, 0.42, 0.44}, {0.4, 0.44, 0.46, 0.442, 0.46}, {0.425, 0.465, 0.485, 0.47, 0.47},
{0.45, 0.49, 0.51, 0.495, 0.5}, {0.475, 0.525, 0.545, 0.495, 0.53}, {0.5, 0.55, 0.57, 0.55, 0.55},
{0.53, 0.58, 0.6, 0.578, 0.6}, {0.56, 0.61, 0.63, 0.61, 0.62}, {0.6, 0.65, 0.67, 0.65, 0.66},
{0.63, 0.68, 0.7, 0.68, 0.69}, {0.67, 0.72, 0.75, 0.72, 0.75}, {0.71, 0.76, 0.79, 0.77, 0.78},
{0.75, 0.81, 0.84, 0.81, 0.83}, {0.8, 0.86, 0.89, 0.86, 0.89}, {0.85, 0.91, 0.94, 0.91, 0.94},
{0.9, 0.96, 0.99, 0.96, 0.99}, {0.93, 0.99, 1.02, 0.99, 1.02}, {0.95, 1.01, 1.04, 1.02, 1.04},
{1.0, 1.07, 1.1, 1.07, 1.11}, {1.06, 1.13, 1.16, 1.14, 1.16}, {1.08, 1.16, 1.19, 1.16, 1.19},
{1.12, 1.19, 1.22, 1.2, 1.23}, {1.18, 1.26, 1.28, 1.26, 1.26}, {1.25, 1.33, 1.35, 1.33, 1.36},
{1.32, 1.4, 1.42, 1.4, 1.42}, {1.4, 1.48, 1.51, 1.48, 1.51}, {1.45, 1.53, 1.56, 1.53, 1.56},
{1.5, 1.58, 1.61, 1.58, 1.61}, {1.56, 1.63, 1.67, 1.64, 1.67}, {1.6, 1.68, 1.71, 1.68, 1.71},
{1.7, 1.78, 1.81, 1.78, 1.81}, {1.74, 1.82, 1.85, 1.82, 1.85}, {1.8, 1.89, 1.92, 1.89, 1.92},
{1.9, 1.99, 2.02, 1.99, 2.02}, {2.0, 2.1, 2.12, 2.1, 2.12}, {2.12, 2.21, 2.24, 2.22, 2.24},
{2.24, 2.34, 2.46, 2.34, 2.46}, {2.36, 2.46, 2.48, 2.36, 2.48}, {2.5, 2.6, 2.63, 2.6, 2.62}};
D = D / 10;
lk = lk / 10;
k = k / 10;
c = c /10;
bTmp = 0;
for (int z = 0; z < 67; ++z){
dw = aWire[z][0] / 10;
Ltotal = 0;
// initialize variable of total self-inductance
lw = 0;
r0 = (D + k) / 2;
n = 0;
Nl = (int) floor(lk / k);
if (isOrthocyclic)
Nl = (int) floor((lk - 0.5 * k) / k);
g = exp(-0.25) * dw / 2;
tmpR = 0;
while (tmpR <= Rm){
n++;
Nc = (n - 1) % Nl;
nLayer = (int) floor((n - 1) / Nl);
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
nx = Nc * k + 0.5 * k;
} else
nx = Nc * k;
if (isOrthocyclic){
ny = r0 + dens * k * nLayer;
} else
ny = r0 + k * nLayer;
Lns = Mut(ny, ny, g, 0);
// self inductance of current turn
lw +=find_Helix_turn_length(ny, k);
M = 0;
if (n > 1){
for (j = n; j >= 2; j--){
Jc = (j - 2) % Nl;
if ((isOrthocyclic) && ((nLayer % 2) != 0)){
jx = Jc * k + 0.5 * k;
} else
jx = Jc * k;
jLayer = (int) floor((j - 2) / Nl);
if (isOrthocyclic){
jy = r0 + dens * k * jLayer;
} else
jy = r0 + k * jLayer;
M = M + 2 * Mut(ny, jy, nx - jx, g);
}
}
Ltotal += Lns + M;
double Resistivity = mtrl[Cu][Rho] * 1e2;
tmpR = (Resistivity * lw * 4) / (M_PI * dw * dw);
}
if (isOrthocyclic)
bTmp = (nLayer * dens * k + k);
else
bTmp = (nLayer + 1) * k;
if (bTmp > (c - k))
break;
else
result->N = Ltotal;
}
N1 = n - Nl;
N2 = n + Nl;
result->sec = Ltotal;
result->thd = N1;
result->fourth = N2;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerI_rectFormer(double a, double b, double l, double c, double dw, double k, _CoilResult *result){
double a0, b0, D, Db, Da, nx, ny, jx, jy, lengthNa, lengthNb, lengthJa, lengthJb, Ltotal, Ladd, Lsub, Madd,
Msub, lw, Km, Ks, Lcor, cTmp = 0, nTmp = 0, ind1 = 0, ind2, N1, N2;
int n, Nc, Nl, Jc, nLayer, jLayer;
a = a / 10;
b = b / 10;
l = l / 10;
c = c / 10;
dw = dw / 10;
k = k / 10;
n = 0;
Ltotal = 0;
a0 = a + k;
b0 = b + k;
lw = 0;
nLayer = 0;
Nl = floor(l / k); // Number of turns in layer
while (cTmp < (c + k)) {
n++;
Nc = (n - 1) % Nl; // Position of the turn on x
nLayer = floor((n - 1) / Nl); // Position of the turn on y
nx = Nc * k; // x-offset of current turn
ny = nLayer * k; // y-offset of current turn
lengthNa = a0 + 2 * k * (nLayer); // lenght of straight conductor of current turn (side a)
lengthNb = b0 + 2 * k * (nLayer); // lenght of straight conductor of current turn (side b)
lw = lw + 2 * (a0 + b0 + 2 * k * (nLayer));
Ladd = SelfInductanceStraightWire(lengthNa, dw) + SelfInductanceStraightWire(lengthNb, dw); // half of self-inductance of the current turn
Db = 2 * ny + a0; // distance to opposite cunductor of the same turn (side b)
Da = 2 * ny + b0; // distance to opposite cunductor of the same turn (side a)
Lsub = 2 * MutInductanceStraightWire(lengthNa, lengthNa, Da) + 2 * MutInductanceStraightWire(lengthNb, lengthNb, Db);
// half mutual inductance with opposite conductor of current turn
Madd = 0;
Msub = 0;
if (n > 1){
for (int j = n; j >= 2; j--){
Jc = (j - 2) % Nl; // position of previous turn on x
jx = Jc * k; // x-offset of previous turn
jLayer = floor((j - 2) / Nl); // Position of the turn on y
jy = k * jLayer; // y-offset of previous turn
lengthJa = a0 + 2 * k * (nLayer + 1); // lenght of straight conductor of previous turn (side a)
lengthJb = b0 + 2 * k * (nLayer + 1); // lenght of straight conductor of previous turn (side b)
D = sqrt(pow(nx - jx, 2) + pow(ny - jy, 2)); // distance to in-phase straight conductor of previous turn
Madd = Madd + 2 * MutInductanceStraightWire(lengthNa, lengthJa, D) + 2 * MutInductanceStraightWire(lengthNb, lengthJb, D);
// half mutual inductance with in-phase conductor in previous turn
Db = sqrt(pow(nx - jx, 2) + pow(ny + jy + a0, 2));
// distance to opposite cunductor between the current turn and previous (side b)
Da = sqrt(pow(nx - jx, 2) + pow(ny + jy + b0, 2));
// distance to opposite cunductor between the current turn and previous (side a)
Msub = Msub + 2 * MutInductanceStraightWire(lengthNa, lengthJa, Da) + 2 * MutInductanceStraightWire(lengthNb, lengthJb, Db);
// half mutual inductance with opposite conductor in previous turn
}
}
Ltotal += 2 * (Ladd - Lsub + Madd - Msub);
Ks = rosaKs(k / dw);
Km = rosaKm(n);
Lcor = 0.0002 * M_PI * (a + b) * n * (Ks + Km);
Ltotal -= Lcor;
if (nTmp < c) {
nTmp = (nLayer + 1) * k;
ind1 = Ltotal;
}
cTmp = (nLayer + 1) * k;
}
N1 = n - Nl;
N2 = n + Nl;
ind2 = Ltotal;
result->N = ind1;
result->sec = ind2;
result->thd = N1;
result->fourth = N2;
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerN_rectFormer(double Ind, double a, double b, double l, double dw, double k, _CoilResult *result){
//Calculation formulas of multilayer inductor with rectangular former https://coil32.net/multilayer-rectangular.html
double a0, b0, D, Db, Da, nx, ny, jx, jy, lengthNa, lengthNb, lengthJa, lengthJb, Ltotal, Ladd, Lsub, Madd, Msub, lw, Km, Ks, Lcor, Rdc;
int n, Nc, Nl, Jc, nLayer, jLayer;
a = a / 10;
b = b / 10;
l = l / 10;
dw = dw / 10;
k = k / 10;
n = 0;
Ltotal = 0;
a0 = a + k;
b0 = b + k;
lw = 0;
nLayer = 0;
Nl = floor(l / k); // Number of turns in layer
while (Ltotal < Ind){
n++;
Nc = (n - 1) % Nl; // Position of the turn on x
nLayer = floor((n - 1) / Nl); // Position of the turn on y
nx = Nc * k; // x-offset of current turn
ny = nLayer * k; // y-offset of current turn
lengthNa = a0 + 2 * k * (nLayer); Rdc = (0.0175 * lw * 1E-4 * 4) / (M_PI * dw * dw);// lenght of straight conductor of current turn (side a)
lengthNb = b0 + 2 * k * (nLayer); // lenght of straight conductor of current turn (side b)
lw += 2 * (a0 + b0 + 2 * k * (nLayer));
Ladd = SelfInductanceStraightWire(lengthNa, dw) + SelfInductanceStraightWire(lengthNb, dw); // half of self-inductance of the current turn
Db = 2 * ny + a0; // distance to opposite cunductor of the same turn (side b)
Da = 2 * ny + b0; // distance to opposite cunductor of the same turn (side a)
Lsub = 2 * MutInductanceStraightWire(lengthNa, lengthNa, Da) + 2 * MutInductanceStraightWire(lengthNb, lengthNb, Db);
// half mutual inductance with opposite conductor of current turn
Madd = 0;
Msub = 0;
if (n > 1){
for (int j = n; j >= 2; j--){
Jc = (j - 2) % Nl; // position of previous turn on x
jx = Jc * k; // x-offset of previous turn
jLayer = floor((j - 2) / Nl); // Position of the turn on y
jy = k * jLayer; // y-offset of previous turn
lengthJa = a0 + 2 * k * (nLayer + 1); // lenght of straight conductor of previous turn (side a)
lengthJb = b0 + 2 * k * (nLayer + 1); // lenght of straight conductor of previous turn (side b)
D = sqrt(pow(nx - jx, 2) + pow(ny - jy, 2)); // distance to in-phase straight conductor of previous turn
Madd = Madd + 2 * MutInductanceStraightWire(lengthNa, lengthJa, D) + 2 * MutInductanceStraightWire(lengthNb, lengthJb, D);
// half mutual inductance with in-phase conductor in previous turn
Db = sqrt(pow(nx - jx, 2) + pow(ny + jy + a0, 2));
// distance to opposite cunductor between the current turn and previous (side b)
Da = sqrt(pow(nx - jx, 2) + pow(ny + jy + b0, 2));
// distance to opposite cunductor between the current turn and previous (side a)
Msub = Msub + 2 * MutInductanceStraightWire(lengthNa, lengthJa, Da) + 2 * MutInductanceStraightWire(lengthNb, lengthJb, Db);
// half mutual inductance with opposite conductor in previous turn
}
}
Ltotal += 2 * (Ladd - Lsub + Madd - Msub);
Ks = rosaKs(k / dw);
Km = rosaKm(n);
Lcor = 0.0002 * M_PI * (a + b) * n * (Ks + Km);
Ltotal -= Lcor;
}
double Resistivity = mtrl[Cu][Rho]*1e2;
Rdc = (Resistivity * lw * 4) / (M_PI * dw * dw);
result->N = n; //number of turns
result->sec = nLayer + 1; //number of layers
result->thd = lw * 0.01; //length of wire
result->fourth = Rdc; //resistance to DC
result->five = (nLayer + 1) * k * 10; //coil thickness
}
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
void getMultiLayerI_rectFormer_byN(double N, double a, double b, double l, double dw, double k, _CoilResult *result){
double a0, b0, D, Db, Da, nx, ny, jx, jy, lengthNa, lengthNb, lengthJa, lengthJb, Ltotal, Ladd, Lsub, Madd, Msub, lw, Km, Ks, Lcor;
int Nc, Nl, Jc, nLayer, jLayer;
a = a / 10;
b = b / 10;
l = l / 10;
dw = dw / 10;
k = k / 10;
Ltotal = 0;
a0 = a + k;
b0 = b + k;
lw = 0;
nLayer = 0;
Nl = floor(l / k); // Number of turns in layer
for (int n = 1; n < N + 1; n++){