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Add extended radial stub model
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@ra3xdh
ra3xdh committed Mar 20, 2024
1 parent d95b85e commit 7818450
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Showing 2 changed files with 258 additions and 12 deletions.
266 changes: 254 additions & 12 deletions src/components/microstrip/msrstub.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -38,11 +38,11 @@ msrstub::msrstub () : circuit (1) {

// Returns the microstrip radial stub reactance.
nr_double_t msrstub::calcReactance (nr_double_t r1, nr_double_t r2,
nr_double_t alpha, nr_double_t er,
nr_double_t phi, nr_double_t er,
nr_double_t h, nr_double_t frequency) {

nr_double_t l0 = C0 / frequency;
nr_double_t W = (r1 + (r2 - r1) / 2) * deg2rad (alpha);
nr_double_t W = (r1 + (r2 - r1) / 2) * (phi);
nr_double_t ereff = (er + 1.0) / 2 + (er - 1.0) /
(2.0 * qucs::sqrt (1 + 10.0 * h / W));
nr_double_t k = 2.0 * pi * qucs::sqrt (ereff) / l0;
Expand All @@ -55,7 +55,7 @@ nr_double_t msrstub::calcReactance (nr_double_t r1, nr_double_t r2,
nr_double_t phi_1 = qucs::atan (-j1 (a) / y1 (a));
nr_double_t phi_2 = qucs::atan (-j1 (b) / y1 (b));

nr_double_t X1 = h * Z_0 / (2.0 * pi * r1) * 360.0 / alpha *
nr_double_t X1 = h * Z_0 / (2.0 * pi * r1) * (2.0 * pi / phi) *
qucs::cos (theta_1 - phi_2) / qucs::sin (phi_1 - phi_2);

return X1;
Expand All @@ -67,17 +67,248 @@ void msrstub::calcSP (nr_double_t frequency) {

nr_complex_t msrstub::calcZ (nr_double_t frequency) {

/* get properties of this component */
nr_double_t r1 = getPropertyDouble ("ri");
nr_double_t r2 = getPropertyDouble ("ro");
nr_double_t al = getPropertyDouble ("alpha");

/* get properties of the substrate */
//radial stub - get parameters
substrate * subst = getSubstrate ();
nr_double_t er = subst->getPropertyDouble ("er");
nr_double_t h = subst->getPropertyDouble ("h");
nr_double_t r_i = getPropertyDouble ("ri"); //inner radius
nr_double_t r_o = getPropertyDouble ("ro"); //outer radius
nr_double_t phi = deg2rad(getPropertyDouble ("alpha")); //stub radius (called phi in formulas, although left alpha in UI)
nr_double_t w = getPropertyDouble ("Wf"); //feed line width
nr_double_t h = subst->getPropertyDouble ("h"); //substrate thickness
nr_double_t t = subst->getPropertyDouble ("t"); //metal thickness
nr_double_t eps_r = subst->getPropertyDouble ("er"); //substrate relative permittivity
nr_double_t resist = subst->getPropertyDouble ("rho"); //metal resistivity
nr_double_t loss_tan = subst->getPropertyDouble ("tand"); //loss tangent of substrate
const char * EffDimens = getPropertyString ("EffDimens");
const char * Model = getPropertyString ("Model");

////////////////////////////////////////////
//corrected dimensions of the stub to account for fringing fields:
nr_double_t p = r_i * qucs::cos(phi/2); //the following intermediate values can be put into conditions to speed up calculations of siple models, like no corrections at all
nr_double_t u = w / h;
nr_double_t del_u1 = t / pi * qucs::log(1 + 4*euler / (t * qucs::pow(qucs::coth(qucs::sqrt(6.517*u)), 2.0)));
nr_double_t w_e = w + h * del_u1 / 2 * (1 + 1 / (qucs::cosh(qucs::sqrt(eps_r - 1))));
nr_double_t r_s = (2 * p + w_e - w) / (2 * qucs::cos(phi/2));

nr_double_t u_rad = (phi * r_s) / h;
nr_double_t del_u1_rad = t / pi * qucs::log(1 + 4*euler / (t * qucs::pow(qucs::coth(qucs::sqrt(6.517*u_rad)), 2.0)));
nr_double_t w_e_phi_r_s = (phi * r_s) + h * del_u1_rad / 2 * (1 + 1 / (qucs::cosh(qucs::sqrt(eps_r - 1))));
nr_double_t del_rs = (w_e_phi_r_s - phi * r_s) / 2;

nr_double_t w_g = (2 * p + w_e - w) * qucs::tan(phi/2);
nr_double_t w_ge = w_g + 2 * del_rs / qucs::cos(phi/2);

nr_double_t r_ie;
nr_double_t r_oe;

if (!strcmp (EffDimens, "Chew_Kong")) {
r_ie = r_s + del_rs / qucs::tan(phi/2) + del_rs * qucs::tan(phi/2);
r_oe = r_o * qucs::sqrt(1 + 2 * h / (pi * eps_r * r_o) * (qucs::log(pi * r_o / (2 * h)) + 1.7726));
}
else if (!strcmp (EffDimens, "Giannini")) {
r_ie = w_e / (2 * qucs::sin(phi/2));
r_oe = r_o * qucs::sqrt(1 + 2 * h / (pi * r_o) * (qucs::log(pi * r_o / (2 * h)) + 1.7726)) + (w_e - w) / (2 * qucs::sin(phi/2));
}
else
{
r_ie = r_i;
r_oe = r_o;
}


if (!strcmp (Model, "March")) {

// effective dielectric constant of line with width (r_o + r_i) * sin(phi/2)
nr_double_t w_eq_stub = (r_o + r_i) * qucs::sin(phi/2);
nr_double_t u_eq_stub = w_eq_stub / h;
nr_double_t a_feed_eq_stub = 1.0 + 1.0/49.0 * qucs::log((qucs::pow(u_eq_stub, 4.0) + qucs::pow(u_eq_stub/52.0, 2.0)) / (qucs::pow(u_eq_stub, 4.0) + 0.432)) + 1.0/18.7 * qucs::log(1.0 + qucs::pow(u_eq_stub/18.1, 3.0));
nr_double_t b_feed_eq_stub = 0.564 * qucs::pow((eps_r - 0.9) / (eps_r + 3), 0.053);
nr_double_t eps_e1_eq_stub = (eps_r + 1.0) / 2.0 + (eps_r - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/u_eq_stub, -a_feed_eq_stub * b_feed_eq_stub);
nr_double_t eps_e_eq_stub = eps_e1_eq_stub; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
//complex propagation constant (with losses):
nr_double_t depth = qucs::sqrt(resist / (pi * frequency * 1 * MU0)); //calculate skin depth (assume mu relative 1)
if(depth > t)
depth = t;
nr_double_t Rsurf = resist / depth; //surface resistivity
nr_double_t k_beta = 2 * pi * frequency * qucs::sqrt(eps_e_eq_stub) / C0; //real part of complex wavenumber
nr_double_t k_alpha = Rsurf * qucs::sqrt(eps_e_eq_stub) / (Z0) + k_beta / 2 * loss_tan; //imaginary part of complex wavenumber (losses)
nr_complex_t k = nr_complex_t(k_beta, -k_alpha);

//impedance calculation
nr_double_t Z0_rie = Z0 * h / (r_ie * phi * qucs::sqrt(eps_e_eq_stub));
nr_complex_t cot_krie_kroe = (yn(0, k * r_ie) * jn(1, k * r_oe) - jn(0, k * r_ie) * yn(1, k * r_oe)) /
(jn(1, k * r_ie) * yn(1, k * r_oe) - yn(1, k * r_ie) * jn(1, k * r_oe));
nr_complex_t Zin = nr_complex_t(0, -1) * Z0_rie * cot_krie_kroe;
return Zin;
}

else if (!strcmp (Model, "Giannini")) {

// Solving equation for k0n:
// J'0(k0n*r_oe) * Y'0(k0n*r_ie) - J'0(k0n*r_ie) * Y'0(k0n*r_oe) = 0
// note that J'0(x)=-J1(x)
int n_max = 20; //how long is the series to calculate - adjust for acceptable accuracy and computation time
nr_double_t k0n_steps = 2 * pi / (4 * r_o) * 0.002; // estimate step in finding the roots numerically (estimate wavenember of first resonance of lambda/4 stub, step is 0.2%)
nr_double_t k0n_root[n_max], k0n_x, k0n_x_inc;
for(int i_root = 0, zeros_cnt = 0; zeros_cnt < n_max; ++i_root)
{
k0n_x = i_root * k0n_steps;
k0n_x_inc = (i_root+1) * k0n_steps;
if ((jn(1, k0n_x*r_oe) * yn(1, k0n_x*r_ie) - jn(1, k0n_x*r_ie) * yn(1, k0n_x*r_oe)) *
(jn(1, k0n_x_inc*r_oe) * yn(1, k0n_x_inc*r_ie) - jn(1, k0n_x_inc*r_ie) * yn(1, k0n_x_inc*r_oe)) < 0)
{
k0n_root[zeros_cnt] = k0n_x;
++zeros_cnt;
}
}


// free space wavenumber
nr_double_t k = 2.0 * pi * frequency / C0;

return nr_complex_t (0, calcReactance (r1, r2, al, er, h, frequency));
// kg - wavenumber of feed line
nr_double_t a_feed = 1.0 + 1.0/49.0 * qucs::log((qucs::pow(u, 4.0) + qucs::pow(u/52.0, 2.0)) / (qucs::pow(u, 4.0) + 0.432)) + 1.0/18.7 * qucs::log(1.0 + qucs::pow(u/18.1, 3.0));
nr_double_t b_feed = 0.564 * qucs::pow((eps_r - 0.9) / (eps_r + 3), 0.053);
nr_double_t eps_e1_feed_eff = (eps_r + 1.0) / 2.0 + (eps_r - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/u, -a_feed * b_feed);
nr_double_t eps_e_feed_eff = eps_e1_feed_eff; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
nr_double_t kg = 2.0 * pi * frequency * qucs::sqrt(eps_e_feed_eff) / C0; // feed line wavenumber (should be complex?)

// characteristic impedance of the radial stub
nr_double_t Z0rs = Z0 * h / (r_ie * phi * qucs::sqrt(eps_r));

// static mode Qt and P coefficients
nr_double_t Qt0 = 1.0 / loss_tan;
nr_double_t P0 = qucs::sqrt((2.0 * w_ge) / (phi * (qucs::pow(r_oe, 2.0) - qucs::pow(r_ie, 2.0)))); // is the alpha the same as phi (angle of stub)?


// impedance and phase velocity in annular and radial directions for capacitances calculations
// annular:
nr_double_t w_ann = r_o - r_i;
nr_double_t del_u1_ann = t / pi * qucs::log(1.0 + 4.0 * euler / (t * qucs::pow((qucs::coth(qucs::sqrt(6.517 * w_ann/h))), 2.0))); //not sure if correction for effective width is needed here, probably doesn't matter much
nr_double_t we_ann = w_ann + h * del_u1_ann / 2.0 * (1.0 + 1.0 / (qucs::cosh(qucs::sqrt(eps_r - 1))));
nr_double_t ue_ann = we_ann / h;
nr_double_t u_ann = w_ann / h; // TODO need separate w/h and weffective/h ?
nr_double_t f_ann = 6.0 + (2.0 * pi - 6.0) * qucs::exp(-qucs::pow(30.666/ue_ann, 0.7528));
nr_double_t a_ann = 1.0 + 1.0/49.0 * qucs::log((qucs::pow(u_ann, 4.0) + qucs::pow((u_ann/52), 2.0)) / (qucs::pow(u_ann, 4.0) + 0.432)) + 1/18.7 * qucs::log(1.0 + qucs::pow(u_ann/18.1, 3.0));
nr_double_t b_ann = 0.564 * qucs::pow((eps_r - 0.9) / (eps_r + 3), 0.053);
nr_double_t Z01_we_ann = 60.0 * qucs::log(f_ann / ue_ann + qucs::sqrt(1.0 + 4.0 / qucs::pow(ue_ann, 2.0)));
nr_double_t eps_e1_ann = (eps_r + 1.0) / 2.0 + (eps_r - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/ue_ann, -a_ann*b_ann);
nr_double_t Z0_ann = Z01_we_ann / qucs::sqrt(eps_e1_ann);
nr_double_t eps_e_ann = eps_e1_ann; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
nr_double_t Zphi = Z0_ann;
nr_double_t vphi = C0 / qucs::sqrt(eps_e_ann);
// as above but free for free space (eps_r=1)
nr_double_t we_ann_eps0 = w_ann + h * del_u1_ann;
nr_double_t ue_ann_eps0 = we_ann_eps0 / h;
nr_double_t f_ann_eps0 = 6.0 + (2.0 * pi - 6.0) * qucs::exp(-qucs::pow(30.666/ue_ann_eps0, 0.7528));
nr_double_t a_ann_eps0 = 1.0 + 1.0/49.0 * qucs::log((qucs::pow(ue_ann_eps0, 4.0) + qucs::pow((ue_ann_eps0/52), 2.0)) / (qucs::pow(ue_ann_eps0, 4.0) + 0.432)) + 1/18.7 * qucs::log(1.0 + qucs::pow(ue_ann_eps0/18.1, 3.0));
nr_double_t b_ann_eps0 = 0.564 * qucs::pow((1 - 0.9) / (1 + 3), 0.053);
nr_double_t Z01_we_ann_eps0 = 60.0 * qucs::log(f_ann_eps0 / ue_ann_eps0 + qucs::sqrt(1.0 + 4.0 / qucs::pow(ue_ann_eps0, 2.0)));
nr_double_t eps_e1_ann_eps0 = (1.0 + 1.0) / 2.0 + (1.0 - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/ue_ann_eps0, -a_ann_eps0*b_ann_eps0);
nr_double_t Z0_ann_eps0 = Z01_we_ann_eps0 / qucs::sqrt(eps_e1_ann_eps0);
nr_double_t eps_e_ann_eps0 = eps_e1_ann_eps0; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
nr_double_t Zphi_eps0 = Z0_ann_eps0;
nr_double_t vphi_eps0 = C0 / qucs::sqrt(eps_e_ann_eps0);
// radial (calculate average width):
int int_steps = 100;
nr_double_t Zr_vr_int_sum = 0;
nr_double_t step_rad = phi * (r_i + (r_o - r_i) * 2.0 / (int_steps-1.0)) - phi * (r_i + (r_o - r_i) * 1.0 / (int_steps-1.0));
nr_double_t w_rad, del_u1_rad, we_rad, ue_rad, u_rad, f_rad, a_rad, b_rad, Z01_we_rad, eps_e1_rad, Z0_rad, eps_e_rad, Zrad, vrad;
for(int i_rad = 0; i_rad < int_steps; ++i_rad)
{
w_rad = phi * (r_i + (r_o - r_i) * i_rad / (int_steps-1.0)); // width in radial direction
del_u1_rad = t / pi * qucs::log(1.0 + 4.0 * euler / (t * qucs::pow((qucs::coth(qucs::sqrt(6.517 * w_rad/h))), 2.0))); //not sure if correction for effective width is needed here, probably doesn't matter much
we_rad = w_rad + h * del_u1_rad / 2.0 * (1.0 + 1.0 / (qucs::cosh(qucs::sqrt(eps_r - 1))));
ue_rad = we_rad / h;
u_rad = w_rad / h; // TODO need separate w/h and weffective/h ?
f_rad = 6.0 + (2.0 * pi - 6.0) * qucs::exp(-qucs::pow(30.666/ue_rad, 0.7528));
a_rad = 1.0 + 1.0/49 * qucs::log((qucs::pow(u_rad, 4.0) + qucs::pow((u_rad/52.0), 2.0)) / (qucs::pow(u_rad, 4.0) + 0.432)) + 1/18.7 * qucs::log(1.0 + qucs::pow(u_rad/18.1, 3.0));
b_rad = 0.564 * qucs::pow((eps_r - 0.9) / (eps_r + 3), 0.053);
Z01_we_rad = 60.0 * qucs::log(f_rad / ue_rad + qucs::sqrt(1.0 + 4.0 / qucs::pow(ue_rad, 2.0)));
eps_e1_rad = (eps_r + 1.0) / 2.0 + (eps_r - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/ue_rad, -a_rad*b_rad);
Z0_rad = Z01_we_rad / qucs::sqrt(eps_e1_rad);
eps_e_rad = eps_e1_rad; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
Zrad = Z0_rad;
vrad = C0 / qucs::sqrt(eps_e_rad);
Zr_vr_int_sum += 1.0 / (Zrad * vrad) * step_rad;
}
nr_double_t ZrVr = 1.0 / (1.0 / (phi * (r_o - r_i)) * Zr_vr_int_sum);
// as above but free for free air (eps_r=1)
nr_double_t Zr_vr_int_sum_eps0 = 0;
nr_double_t w_rad_eps0, del_u1_rad_eps0, we_rad_eps0, ue_rad_eps0, u_rad_eps0, f_rad_eps0, a_rad_eps0, b_rad_eps0, Z01_we_rad_eps0, eps_e1_rad_eps0, Z0_rad_eps0, eps_e_rad_eps0, Zrad_eps0, vrad_eps0;
for(int i_rad = 0; i_rad < int_steps; ++i_rad)
{
w_rad_eps0 = phi * (r_i + (r_o - r_i) * i_rad / (int_steps-1.0)); // width in radial direction
del_u1_rad_eps0 = t / pi * qucs::log(1.0 + 4.0 * euler / (t * qucs::pow((qucs::coth(qucs::sqrt(6.517 * w_rad_eps0/h))), 2.0))); //not sure if correction for effective width is needed here, probably doesn't matter much
we_rad_eps0 = w_rad_eps0 + h * del_u1_rad_eps0;
ue_rad_eps0 = we_rad_eps0 / h;
u_rad_eps0 = w_rad_eps0 / h; // TODO need separate w/h and weffective/h ?
f_rad_eps0 = 6.0 + (2.0 * pi - 6.0) * qucs::exp(-qucs::pow(30.666/u_rad_eps0, 0.7528));
a_rad_eps0 = 1.0 + 1.0/49 * qucs::log((qucs::pow(u_rad_eps0, 4.0) + qucs::pow((u_rad_eps0/52), 2.0)) / (qucs::pow(u_rad_eps0, 4.0) + 0.432)) + 1/18.7 * qucs::log(1.0 + qucs::pow(u_rad_eps0/18.1, 3.0));
b_rad_eps0 = 0.564 * qucs::pow((1 - 0.9) / (1 + 3), 0.053);
Z01_we_rad_eps0 = 60.0 * qucs::log(f_rad_eps0 / ue_rad_eps0 + qucs::sqrt(1.0 + 4.0 / qucs::pow(ue_rad_eps0, 2.0)));
eps_e1_rad_eps0 = (1.0 + 1.0) / 2.0 + (1.0 - 1.0) / 2.0 * qucs::pow(1.0 + 10.0/ue_rad_eps0, -a_rad_eps0*b_rad_eps0);
Z0_rad_eps0 = Z01_we_rad_eps0 / qucs::sqrt(eps_e1_rad_eps0);
eps_e_rad_eps0 = eps_e1_rad_eps0; // TODO, eq 4.6 - skipped the correction (copper thickness?), to clarify, maybe check https://pure.tue.nl/ws/files/46936050/640261-1.pdf
Zrad_eps0 = Z0_rad_eps0;
vrad_eps0 = C0 / qucs::sqrt(eps_e_rad_eps0);
Zr_vr_int_sum_eps0 += 1.0 / (Zrad_eps0 * vrad_eps0) * step_rad;
}
nr_double_t ZrVr_eps0 = 1.0 / (1.0 / (phi * (r_o - r_i)) * Zr_vr_int_sum_eps0);

// calculations of capacitances for dynamic permittivity calculations
nr_double_t Cd0_eps_r = E0 * eps_r * phi * (qucs::pow(r_o, 2.0) - qucs::pow(r_i, 2.0)) / (2.0 * h);
nr_double_t Cdf_eps_r = (r_o + r_i) * phi / 2.0 * (1.0 / (Zphi * vphi) - E0 * eps_r * (r_o - r_i) / h);
nr_double_t Cdf_eps0 = (r_o + r_i) * phi / 2.0 * (1.0 / (Zphi_eps0 * vphi_eps0) - E0 * 1 * (r_o - r_i) / h);
nr_double_t Cds_eps_r = (r_o - r_i) / 2.0 * (1.0 / (ZrVr) - E0 * eps_r * (r_o + r_i) * phi / (2.0 * h));
nr_double_t Cds_eps0 = (r_o - r_i) / 2.0 * (1.0 / (ZrVr_eps0) - E0 * 1 * (r_o + r_i) * phi / (2.0 * h));

// static mode dynamic permittivity
nr_double_t eps_d0 = (Cd0_eps_r + Cdf_eps_r + 2 * Cds_eps_r) / (Cd0_eps_r / eps_r + Cdf_eps0 + 2 * Cds_eps0);

// higher modes
nr_complex_t sum_part_zin = nr_complex_t(0, 0);
nr_double_t Kn, A0n, B0n, P0n, Cd0n_eps_r, eps_d0n, omega0n, Rs, K, Itheta, dItheta, Qc0n, Qr0n, Qt0n;
for(int i_loop = 0; i_loop < n_max; ++i_loop)
{
// coefficients ...
Kn = -jn(1, k0n_root[i_loop]*r_oe) / yn(1, k0n_root[i_loop]*r_oe);
A0n = qucs::sqrt(2/phi) / qucs::sqrt(qucs::pow(r_oe, 2.0) * qucs::pow(jn(0, k0n_root[i_loop]*r_oe) + Kn*yn(0, k0n_root[i_loop]*r_oe), 2.0) - qucs::pow(r_ie, 2.0) * qucs::pow(jn(0, k0n_root[i_loop]*r_ie) + Kn*yn(0, k0n_root[i_loop]*r_ie), 2.0));
B0n = Kn * A0n;
P0n = qucs::sqrt(w_ge) * (A0n * jn(0, k0n_root[i_loop]*r_ie) + B0n * yn(0, k0n_root[i_loop]*r_ie));

// calculation of capacitance Cd0n and dynamic permittivity (higher modes)
Cd0n_eps_r = E0 * eps_r * phi / (2.0 * h) * (qucs::pow(r_o, 2.0) - qucs::pow(r_i, 2.0) * qucs::pow((jn(0, k0n_root[i_loop] * r_oe) + Kn * yn(0, k0n_root[i_loop] * r_oe)) / (jn(0, k0n_root[i_loop] * r_ie) + Kn * yn(0, k0n_root[i_loop] * r_ie)), 2.0));
eps_d0n = (Cd0n_eps_r + Cdf_eps_r + Cds_eps_r) / (Cd0n_eps_r / eps_r + Cdf_eps0 + Cds_eps0);

// quality factors calculations
omega0n = k0n_root[i_loop] * C0 / qucs::sqrt(eps_d0n); //TODO - correct?
Rs = qucs::sqrt(omega0n * MU0 / (2.0 * 1.0 / resist)); //TODO - what kind of resistivity? what with skin effect?
K = 1.0 -
(qucs::pow(r_ie, 2.0) * qucs::pow(jn(0, k0n_root[i_loop]*r_ie) * yn(1, k0n_root[i_loop]*r_ie) - jn(1, k0n_root[i_loop]*r_ie) * yn(0, k0n_root[i_loop]*r_ie), 2.0)) /
(qucs::pow(r_oe, 2.0) * qucs::pow(jn(0, k0n_root[i_loop]*r_oe) * yn(1, k0n_root[i_loop]*r_oe) - jn(1, k0n_root[i_loop]*r_ie) * yn(0, k0n_root[i_loop]*r_oe), 2.0));
Itheta = 0;
for(int i_theta = 1; i_theta <= 180; ++i_theta) // integrate numerically (each step 1deg)
{
dItheta = 1.0/180.0 * qucs::pow(jn(1, K * r_oe * qucs::sin(deg2rad(i_theta))), 2.0) * qucs::sin(deg2rad(i_theta));
Itheta += dItheta;
}
Qc0n = omega0n * MU0 * h / (2.0 * Rs);
Qr0n = 1.0 / (omega0n * h * Itheta / (eps_d0 * K * C0));
Qt0n = 1.0 / (1.0 / Qt0 + 1.0 / Qc0n + 1.0 / Qr0n);

// part of stub impedance (higher modes)
sum_part_zin += (kg * qucs::pow(P0n, 2.0)) / (qucs::pow(k0n_root[i_loop], 2.0) * (1.0 + nr_complex_t(0,1) / Qt0n) - qucs::pow(k, 2.0) * eps_d0n);
}

//normalized impedance and impedance calculations
nr_complex_t z_in = (1.0 / Qt0 - nr_complex_t(0,1) * kg * qucs::pow(P0, 2.0)) / (qucs::pow(k, 2.0) * eps_d0) + nr_complex_t(0,1) * sum_part_zin;
nr_complex_t Zin = Z0rs * z_in;
return Zin;
}

else {
return nr_complex_t (0, calcReactance (r_ie, r_oe, phi, eps_r, h, frequency)); //old model used in qucs
}
}

void msrstub::initDC (void) {
Expand All @@ -93,10 +324,21 @@ void msrstub::calcAC (nr_double_t frequency) {
PROP_REQ [] = {
{ "ri", PROP_REAL, { 1e-3, PROP_NO_STR }, PROP_POS_RANGE },
{ "ro", PROP_REAL, { 10e-3, PROP_NO_STR }, PROP_POS_RANGE },
{ "Wf", PROP_REAL, { 1e-3, PROP_NO_STR }, PROP_POS_RANGE },
{ "alpha", PROP_REAL, { 90, PROP_NO_STR }, PROP_RNGII (0, 180) },
{ "Subst", PROP_STR, { PROP_NO_VAL, "Subst1" }, PROP_NO_RANGE },
{ "EffDimens", PROP_STR, { PROP_NO_VAL, "OldQucsNoCorrection" }, PROP_RNG_MRSCORR },
{ "Model", PROP_STR, { PROP_NO_VAL, "OldQucsModel" }, PROP_RNG_MRSMOD },
PROP_NO_PROP };
PROP_OPT [] = {
PROP_NO_PROP };
struct define_t msrstub::cirdef =
{ "MRSTUB", 1, PROP_COMPONENT, PROP_NO_SUBSTRATE, PROP_LINEAR, PROP_DEF };


// Literature
// Design of a rectenna for wireless low-power transmission, Akkermans, J.A.G.
// A New Simple and Accurate Formula for Microstrip Radial Stub, Roberto Sorrentino, Luca Roselli
// A Crooked U-Slot Dual-Band Antenna With RadialStub Feeding, Hyo Rim Bae, Soon One So, Choon Sik Cho, Member, IEEE, Jae W. Lee, Member, IEEE, and Jaeheung Kim, Member, IEEE
// Performance Characterization of Radial Stub Microstrip Bow-Tie Antenna, B.T.P.Madhav, 2S.S.Mohan Reddy, 3Neha Sharma, 3J. Ravindranath Chowdary 3Bala Rama Pavithra, 3K.N.V.S. Kishore, 3G. Sriram, 3B. Sachin Kumar 1Associate Professor, Department of ECE, K L University, Guntur DT, AP, India 2Associate Professor, Department of ECE, SRKR Engineering College, Bhimavaram, AP, India 3Project Students, Department of ECE, K L University, Guntur DT, AP, India, Performance Characterization of Radial Stub Microstrip Bow-Tie Antenna. Available from: https://www.researchgate.net/publication/286889155_Performance_Characterization_of_Radial_Stub_Microstrip_Bow-Tie_Antenna [accessed Oct 19 2021].
//https://www.jpier.org/PIERL/view/12012009/
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