def dipole():
s1p_file = './resource/single_dipole.s1p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s1p_file)
cs = freq * 2j * np.pi
# Try to fit S
# f_out = vecfit.fit_s(s_data, cs, n_pole=3, n_iter=20, s_inf=-1)
# f_out = vecfit.fit_s(s_data, cs, n_pole=6, n_iter=20, s_inf=-1, bound_wt=0.3)
# f_out = vecfit.bound_tightening(s_data, cs) # np.inf, -1
f_out, log = vecfit.bound_tightening_sweep(s_data, cs)
bound, bw = f_out.bound(np.inf, f0=2.4e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
# ant_integral = f_out.bound_integral(cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, BW is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bw, bound_error, ant_integral))
ax1 = vecfit.plot_freq_resp(cs, s_data, y_scale='db')
f_out.plot(cs, ax=ax1, y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs,
s_data - f_out.model(cs),
ax=ax1,
y_scale='db',
linestyle='--')
ax2 = f_out.plot_improved_bound(1e11, 4e10)
def coupled_siw():
s2p_file = './resource/two_SIW_antenna_39GHz_50mil.s2p'
freq, n, z, s, z0 = vecfit.read_snp(s2p_file)
s_z0 = np.zeros(z.shape, dtype=z.dtype)
cs = freq * 2j * np.pi
# z0 = 50
z0 = 190
for i in range(len(freq)):
s_z0[:, :,
i] = np.matrix(z[:, :, i] / z0 - np.identity(n)) * np.linalg.inv(
np.matrix(z[:, :, i] / z0 + np.identity(n)))
s_model, bound = vecfit.mode_fitting(s_z0, cs, True)
bound_error = s_model.bound_error(s_z0, cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_z0, cs, np.inf)
print(
'Bound is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bound_error, ant_integral))
# plots
axs = vecfit.plot_freq_resp_matrix(cs, s_z0, y_scale='db')
s_model.plot(cs, axs=axs, y_scale='db', linestyle='--')
vecfit.plot_freq_resp_matrix(cs,
s_z0 - s_model.model(cs),
axs=axs,
y_scale='db',
linestyle='--')
def single_siw():
s1p_file = './resource/single_SIW_antenna_39GHz_50mil.s1p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s1p_file)
z0 = 190
s_data = (z_data - z0) / (z_data + z0)
cs = freq * 2j * np.pi
# Try to fit S
# f_out = vecfit.fit_s(s_data, cs, n_pole=18, n_iter=20, s_dc=0, s_inf=1, bound_wt=0.27)
f_out = vecfit.bound_tightening(s_data, cs)
bound, bw = f_out.bound(np.inf, f0=39e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
# ant_integral = f_out.bound_integral(cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, BW is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bw, bound_error, ant_integral))
ax1 = vecfit.plot_freq_resp(cs, s_data, x_scale='log', y_scale='db')
f_out.plot(cs, ax=ax1, x_scale='log', y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs,
s_data - f_out.model(cs),
ax=ax1,
x_scale='log',
y_scale='db',
linestyle='--')
ax2 = f_out.plot_improved_bound(1.2e10, 4e11)
def coupled_siw_even_odd():
s2p_file = './resource/two_SIW_antenna_39GHz_50mil.s2p'
freq, n, z, s, z0 = vecfit.read_snp(s2p_file)
s_z0 = np.zeros(z.shape, dtype=z.dtype)
cs = freq * 2j * np.pi
# z0 = 50
z0 = 190
for i in range(len(freq)):
s_z0[:, :,
i] = np.matrix(z[:, :, i] / z0 - np.identity(n)) * np.linalg.inv(
np.matrix(z[:, :, i] / z0 + np.identity(n)))
# Fit even and odd mode separately
s_even = ((s_z0[0, 0, :] + s_z0[0, 1, :] + s_z0[1, 0, :] + s_z0[1, 1, :]) /
2).reshape(len(freq))
s_odd = ((s_z0[0, 0, :] - s_z0[0, 1, :] - s_z0[1, 0, :] + s_z0[1, 1, :]) /
2).reshape(len(freq))
# Even mode
# f_even = vecfit.fit_s(s_even, cs, n_pole=19, n_iter=20, s_inf=1, bound_wt=1.1)
f_even = vecfit.bound_tightening(s_even, cs)
bound_even, bw_even = f_even.bound(np.inf, f0=39e9)
bound_error_even = f_even.bound_error(s_even, cs, reflect=np.inf)
# integral_even = f_even.bound_integral(cs, reflect=np.inf)
integral_even = vecfit.bound_integral(s_even, cs, np.inf)
# Odd mode
# f_odd = vecfit.fit_s(s_odd, cs, n_pole=17, n_iter=20, s_inf=1, bound_wt=0.62)
f_odd = vecfit.bound_tightening(s_odd, cs)
bound_odd, bw_odd = f_odd.bound(np.inf, f0=39e9)
bound_error_odd = f_odd.bound_error(s_odd, cs, reflect=np.inf)
# integral_odd = f_odd.bound_integral(cs, reflect=np.inf)
integral_odd = vecfit.bound_integral(s_odd, cs, np.inf)
print(
'Even mode: bound is {:.5e}, BW is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound_even, bw_even, bound_error_even, integral_even))
print(
'Odd mode: bound is {:.5e}, BW is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound_odd, bw_odd, bound_error_odd, integral_odd))
# plots
ax1 = vecfit.plot_freq_resp(cs, s_even, y_scale='db')
f_even.plot(cs, ax=ax1, y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs,
s_even - f_even.model(cs),
ax=ax1,
y_scale='db',
linestyle='--')
ax2 = f_even.plot_improved_bound(2e10, 4e11)
ax3 = vecfit.plot_freq_resp(cs, s_odd, y_scale='db')
f_odd.plot(cs, ax=ax3, y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs,
s_odd - f_odd.model(cs),
ax=ax3,
y_scale='db',
linestyle='--')
ax4 = f_odd.plot_improved_bound(2e10, 4e11)
def coupled_dipole():
s2p_file = './resource/coupled_dipoles.s2p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s2p_file)
cs = freq * 2j * np.pi
# Fit even and odd mode separately
s_even = ((s_data[0, 0, :] + s_data[0, 1, :] + s_data[1, 0, :] +
s_data[1, 1, :]) / 2).reshape(len(freq))
s_odd = ((s_data[0, 0, :] - s_data[0, 1, :] - s_data[1, 0, :] +
s_data[1, 1, :]) / 2).reshape(len(freq))
# Even and odd mode
# f_even = vecfit.fit_s(s_even, cs, n_pole=3, n_iter=20, s_inf=-1)
# f_odd = vecfit.fit_s(s_odd, cs, n_pole=3, n_iter=20, s_inf=-1)
# f_even = vecfit.bound_tightening(s_even, cs)
# f_odd = vecfit.bound_tightening(s_odd, cs)
f_even, log_even = vecfit.bound_tightening_sweep(s_even, cs, np.inf)
f_odd, log_odd = vecfit.bound_tightening_sweep(s_odd, cs, np.inf)
bound_even, bw_even = f_even.bound(np.inf, f0=2.4e9)
bound_error_even = f_even.bound_error(s_even, cs, reflect=np.inf)
bound_odd, bw_odd = f_odd.bound(np.inf, f0=2.4e9)
bound_error_odd = f_odd.bound_error(s_odd, cs, reflect=np.inf)
print('Manual even/odd mode decomposition:')
print(
'Even mode, # poles {}, bound {:.5e}, bound error {:.5e}, sum {:.5e}'.
format(len(f_even.pole), bound_even, bound_error_even,
bound_even + bound_error_even))
print('Odd mode, # poles {}, bound {:.5e}, bound error {:.5e}, sum {:.5e}'.
format(len(f_odd.pole), bound_odd, bound_error_odd,
bound_odd + bound_error_odd))
fig = plt.figure(figsize=(8, 5.5))
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
vecfit.plot_freq_resp(cs, s_even, ax=ax1, y_scale='db')
f_even.plot(cs, ax=ax1, y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs, s_odd, ax=ax2, y_scale='db')
f_odd.plot(cs, ax=ax2, y_scale='db', linestyle='--')
# Try to fit S
# fixed_pole = np.concatenate([f_even.pole, f_odd.pole])
# s_model = vecfit.matrix_fitting_rescale(s_data, cs, n_pole=6, n_iter=20, has_const=True, has_linear=False, fixed_pole=fixed_pole)
# s_model = s_model.rank_one()
# s_model = vecfit.matrix_fitting_rank_one_rescale(s_data, cs, n_pole=6, n_iter=50, has_const=True, has_linear=True)
s_model, bound = vecfit.mode_fitting(s_data, cs, True)
bound_error = s_model.bound_error(s_data, cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bound_error, ant_integral))
axs = vecfit.plot_freq_resp_matrix(cs, s_data, y_scale='db')
s_model.plot(cs, axs=axs, y_scale='db', linestyle='--')
def four_ifa():
snp_file = './resource/4Port_IFA_Free_Space.s4p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(snp_file)
cs = freq * 2j * np.pi
# Fit modes separately
s_matrix, bound = vecfit.mode_fitting(s_data, cs, True)
bound_error = s_matrix.bound_error(s_data, cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bound_error, ant_integral))
# plot the s_matrix
axs = vecfit.plot_freq_resp_matrix(cs, s_data, y_scale='db')
s_matrix.plot(cs, axs=axs, y_scale='db', linestyle='--')
def skycross_antennas():
snp_file = './resource/Skycross_4_parallel_fine2.s4p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(snp_file)
cs = freq * 2j * np.pi
s_matrix, bound = vecfit.mode_fitting(s_data, cs, True)
bound_error = s_matrix.bound_error(s_data, cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bound_error, ant_integral))
# plot per mode response
# calculate the bound error
s_fit = s_matrix.model(cs)
s_error = s_fit - s_data
u, sigma, vh = np.linalg.svd(np.moveaxis(s_error, -1, 0))
sigma_error = sigma[:, 0].flatten()
u, sigma, vh = np.linalg.svd(np.moveaxis(s_data, -1, 0))
sigma_max = sigma[:, 0].flatten()
sigma_min = sigma[:, -1].flatten()
rho = (2 * sigma_error) / (
1 - np.power(sigma_max, 2)) * np.sqrt(1 +
(sigma_max**2 - sigma_min**2) /
(1 - sigma_max)**2)
tau = 0.3162278
int_fct = vecfit.f_integral(
cs.imag, 0) / 2 * np.log(1 + (1 - tau**2) / tau**2 * rho)
delta_b = vecfit.num_integral(cs.imag, int_fct)
print('Bound error is {:.2e}'.format(delta_b))
int_fct = vecfit.f_integral(cs.imag, 0) * (1 - np.sum(sigma**2, 1) / n)
unmatched_integral = vecfit.num_integral(cs.imag, int_fct)
print('Unmatched integral is {:.2e}'.format(unmatched_integral))
# plot the s_matrix
axs = vecfit.plot_freq_resp_matrix(cs, s_data, y_scale='db')
s_matrix.plot(cs, axs=axs, y_scale='db', linestyle='--')
def skycross_antennas_old():
snp_file = './resource/Skycross_4_parallel_fine2.s4p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(snp_file)
# z0 = 50
# s_data = (z_data-z0) / (z_data+z0)
cs = freq * 2j * np.pi
cs_all = np.logspace(0, 15, 10000) * 2j * np.pi
# Fit modes separately
s_inf = 1
inf_weight = 1e6
s_data = np.concatenate(
[s_data, np.reshape(inf_weight * np.identity(n), [n, n, 1])], 2)
u_a, Lambda_A, vh_a, A_remain, err_norm, orig_norm = vecfit.joint_svd(
s_data)
s_data = s_data[:, :, :-1]
Lambda_A = Lambda_A[:, :, :-1]
A_remain = A_remain[:, :, :-1]
# poles_by_mode = [5, 7, 9, 6]
poles_by_mode = [5, 8, 5, 7] # s_inf = 1
f_by_mode = []
total_bound = 0.0
for i in range(n):
s_mode = Lambda_A[i, i, :]
f_mode = vecfit.fit_s(s_mode * np.exp(1j * np.pi * 0),
cs,
n_pole=poles_by_mode[i],
n_iter=20,
s_dc=s_inf)
mode_bound = f_mode.bound(0)
print('Mode {} bound is {:.2e}'.format(i, mode_bound[0]))
total_bound += mode_bound[0]
f_by_mode.append(f_mode)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(np.abs(cs) / 2 / np.pi, 20 * np.log10(np.abs(s_mode)), 'b-')
ax.semilogx(
np.abs(cs_all) / 2 / np.pi,
20 * np.log10(np.abs(f_mode.model(cs_all))), 'r--')
ax.grid(True)
ax.set_xlabel('Frequency (Hz)')
ax.set_ylabel('S even Amplitude (dB)')
total_bound /= n
print('Total bound is {:.2e}'.format(total_bound))
# Put the modes back to matrix
pole = np.zeros([np.sum(poles_by_mode)], dtype=np.complex128)
residue = np.zeros([n, n, np.sum(poles_by_mode)], dtype=np.complex128)
const = np.zeros([n, n], dtype=np.complex128)
idx = 0
for i in range(n):
tmp_matrix = np.zeros([n, n], dtype=np.complex128)
tmp_matrix[i, i] = 1
pole_range = np.array(range(idx, idx + poles_by_mode[i]))
pole[pole_range] = f_by_mode[i].pole
for j in range(poles_by_mode[i]):
residue_matrix = np.dot(
np.dot(u_a, f_by_mode[i].residue[j] * tmp_matrix), vh_a)
residue[:, :, pole_range[j]] = residue_matrix
const += np.dot(np.dot(u_a, f_by_mode[i].const * tmp_matrix), vh_a)
idx += poles_by_mode[i]
s_matrix = vecfit.RationalMtx(pole, residue, const)
# # do another fit for the remaining errors
# s_inf = -1
# inf_weight = 1e6
# s_remain = np.concatenate([A_remain, np.reshape(inf_weight * np.identity(n), [n, n, 1])], 2)
# u_a, Lambda_A, vh_a, A_remain, err_norm, orig_norm = vecfit.joint_svd(s_remain)
# s_remain = s_remain[:, :, :-1]
# Lambda_A = Lambda_A[:, :, :-1]
# A_remain = A_remain[:, :, :-1]
#
# poles_by_mode = [7, 11, 8, 9]
# f_by_mode = []
# total_bound = 0.0
# for i in range(n):
# s_mode = Lambda_A[i, i, :]
# f_mode = vecfit.fit_s(s_mode * np.exp(1j*np.pi*0), cs, n_pole=poles_by_mode[i], n_iter=20, s_inf=s_inf)
# mode_bound = f_mode.bound(np.inf)
# print('Mode {} bound is {:.2e}'.format(i, mode_bound[0]))
# total_bound += mode_bound[0]
# f_by_mode.append(f_mode)
# fig = plt.figure()
# ax = fig.add_subplot(111)
# ax.plot(np.abs(cs) / 2 / np.pi, 20 * np.log10(np.abs(s_mode)), 'b-')
# ax.semilogx(np.abs(cs_all) / 2 / np.pi, 20 * np.log10(np.abs(f_mode.model(cs_all))), 'r--')
# ax.grid(True)
# ax.set_xlabel('Frequency (Hz)')
# ax.set_ylabel('S even Amplitude (dB)')
# total_bound /= n
# print('Total bound is {:.2e}'.format(total_bound))
# # Put the modes back to matrix
# pole = np.zeros([np.sum(poles_by_mode)], dtype=np.complex128)
# residue = np.zeros([n, n, np.sum(poles_by_mode)], dtype=np.complex128)
# const = np.zeros([n, n], dtype=np.complex128)
# idx = 0
# for i in range(n):
# tmp_matrix = np.zeros([n, n], dtype=np.complex128)
# tmp_matrix[i, i] = 1
# pole_range = np.array(range(idx, idx+poles_by_mode[i]))
#
# pole[pole_range] = f_by_mode[i].pole
# for j in range(poles_by_mode[i]):
# residue_matrix = np.dot(np.dot(u_a, f_by_mode[i].residue[j]*tmp_matrix), vh_a)
# residue[:, :, pole_range[j]] = residue_matrix
# const += np.dot(np.dot(u_a, f_by_mode[i].const*tmp_matrix), vh_a)
# idx += poles_by_mode[i]
# s_matrix = vecfit.RationalMtx(pole, residue, const) + s_matrix
# calculate the bound error
s_fit = s_matrix.model(cs)
s_error = s_fit - s_data
u, sigma, vh = np.linalg.svd(np.moveaxis(s_error, -1, 0))
sigma_error = sigma[:, 0].flatten()
u, sigma, vh = np.linalg.svd(np.moveaxis(s_data, -1, 0))
sigma_max = sigma[:, 0].flatten()
sigma_min = sigma[:, -1].flatten()
rho = (2 * sigma_error) / (
1 - np.power(sigma_max, 2)) * np.sqrt(1 +
(sigma_max**2 - sigma_min**2) /
(1 - sigma_max)**2)
tau = 0.3162278
int_fct = vecfit.f_integral(
cs.imag, 0) / 2 * np.log(1 + (1 - tau**2) / tau**2 * rho)
delta_b = vecfit.num_integral(cs.imag, int_fct)
print('Bound error is {:.2e}'.format(delta_b))
int_fct = vecfit.f_integral(cs.imag, 0) * (1 - np.sum(sigma**2, 1) / n)
unmatched_integral = vecfit.num_integral(cs.imag, int_fct)
print('Unmatched integral is {:.2e}'.format(unmatched_integral))
# plot the s_matrix
s = 2j * np.pi * freq
s_model = s_matrix.model(s)
fig1 = plt.figure()
ax1 = fig1.add_subplot(321)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[0, 0, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[0, 0, :].flatten())), 'r--')
# ax1.plot(freq, 20 * np.log10(np.abs((s_data - s_model)[0, 0, :].flatten())), 'k--')
ax1 = fig1.add_subplot(322)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[0, 1, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[0, 1, :].flatten())), 'r--')
ax1 = fig1.add_subplot(323)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[0, 2, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[0, 2, :].flatten())), 'r--')
ax1 = fig1.add_subplot(324)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[0, 3, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[0, 3, :].flatten())), 'r--')
ax1 = fig1.add_subplot(325)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[1, 1, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[1, 1, :].flatten())), 'r--')
ax1 = fig1.add_subplot(326)
ax1.plot(freq, 20 * np.log10(np.abs(s_model[1, 2, :].flatten())), 'b-')
ax1.plot(freq, 20 * np.log10(np.abs(s_data[1, 2, :].flatten())), 'r--')
plt.show()
def long_dipole_bound_vs_pole():
s1p_file = './resource/single_dipole_wideband.s1p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s1p_file)
cs = freq * 2j * np.pi
s_all = np.logspace(
np.log10(np.min(np.abs(cs))) - 3,
np.log10(np.max(np.abs(cs))) + 3, int(1e5)) * 1j
# plot 1: bound vs pole with reflection inf
# ax1 = vecfit.plot_freq_resp(cs, s_data, y_scale='db')
pole_list = []
bound_list = []
bound_error_list = []
for i in range(1, 15):
f_out = vecfit.fit_s_v2(s_data, cs, n_pole=i, n_iter=20, s_inf=-1)
passive = np.all(np.abs(f_out.model(s_all)) <= 1)
print('Pole {}, passive {}, stable {}'.format(i, passive,
f_out.stable))
bound, bw = f_out.bound(np.inf, f0=2.4e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
pole_list.append(i)
bound_list.append(bound)
bound_error_list.append(bound_error)
# f_out.plot(cs, ax=ax1, y_scale='db', linestyle='--')
# vecfit.plot_freq_resp(cs, s_data - f_out.model(cs), ax=ax1, y_scale='db', linestyle='--')
fig = plt.figure(figsize=(8, 5.5))
ax = fig.add_subplot(111)
ax.plot(pole_list, bound_list, '--')
ax.plot(pole_list, bound_error_list, '--')
ax.plot(pole_list, np.array(bound_list) + np.array(bound_error_list))
ax.set_xlabel(r'Number of poles $N_p$')
ax.set_ylabel(r'Bound ($s_0=\infty$)')
ax.legend([r'$B$', r'$\delta B$', r'$B+\delta B$'])
ax.grid(True, which='both', linestyle='--')
# plot 2: bound vs weight with reflection inf
wt_list = []
bound_list = []
bound_error_list = []
wt = 0
wt_step = 0.2
while wt <= 20:
f_out = vecfit.fit_s_v2(s_data,
cs,
n_pole=7,
n_iter=20,
s_inf=-1,
bound_wt=wt)
passive = np.all(np.abs(f_out.model(s_all)) <= 1)
if passive and f_out.stable:
bound, bw = f_out.bound(np.inf, f0=2.4e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
wt_list.append(wt)
bound_list.append(bound)
bound_error_list.append(bound_error)
wt += wt_step
else:
print('Stop at weight {:g}, passive {}, stable {}'.format(
wt, passive, f_out.stable))
break
fig = plt.figure(figsize=(8, 5.5))
ax = fig.add_subplot(111)
ax.plot(wt_list, bound_list, '--')
ax.plot(wt_list, bound_error_list, '--')
ax.plot(wt_list, np.array(bound_list) + np.array(bound_error_list))
ax.set_xlabel(r'Weight $\alpha$')
ax.set_ylabel(r'Bound ($s_0=\infty$)')
ax.legend([r'$B$', r'$\delta B$', r'$B+\delta B$'])
ax.grid(True, which='both', linestyle='--')
def long_dipole_paper():
s1p_file = './resource/single_dipole_wideband.s1p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s1p_file)
cs = freq * 2j * np.pi
z0 = 50
z_data = (1 + s_data) / (1 - s_data) * z0
fz = interp1d(freq, z_data)
fr = interp1d(freq, np.real(z_data))
fx = interp1d(freq, np.imag(z_data))
f0 = 2.4e9
f1 = optimize.bisect(fx, 2e9, 2.5e9)
f2 = optimize.bisect(fx, 4e9, 4.2e9)
f3 = optimize.bisect(fx, 6.8e9, 7.2e9)
f4 = optimize.bisect(fx, 8.5e9, 8.8e9)
# Equivalent circuit of dipole antenna of arbitrary length
# proposed structure: C0 + L0 + (R1 // L1 // C1) + (R2 // L2 // C2)
C0 = -1 / (2 * np.pi * f0 / 10 * fx(f0 / 10)) # determined by 0.1 * lambda
L0 = 1 / (2 * np.pi *
(3 * f1))**2 / C0 # determined by 0.5 * lambda and C0
R1 = fr(f2) # determined by 1 * lambda
C1 = 1e-13 # determined by 0.5 * lambda and 1 * lambda
L1 = 1 / (2 * np.pi *
f2)**2 / C1 # determined by 0.5 * lambda and 1 * lambda
R2 = fr(f4) # determined by 2 * lambda
C2 = 1.2e-13 # determined by 1.5 * lambda and 2 * lambda
L2 = 1 / (
2 * np.pi *
(1.018 * f4))**2 / C2 # determined by 1.5 * lambda and 2 * lambda
p1 = (-1 / R1 / C1 + cmath.sqrt(1 / R1**2 / C1**2 - 4 / L1 / C1)) / 2
p2 = (-1 / R1 / C1 - cmath.sqrt(1 / R1**2 / C1**2 - 4 / L1 / C1)) / 2
r1 = 1 / C1 / (1 - p2 / p1)
r2 = 1 / C1 / (1 - p1 / p2)
p3 = (-1 / R2 / C2 + cmath.sqrt(1 / R2**2 / C2**2 - 4 / L2 / C2)) / 2
p4 = (-1 / R2 / C2 - cmath.sqrt(1 / R2**2 / C2**2 - 4 / L2 / C2)) / 2
r3 = 1 / C2 / (1 - p4 / p3)
r4 = 1 / C2 / (1 - p3 / p4)
pole_model = [0, p1, p2, p3, p4]
zero_model = [1 / C0, r1, r2, r3, r4]
z_model = vecfit.RationalFct(pole_model, zero_model, 0, L0)
s_tmp = (z_model.model(cs) - z0) / (z_model.model(cs) + z0)
s_model = vecfit.fit_s(s_tmp, cs, n_pole=6, n_iter=20, s_inf=1)
paper_bound, paper_bw = s_model.bound(np.inf, f0=2.4e9)
paper_bound_error = s_model.bound_error(s_data, cs, reflect=np.inf)
zl = z_model.model(cs)
zl2 = 1 / (cs * C0) + cs * L0 + 1 / (1 / R1 + 1 / (cs * L1) +
cs * C1) + 1 / (1 / R2 + 1 /
(cs * L2) + cs * C2)
# zl2 = 1/(cs*C0) + cs*L0 + 1/(1/R1 + 1/(cs*L1) + cs*C1)
# zl2 = 1/(cs*C0) + cs*L0
# zl2 = 1/(1/R1 + 1/(cs*L1) + cs*C1)
# Use algorithm to fit S
# f_out = vecfit.fit_s(s_data, cs, n_pole=6, n_iter=20, s_inf=1)
# f_out = vecfit.bound_tightening(s_data, cs)
f_out, log = vecfit.bound_tightening_sweep(s_data, cs, np.inf) # -1
z_fit = (1 + f_out.model(cs)) / (1 - f_out.model(cs)) * z0
bound, bw = f_out.bound(np.inf, f0=2.4e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
# Use manual algorithm to fit S
# f_out2 = vecfit.fit_s(s_data, cs, n_pole=6, n_iter=20, s_inf=1)
f_out2 = vecfit.fit_s_v2(s_data, cs, n_pole=6, n_iter=20, s_inf=1)
z_fit2 = (1 + f_out2.model(cs)) / (1 - f_out2.model(cs)) * z0
bound2, bw2 = f_out2.bound(np.inf, f0=2.4e9)
bound_error2 = f_out2.bound_error(s_data, cs, reflect=np.inf)
# plots
ax = vecfit.plot_freq_resp(cs, s_data, y_scale='db')
vecfit.plot_freq_resp(cs, s_tmp, ax=ax, y_scale='db', linestyle='--')
f_out.plot(cs, ax=ax, y_scale='db', linestyle='--')
f_out2.plot(cs, ax=ax, y_scale='db', linestyle='--')
ax.set_ylabel(r'Reflection coefficient $\Gamma$ (dB)')
ax.legend(['Simulation', 'Paper [16?]', 'Algorithm 2', 'Impedance Method'])
ax.grid(True, which='both', linestyle='--')
# bound values
print('Paper:')
print('Poles {}, bound {:.5e}, error {:.5e}, sum {:.5e}'.format(
len(s_model.pole), paper_bound, paper_bound_error,
paper_bound + paper_bound_error))
print('Algorithm:')
print('Poles {}, bound {:.5e}, error {:.5e}, sum {:.5e}'.format(
len(f_out.pole), bound, bound_error, bound + bound_error))
print('Manual comparison:')
print('Poles {}, bound {:.5e}, error {:.5e}, sum {:.5e}'.format(
len(f_out2.pole), bound2, bound_error2, bound2 + bound_error2))
def dipole_paper():
# Equivalent circuit of a dipole antenna using frequency-independent lumped elements
# https://ieeexplore.ieee.org/document/210122
s1p_file = './resource/single_dipole.s1p'
freq, n, z_data, s_data, z0_data = vecfit.read_snp(s1p_file)
cs = freq * 2j * np.pi
z0 = 50
# [2] three-element
# [3] four-element
# proposed four-element: C1 + (C2 // L1 // R1)
h = 62.5e-3 / 2
a = 2.5e-3 / 2
# h = 0.9
# a = 0.00264
C1 = 12.0674 * h / (np.log10(2 * h / a) - 0.7245) * 1e-12 # pF
C2 = 2 * h * (0.89075 / (np.power(np.log10(2 * h / a), 0.8006) - 0.861) -
0.02541) * 1e-12 # pF
L1 = 0.2 * h * (np.power(1.4813 * np.log10(2 * h / a), 1.012) -
0.6188) * 1e-6 # uH
R1 = (0.41288 * np.power(np.log10(2 * h / a), 2) +
7.40754 * np.power(2 * h / a, -0.02389) - 7.27408) * 1e3 # k Ohm
C1 *= z0
C2 *= z0
L1 /= z0
R1 /= z0
p1 = (-1 / R1 / C2 + cmath.sqrt(1 / R1**2 / C2**2 - 4 / L1 / C2)) / 2
p2 = (-1 / R1 / C2 - cmath.sqrt(1 / R1**2 / C2**2 - 4 / L1 / C2)) / 2
r1 = 1 / C2 / (1 - p2 / p1)
r2 = 1 / C2 / (1 - p1 / p2)
pole_model = [0, p1, p2]
zero_model = [1 / C1, r1, r2]
z_model = vecfit.RationalFct(pole_model, zero_model, 0, 0)
s_model = (z_model.model(cs) - 1) / (z_model.model(cs) + 1)
# Try to fit S
# f_out = vecfit.bound_tightening(s_data, cs)
f_out, log = vecfit.bound_tightening_sweep(s_data, cs)
bound, bw = f_out.bound(np.inf, f0=2.4e9)
bound_error = f_out.bound_error(s_data, cs, reflect=np.inf)
# ant_integral = f_out.bound_integral(cs, reflect=np.inf)
ant_integral = vecfit.bound_integral(s_data, cs, np.inf)
print(
'Bound is {:.5e}, BW is {:.5e}, Bound error is {:.5e}, The integral of the antenna is {:.5e}'
.format(bound, bw, bound_error, ant_integral))
ax1 = vecfit.plot_freq_resp(cs, s_data, y_scale='db')
f_out.plot(cs, ax=ax1, y_scale='db', linestyle='--')
vecfit.plot_freq_resp(cs, s_model, ax=ax1, y_scale='db')
vecfit.plot_freq_resp(cs,
s_data - f_out.model(cs),
ax=ax1,
y_scale='db',
linestyle='--')
vecfit.plot_freq_resp(cs,
s_data - s_model,
ax=ax1,
y_scale='db',
linestyle='--')
ax2 = f_out.plot_improved_bound(1e11, 4e10)
