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example_3.py
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example_3.py
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"""
Example comparing the statistical performance of different mTRL calibrations.
"""
import os
# need to be installed via pip
import skrf as rf
import numpy as np
import matplotlib.pyplot as plt
# my script (MultiCal.py and TUGmTRL.py must also be in same folder)
from mTRL import mTRL
class PlotSettings:
# to make plots look better for publication
# https://matplotlib.org/stable/tutorials/introductory/customizing.html
def __init__(self, font_size=10, latex=False):
self.font_size = font_size
self.latex = latex
def __enter__(self):
plt.style.use('seaborn-v0_8-paper')
# make svg output text and not curves
plt.rcParams['svg.fonttype'] = 'none'
# fontsize of the axes title
plt.rc('axes', titlesize=self.font_size*1.2)
# fontsize of the x and y labels
plt.rc('axes', labelsize=self.font_size)
# fontsize of the tick labels
plt.rc('xtick', labelsize=self.font_size)
plt.rc('ytick', labelsize=self.font_size)
# legend fontsize
plt.rc('legend', fontsize=self.font_size*1)
# fontsize of the figure title
plt.rc('figure', titlesize=self.font_size)
# controls default text sizes
plt.rc('text', usetex=self.latex)
#plt.rc('font', size=self.font_size, family='serif', serif='Times New Roman')
plt.rc('lines', linewidth=1.5)
def __exit__(self, exception_type, exception_value, traceback):
plt.style.use('default')
def add_white_noise(NW, sigma=0.01):
# add white noise to a network's S-parameters
freq = NW.frequency
noise = (np.random.standard_normal((len(freq.f),2,2))
+ 1j*np.random.standard_normal((len(freq.f),2,2)))*sigma
S = NW.s + noise
return rf.Network(frequency=freq, s=S)
def add_uniform_noise(NW, lower=-0.01, upper=0.01):
# add uniform noise to a network's S-parameters
freq = NW.frequency
noise = np.random.uniform(lower, upper, (len(freq.f),2,2)) + \
1j*np.random.uniform(lower, upper, (len(freq.f),2,2))
S = NW.s + noise
return rf.Network(frequency=freq, s=S)
def add_phase_error(NW, lower=-5, upper=5):
# add uniform phase noise (in degrees) to a network's S-parameters
freq = NW.frequency
noise = np.random.uniform(lower, upper, (len(freq.f),2,2))
S = abs(NW.s)*np.exp(1j*np.deg2rad(np.angle(NW.s, deg=True) + noise))
return rf.Network(frequency=freq, s=S)
def coef_MAE(coef_MC, coefs_ideal, name, name2=None):
name2 = name if name2 is None else name2
return np.array([ abs(x[name]-coefs_ideal[name2]) for x in coef_MC ]).mean(axis=0)
# main script
if __name__ == '__main__':
# useful functions
c0 = 299792458 # speed of light in vacuum (m/s)
mag2db = lambda x: 20*np.log10(abs(x))
db2mag = lambda x: 10**(x/20)
gamma2ereff = lambda x,f: -(c0/2/np.pi/f*x)**2
ereff2gamma = lambda x,f: 2*np.pi*f/c0*np.sqrt(-(x-1j*np.finfo(complex).eps)) # eps to ensure positive square-root
gamma2dbmm = lambda x: mag2db(np.exp(x.real*1e-3)) # losses dB/mm
# load the measurements
# files' path are reference to script's path
s2p_path = os.path.dirname(os.path.realpath(__file__)) + '\\s2p_example_1\\'
# Calibration standards
L1 = rf.Network(s2p_path + 'Cascade_line_0200u.s2p')
L2 = rf.Network(s2p_path + 'Cascade_line_0450u.s2p')
L3 = rf.Network(s2p_path + 'Cascade_line_0900u.s2p')
L4 = rf.Network(s2p_path + 'Cascade_line_1800u.s2p')
L5 = rf.Network(s2p_path + 'Cascade_line_3500u.s2p')
L6 = rf.Network(s2p_path + 'Cascade_line_5250u.s2p') # used as well as DUT
SHORT = rf.Network(s2p_path + 'Cascade_short.s2p')
freq = L1.frequency
f = freq.f
lines = [L1, L2, L3, L4, L5, L6]
line_lengths = [200e-6, 450e-6, 900e-6, 1800e-6, 3500e-6, 5250e-6]
reflect = [SHORT]
reflect_est = [-1]
reflect_offset = [-100e-6]
# DUT noiseless
cal = mTRL(lines=lines, line_lengths=line_lengths, reflect=reflect,
reflect_est=reflect_est, reflect_offset=reflect_offset, ereff_est=6.2-0.0001j)
print('\nNoiseless case...')
cal.run_multical() # use MultiCal as reference
coefs_ideal = cal.coefs
gamma_ideal = cal.gamma
# Monte Carlo Analysis
print('\n\nWith noise...')
M = 10 # number of trials
sigma_noise = 0.2
coefs_NIST = []
coefs_TUG = []
coefs_skrf = []
gamma_NIST = []
gamma_TUG = []
gamma_skrf = []
for inx in range(M):
# additive noise
lines_n = [add_white_noise(NW, sigma_noise) for NW in lines]
reflect_n = [add_white_noise(NW, sigma_noise) for NW in reflect]
#lines_n = [add_phase_error(NW, -20, 20) for NW in lines]
#reflect_n = [add_phase_error(NW, -20, 20) for NW in reflect]
# calibration object
cal = mTRL(lines=lines_n, line_lengths=line_lengths, reflect=reflect_n,
reflect_est=reflect_est, reflect_offset=reflect_offset, ereff_est=6.2-0.0001j)
# using NIST MultiCal mTRL
cal.run_multical()
coefs_NIST.append(cal.coefs)
gamma_NIST.append(cal.gamma)
# using TUG mTRL
cal.run_tug()
coefs_TUG.append(cal.coefs)
gamma_TUG.append(cal.gamma)
# use skrf
measured = [lines_n[0]] + [reflect_n[0]] + lines_n[1:]
offset = line_lengths[0]
cal_skrf = rf.NISTMultilineTRL(
measured = measured,
Grefls = [-1],
l = [i - offset for i in line_lengths],
refl_offset = reflect_offset,
er_est = 6.2-0.0001j)
cal_skrf.run()
coefs_skrf.append(cal_skrf.coefs)
gamma_skrf.append(cal_skrf.gamma)
print(f'\nMC Index: {inx+1} out of {M} done.')
EDF_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'EDF')
ESF_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ESF')
ERF_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ERF')
EDR_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'EDR')
ESR_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ESR')
ERR_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ERR')
ETF_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ETF')
ETR_NIST = coef_MAE(coefs_NIST, coefs_ideal, 'ETR')
EDF_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'EDF')
ESF_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ESF')
ERF_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ERF')
EDR_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'EDR')
ESR_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ESR')
ERR_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ERR')
ETF_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ETF')
ETR_TUG = coef_MAE(coefs_TUG, coefs_ideal, 'ETR')
EDF_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'forward directivity', 'EDF')
ESF_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'forward source match', 'ESF')
ERF_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'forward reflection tracking', 'ERF')
EDR_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'reverse directivity', 'EDR')
ESR_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'reverse source match', 'ESR')
ERR_skrf = coef_MAE(coefs_skrf, coefs_ideal, 'reverse reflection tracking', 'ERR')
with PlotSettings(14):
fig, axs = plt.subplots(3,2, figsize=(10,11))
fig.set_dpi(600)
fig.tight_layout(pad=2)
ax = axs[0,0]
ax.plot(f*1e-9, mag2db(EDF_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(EDF_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(EDF_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Forward directivity')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
ax = axs[1,0]
ax.plot(f*1e-9, mag2db(ESF_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ESF_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ESF_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Forward source match')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
ax = axs[2,0]
ax.plot(f*1e-9, mag2db(ERF_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ERF_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ERF_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Forward reflection tracking')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
ax = axs[0,1]
ax.plot(f*1e-9, mag2db(EDR_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(EDR_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(EDR_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Reverse directivity')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
ax = axs[1,1]
ax.plot(f*1e-9, mag2db(ESR_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ESR_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ESR_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Reverse source match')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
ax = axs[2,1]
ax.plot(f*1e-9, mag2db(ERR_NIST), lw=2, label='NIST MultiCal',
marker='^', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ERR_TUG), lw=2, label='TUG mTRL',
marker='v', markevery=50, markersize=10)
ax.plot(f*1e-9, mag2db(ERR_skrf), lw=2, label='skrf',
marker='>', markevery=50, markersize=10)
ax.set_xlabel('Frequency (GHz)')
ax.set_ylabel('Reverse reflection tracking')
ax.set_xlim(0,150)
ax.set_xticks(np.arange(0,151,30))
handles, labels = ax.get_legend_handles_labels()
fig.legend(handles, labels, bbox_to_anchor=(0.5, 0.98),
loc='lower center', ncol=3, borderaxespad=0
)
plt.suptitle(f"Mean Absolute Error (MAE) in dB of calibration coefficients. Noise std = {sigma_noise:.2f}", verticalalignment='bottom').set_y(1.02)
plt.show()
# EOF