189 lines
4.5 KiB
Python
189 lines
4.5 KiB
Python
|
# coding: utf-8
|
|||
|
|
from __future__ import print_function, division, unicode_literals
|
|||
|
|
|
|||
|
|
import numpy as np
|
|||
|
|
import uncertainties.umath as um
|
|||
|
|
import matplotlib.pyplot as plt
|
|||
|
|
from lab import *
|
|||
|
|
|
|||
|
|
## Impedence of an inductor (I)
|
|||
|
|
## (all SI units)
|
|||
|
|
|
|||
|
|
R = ufloat(996, 4) # resistor
|
|||
|
|
L = ufloat(0.014561, 0.000009)
|
|||
|
|
C = ufloat(10e-12, 1e-12)
|
|||
|
|
|
|||
|
|
# frequency
|
|||
|
|
nu = array( 2e3, 10e3, 25e3, 50e3, 75e3, 100e3, 125e3, 150e3, 175e3, 200e3,
|
|||
|
|
225e3, 250e3, 260e3, 270e3, 275e3, 285e3, 300e3, 350e3, 375e3)
|
|||
|
|
|
|||
|
|
# V input
|
|||
|
|
Va = array(10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0, 10.0,
|
|||
|
|
10.0, 10.0, 8.2, 10.0, 10.0, 8.20, 10.0, 10.0, 10.0)/2
|
|||
|
|
|
|||
|
|
# V output
|
|||
|
|
Vb = array( 10.0, 9.4, 7.8, 5.0, 3.28, 2.20, 1.44, 0.96, 0.56, 0.32, 0.144,
|
|||
|
|
0.085, 0.0396, 0.069, 75.4e-3, 0.144, 0.194, 0.320, 0.360)/2
|
|||
|
|
|
|||
|
|
# time offset Va - Vb
|
|||
|
|
Oab = array( 12e-6, 6.0e-6, 5.2e-6, 4.2e-6, 3.5e-6, 3.08e-6, 2.64e-6, 2.36e-6,
|
|||
|
|
2.08e-6, 1.88e-6, 1.71e-6, 260e-9, 260e-9, 280e-9, 280e-9, 300e-9,
|
|||
|
|
250e-9, 220e-9, 180e-9)
|
|||
|
|
|
|||
|
|
# time offset I - V
|
|||
|
|
Oiv = array( 110e-6, 26.0e-6, 11.2e-6, 5.9e-6, 4.2e-6, 3.36e-6, 2.80e-6, 2.40e-6,
|
|||
|
|
2.12e-6, 1.90e-6, 1.74e-6, 280e-9, 260e-9, 270e-9, 280e-9, 280e-9,
|
|||
|
|
260e-9, 220e-9, 184e-9)
|
|||
|
|
|
|||
|
|
|
|||
|
|
om = 2*np.pi*nu # angular frequency
|
|||
|
|
I = Vb/R.n # output current
|
|||
|
|
Vab = Va - Vb # tension drop
|
|||
|
|
Fab = om * Oab # phase difference Vᵢ - Vₒ
|
|||
|
|
Fiv = om * Oiv # phase difference I - Vₒ
|
|||
|
|
|
|||
|
|
Z = Vab/I * np.exp(1j*Fiv) # impedance
|
|||
|
|
H1 = Vab/Vb * np.exp(1j*Fab) # transfer function ΔV→Vb
|
|||
|
|
H2 = Vb/Va * np.exp(1j*Fab) # transfer function Va→Vb
|
|||
|
|
|
|||
|
|
|
|||
|
|
# estimate uncertainties
|
|||
|
|
Evb, Eva = ufloat(Vb[0], 1e-3), ufloat(Va[0], 0.1)
|
|||
|
|
sigmaF = (om[0]*ufloat(Oiv[0], 3e-5)).s
|
|||
|
|
sigmaZ = (R*(Eva - Evb)/Evb).s
|
|||
|
|
sigmaH1 = ((Eva - Evb)/Evb).s
|
|||
|
|
sigmaH2 = ((Evb - Eva)/Evb).s
|
|||
|
|
|
|||
|
|
|
|||
|
|
# plot and fit Z(ν)
|
|||
|
|
plt.figure(4)
|
|||
|
|
plt.clf()
|
|||
|
|
|
|||
|
|
# magnitude
|
|||
|
|
plt.subplot(2, 1, 1)
|
|||
|
|
plt.title('impedance (RL circuit)')
|
|||
|
|
plt.ylabel('magnitude (kΩ)')
|
|||
|
|
plt.semilogx(nu, abs(Z)/1e3, 'o', color="#36913d", markersize=4.5)
|
|||
|
|
|
|||
|
|
# fit Y=kX where Y=|Z|, X=ν, k=2πL
|
|||
|
|
k = simple_linear(nu, abs(Z), sigmaZ)
|
|||
|
|
L = k/(2*np.pi)
|
|||
|
|
f = lambda x: k.n*x
|
|||
|
|
|
|||
|
|
x = np.arange(nu.min()-10, nu.max(), 10)
|
|||
|
|
plt.semilogx(x, f(x)/1e3, color='#589f22')
|
|||
|
|
|
|||
|
|
# phase
|
|||
|
|
plt.subplot(2, 1, 2)
|
|||
|
|
plt.xlabel('frequency (Hz)')
|
|||
|
|
plt.ylabel('phase (rad)')
|
|||
|
|
plt.semilogx(nu, Fiv, 'o', color="#36913d", markersize=4.5)
|
|||
|
|
plt.show()
|
|||
|
|
|
|||
|
|
|
|||
|
|
alpha = chi_squared_fit(nu, abs(Z), f, sigmaZ)
|
|||
|
|
|
|||
|
|
print(mformat('''
|
|||
|
|
k: {}
|
|||
|
|
L: {} H
|
|||
|
|
|
|||
|
|
χ² test:
|
|||
|
|
α={:.2f}, α>ε: {}
|
|||
|
|
''', k, L,
|
|||
|
|
alpha, alpha>epsilon))
|
|||
|
|
|
|||
|
|
|
|||
|
|
|
|||
|
|
# plot, fit H₁(ν)
|
|||
|
|
plt.figure(5)
|
|||
|
|
plt.clf()
|
|||
|
|
|
|||
|
|
# magnitude
|
|||
|
|
plt.subplot(2,1,1)
|
|||
|
|
plt.title('transfer function 1')
|
|||
|
|
plt.ylabel('magnitude (Vout-Vin / Vout)')
|
|||
|
|
plt.semilogx(nu, abs(H1), 'o', color="#9b2e83", markersize=4.5)
|
|||
|
|
|
|||
|
|
# fit Y=kX where Y=|H1|, X=ν, k=2πL/R
|
|||
|
|
k = simple_linear(nu, abs(H1), sigmaH1)
|
|||
|
|
L = k*R/(2*np.pi)
|
|||
|
|
f = lambda x: k.n/x
|
|||
|
|
|
|||
|
|
x = np.arange(nu.min()-10, nu.max(), 10)
|
|||
|
|
plt.semilogx(x, f(x), color='#9b2e83')
|
|||
|
|
|
|||
|
|
# phase
|
|||
|
|
plt.subplot(2,1,2)
|
|||
|
|
plt.xlabel('frequency (Hz)')
|
|||
|
|
plt.ylabel('phase (rad)')
|
|||
|
|
plt.semilogx(nu, Fab, 'o', color="#3a44ad", markersize=4.5)
|
|||
|
|
plt.show()
|
|||
|
|
|
|||
|
|
alpha = check_measures(R*C, RCo)
|
|||
|
|
beta = chi_squared_fit(nu, abs(H1), f, sigmaH1)
|
|||
|
|
|
|||
|
|
print(mformat('''
|
|||
|
|
k: {} Hz
|
|||
|
|
RC: {} s
|
|||
|
|
RCₒ: {} s
|
|||
|
|
|
|||
|
|
compatibility test:
|
|||
|
|
α={:.2f}, α>ε: {}
|
|||
|
|
|
|||
|
|
χ² test:
|
|||
|
|
β={:.2f}, β>ε: {}
|
|||
|
|
''', k, R*C, RCo,
|
|||
|
|
alpha, alpha>epsilon,
|
|||
|
|
beta, beta>epsilon))
|
|||
|
|
|
|||
|
|
|
|||
|
|
# plot, fit H₂(ν)
|
|||
|
|
plt.figure(6)
|
|||
|
|
plt.clf()
|
|||
|
|
|
|||
|
|
# magnitude
|
|||
|
|
plt.subplot(2,1,1)
|
|||
|
|
plt.title('transfer function 2')
|
|||
|
|
plt.ylabel('magnitude (Vout / Vin)')
|
|||
|
|
plt.semilogx(nu, abs(H2), 'o', color="#9b2e83", markersize=4.5)
|
|||
|
|
|
|||
|
|
# fit Y=a+bX where Y=1/|H₂|², X=1/ν², a=1, b=1/(2πRC)²
|
|||
|
|
a,b = linear(1/nu**2, 1/abs(H2)**2, 0.01)
|
|||
|
|
RCo = 1/(2*np.pi*um.sqrt(b))
|
|||
|
|
f = lambda x: 1/np.sqrt(1 + b.n/x**2) # magnitude
|
|||
|
|
g = lambda x: -np.pi/2 + np.arctan(2*np.pi*x*R.n*C.n) # phase
|
|||
|
|
|
|||
|
|
x = np.arange(nu.min()-10, nu.max(), 10)
|
|||
|
|
plt.semilogx(x, f(x), color='#9b2e83')
|
|||
|
|
|
|||
|
|
# phase
|
|||
|
|
plt.subplot(2,1,2)
|
|||
|
|
plt.xlabel('frequency (Hz)')
|
|||
|
|
plt.ylabel('phase (rad)')
|
|||
|
|
plt.semilogx(nu, Fab, 'o', color="#3a44ad", markersize=4.5)
|
|||
|
|
plt.semilogx(x, g(x))
|
|||
|
|
plt.show()
|
|||
|
|
|
|||
|
|
alpha = check_measures(R*C, RCo)
|
|||
|
|
beta = chi_squared_fit(nu, abs(H2), f, sigmaH2)
|
|||
|
|
gamma = chi_squared_fit(nu, Fab, g, sigmaF)
|
|||
|
|
|
|||
|
|
print(mformat('''
|
|||
|
|
b: {}
|
|||
|
|
RC: {} s
|
|||
|
|
RCₒ: {} s
|
|||
|
|
|
|||
|
|
compatibility test:
|
|||
|
|
α={:.2f}, α>ε: {}
|
|||
|
|
|
|||
|
|
χ² test (magnitude):
|
|||
|
|
β={:.2f}, β>ε: {}
|
|||
|
|
|
|||
|
|
χ² test (phase):
|
|||
|
|
γ={:.2f}, γ>ε: {}
|
|||
|
|
''', b, R*C, RCo,
|
|||
|
|
alpha, alpha>epsilon,
|
|||
|
|
beta, beta>epsilon,
|
|||
|
|
gamma, gamma>epsilon))
|
|||
|
|
|