180 lines
4.1 KiB
Python
180 lines
4.1 KiB
Python
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# coding: utf-8
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from __future__ import print_function, division, unicode_literals
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from lab import *
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import numpy as np
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import uncertainties.umath as um
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import matplotlib.pyplot as plt
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##
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## Internal resistance
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##
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Req = array(2.021, 3.048) / \
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array(2.25e-6, 1.19e-6) # potential/current
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Rn = array(0.98e6, 3.322e6) # nominal value
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Rv = sample(Rn*Req/(Rn - Req)).val() # internal resistance
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Req = array(1.101, 1.104, 1.108) / \
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array(70.08e-3, 34.545e-3, 23.555e-3) # potential/current
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Rn = array(9.88, 21.66, 32.64) # nominal value
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Ra = sample(Req - Rn).val() # internal resistance
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print(mformat("""
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Internal resistance:
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{} Ω (voltmeter)
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{} Ω (amperometer)
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""", Ra, Rv))
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##
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## Ohm Law
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##
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# 10Ω resistor
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I = array(44.10, 52.65, 61.60, 66.00, 70.60, 75.07, 79.12, 83.66,
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88.39, 92.41, 96.44, 101.28, 105.69, 109.83, 114.23, 118.67,
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123.35, 127.40, 132.13, 140.52)/1e3
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V = array(0.432, 0.515, 0.604, 0.646, 0.691, 0.734, 0.774, 0.820, 0.864, 0.904,
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0.944, 0.991, 1.034, 1.074, 1.117, 1.161, 1.207, 1.247, 1.293, 1.375)
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# linear fit y=a+bx where y=V and x=I
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x = np.linspace(40, 145, 100)/1e3
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a, b = linear(I, V, 1e-3)
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f = lambda x: a.n + b.n*x
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R = b
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alpha = chi_squared_fit(I, V, f, sigma=1e-3)
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# plot y=a+bx
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plt.figure(1)
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plt.xlabel('I (A)')
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plt.ylabel('dV (V)')
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plt.scatter(I, V, color='#ba6b88')
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plt.plot(x, f(x), '#ba6b88')
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plt.show()
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print(mformat('''
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R={} Ω
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χ² test:
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α={:.3f}, α>ε: {}
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''', R, alpha, alpha>epsilon))
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# 1kΩ resistor
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V = array(0.738, 0.828, 0.922, 1.011, 1.103, 1.198, 1.288, 1.377, 1.472, 1.568,
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1.658, 1.751, 1.846, 1.936, 2.028, 2.114, 2.213, 2.300, 2.391, 2.487)
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I = array(0.7445, 0.8350, 0.9304, 1.0194, 1.1127, 1.2089, 1.2993, 1.3897, 1.4850,
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1.5824, 1.6732, 1.7670, 1.8625, 1.9537, 2.0474, 2.1339, 2.2334, 2.3213,
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2.4134, 2.5099)/1e3
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# linear fit y=a+bx where y=V and x=I
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x = np.linspace(0.7, 2.6, 100)/1e3
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a, b = linear(I, V, 1e-3)
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f = lambda x: a.n + b.n*x
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R = b
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alpha = chi_squared_fit(I, V, f, sigma=1e-3)
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# plot y=a+bx
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plt.figure(2)
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plt.xlabel('I (mA)')
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plt.ylabel('dV (V)')
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plt.scatter(I*1e3, V, color='#3e49ba')
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plt.plot(x*1e3, f(x), '#3e49ba')
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plt.show()
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print(mformat('''
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R={} Ω
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χ² test:
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α={:.3f}, α>ε: {}
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''', R, alpha, alpha>epsilon))
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# 1MΩ resistor
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V = array(1.012, 1.118, 1.214, 1.317, 1.421, 1.524, 1.621, 1.722, 1.823, 1.924,
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2.030, 2.130, 2.230, 2.330, 2.434, 2.534, 2.640, 2.739, 2.845, 2.940)
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I = array(1.12, 1.24, 1.34, 1.46, 1.58, 1.69, 1.80, 1.91, 2.03, 2.14, 2.26, 2.37,
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2.47, 2.58, 2.71, 2.82, 2.94, 3.04, 3.16, 3.26)/1e6
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# linear fit y=a+bx where y=V and x=I
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x = np.linspace(1.10, 3.30, 100)/1e6
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a, b = linear(I, V, 5e-3)
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f = lambda x: a.n + b.n*x
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R = b
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alpha = chi_squared_fit(I, V, f, sigma=5e-3)
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# plot y=a+bx
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plt.figure(3)
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plt.xlabel('I (muA)')
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plt.ylabel('dV (V)')
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plt.scatter(I*1e6, V, color='#d5b647')
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plt.plot(x*1e6, f(x), '#d5b647')
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plt.show()
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print(mformat('''
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R={} Ω
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χ² test:
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α={:.3f}, α>ε: {}
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''', R, alpha, alpha>epsilon))
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##
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## Diode
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##
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V = array(3.172, 3.293, 3.393, 3.471, 3.529, 3.579, 3.619, 3.651)
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I = array(1.22, 86.77, 323.60, 749.20, 1260.20, 1880.90, 2597.5, 3351.45)/1e6
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sigmaI = 3e-5
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# fit
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x = np.linspace(3.0, 3.7, 100)
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shockley = lambda V, a, b, c: a*V + b*(np.exp(c*V) - 1)
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f, (a, b, c) = curve(V, I, shockley, sigmaI, guess=[1, 1e-10, 10])
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y = np.linspace(0, 5000, 100)/1e6
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threshold = lambda I, Vth: Vth
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h, (Vth,) = curve(I[4:], V[4:], threshold, sigmaI)
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# parameters
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e = 1.602e-19 # elementary charge
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k = 1.380e-23 # boltzmann constant
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T = 298 # temperature
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g = e/(k*T*c)
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# χ² test
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alpha = chi_squared_fit(V, I, f, sigmaI, s=3)
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print(mformat('''
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a: {} Ω⁻¹
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I₀: {} A
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g: {}
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Vth: {} V
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χ² test:
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α={:.3f}, α>ε: {}
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''', a, b, g, Vth, alpha, alpha>epsilon))
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# plot I - V
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plt.figure(4)
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plt.title('Shockley law')
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plt.xlabel('ΔV (V)')
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plt.ylabel('I (mA)')
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# shockley curve
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plt.scatter(V, I*1e3, color='#3363aa')
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plt.plot(x, f(x)*1e3, color='#2a518c')
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# threshold line
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plt.plot(np.repeat(h(y), len(y)), y*1e3, color='#91375b')
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plt.text(Vth.n+0.01, 0.01, 'Vth')
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plt.show()
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