60 lines
1.3 KiB
Python
60 lines
1.3 KiB
Python
# coding: utf-8
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from __future__ import print_function
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from sympy import *
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from sympy.utilities.lambdify import lambdify
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import matplotlib.pyplot as plt
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import numpy as np
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##
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## Transfer function calculator
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##
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I # imaginary unit
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i = Symbol('i', positive=True, real=True) # current
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R = Symbol('R', positive=True, real=True) # resistance
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Rl = Symbol('Rl', positive=True, real=True) # resistance
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L = Symbol('L', positive=True, real=True) # inductance
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C = Symbol('C', positive=True, real=True) # capacitance
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w = Symbol('w', positive=True, real=True) # angular frequency
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# impedances
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Zl = Rl+I*w*L
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Zc = 1/(I*w*C)
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Zr = R
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# input/output tensions
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Va = (Zc+Zr+Zl)*i
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Vb = (Zc)*i
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# transfer function
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H = Vb/Va
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phase = simplify(atan2(re(H), im(H)))
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magn = simplify(sqrt(re(H)**2 + im(H)**2))
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print('arg H =', phase)
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print(' |H| =', magn)
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##
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## Plot function
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##
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p = (9.94e3, 20, 3.8e-3, 4.45e-8) # R,Rl,L,C
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x = np.linspace(100, 150e3, 1500)
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f = np.vectorize(lambda nu: lambdify((w, R, Rl, L, C), magn)(2*pi*nu, *p))
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g = np.vectorize(lambda nu: lambdify((w, R, Rl, L, C), phase)(2*pi*nu, *p))
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plt.subplot(2, 1, 1)
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plt.title('transfer function')
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plt.xscale('log')
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plt.ylabel('magnitude')
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plt.plot(x, f(x))
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plt.subplot(2, 1, 2)
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plt.xscale('log')
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plt.plot(x, g(x))
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plt.xlabel('frequency (Hz)')
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plt.ylabel('phase (rad)')
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plt.show()
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