RC circuit response for chirp signal
This post presents next experiment with RC circuit. Response for chirp signal will be simulated and measured. Firstly chirp signal will be described. Then will be presented simulation and experiment. Jupyter notebook could be found here
Chirp is a sinus signal that constantly change its frequency:
where is amplitued, - is length of signal, is frequency at time 0, and at time . It is very useful for determining the Bode characteristic of dynamics system.
import numpy
import scipy
import matplotlib.pyplot as plt
from sympy import init_session
init_session()
import scipy.signal as sig
import scipy.optimize as opt
from IPython.display import Image
import scipy.signal as sig
%matplotlib inline
IPython console for SymPy 1.0 (Python 3.5.2-64-bit) (ground types: python)
These commands were executed:
>>> from __future__ import division
>>> from sympy import *
>>> x, y, z, t = symbols('x y z t')
>>> k, m, n = symbols('k m n', integer=True)
>>> f, g, h = symbols('f g h', cls=Function)
>>> init_printing()
Documentation can be found at http://docs.sympy.org/1.0/
For experimet RC circuit form last post was used. Firstly transfer function was created:
RC = 0.0085
G = sig.TransferFunction(np.array([1]), np.array([RC, 1]))
Then chirp signal was generated. Sampling frequency was choosen to so maximum generated frequency is (Nyquist frequency).
T = 5
Ts = 0.001
f0 = 1
f1 = 500
t=numpy.linspace(0,T,T/Ts+1)
u=sig.chirp(t,f0=f0,t1=T,f1=f1)
STM32 contain 12 bit DAC. So signal must be shifted and scaled to take values beetween 0 and 4095. Then it will be rounded to integers:
u_int = (u+1)/2*4095
u_int = u_int+0.5
u_int = u_int.astype(int)
In experimental set-up range of output voltage is beetween and :
u_v = u_int*3.3/4095.0
Now all data for simulation are prepared. Outcome is presented on belowe chart. Blue curve is input signal and green output. This plot show how amplitued of output signal is determined by its frequency. It is so called Bode characteristics. RC circuit is a low pass filter.
f = numpy.linspace(f0,f1, T/Ts+1)
y=G.output(u_v,T=t)
fig = plt.axes()
input, = fig.plot(f,u_v,label='input')
output, = fig.plot(f,y[1],label='output')
fig.set_xlabel('f, Hz')
fig.set_ylabel('Amplitude, V')
plt.legend(handles=[input, output])
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=3, mode="expand", borderaxespad=0.)
<matplotlib.legend.Legend at 0x14f9e379c50>
Now header file with chipr signal will be generated. It will be used in microcontroler to generate testing signal:
file_chirp = open('chirp.h', 'w')
file_chirp.write('#ifndef CHIRP_H\n')
file_chirp.write('#define CHIRP_H\n')
file_chirp.write('const uint16_t chirp_size = ' + repr(np.size(u_int)) + ';\n')
file_chirp.write('const uint16_t chirp[] = {\n')
for value in u_int:
file_chirp.write(' ' + repr(value) + ',\n')
file_chirp.write('};\n')
file_chirp.write('#endif\n')
file_chirp.write('\n')
file_chirp.close()
STM32F429DISC0 discovery generate signal and measuring response of circuit. Configuration was generated in STM32CubeMX and code was written in Atolic TrueStudio. Project is avaiable on github. Below figure show connection beetween STM32 and RC:
Firstly DAC output was connected directly to ADC input. Just to prove if it work. The result is show belowe:
data_dac = numpy.transpose(numpy.loadtxt('dac.txt'));
data_dac = data_dac*3.3/4095.0
fig = plt.axes()
fig.plot(t, data_dac)
fig.set_xlabel('t, s')
fig.set_ylabel('Amplitude, V')
<matplotlib.text.Text at 0x14f9cf3c470>
Then DAC and ADC was connected to RC circuit. Belowe figure show simulated and real data.
data_rc = numpy.transpose(numpy.loadtxt('rc.txt'));
data_rc = data_rc*3.3/4095.0
fig = plt.axes()
simulated, = fig.plot(f, y[1], label='simulated')
real, = fig.plot(f, data_rc, label='real')
fig.set_xlabel('f, Hz')
fig.set_ylabel('Amplitude, V')
plt.legend(handles=[input, output])
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=3, mode="expand", borderaxespad=0.)
<matplotlib.legend.Legend at 0x14f9e2fce48>
For clarity view only the wraper was drawn:
max_data = numpy.r_[True, data_rc[1:] > data_rc[:-1]] & numpy.r_[data_rc[:-1] > data_rc[1:], True]
max_sim = numpy.r_[True, y[1][1:] > y[1][:-1]] & numpy.r_[y[1][:-1] > y[1][1:], True]
fig = plt.axes()
simulated, = fig.plot(f[o2], y[1][o2]-3.3/2, label='simulated')
real, = fig.plot(f[o1], data_rc[o1]-3.3/2, label='real')
fig.set_xlabel('f, Hz')
fig.set_ylabel('Amplitude, V')
plt.legend(handles=[input, output])
plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
ncol=3, mode="expand", borderaxespad=0.)
<matplotlib.legend.Legend at 0x14f9e5ee7b8>
For lower frequences amplitued is lower then simulated. For biger probably noise is bigger then system output.