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utils.py
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utils.py
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"""Functions for Channel Modelling
Notes
-----
Based off of https://github.com/tchancarusone/Wireline-ChModel-Matlab
"""
#TODO: change comments to docstring
import numpy as np
import matplotlib.pyplot as plt
def abcd2dbca(ABCD):
A = ABCD[:,0,0]
B = ABCD[:,0,1]
C = ABCD[:,1,0]
D = ABCD[:,1,1]
DBCA = np.copy(ABCD)
DBCA[:,0,0] = D
DBCA[:,0,1] = B
DBCA[:,1,0] = C
DBCA[:,1,1] = A
return DBCA
def rlgc2abcd(r,l,g,c,d,f):
"""
Parameters
----------
r : TYPE
r = resistance along the line per unit length [?/m]
l : TYPE
inductance along the line per unit length [H/m]
g : TYPE
conductance shunting the line per unit length [S/m]
c : TYPE
capacitance shunting the line per unit length [F/m]
d : TYPE
transmissioin line length
f : TYPE
frequency, row vector.
Returns
-------
ABCD : TYPE
ABCD matrix.
"""
w = 2*np.pi*f
gammad = d*np.sqrt( np.multiply( (r+1j * np.multiply(w,l)),(g+ 1j * np.multiply(w,c)) ) );
z0 = np.sqrt( np.divide((r + 1j*np.multiply(w,l) ),(g+1j*np.multiply(w,c))) );
A = np.cosh(gammad)
B = np.multiply(z0,np.sinh(gammad))
C = np.divide(np.sinh(gammad),z0)
D = A
ABCD = np.zeros((f.size,2,2),dtype=np.complex_)
ABCD[:,0,0] = A
ABCD[:,0,1] = B
ABCD[:,1,0] = C
ABCD[:,1,1] = D
return ABCD
def impedance2abcd(z):
"""
Parameters
----------
z : TYPE
2-port network with series impedance z (z is array if frequency dependent)
Returns
-------
ABCD : TYPE
ABCD matrix
"""
l = z.size
ABCD = np.zeros((l,2,2),dtype=np.complex_)
ABCD[:,0,0] = np.ones(l)
ABCD[:,0,1] = z
ABCD[:,1,0] = np.zeros(l)
ABCD[:,1,1] = np.ones(l)
return ABCD
def admittance2abcd(y):
"""
Parameters
----------
y : TYPE
for 2-port network with shunt admittance y (y is array if frequency dependent)
Returns
-------
ABCD : TYPE
ABCD matrix.
"""
l = y.size
ABCD = np.zeros((l,2,2),dtype=np.complex_)
ABCD[:,0,0] = np.ones(l)
ABCD[:,0,1] = np.zeros(l)
ABCD[:,1,0] = y
ABCD[:,1,1] = np.ones(l)
return ABCD
def series(ABCD1, ABCD2, *arg):
"""
Series combination of two or more 2-port networks, ABCD1 followed by ABCD2
Parameters
----------
ABCD1: TYPE
ABCD matrix 1.
ABCD2: TYPE
ABCD matrix 2 following ABCD matrix 1.
*arg: tuples:
more ABCD matrices following ABCD2
Returns
-------
ABCD_cascade: TYPE
Cascading ABCD matrix of ABCD1 and ABCD2
"""
ABCD_cascade = ABCD1 @ ABCD2
if len(arg) != 0:
for i in range(len(arg)):
ABCD_cascade = ABCD_cascade @ arg[i]
return ABCD_cascade
def freq2impulse(H, f):
"""
Returns the impulse response, h, and (optionally) the step response,
hstep, for a system with complex frequency response stored in the array H
and corresponding frequency vector f. The time array is
returned in t. The frequency array must be linearly spaced.
Parameters
----------
H : TYPE
(complex) frequency response.
f : TYPE
frequency.
Returns
-------
h : TYPE
impluse response.
t : TYPE
time vector.
"""
Hd = np.concatenate((H,np.conj(np.flip(H[1:H.size-1]))))
h = np.real(np.fft.ifft(Hd))
hstep = np.convolve(h,np.ones(h.size))
hstep = hstep[0:h.size]
t= np.linspace(0,1/f[1],h.size+1)
t = t[0:-1]
return h,t,hstep
def s2abcd(sparams,f, z0=50):
"""
ABCD matrix description of a 2-port network with S-parameters
specified at the frequencies f in row vectors s11,s12,s21,s22
f should be a row vector
z0 is the characteristic impedance used for the S-parameter
measurements
Returns a structure containing the 2-port A,B,C,D matrix entries
at the frequencies in f: s.A, s.B, s.C, s.D
Parameters
----------
sparams : TYPE
sparams.
f : TYPE
frequency.
z0 : TYPE
characteristic impedance.
Returns
-------
ABCD : TYPE
ABCD matrix.
"""
ABCD = np.zeros((f.size,2,2),dtype=np.complex_)
s11 = sparams[:,0,0]
s12 = sparams[:,0,1]
s21 = sparams[:,1,0]
s22 = sparams[:,1,1]
ABCD[:,0,0] = ((1+s11)*(1-s22) + s12*s21) / (2*s21)
ABCD[:,0,1] = z0 * ((1+s11)*(1+s22) - s12*s21) / (2*s21)
ABCD[:,1,0] = (1/z0) * ((1-s11)*(1-s22) - s12*s21) / (2*s21)
ABCD[:,1,1] = ((1-s11)*(1+s22) + s12*s21) / (2*s21)
return ABCD
def abcd2s(ABCD, f, z0=50):
sparams = np.zeros((f.size,2,2),dtype=np.complex_)
A = ABCD[:,0,0]
B = ABCD[:,0,1]
C = ABCD[:,1,0]
D = ABCD[:,1,1]
s11 = (A + B/z0 - C*z0 - D) / (A + B/z0 + C*z0 + D)
s12 = 2*(A*D-B*C) / (A + B/z0 + C*z0 + D)
s21 = 2/(A + B/z0 + C*z0 + D)
s22 = (-A + B/z0 - C*z0 + D) / (A + B/z0 + C*z0 + D)
sparams[:,0,0] = s11
sparams[:,0,1] = s12
sparams[:,1,0] = s21
sparams[:,1,1] = s22
return sparams
def channel_coefficients(pulse_response, main_idx, t, samples_per_symbol, n_precursors, n_postcursors, title="Channel Coefficients", plot=True, all=False):
if all == False:
n_cursors = n_precursors + n_postcursors + 1
channel_coefficients = np.zeros(n_cursors)
else:
n_precursors = 0
n_postcursors = 0
while main_idx - samples_per_symbol*n_precursors > 0:
n_precursors = n_precursors + 1
while main_idx + samples_per_symbol*n_postcursors < len(pulse_response) - 2*samples_per_symbol:
n_postcursors = n_postcursors + 1
n_cursors = n_precursors + n_postcursors + 1
channel_coefficients = np.zeros(n_cursors)
t_vec = np.zeros(n_cursors)
xcoords = []
half_symbol = int(round(samples_per_symbol/2))
#find peak of pulse response
# main_idx = np.argmax(abs(pulse_response))
for cursor in range(n_cursors):
a = cursor - n_precursors
channel_coefficients[cursor] = pulse_response[main_idx+a*samples_per_symbol]
#for plotting
xcoords = xcoords + [1e9*t[main_idx+a*samples_per_symbol-half_symbol]]
t_vec[a+n_precursors] = t[main_idx + a*samples_per_symbol]
xcoords = xcoords + [1e9*t[main_idx+(n_postcursors+1)*samples_per_symbol-half_symbol]]
if plot==True:
#plot pulse response and cursor samples
plt.figure()
plt.plot(t_vec*1e9, channel_coefficients, 'o', label = 'Cursor samples')
plt.plot(t*1e9,pulse_response, label = 'Pulse response', linewidth=2)
plt.xlabel("Time [ns]", weight='bold')
plt.ylabel("Amplitude [V]", weight='bold')
ll = t[main_idx-samples_per_symbol*(n_precursors+2)]*1e9
ul = t[main_idx+samples_per_symbol*(n_postcursors+2)]*1e9
#print(ll,ul)
plt.xlim([ll,ul])
plt.title(title)
plt.legend()
for xc in xcoords:
plt.axvline(x=xc,color = 'grey',label ='UIs', ls='--')
return channel_coefficients
def pam4_input(samples_per_symbol, data_in, voltage_levels):
"""Genterates ideal, square, PAM-4 transmitter waveform from binary sequence
Parameters
----------
samples_per_symbol: int
timesteps per bit
length: int
length of desired time-domain signal
data_in: array
quaternary sequence to input, must be longer than than length/samples_per_symbol
voltage levels: array
definition of voltages corresponding to symbols.
voltage_levels[0] = voltage corresponding to 0 symbol,
voltage_levels[1] = voltage corresponding to 1 symbol
voltage_levels[2] = voltage corresponding to 2 symbol
voltage_levels[3] = voltage corresponding to 3 symbol
length: float
timestep of time domain signal
Returns
-------
signal: array
square waveform at trasmitter corresponding to data_in
"""
signal = np.zeros(samples_per_symbol*data_in.size)
for i in range(data_in.size):
if (data_in[i]==0):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[0]
elif (data_in[i]==1):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[1]
elif (data_in[i]==2):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[2]
elif (data_in[i]==3):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[3]
else:
print('unexpected symbol in data_in')
return False
if (i%100000 == 0):
print('i=',i)
return signal
def nrz_input(samples_per_symbol, data_in, voltage_levels):
"""Genterates ideal, square, NRZ (PAM-2) transmitter waveform from binary sequence
Parameters
----------
samples_per_symbol: int
timesteps per bit
length: int
length of desired time-domain signal
data_in: array
binary sequence to input, must be longer than than length/samples_per_symbol
voltage levels: array
definition of voltages corresponding to 0 and 1.
voltage_levels[0] = voltage corresponding to 0 bit,
voltage_levels[1] = voltage corresponding to 1 bit
length: float
timestep of time domain signal
Returns
-------
signal: array
square waveform at trasmitter corresponding to data_in
"""
signal = np.zeros(samples_per_symbol*data_in.size)
for i in range(data_in.size):
if (data_in[i] == 0):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[0]
elif(data_in[i] == 1):
signal[i*samples_per_symbol:(i+1)*samples_per_symbol] = np.ones(samples_per_symbol)*voltage_levels[1]
else:
print('unexpected symbol in data_in')
return False
#if (i%100000 == 0):
# print('i=',i)
return signal