Finished ECOMMS homework 3

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Aidan Sharpe
2024-11-11 19:15:36 -05:00
parent 660744cf30
commit 655a0ecfde
6 changed files with 43 additions and 17 deletions

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### 3c
If the RF waveform appears across a 50$\Omega$ load, determine the average power and the PEP.
The average power of the signal is:
$$\langle s^2(t) \rangle = \frac{1}{T} \int\limits_{-T/2}^{T/2} 500\cos(\omega_c t + 20\cos(\omega_1 t)) dt$$
The average power and the PEP are the same: $\frac{A_c^2}{2} \times \frac{1}{50} = 2.5$kW.

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import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
f_c = 100E+6
f_m = 1E3
T_c = 1/f_c
f_s = 1E9
T_s = 1/f_s
A_c = 500
D_p = 100
D_f = 1E+6
omega_m = 2*np.pi*f_m
omega_c = 2*np.pi*f_c
# Time samples to 10 seconds at a samplig frequency of 8kHz
t = np.arange(0,10*T_c,T_s)
m_p = 0.2*np.cos(omega_m * t)
m_f = -2E-5*omega_m*np.sin(omega_m * t)
M_f = 2E-5*np.cos(omega_m*t)
theta = D_f * M_f
# The phase modulated signal
s_p = A_c*np.cos(omega_c*t + D_p*m_p)
s_f = A_c*np.cos(omega_c*t + theta)
c = A_c*np.cos(omega_c *t)
plt.plot(t, s_p, label="Phase Modulated Signal")
plt.plot(t, s_p-c)
#plt.plot(t, s_f, label="Frequency Modulated Signal")
plt.show()