Chapter 7: Radio Transmitters and Receivers

Example 7.1, page no. 153

In [2]:
# Variable Declaration
fs1    = 1.00*pow(10,6)             # Sampling Frequency (Hz)
fs2    = 25.00*pow(10,6)            # Sampling Frequency (Hz)
fi     = 455.00*pow(10,3)           # Intermediate Frequency (Hz)
Q      = 100.00                     # Loaded Q of the antenna coupling circuit                

# Calculation
import math                         # Math Library
fsi1   = fs1+2*fi                   # Image Frequency (Hz)
rho1   = fsi1/fs1-fs1/fsi1          # Constant 1
alpha1 = math.sqrt(1+pow(Q*rho1,2)) # Rejection Ratio 1
fsi2   = fs2+2*fi                   # Image Frequency (Hz) 
rho2   = fsi2/fs2-fs2/fsi2          # Constant 2
alpha2 = math.sqrt(1+pow(Q*rho2,2)) # Rejection Ratio 2

# Result
print "(a) Image Frequency, fsi   =",fsi1/pow(10,3),"kHz"
print "                     rho   =",round(rho1,3)
print "    Image Rejection, Alpha =",round(alpha1,1)
print "(b) Image Frequency, fsi   =",fsi2/pow(10,6),"MHz"
print "                     rho   =",round(rho2,4)
print "    Image Rejection, Alpha =",round(alpha2,2)

(a) Image Frequency, fsi   = 1910.0 kHz
                     rho   = 1.386
    Image Rejection, Alpha = 138.6
(b) Image Frequency, fsi   = 25.91 MHz
                     rho   = 0.0715
    Image Rejection, Alpha = 7.22

Example 7.2, page no. 153

In [3]:
# Variable Declaration
alpha1   = 138.6                                 # Image Rejection From Example 7.1
alpha2   = 7.22                                  # Image Rejection From Example 7.1
rho      = 0.0715                                # Constant From Example 7.1
Q        = 100.00                                # Loaded Q From Example 7.1
fsi_dash = 1.91*pow(10,6)                        # Image Frequency (Hz)
fs_dash  = 1.00*pow(10,6)                        # Sampling Frequency 1 (Hz)
fs       = 25.00*pow(10,6)                       # Sampling Frequency 2 (Hz)


# Calculation
import math                                      # Math Library
Q_dash   = math.sqrt(pow(alpha1/alpha2,2)-1)/rho # Loaded Q of the RF amplifier
fi_dash  = (fsi_dash/fs_dash*fs-fs)/2            # Intermediate Frequency (Hz) 

# Result
print "(a) The Q of the circuit is",round(math.sqrt(Q*Q_dash)),", which is the geometric mean of",round(Q),"and",round(Q_dash)
print "(b) Intermediate Frequency, fi_dash =",round(fi_dash/pow(10,6),1),"MHz"

(a) The Q of the circuit is 164.0 , which is the geometric mean of 100.0 and 268.0
(b) Intermediate Frequency, fi_dash = 11.4 MHz

Example 7.3, page no. 164

In [4]:
# Variable Declaration
R1    = 110.00*pow(10,3)                # RESISTANCE 1 (Ohms)
R2    = 220.00*pow(10,3)                # RESISTANCE 2 (Ohms)
R3    = 470.00*pow(10,3)                # RESISTANCE 3 (Ohms)
R4    = 1.00*pow(10,6)                  # RESISTANCE 4 (Ohms)

# Calculation
import math                             # Math Library
Rc    = R1+R2                           # Resistance (Ohm)
Zm    = R2*R3*R4/(R2*R3+R3*R4+R2*R4)+R1 # Impedance (Ohm)
m_max = Zm/Rc                           # Maximum Modulation Index

# Result
print "Maximum Modulation Index, m_max =",round(m_max*pow(10,2)),"%"

Maximum Modulation Index, m_max = 73.0 %