Chapter 6 : Amplitude Modulation Methods

Example 6.1 Page No : 186

In [1]:
# Variables
#All frequencies in kHz
fc = 1*10**3; #in kHz
W = 15;  

# Calculations and Results
DSBl = fc-W;  #lowest freq of DSB signal
DSBh = fc+W;  #highest freq of DSB signal
print '(a)  The range of freq is from ',DSBl,'to',DSBh

BT = 2*W;
print '(b)  Transmission bandwidth is ',BT
(a)  The range of freq is from  985 to 1015
(b)  Transmission bandwidth is  30

Example 6.2 Page No : 186

In [2]:
# Variables
#All frequencies in kHz
fi = 250.;  #input freq

# Calculations and Results
LSB = [fi-1,fi-3,fi-5];
USB = [fi+1,fi+3,fi+5];
print '(a)  The upper sideband and lower sideband ,USB:' ,USB,'and LSB:',LSB
BT = 2*5;
print 'The net transmission bandwidth is ',BT
(a)  The upper sideband and lower sideband ,USB: [251.0, 253.0, 255.0] and LSB: [249.0, 247.0, 245.0]
The net transmission bandwidth is  10

Example 6.3 Page No : 190

In [3]:
# Variables
fc = 1*10**3; #in kHz
W = 15;  

# Calculations and Results
LSBl = fc-W;  #lowest freq of LSB
USBh = fc+W;  #highest freq of USB
print '(a)  The range of freq(in kHz) for LSB is from ',LSBl,'to',fc
print '(b)  The range of freq(in kHz) for USB is from ',fc,'to',USBh
BT = W;
print '(b)  Transmission bandwidth is ',BT
(a)  The range of freq(in kHz) for LSB is from  985 to 1000
(b)  The range of freq(in kHz) for USB is from  1000 to 1015
(b)  Transmission bandwidth is  15

Example 6.4 Page No : 190

In [4]:
# Variables
#All frequencies in kHz
fi = 250;  #input freq

# Calculations and Results
LSB = [fi-1, fi-3, fi-5];
USB = [fi+1, fi+3, fi+5];
print '(a)  For LSB transmission freq are' ,LSB
print '(b)  For USB transmission freq are',USB

W = 5;
BT = W;
print '(c)  The transmission bandwidth is ',BT
(a)  For LSB transmission freq are [249, 247, 245]
(b)  For USB transmission freq are [251, 253, 255]
(c)  The transmission bandwidth is  5

Example 6.5 Page No : 195

In [6]:
from numpy import array
#All frequencies in kHz
#refer Ex 6.4
fi = 250;  #input freq
LSB = array([fi-1, fi-3, fi-5]);  #from Ex 6.4

# Calculations
fc = 250;  #carrier freq
f0sum = fc+LSB;
f0diff = fc-LSB;

# Results
print '(a)  The output frequencies (in kHz) are ',f0diff,f0sum
print '(b)  At low pass filter,the actual frequencies (in kHz) are ',f0diff
(a)  The output frequencies (in kHz) are  [1 3 5] [499 497 495]
(b)  At low pass filter,the actual frequencies (in kHz) are  [1 3 5]

Example 6.6 Page No : 195

In [7]:
from numpy import array

# Variables
#All frequencies in kHz
fi = 250;  #input freq
USB = array([fi+1, fi+3, fi+5]); #from Ex 6.4
#
# Calculations
fc = 250;  #carrier freq
f0sum = fc+USB;
f0diff = USB-fc;

# Results
print '(a)  The output frequencies (in kHz) are ',f0sum,f0diff
print '(b)  At low pass filter,the actual frequencies (in kHz) are',f0diff
(a)  The output frequencies (in kHz) are  [501 503 505] [1 3 5]
(b)  At low pass filter,the actual frequencies (in kHz) are [1 3 5]

Example 6.7 Page No : 195

In [8]:
from numpy import array

#All frequencies in kHz
#refer Ex 6.4

# Variables
fi = 250.;  #input freq
LSB = array([fi-1, fi-3, fi-5]);  #from Ex 6.7

# Calculations
fc = 250.1;  #carrier freq
f0sum = fc+LSB;
f0diff = fc-LSB;

# Results
print '(a)  The output frequencies (in kHz) are ',f0sum,f0diff
print '(b)  At low pass filter,the frequencies (in kHz) are ',f0diff
(a)  The output frequencies (in kHz) are  [ 499.1  497.1  495.1] [ 1.1  3.1  5.1]
(b)  At low pass filter,the frequencies (in kHz) are  [ 1.1  3.1  5.1]

Example 6.8 Page No : 200

In [10]:
# Variables
fc = 250;  #carrier freq

# Calculations and Results
LSB = [fc-1, fc-3, fc-5];
USB = [fc+1, fc+3, fc+5];
print '(a)  The spectrum contains following freq.LSB:' ,LSB
print 'USB:',USB,
print 'carrier:',fc

W = 5;
BT = 2*W;
print 'The transmission bandwidth is ',BT
(a)  The spectrum contains following freq.LSB: [249, 247, 245]
USB: [251, 253, 255] carrier: 250
The transmission bandwidth is  10

Example 6.9 Page No : 200

In [11]:
# Variables
#All voltage in V
m = 0.6;   #modulation factor
A = 100;   #peak carrier level (in V)

# Calculations
Vmax = A*(1+m);
Vmin = A*(1-m);

# Results
print 'The maximum and minimum values of positive envelope is','Vmax:',Vmax,'Vmin:',Vmin
The maximum and minimum values of positive envelope is Vmax: 160.0 Vmin: 40.0

Example 6.10 Page No : 201

In [12]:
# Variables
Ratio = .5/2;  #  Ratio = Vmin/Vmax

# Calculations
m = (1-Ratio)/(1+Ratio);   #modulation factor

# Results
print 'The modulation factor is ',m
print 'The %age modulation is ',m*100
The modulation factor is  0.6
The %age modulation is  60.0

Example 6.11 Page No : 201

In [13]:
# Calculations
def sideband_amplitude(m,A):
    return m*A/2;  #As:sideband amplitude
               #m:modulation factor
               #A:carrier amplitude
# Variables
A = 10.;
m = 0;

# Results
print '(a) For m = 0, sideband amplitude is ',sideband_amplitude(m,A)
m = 0.5;
print '(b) For m = 0.5, sideband amplitude is ',sideband_amplitude(m,A)
m = 1.;
print '(c) For m = 1, sideband amplitude is ',sideband_amplitude(m,A)
(a) For m = 0, sideband amplitude is  0.0
(b) For m = 0.5, sideband amplitude is  2.5
(c) For m = 1, sideband amplitude is  5.0

Example 6.12 Page No : 203

In [14]:
# Variables
fc = 455.;  #in kHz

# Calculations and Results
Tc = (1./fc)*10**3;  #in micro sec
print '(a)  The carrier period is',Tc,'micro s'

tau = 10*Tc;  #in micro sec
print 'The time consmath.tant is selected 10Tc:',tau,'micro s'

C = 0.01*10**-6;  #in F
R = (tau*10**-6)/C;  #ohm
print 'R is determined',R,'ohm'

W = 5.;  #in kHz
Tm = 1/W*10**3;  #micro sec
print 'The shortest modulation period Tm = ',Tm,'micro sec'
(a)  The carrier period is 2.1978021978 micro s
The time consmath.tant is selected 10Tc: 21.978021978 micro s
R is determined 2197.8021978 ohm
The shortest modulation period Tm =  200.0 micro sec

Example 6.14 Page No : 208

In [15]:
# Variables
A = 200.;  # in Volts
R = 50.;   #in ohm

# Calculations and Results
P = A**2/(4*R);  #in W
print '(a)   The sverage power is ',P,'W'

Pp = A**2/(2*R);  #in W
print '(b)   The peak envelop power is ',Pp,"W"
(a)   The sverage power is  200.0 W
(b)   The peak envelop power is  400.0 W

Example 6.15 Page No : 208

In [16]:
import math 

# Variables
P = 1000.;  #in watts
R = 50.;  #in ohm

# Calculations
Vrms = math.sqrt(R*P);  #in V
Irms = math.sqrt(P/R);  #in A

# Results
print 'The unmodulated rms carrier voltage is ',Vrms,"V"
print 'The unmodulated rms carrier current is ',Irms,"A"
The unmodulated rms carrier voltage is  223.60679775 V
The unmodulated rms carrier current is  4.472135955 A

Example 6.16 Page No : 209

In [17]:
import math 

# Calculations
#All power in Watts
Pc = 1000.;

def avg_P(m):           #function for total average power
    return (1+(m**2/2))*Pc;

def peak_P(m):          #function for peak power
    return (1+m)**2*Pc;

def SB_P(m):          #function for SB power
    return avg_P(m)-Pc;

def lay(m):          #function for print laying table
    table = [m*100, avg_P(m), peak_P(m), SB_P(m)];
    print (table);


# Results
print ('Summary for the result is print layed in the table ');
print ('Mod**n_%  Avg_Pwr  Peak_Pwr SB_Pwe');
m = 0.;   #for m = 0
lay(m);
m = 0.5;   #for m = 0.5
lay(m);
m = 1.;      #for m = 1
lay(m);
Summary for the result is print layed in the table 
Mod**n_%  Avg_Pwr  Peak_Pwr SB_Pwe
[0.0, 1000.0, 1000.0, 0.0]
[50.0, 1125.0, 2250.0, 125.0]
[100.0, 1500.0, 4000.0, 500.0]

Example 6.17 Page No : 210

In [18]:
import math 

# Variables
#All power in Watts
#All voltage in volts
#All current in ampere
R = 50;   
m = 0.5;
P = 1125;  #for m = 0.5

# Calculations and Results
Vrms = math.sqrt(R*P);
Irms = math.sqrt(P/R);
print '(a)  For m = 0.5, Vrms and Irms are:',Vrms,'V',Irms,'A'
m = 1.;
P = 1500.;  #For m = 1
Vrms = math.sqrt(R*P);
Irms = math.sqrt(P/R);
print '(b)  For m = 1, Vrms and Irms are:',Vrms,'V',Irms,'A'
(a)  For m = 0.5, Vrms and Irms are: 237.170824513 V 4.69041575982 A
(b)  For m = 1, Vrms and Irms are: 273.861278753 V 5.47722557505 A