# Chapter 4 : Angle Modulation¶

## Example 4.2 Page No : 199¶

In [1]:
import math

#Given angle modulated signal is x  =  3*math.cos[2*pi*(10**6)*t+2*math.sin(2*pi*10**3*t)]

#So, phase of the angle modulates signal is Q  =  2*pi*(10**6*t)+2*math.sin(2*pi*(10**3)*t)

#Insmath.tanmath.taneous frequency  =  dQ/dt  =  2*pi*(10**6)+ 4*pi*(10**3)*math.sin(2*pi*(10**3)*t)

#For Insmath.tanmath.taneous frequency at 0.25ms, Substituting t  =  0.25ms in Insmath.tanmath.taneous frequency
#Insmath.tanmath.taneous frequency is expressed as f1_rad for frequency in radians per second

#Insmath.tanmath.taneous frequency is expressed as f1_hz for frequency in hertz

print 'the Instantaneous frequency at time t = 0.25ms is ',f1_rad,' rad/sec  =  ',f1_hz,' Hz'

#For Insmath.tanmath.taneous frequency at 0.25ms, Substituting t  =  0.5ms in Insmath.tanmath.taneous frequency
#Insmath.tanmath.taneous frequency is expressed as f2rad for frequency in radians per second

#Insmath.tanmath.taneous frequency is expressed as f2hz for frequency in hertz

print 'the Instantaneous frequency at time t = 0.5ms is ',f2_rad,' rad/sec  =  ',f2_hz,' Hz'

#Maximum phase deviation  =  max[2*math.sin(2*pi*(10**3)*t)]  =  2*1
maxDp  =  2;

print 'Maximum phase deviation is ',maxDp,' rad'

#Maximum frequency deviation  =  max[4*pi*(10**3)*math.sin(2*pi*(10**3)*t)]  =  4*pi*(10**3)*1
maxDf  =  4*math.pi*(10**3)*1;

print 'Maximum frequency deviation is %.4f'%maxDf,' Hz'
#print ('in rad',maxDf,'Maximum frequency deviation is')

#In the textbook the calculated value of max frequency devaition is  =  2000 Hz, in reality the value  =  12566.371 Hz

the Instantaneous frequency at time t = 0.25ms is  6295751.67779  rad/sec  =   1002000.0  Hz
the Instantaneous frequency at time t = 0.5ms is  6283185.30718  rad/sec  =   1000000.0  Hz
Maximum phase deviation is  2  rad
Maximum frequency deviation is 12566.3706  Hz


## Example 4.4 Page No : 208¶

In [2]:
import math

#Given modulating signal m(t)  =  2*math.sin(2*pi*(10**3)*t), B for phase modulation Bp  =  10 & for fequency modulation Bf  =  10
Bp  =  10.
Bf  =  10.
#So Amplitude of modulating signal is Am = 2 metres
Am  =  2.
#Frequency of modulating signal is fm  =  1000 hertz
fm = 1000.

#Bandwidth  =  2*(1+B)*fm
#Bandwidth for phase modulation with modulating signal m(t) is bw_pm  =  2*(1+Bp)*fm
bw_pm  =  2.*(1+10)*1000
#Bandwidth for frequency modulation with modulating signal m(t) is bw_fm  =  2*(1+Bf)*fm
bw_fm  =  2*(1+10)*1000.

print 'Bandwidth for phase modulation ',bw_pm,' Hz'
print 'Bandwidth for frequency modulation ',bw_fm,' Hz'

#Bandwidth for phase & frequency modulation if frequency of modulating signal is doubled i.e fm  =  2000 hertz

#Bp & Bf after frequency of modulating signal is doubled

#Bp  =  kp*Am, observing the equation as there is no change in amplitude Bp  =  10
Bp  =  10.
#Bf  =  kf*Am/fm, observing the equation as there is change in frequency  Bf  =  10/2  =  5
Bf  =  5.

#Bandwidth for phase modulation if frequency of modulating signal is doubled is bw_double_pm  =  2*(1+Bp)*fm
bw_double_pm  =  2.*(1+10)*2000
#Bandwidth for frequency modulation if frequency of modulating signal is doubled is bw_double_fm  =  2*(1+Bf)*fm
bw_double_fm  =  2*(1+5)*2000.

print 'Bandwidth for phase modulation for doubled frequency ',bw_double_pm,' Hz'
print 'bandwidth for frequency modulation for doubled frequency ',bw_double_fm,' Hz'

#Bandwidth for phase & frequency modulation if amplitude of modulating signal is halfed i.e Am  =  1 metre

#Bp & Bf after amplitude of modulating signal is halfed

#Bp  =  kp*Am, observing the equation as there is change in amplitude Bp  =  10/2  =  5
Bp  =  5

#Bf  =  kf*Am/fm, observing the equation as there is change in amplitude Bf  =  5/2  =  2.5
Bf  =  2.5

#Bandwidth for phase modulation if frequency of modulating signal is doubled is bw_halfed_pm  =  2*(1+Bp)*fm
bw_halfed_pm  =  2*(1+5)*2000

#Bandwidth for frequency modulation if frequency of modulating signal is doubled is bw_halfed_fm  =  2*(1+Bf)*fm
bw_halfed_fm  =  2*(1+2.5)*2000

print 'Bandwidth for phase modulation for halfed amplitude ',bw_halfed_pm,' Hz'
print 'Bandwidth for frequency modulation for halfed amplitude ',bw_halfed_fm,' Hz'

Bandwidth for phase modulation  22000.0  Hz
Bandwidth for frequency modulation  22000.0  Hz
Bandwidth for phase modulation for doubled frequency  44000.0  Hz
bandwidth for frequency modulation for doubled frequency  24000.0  Hz
Bandwidth for phase modulation for halfed amplitude  24000  Hz
Bandwidth for frequency modulation for halfed amplitude  14000.0  Hz