# Chapter 15 - Communication System¶

## Example E1 - Pg 773¶

In [1]:
#Ex15_1 Pg-773
#calculte Total power
Pc=10000. #carrier input power in watt
m=30./100. #modulation of 30%
print '%s' %("Total power = carrier power*(1+m**2/2)")
Pt=Pc*(1.+m**2./2.) #total power
print '%s %.2f' %("            = W",Pt*1e-3)

Total power = carrier power*(1+m**2/2)
= W 10.45


## Example E2 - Pg 774¶

In [2]:
#Ex15_2 Pg-774
#calculte Total current
import math
Ic=100. #carrier current in A
m=80./100. #modulation of 80%
print '%s' %("Total current = carrier current*(1+m**2/2)")
It=Ic*math.sqrt(1.+m**2./2.) #total power
print '%s %.1f' %("              = A",It)
change_I=It-Ic #change in current
print '%s %.1f' %("Therefore, increase in current due to modulation = A",change_I)

Total current = carrier current*(1+m**2/2)
= A 114.9
Therefore, increase in current due to modulation = A 14.9


## Example E3 - Pg 774¶

In [3]:
#Ex15_3 Pg-774
#calculte Modulation Factor,Amplitude of each sideband,Frequenc of sidebands,Bandwidth of the wave
Em=5. #modulated wave amplitude
Ec=100. #carrier wave amplitude
Fm=50. #frequency of modulated wave
Fc=10.*10.**(3.) #frequency of carrier wave
print '%s' %("(1)Modulation Factor")
m=Em/Ec #modulation factor
per_m=m*100. #modulation factor in percentage
print '%s %.0f' %("m =",per_m)
print '%s' %("(2)Amplitude of each sideband = m*Ec/2")
Amp=m*Ec/2. #amplitude of each sideband
print '%s %.1f' %("=",Amp)
USB=Fc+Fm #upper side band
LSB=Fc-Fm #lower side band
print '%s' %("(3)Frequenc of sidebands")
print '%s %.0f' %("USB = Hz",USB)
print '%s %.0f' %("LSB = Hz",LSB)
print '%s' %("(4) Bandwidth of the wave")
BW=2*Fm #Bandwidth
print '%s %.0f' %("BW =",BW)

(1)Modulation Factor
m = 5
(2)Amplitude of each sideband = m*Ec/2
= 2.5
(3)Frequenc of sidebands
USB = Hz 10050
LSB = Hz 9950
(4) Bandwidth of the wave
BW = 100


## Example E4 - Pg 774¶

In [4]:
#Ex15_4 Pg-774
#calculte Modulation factor
Vmax=600. #peak to peak voltage
Vmin=100. #valley to valley voltage
print '%s' %("From figure 15.49, we have")
m=(Vmax-Vmin)/(Vmax+Vmin) #modulation factor
per_m=m*100. #modulation factor in percentage
print '%s %.1f' %("Modulation factor = ",per_m )

From figure 15.49, we have
Modulation factor =  71.4


## Example E5 - Pg 775¶

In [5]:
#Ex15_5 Pg-775
#calculte Modulation factor,Carrier Amplitude,omega,Signal frequency,Emax ,Emin,BW
import math
print '%s' %("The standard equation of AM wave is")
print '%s' %(" e = Ec*(1+m*sin(omega_m*t)*sin(omega_c*t)) -->eqn 1")
print '%s' %("Given the equation")
print '%s' %(" e = 20*(1+0.7*sin(6280*t)*sin(628000*t))   --eqn 2")
print '%s' %("Comparing eqn 1 and eqn 2 one obtains")
print '%s' %("(1)Modulation factor, m = 0.7")
m=0.7 #modulation factor
print '%s' %("(2)Carrier Amplitude, Ec = 20 V")
Ec=20. #carrier wave amplitude in V
print '%s' %("(3)omega_m = 6280")
omega_m=6280 #modulating frequency
Fm=omega_m/(2.*math.pi) #signal frequency
print '%s %.0f' %("Signal frequency = kHz",Fm*1e-3)
omega_c=628000. #carrier frequency in Hz
Fc=omega_c/(2.*math.pi)
print '%s %.0f' %("(4)Signal frequency = kHz",Fc*1e-3)
Emax=Ec+m*Ec #minimum amplitude of wave
print '%s %.0f' %("(5)Emax = V",Emax)
Emin=Ec-m*Ec #minimum amplitude of wave
print '%s %.0f' %("(5)Emin = V",Emin)
BW=2.*Fm #Bandwidth
print '%s %.0f' %("(6)BW = kHZ",BW*1e-3)

The standard equation of AM wave is
e = Ec*(1+m*sin(omega_m*t)*sin(omega_c*t)) -->eqn 1
Given the equation
e = 20*(1+0.7*sin(6280*t)*sin(628000*t))   --eqn 2
Comparing eqn 1 and eqn 2 one obtains
(1)Modulation factor, m = 0.7
(2)Carrier Amplitude, Ec = 20 V
(3)omega_m = 6280
Signal frequency = kHz 1
(4)Signal frequency = kHz 100
(5)Emax = V 34
(5)Emin = V 6
(6)BW = kHZ 2


## Example E6 - Pg 776¶

In [6]:
#Ex15_6 Pg-776
#calculte Total power
Pc=10000. #carrier power in watt
m=0.9 #modulation factor
print '%s' %("We have")
print '%s' %("Total power = carrier power*(1+m**2/2)")
Pt=Pc*(1.+m**2./2.) #total power
print '%s %.0f' %("            = kW",Pt*1e-3)
print '%s' %("This will be the maximum power handeled by the transmitter.\nNow,increased unmodulated carrier power can be obtained by")
m=40./100. #modulation in terms of percentage
Pt=14000. #total power
Pc=Pt/(1.+m**2./2.) #neew carrier power
print '%s %.2f' %("Pc = kW",Pc*1e-3)

We have
Total power = carrier power*(1+m**2/2)
= kW 14
This will be the maximum power handeled by the transmitter.
Now,increased unmodulated carrier power can be obtained by
Pc = kW 12.96


## Example E7 - Pg 776¶

In [7]:
#Ex15_7 Pg-776
#calculte standard equations for modulated voltage wave
import math
print '%s' %("Given the equation")
print '%s' %("\nE = 100*sin(628000*t)+25*sin(621720*t)\n-25*cos(634280*t))\n")
m=50./100. #modulation factor in percentage
Ec=100. #carrier wave amplitude in V
Em=10. #modulated wave amplitude in V
Fc=100000. #carier frequency in Hz
Fm=1000. #modulating frequency in Hz
pi=3.14
omega_c=2.*pi*Fc #carier frequency
omega_m=2.*pi*Em #modulating frequency
print '%s' %("Now,putting these equation in the standard equations for modulated voltage wave,")
print '%s' %("  e = Ec*sin(omega_c*t)+m*Ec/2*cos(omega_c-omega_m)*t-m*Ec/2*cos(omega_c-omega_m)*t")
USB=omega_c+omega_m #upper sideband
LSB=omega_c-omega_m #lower sideband
mEc=m*Ec/2.
print '%s %.0f' %("\n=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t))",mEc)
print '%s %.0f' %("\n=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t))",USB)
print '%s %.0f' %("\n=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t))",mEc)
print '%s %.0f' %("\n=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t))",LSB)

Given the equation

E = 100*sin(628000*t)+25*sin(621720*t)
-25*cos(634280*t))

Now,putting these equation in the standard equations for modulated voltage wave,
e = Ec*sin(omega_c*t)+m*Ec/2*cos(omega_c-omega_m)*t-m*Ec/2*cos(omega_c-omega_m)*t

=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t)) 25

=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t)) 628063

=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t)) 25

=100*sin(628000*t)+%.0f*sin(%.0f*t)-%.0f*cos(%.0f*t)) 627937