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Q/As :

1. Calculation of the modulation index and power of the modulated signal from the

experimental data is given below:

Calculation of modulation index for first case:

Amax= 3.939V

Amin = .3V

!odulation "ndex# a = $Amax % Amin& ' $Amax( Amin& = .99) * 1

Calculation of power for first case:

+ighest pea, $of carrier& from fre-uenc spectrum# / = 0.d2

1log1$& = /

= 1 $/ ' 1&= 3.999445

6o# +ighest pea, $of carrier& from fre-uenc spectrum# = 3.999445

Another pea, $of message and carrier& from fre-uenc spectrum# + = % .9d2

1log1$7& = +

7 = 1 $+ ' 1&= .93840

6o# +ighest pea, $of carrier& from fre-uenc spectrum# 7 = .93840

ower = ( 47= 38.491

Figure 1 : PSD of the modulated signal for this case(a=1)

Calculation of modulation index for 6econd case:

Amax= 8.143V

Amin = %.9)4V

!odulation "ndex# a = $Amax % Amin& ' $Amax( Amin& = 1.453

Calculation of power for 6econd case:

+ighest pea, $of carrier& from fre-uenc spectrum# / = 0.d2

1log1$& = / = 1 $/ ' 1&= 3.999445

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6o# +ighest pea, $of carrier& from fre-uenc spectrum# = 3.999445

Another pea, $of message and carrier& from fre-uenc spectrum# + = 3.54d2

1log1$7& = +

7 = 1 $+ ' 1&= .3089196o# +ighest pea, $of carrier& from fre-uenc spectrum# 7 = .308919

ower = ( 47= 84.3)1

Figure 2 : PSD of the modulated signal for this case(a>1)

Calculation of modulation index for third case:

Amax= 3.3)9V

Amin = .03V

!odulation "ndex# a = $Amax % Amin& ' $Amax( Amin& = .0)80

Calculation of power for third case:

+ighest pea, $of carrier& from fre-uenc spectrum# / = 8.94d2

1log1$& = /

= 1 $/ ' 1&= 3.90449

6o# +ighest pea, $of carrier& from fre-uenc spectrum# = 3.90449

Another pea, $of message and carrier& from fre-uenc spectrum# + = %3.9d2

1log1$7& = +

7 = 1 $+ ' 1&= .40))13

6o# +ighest pea, $of carrier& from fre-uenc spectrum# 7 = .40))13

ower = ( 47= 31.513

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Figure 3: PSD of the modulated signal for this case(a and ?ero

when u$t&. he message signal is recovered b passing the rectified signal through a

lowpass filter whose bandwidth matches that of the message signal. he dc

component can then be eliminated b passing this output through a transformer.

@utput of the transformer is amplified'attenuated version of the message signal.

he simplicit of the demodulator has made conventional 62 A! a practical choice

for A! radio broadcasting. 6ince there are literall billions of radio receivers# an

inexpensive implementation of the demodulator is extremel important. he power

inefficienc of conventional A! is justifiedb the fact that there are few broadcast

transmitters relative to the number of receivers. Conse-uentl# it is cost effective to

construct powerful transmitters and sacrifice power efficienc in order to simplif the

signal demodulation at the receivers.

hatBs wh hough 62 is an inefficient modulation method in terms of power#

because of eas detection# itBs preferred over 62%6C in A! modulation.D

3. !AEA2 code for a conventional A! signal generation and plot of modulated signal

for the as,ed values of Fa is given below:

clc

clf

clear all

del=1G%0H

am=1H

fm=33HAc=H

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fc=0H

t=:del:.1H

mt=amIcos$IpiIfm.It&H

ct=AcIcos$IpiIfc.It&H

Fa1=.5

ut1=AcI$1(Fa1IamIcos$IpiIfm.It&&.Icos$IpiIfc.It&HFa=1

ut=AcI$1(FaIamIcos$IpiIfm.It&&.Icos$IpiIfc.It&H

Fa3=1.0

ut3=AcI$1(Fa3IamIcos$IpiIfm.It&&.Icos$IpiIfc.It&H

figure$1&

subplot$311&

plot$t#ut1&

grid on

xlabel$Jtime# tJ&

label$Jmodulated signal#u$t&J&

title$Ju$t& vs t plot for Fa=.5J&subplot$31&

plot$t#ut&

grid on

xlabel$Jtime# tJ&

label$Jmodulated signal#u$t&J&

title$Ju$t& vs t plot for Fa=1J&

subplot$313&

plot$t#ut3&

grid on

xlabel$Jtime# tJ&

label$Jmodulated signal#u$t&J&

title$Ju$t& vs t plot for Fa=1.0J&

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0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-40

-20

0

20

40

time, t

modulate

dsignal,u(t)

u(t) vs t plot for Ka=0.7

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-40

-20

0

20

40

time, t

modulatedsignal,u(t)

u(t) vs t plot for Ka=1

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-100

-50

0

50

100

time, t

modulatedsignal,u(t)

u(t) vs t plot for Ka=1.6

Reference:

1. Communication 6stems Kngineering# ndKditionH Author: Lohn /. roa,is# !asoud

6alehi