2 Amplitude_Modulation.pdf

AM

1. Module-II
Linear Modulation
Prof.Dr.G.Aarthi,
Associate Professor, SENSE

2. Text books:
Electronic communication systems-George Kennedy

3. AMgeneration
•AMexpression
•Frequency Spectrum of AM wave
•Powercalculation
•Currentcalculation
•Modulationindex
•Problems

4. Amplitudemodulation

5. Amplitudemodulation
•Theamplitudeofacarriersignalismadeproportionaltotheinstantaneous
amplitude of the modulating voltage
•Let the Carrier voltage be
•and the Message voltagebe
=v
cV
c sin
ct
v
mV
m sin
mt

6. Amplitudemodulation

7. Modulation index:
Modulation index:
Defined as the ratio between modulating signal voltage and carrier signal
voltage
The above ratio is called Modulationindex/Percentageof modulation/
Modulation factor/Degree of Modulationand lies between 0 and1.

8. The amplitude of the Modulatedsignal is:
A

9. The instantaneous voltage of the resultant AM waveis:
ThustheequationoftheAMwavehasthreecomponents-
thefirsttermistheunmodulatedcarrier
secondandthirdtermsrepresenttheloweranduppersidebands(LSBand
USB).
Bandwidthrequiredforamplitudemodulationistwicethefrequencyof
themodulatingsignal-2f
m

10. Frequency spectrum of the AM wave/Components of am
AMwave
•Frequencies present in an AMwave:
Carrierfrequency and the first pair of sidebandfrequencies

11. Frequency spectrum of AM wave/Components of am AMwave
•AM is shown as consisting of three discretefrequencies.
•Carrier frequency and the first pair of sidebandfrequencies
•The central carrier frequency has the highestamplitude
•The other two have amplitudes equal to each other, can never exceed half the
carrier amplitude.

12. Frequency spectrum of AM wave/Components of am AMwave
•Side band frequency, f
SB= f
c+nf
m
•For first pair, n=1
•Bandwidth of the AM signal
•BW= f
c+ f
m-(f
c–f
m)
•BW= 2f
m
•Bandwidth required for an AM signal is twice the frequency of the modulating
signal.
•In modulation by several sinewaves simultaneously as in AM broadcasting
service, the BW required is twice the highest modulating frequency.

13. Representation of AM –Timedomain

14. Representation of AMcontd..
•Refer to diagram in previousslide:
•Topenvelope:
•Bottom envelope:
The Modulated wave extends between these twolimitingenvelopes and has a
repetition rate equal to the unmodulated carrierfrequency.

15. ModulationIndex
•Modulation index can be derived in terms of V
max and V
min.

16. Critical modulation,
m=1
Vm=Vc
The maximum percent
modulation that can be
obtained without
causing excessive
distortion
Under modulation,
m<1
Vm< Vc
Over modulation,
m>1
Vm> Vc
Envelope no longer
resembles the
modulating signal and
the information cannot
be retrieved in this case

17. Importance of Modulation factor

19. The tuned circuit of an oscillator in a simple AMtransmitter employs a 50μHcoil
and1nF capacitor. If the oscillator output ismodulated by audio frequency upto
10KHz. What is thefrequency range occupied by the side bands inKHz.

21. Power relations in AMwave
•The modulated wave contains extra energy in the twosidebands.
•Since amplitude of sidebands depend on the modulation index, it is anticipated
that total power will also depend on the modulationindex.

22. •Total power in the modulated waveis
The first term is the unmodulated carrierpower
mVc/2 mVc/2
Vc

23. Substituting these in the equation forPt,
Maximum power in an AM is P
t=1.5P
c.(when m=1)
This is the maximum power amplifiers must be able to handle withoutdistortion

24. Currentrelations:
LetI
cbetheunmodulatedcurrentandI
tthetotalormodulated
currentofandAMtransmitterbothbeingrmsvalues:
IfRistheresistanceinwhichthesecurrentsflow,then

25. A400Wcarrierismodulatedtoadepthof75percent.Calculate
thetotalpowerinthemodulatedwave.

26. Abroadcastradiotransmitterradiates10kWwhenthemodulation
percentageis60.Howmuchofthisiscarrierpower?

31. Modulation by several sine waves
If V1, V2… etc. be the simultaneous modulating voltages, then the total
modulating voltage Vtwill be the square root of the sum of the squares of
the individual voltage.
Divide both sides by Vc

32. Transmissionefficiency
•Amount of useful power in an AMwave
100
P
t

P
USB P
LSB
100
2
m
2
P
2
c




m
2

P1

c
100
2 m
2
m
2


33. ForanAMDSBFC wavewithpeakunmodulatedcarriervoltage
V
c=10V,loadresistanceR
L=10Ωandamodulationcoefficientm=1.
Calculate
•Powers of the carrier and the upper and lowersidebands
•Total sidebandpower
•Totalpower
•Draw the powerspectrum

34. P
c=5W
P
USB=P
LSB=1.25W
P
TSB=P
USB+ P
LSB=2.5W
P
t=7.5 W

35. ForanAMDSBFC wavewithpeakunmodulatedcarriervoltage
V
c=10V,loadresistanceR
L=10Ωandamodulationcoefficientm=1.
Calculate
•Powers of the carrier and the upper and lowersidebands
•Total sidebandpower
•Totalpower
•Draw the powerspectrum
•P
c=5W
•P
USB=P
LSB=1.25W
•P
TSB=2.5W
•P
t=7.5 W

36. Power spectrum of AMwave

37. Frequency Spectrum of AM wave

38. Amodulatingsignal20sin(2πx10
3
t)isusedtomodulateacarrier
signal 40sin(2π x 10
4
t) .Calculate
•Modulationindex
•Percentagemodulation
•Frequencies of sideband components and theiramplitudes
•Bandwidth of the modulatedsignal
•Draw the powerspectrum

39. Amodulatingsignal20sin(2πx10
3
t)isusedtomodulateacarrier
signal 40sin(2π x 10
4
t) .Calculate
Modulationindex
m=0.5
Percentagemodulation
%m=50%
Frequencies of sideband components and theiramplitudes
f
USB=11KHz
f
LSB=9KHz
V
LSB=V
USB=10V
Bandwidth of the modulatedsignal
B= 2fm = 2 KHz

40. Amodulatingsignal20sin(2πx10
3
t)isusedtomodulateacarrier
signal 40sin(2π x 10
4
t) .Calculate
•Draw the powerspectrum

41. Acertaintransmitterradiates9kWwiththecarrierunmodulated,and10.125
kWwhencarrierissinusoidallymodulated.Calculatethemodulationindex.If
saytwomoresinewaves,correspondingto40%and60%modulationsare
transmittedsimultaneously,determinethetotalradiatedpower.

42. Acertaintransmitterradiates9kWwiththecarrierunmodulated,and10.125
kWwhencarrierissinusoidallymodulated.Calculatethemodulationindex.If
saytwomoresinewaves,correspondingto40%and60%modulationsare
transmittedsimultaneously,determinethetotalradiatedpower.

43. The antenna current of an AM transmitter is 8A when only carrier is sent
but it increases to 8.93 A when a carrier is modulated by a single tone
sinusoid. Find the percentage of modulation. Find antenna current when
depth of modulation changes to 0.8
m = 0.7 = 70.1%
When m = 0.8 ,
I
t= 9.19 A

44. TheantennacurrentofanAMbroadcasttransmitter,modulatedtoa
depthof40percentbyanaudiosinewaveis11A.Itincreasesto12A
asaresultofsimultaneousmodulationbyanotheraudiosinewave.
Whatisthemodulationindexduetothissecondwave?
I
c=10.58A m
t=0.76
m
2=0.643