The document discusses amplitude modulation (AM) generation and its key characteristics. It defines AM expression, modulation index, frequency spectrum of AM waves, and power and current calculations. It explains that the amplitude of the carrier signal is made proportional to the instantaneous amplitude of the modulating signal. The modulation index is defined as the ratio between modulating and carrier signal voltages. It describes that the AM wave contains the carrier frequency along with upper and lower sideband frequencies. The total power and bandwidth of the AM signal depend on the modulation index.

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

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

3. AM generation
• AM expression
• Frequency Spectrum of AM wave
• Power calculation
• Current calculation
• Modulation index
• Problems

4. Amplitude modulation

5. Amplitude modulation
• The amplitude of a carrier signal is made proportional to the instantaneous
amplitude of the modulating voltage
• Let the Carrier voltage be
• and the Message voltage be
=
vc Vc sinct
vm  Vm sinmt

6. Amplitude modulation

7. Modulation index:
Modulation index:
Defined as the ratio between modulating signal voltage and carrier signal
voltage
The above ratio is called Modulation index/ Percentage of modulation/
Modulation factor/Degree of Modulation and lies between 0 and 1.

8. The amplitude of the Modulated signal is:
A

9. The instantaneous voltage of the resultant AM wave is:
Thus the equation of the AM wave has three components-
 the first term is the unmodulated carrier
 second and third terms represent the lower and upper side bands (LSB and
USB).
 Bandwidth required for amplitude modulation is twice the frequency of
the modulating signal-2fm

10. Frequency spectrum of the AM wave/Components of am
AM wave
• Frequencies present in an AM wave:
Carrier frequency and the first pair of sideband frequencies

11. Frequency spectrum of AM wave/Components of am AM wave
• AM is shown as consisting of three discrete frequencies.
• Carrier frequency and the first pair of sideband frequencies
• The central carrier frequency has the highest amplitude
• 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 AM wave
• Side band frequency, fSB= fc + nfm
• For first pair, n=1
• Bandwidth of the AM signal
• BW= fc + fm - (fc – fm)
• BW= 2 fm
• 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 – Time domain

14. Representation of AM contd..
• Refer to diagram in previous slide:
• Top envelope:
• Bottom envelope:
The Modulated wave extends between these two limiting envelopes and has a
repetition rate equal to the unmodulated carrier frequency.

15. Modulation Index
• 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 AM transmitter employs a 50 μH coil
and 1nF capacitor. If the oscillator output is modulated by audio frequency upto
10KHz. What is the frequency range occupied by the side bands in KHz.

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

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

23. Substituting these in the equation for Pt,
Maximum power in an AM is Pt=1.5 Pc. (when m=1)
This is the maximum power amplifiers must be able to handle without distortion

24. Current relations:
Let Ic be the unmodulated current and It the total or modulated
current of and AM transmitter both being rms values:
If R is the resistance in which these currents flow, then

25. A 400 W carrier is modulated to a depth of 75 percent. Calculate
the total power in the modulated wave.

26. A broadcast radio transmitter radiates 10 kW when the modulation
percentage is 60. How much of this is carrier power?

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

32. Transmission efficiency
• Amount of useful power in an AM wave
100
Pt
 
PUSBPLSB
100
2
m2
P
2 c




 m2

P 1
 
c
100
2 m2
m2
 

33. For an AMDSBFC wave with peak unmodulated carrier voltage
Vc=10V, load resistance RL=10Ω and a modulation coefficient m=1.
Calculate
• Powers of the carrier and the upper and lower sidebands
• Total sideband power
• Total power
• Draw the power spectrum

34. Pc= 5 W
PUSB=PLSB=1.25 W
PTSB= PUSB+ PLSB =2.5 W
Pt=7.5 W

35. For an AMDSBFC wave with peak unmodulated carrier voltage
Vc=10V, load resistance RL=10Ω and a modulation coefficient m=1.
Calculate
• Powers of the carrier and the upper and lower sidebands
• Total sideband power
• Total power
• Draw the power spectrum
• Pc= 5 W
• PUSB=PLSB=1.25 W
• PTSB=2.5 W
• Pt=7.5 W

36. Power spectrum of AMwave

37. Frequency Spectrum of AM wave

38. A modulating signal 20sin(2π x 103t) is used to modulate a carrier
signal 40sin(2π x 104t) . Calculate
• Modulation index
• Percentage modulation
• Frequencies of sideband components and their amplitudes
• Bandwidth of the modulated signal
• Draw the power spectrum

39. A modulating signal 20sin(2π x 103t) is used to modulate a carrier
signal 40sin(2π x 104t) . Calculate
Modulation index
m=0.5
Percentage modulation
%m=50%
Frequencies of sideband components and their amplitudes
fUSB=11 KHz
fLSB=9 KHz
VLSB=VUSB=10 V
Bandwidth of the modulated signal
B= 2fm = 2 KHz

40. A modulating signal 20sin(2π x 103t) is used to modulate a carrier
signal 40sin(2π x 104t) . Calculate
• Draw the power spectrum

41. A certain transmitter radiates 9 kW with the carrier unmodulated, and 10.125
kW when carrier is sinusoidally modulated. Calculate the modulation index. If
say two more sine waves, corresponding to 40% and 60% modulations are
transmitted simultaneously, determine the total radiated power.

42. A certain transmitter radiates 9 kW with the carrier unmodulated, and 10.125
kW when carrier is sinusoidally modulated. Calculate the modulation index. If
say two more sine waves, corresponding to 40% and 60% modulations are
transmitted simultaneously, determine the total radiated power.

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 ,
It = 9.19 A

44. The antenna current of an AM broadcast transmitter, modulated to a
depth of 40 percent by an audio sine wave is 11A. It increases to 12A
as a result of simultaneous modulation by another audio sine wave.
What is the modulation index due to this second wave?
Ic=10.58A mt=0.76
m2=0.643