Modulation involves impressing a low frequency signal onto a higher frequency carrier signal to allow for more efficient transmission. Amplitude modulation (AM) varies the amplitude of the carrier signal based on the amplitude of the intelligence signal. The AM signal consists of the carrier signal plus upper and lower sideband frequencies that carry the modulated information. Power in an AM signal is distributed between the carrier and sidebands, with more power in the sidebands for higher modulation indices up to a maximum of 100% modulation.

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L2 - Fundamentals of Amplitude Modulation
Seneca College
Prof Kris Pillay
AM Introduction
1. Why do we use modulation?
a. Antenna size and efficient transmission and reception at higher frequencies.
b. Only one transmission and reception of voice can take place and transmission and
reception of 2nd signal would result in the interference being at the same frequency.
2. What is Modulation and Demodulation?
Modulation is a process of impressing (or translating) a low frequency intelligence signal
onto a higher frequency carrier signal.
Demodulation is the reverse process where the received modulated signal is transformed
back to its original low frequency audio signal.
Amplitude Modulation
3. What is Amplitude Modulation?
In Amplitude Modulation the amplitude of the carrier frequency is changed in accordance
with the amplitude.
4. Figure 2.4 shows the AM wave forms under varying intelligence conditions.

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5. Mathematical description of AM
Mathematical description of AM
• The instantaneous value of an unmodulated carrier is
ec = Ec sin 2 fc t
Where Ec = peak carrier amplitude
fc = Carrier frequency
• The instantaneous value of an intelligence signal
ei = Ei sin 2 fi t
Where Ei = peak intelligence amplitude
fi = Intelligence frequency
6. The instantaneous value of an unmodulated carrier is
ec = Ec sin 2 fc t
Where Ec = peak carrier amplitude
fc = Carrier frequency
7. The instantaneous value of an intelligence signal
ei = Ei sin 2 fi t
Where Ei = peak intelligence amplitude
fi = Intelligence frequency
Mathematical description of AM
8. Since the amplitude of the am signal varies in accordance with the amplitude of the
intelligence signal
eAM = (Ec +Ei sin 2 fi t) sin 2 fc t
eAM = Ec sin 2 fc t +Ei sin 2 fi t x sin 2 fc t
9. The second part is the multiplication of the signals in the frequency domain results in
amplitude modulation
10. Since sin A X sin B = 0.5{cos (A-B) – cos (A+B)}
eAM = Ec sin 2 fc t +Ei sin 2 fi t x sin 2 fc t
eAM = Ec sin 2 fc t +mEc sin 2 fi t x sin 2 fc t [where Ei =mEc ]
eAM = Ec sin 2 fc t +0.5 mEc {cos 2 (fc - fi )t – cos 2(fc + fi )t}

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Amplitude Modulation
11. A 1 MHz carrier signal is modulated by a 5 kHz intelligence signal. Determine the
frequency components of the resulting AM signal and draw the frequency domain
representation.
Amplitude Modulation
12. A 30 MHz carrier signal is modulated by a 10 kHz intelligence signal. Determine the
frequency components of the resulting AM signal, draw the frequency domain
representation, and determine the bandwidth.

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Amplitude Modulation
13. What is Bandwidth of an AM signal?
The total Bandwidth of the AM signal is defined as the difference between the upper and
the lower side frequencies.
14. BW = fUSF- fLSF
15. A closer look at the result reveals that the
BW = 2 fi
Amplitude Modulation
16. A 1000 kHz carrier is modulated by a music signal that has frequency range from 20 Hz to
20 kHz.
a. Determine the range of frequencies generated for the upper sideband and lower
sidebands.
b. Determine the BW
c. Can the music signal be processed in an AM system without distortion?
Amplitude Modulation
17. Solution
a. fUSBmax=fC+ fimax= 1000 kHz + 20 kHz = 1020 kHz
b. fUSBmin=fC+ fimin= 1000 kHz + 20 Hz = 1000.02 kHz
c. fLSBmax=fC- fimax= 1000 kHz - 20 kHz = 980 kHz
d. fLSBmin=fC- fimin= 1000 kHz + 20 Hz = 999.98 kHz
18. BW =fUSBmax-fLSBmax= 1020 kHz -980 kHz =2 x fimax
= 2x 20 kHz = 40 kHz
19. AM designated BW = 10 kHz, hence only frequencies below 5 kHz will be processed and
all fi > 5 kHz will be distorted. No wonder on AM radio music does not sound as good as an
FM band.
Modulation index
20. What is modulation index?
A measure of the extent to which the amplitude of the carrier is varied by the intelligence is
expressed in terms of the modulation index m.
21. Modulation index is given by
M = Ei/Ec = (Emax – Emin) /(Emax + Emin)
where m = modulation index
Ei = Peak amp of intelligence signal
Ec = Peak amp of carrier signal

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22. Graphical Measurement (see fig 2.8)
23. M = (Emax – Emin) /(Emax + Emin)
Min modulation = 0
Max modulation = 100
Over - Modulation
24. What is over modulation?
modulation index = m = Ei/Ec
If Ei = 0, this results in 0% modulation
If Ei = Ec, this results in 100% modulation
25. If E > Ec, this results in over modulation, If this occurs the modulated carrier will be more
than double its un modulated value but will fall to zero for an interval of time as shown in
fig 2.9

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Amplitude Modulation
26. determine the % modulation, and Ei for an un-modulated carrier peak to peak amplitude of
80 V that reaches its max and min values as shown below
S No Emax (V) Emin (V) m% Ei (V)
a. 100 60 25 20
b. 125 35 56.2 45
c. 160 0 100 80
d. 180 0 ? 90
e. 135 25 68.7 55
AM Analaysis
27. The am signal is given by
eAM = Ec sin 2 fc t +0.5 mEc {cos 2 (fc - fi )t – cos 2(fc + fi )t}
eAM=Ec sin 2 fc t +0.5 mEc cos 2 (fc - fi )t – 0.5 mEc cos 2(fc + fi )t
28. Inference: The AM wave consists of carrier, USF and LSF
The amplitude of the side frequencies is 0.5mEc
29. In AM transmission the carrier amplitude Ec and carrier frequency fc always remain
constant , whilst the intelligence amplitude Ei and the intelligence frequencies keep
changing and hence the side bands amplitude and the frequencies keep changing.
30. The carrier contains no intelligence, however max power goes to it.
31. The side bands carry the intelligence and if more power goes to the side bands that contain
info the transmission becomes more efficient. That is why the m is always set to maximum,
but not higher than 100%.
AM power distribution
32. Power distribution in AM signal
The amplitude of the am wave is
eAM=Ec sin 2 fc t +0.5 mEc cos 2 (fc - fi )t – 0.5 mEc cos 2(fc + fi )t
Eam = Ec + 0.5mEc + 0.5 mEc
Pam = Pc + PLSB + PLSB
Since power is proportional to the swquare of the voltage, the power can be expressed as
Pam = Pc + 0.25m2 Pc+ 0.25m2 Pc
33. PT =Pam = Pc + 0.25m2 Pc+ 0.25m2 Pc = Pc (1 + m2 /2)
34. Power is side band is PLSB =PLSB = Pc ( m2 /4)
AM power distribution
35. Power in side band is PLSB =PLSB = Pc ( m2 /2)
36. The effect of m over the power in side bands?
37. Most modulators are set for 90 to 95% modulation to transmit max intelligence power and
at the same time do not exceed 100% modulation.

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Amplitude Modulation
38. A 500 W carrier is to be modulated to a 90% modulation level. Determine the
– The total transmitted power
39.
– The upper side band and lower side band power
Solution
40. PT =Pc (1 + m2 /2) = 500 (1 + .92 /2) = 702.5
41. Power in side band is PLSB =PLSB = Pc ( m2 /4)
= 500 ( .92 /4) = 101.25
Amplitude Modulation
42. An AM broadcast station operates at its max allowed tatal output of 50 kw and at 95%
modulation. Calcualte the
– Carrier power
43.
– Sideband power
Solution
PT =Pc (1 + m2 /2)
50 =Pc (1 + 0.952 /2) = Pc(1 + .857 /2) = 1.429 Pc
50 = 1.429 Pc
1.429 Pc = 50 kW
Carrier Power Pc = 50 / 1.429 kW = 34.99 kw
sideband power = Pc ( 0.952 /2) = Pc(.857 /2) = 0.429 Pc
= 15.01 kw
AM Transmitter system
44. Microphone sound to modulating signal
45. Intelligence signal is amplified.
46. The oscillator generates the carrier frequency
47. The oscillator buffer ensues stability and then amplified
48. The modulator modulates the signal and transmits to the antenna
49. The impedance of the antenna is to be properly matched

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