Amplitude modulation (AM) varies the amplitude of a carrier wave based on the instantaneous amplitude of a message signal. In AM, the frequency and phase of the carrier wave remain constant while the amplitude is varied by the message signal. The modulation index, m, indicates the degree of modulation and is defined as the ratio of the amplitude of the message signal to the carrier amplitude. An AM signal produces a carrier wave along with upper and lower sideband frequencies that contain the message information.

1. Amplitude Modulation

2. To achieve modulation, we need two signals, carrier (high frequency) and message
(low frequency) signals
 In Continuous Wave (CW) modulation schemes, the carrier is a sinusoid.
 The three parameters of a sinusoidal carrier that can be varied are:
 Amplitude,
 Frequency
 Phase
 According to parameters: Types of Modulation
 Amplitude Modulation (AM),
 Frequency Modulation (FM) and
 Phase Modulation (PM).

3. Amplitude
Amplitude is the height, force or power of the wave
Frequency and Phase remains constant, however the height of the wave is
dynamic based on the power of the wave
 The higher power, or amplitude, the higher the wave form peeks.
 The lower the power, or amplitude, the lower the wave form peeks
Standard measure of amplitude = Volts

4. Frequency
Frequent, consistent, and repetitive
Frequency - Number of times a specified event occurs within a
specified time interval
Standard measure of Frequency = Hertz or
cycles per seconds
1. AM Radio: 535-1605 kHz
2. FM Radio: 88-108 MHz
3. TV Broadcasting: VHF Band – 41-68 MHz and 174-230 MHz; UHF
band -470-890MHz
4. Microwave & Satellite Signal – Several GHz
5. Infrared & Fiber Optic Signals – 200 to 300 THz
Frequencies used for
various applications

5. Phase
Phase is the same frequency, same cycle, same wavelength, but are 2 or more wave forms
not exactly aligned together.
The phase involves the relationship between the position of the amplitude crests and
troughs of two waveforms.
Inphase -If the peaks of two signals with the same frequency are in exact alignment at the same time.
Out of phase- If the peaks of two signals with the same frequency are not in exact alignment at the same time
Standard measure of Phase=
distance, time, or degrees

6. In amplitude modulation, the amplitude of the carrier signal is varied in accordance with the
instantaneous value (amplitude) of the modulating signal, but the frequency and phase remains
constant
Mathematical Representation of an AM Wave
Amplitude Modulation
Carrier (High frequency) signal c t or 𝑣𝑐 = 𝑉
𝑐𝑐𝑜𝑠𝜔𝑐𝑡
Modulating (Low frequency/message/baseband/information) signal, m t or 𝑣𝑚 = 𝑉
𝑚𝑐𝑜𝑠𝜔𝑚𝑡
On amplitude modulation, 𝑣𝐴𝑀 = 𝑉𝑐+𝑣𝑚)𝑐𝑜𝑠𝜔𝑐𝑡
𝒗𝑨𝑴 = 𝑽𝒄 𝟏 + 𝒎𝒄𝒐𝒔𝝎𝒎𝒕 𝒄𝒐𝒔𝝎𝒄𝒕

7. 𝑊ℎ𝑒𝑟𝑒, 𝑚 =
𝑉𝑚
𝑉𝑐
, modulation index of AM
Frequency domain representation of AM wave, 𝑽𝑨𝑴 𝒕) = 𝑽𝒄𝒄𝒐𝒔𝝎𝒄𝒕 +
𝒎𝑽𝒄
𝟐
𝒄𝒐𝒔 𝝎𝒄 − 𝝎𝒎 +
𝒎𝑽𝒄
𝟐
𝒄𝒐𝒔 𝝎𝒄 + 𝝎𝒎 𝒕

8. Frequency Spectrum

9. Phasor Diagram

10. Voltage Spectrum

11. Coefficient of Modulation or Modulation Index
𝑚 =
𝑉
𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛
𝑉
𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛
The amount of amplitude change (modulation) present in an AM waveform
Percentage Modulation or Depth of Modulation
Modulation index when expressed in percentage
The range of modulation index is 0 to 1

12.  Under modulation (m < 1 or Vm < Vc).
 Critical modulation (m =1 or Vm = Vc).
 Over modulation (m >1 or Vm > Vc).
Degree of Modulation

13.  𝑃 =
𝑉2
𝑐𝑎𝑟𝑟
𝑅
+
𝑉2
𝐿𝑆𝐵
𝑅
+
𝑉2
𝑈𝑆𝐵
𝑅
 𝑃𝑐 =
𝑉2
𝑐𝑎𝑟𝑟
𝑅
=
𝑉𝑐
2
2
𝑅
= 𝑉𝑐
2
2𝑅
 𝑃𝐿𝑆𝐵 = 𝑃𝑈𝑆𝐵 =
𝑉2
𝑆𝐵
𝑅
=
𝑚𝑉𝑐
2
2
2
𝑅
= 𝑚2𝑉𝑐
2
8𝑅 =
𝑚2
4
×
𝑉𝑐
2
2𝑅
Power Distribution in AM Wave
𝑃𝑇 = 𝑃𝑐 1 +
𝑚2
2
Sub 𝑷𝒄 , 𝑷𝑳𝑺𝑩 𝒂𝒎𝒅 𝑷𝑼𝑺𝑩 𝒊𝒏 𝑷
 𝑃𝑇 =
𝑉𝑐
2
2𝑅
+
𝑚2
4
𝑉𝑐
2
2𝑅
+
𝑚2
4
𝑉𝑐
2
2𝑅
𝑃𝑇 = 𝑃𝑐 +
𝑚2
4
𝑃𝑐 +
𝑚2
4
𝑃𝑐

14. Power Spectrum
The maximum power in the AM wave is
𝑷𝑻 = 𝟏. 𝟓𝑷𝒄 when m=1.

15. 
𝑃𝑇
𝑃𝑐
=
𝐼𝑇
2𝑅
𝐼𝑐
2𝑅
= 1 +
𝑚2
2
 𝐼𝑇 = 𝐼𝑐 1 +
𝑚2
2
 Similarly, 𝑉𝑇 = 𝑉
𝑐 1 +
𝑚2
2
AM current and voltage calculations

16.  %𝜂 =
𝑃𝑜𝑤𝑒𝑟 𝑖𝑛 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑𝑠
𝑇𝑜𝑡𝑎𝑙 𝑃𝑜𝑤𝑒𝑟
× 100 =
𝑃𝐿𝑆𝐵+𝑃𝑈𝑆𝐵
𝑃𝑇
× 100
 %𝜂 =
𝑚2𝑉𝑐
2
8𝑅 + 𝑚2𝑉𝑐
2
8𝑅
𝑉𝑐
2
2𝑅 1+
𝑚2
2
× 100
 %𝜂 =
𝑚2
2+𝑚2 × 100 Assuming m=1, %𝜂 =
1
3
× 100 = 33.3%.
Efficiency of AM
 The amount of useful message power present in AM wave is expressed by the term called
transmission efficiency
 It is the ratio of total sideband power to the total transmitted power
Bandwidth of AM signal
The difference between upper and lower side frequencies will be 2fm and this is the bandwidth of AM signal.

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