Saturday, 3 March 2012

Amplitude Modulation

  • Modulation is the process by which characteristics of carrier are changed according to the message signal.
  • Message signal is also called as baseband signal or modulating signal. The result of modulation is modulated wave. 
  • Demodulation is the process of recovering original message signal from the modulated wave.

Amplitude modulation:
The amplitude of carrier is varied according to the message signal amplitude. Let C (t) = Ac COS (2πfct) is carrier signal and m (t) is message signal, then amplitude modulated wave is given by
S (t) =Ac [1+ka m (t)] COS (2πfct)
K a = amplitude sensitivity of modulator.
 
|Ka m (t)|<1         under modulation
|Ka m (t)|=1         critical modulation
|Ka m (t)|>1         over modulation
Envelope of modulated wave follows message signal. The message signal can be recovered from the modulated signal except in the case of over modulation. The carrier frequency fc must be greater than message signal frequency.

Frequency domain concept:
S (t) =Ac [1+ka m (t)] COS (2πfct)
S (t) = Ac COS (2πfct) + Ac ka m (t) COS (2πfct)
Taking Fourier Transform on both sides
 
Let the message signal is band limited to –w ≤ f ≤ w
 
Band width of AM signal is twice the message signal bandwidth.
BT = 2w
Single tone modulation:
Consider a message signal having single frequency component m (t) = Am COS (2πfmt)
Where Am= amplitude of message signal, fm = frequency of message signal
Let C (t) is a carrier wave of amplitude Ac, and frequency fc
Amplitude modulated wave S (t) = Ac [1+µ cos (2πfmt)] cos (2πfct)
Where µ=ka Am =modulation index (or) % of modulation
µ≤1 for recovering the message signal from S (t), Otherwise envelope distortion occurs.
Frequency domain:
S (t) = Ac cos (2πfct) + µ Ac cos (2πfmt) cos (2πfct)
Taking Fourier transform on both sides
The above figure shows frequency domain representation of single tone AM modulation
Modulation index:
Modulation index µ = Am/Ac
Where Am=amplitude of message signal
Ac=amplitude of carrier signal
µ<1      under modulation (Am< Ac)
µ=1     critical modulation (Am=Ac)
µ>1     over modulation (Am>Ac)
Below figure shows under modulated AM wave  
Amax= Am + Ac = Ac (1+µ)
Amin= Am – Ac = Ac (1+µ)
 
Trapezoidal display:

If modulated signal is applied to vertical deflection plates and modulating signal is applied to horizontal deflection plates of CRO, then in the above figure can be observed on the oscilloscope.
L1=2(Ac + Am)
L2=2(Ac - Am)
   
Below figure shows trapezoidal display of over modulation and distorted AM waves
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