- 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) = A

_{c }COS (2πf_{c}t) is carrier signal and m (t) is message signal, then amplitude modulated wave is given by
S (t) =Ac [1+k

_{a }m (t)] COS (2πf_{c}t)
K

_{a }= amplitude sensitivity of modulator.
|K

_{a }m (t)|<1 under modulation
|K

_{a }m (t)|=1 critical modulation
|K

_{a }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 f

_{c}must be greater than message signal frequency.**Frequency domain concept:**

S (t) =Ac [1+k

_{a }m (t)] COS (2πf_{c}t)
S (t) = Ac COS (2πf

_{c}t) + Ac k_{a }m (t) COS (2πf_{c}t)
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.

B

_{T }= 2w**Single tone modulation:**

Consider a message signal having single frequency component m (t) = A

_{m }COS (2πf_{m}t)
Where A

_{m}= amplitude of message signal, f_{m}= frequency of message signal
Let C (t) is a carrier wave of amplitude A

_{c}, and frequency f_{c}
Amplitude modulated wave S (t) = Ac [1+µ cos (2πf

_{m}t)] cos (2πf_{c}t)
Where µ=k

_{a}A_{m}=modulation index (or) % of modulation
µ≤1 for recovering the message signal from S (t), Otherwise envelope
distortion occurs.

**Frequency domain:**

S (t) = A

_{c}cos (2πf_{c}t) + µ A_{c}cos (2πf_{m}t) cos (2πf_{c}t)
Taking Fourier transform on both sides

The above figure
shows frequency domain representation of single tone AM modulation

**Modulation index:**

Modulation index µ
= A

_{m}/A_{c}
Where A

_{m}=amplitude of message signal
A

_{c}=amplitude of carrier signal
µ<1 under modulation (A

_{m}< A_{c})
µ=1 critical modulation (A

_{m}=A_{c})
µ>1 over modulation (A

_{m}>A_{c})
Below figure shows
under modulated AM wave

A

_{max}= A_{m}+ A_{c}= A_{c}(1+µ)
A

_{min}= A_{m}– A_{c}= A_{c}(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.

L

_{1}=2(A_{c}+ A_{m})
L

_{2}=2(A_{c}- A_{m})
Below figure shows
trapezoidal display of over modulation and distorted AM waves

## No comments:

## Post a Comment