The amplitude of the carrier signal varies in accordance with the instantaneous amplitude of the modulating signal in Amplitude Modulation. That is the amplitude of the carrier signal containing no information varies as per the amplitude of the signal containing information, at each instant.

**Concept of Amplitude Modulation**

Consider the following diagram

The message signal shown above is in the form of a modulating wave. Then there is a carrier wave signal which has a higher frequency. This carrier wave has no information. At last shown is the modulated wave form. There is interconnection between the positive and negative ends of the carrier wave which helps to recover the exact shape of the modulating signal. This is called an Envelope. This is exactly the same as the message signal.

Therefore, we can say that Amplitude Modulation is the process of changing the amplitude of a carrier signal in accordance with the amplitude of the modulating signal. The carrier amplitude varies linearly by the modulating signal which usually consists of a range of audio frequencies. Then there is no effect on the frequency of the carrier.

**Forms**

The basic forms of AM are:

- Double Sideband Large carrier modulation (DSBLC) /Double Sideband Full Carrier (DSBFC)
- Double Sideband Suppressed carrier (DSBSC) modulation.
- Single Sideband (SSB) modulation

**Generation of DSB-FC (Double Side Band Full Wave Carrier)**

**Time-Domain Representation**

Let the us consider the modulating signal as,

Let the carrier signal be

Where:

A_{m} : It is the Amplitude of the modulating signal

A_{c} : Amplitude of carrier signal respectively.

f_{m} : It is the Frequency of the modulating signal

f_{c} : The carrier signal frequency.

Then Amplitude modulated wave will be

Then modulation index will be

**Modulation index**

If A_{max} :The maximum amplitudes of the modulated wave

A_{min} :The minimum amplitudes of the modulated wave.

When cos(2πf_{m}t) is 1, We will get the maximum amplitude of the modulated wave

A_{max}=A_{c} + A_{m}

When cos(2πf_{m}t) is -1, We will get the minimum amplitude of the modulated wave

A_{min} = A_{c} – A_{m}

A_{max} + A_{min} = Ac + A_{m} + A_{c} –A_{m }= 2A_{c}

A_{c} = A_{max} + A_{min}/2

Hence we can write,

A_{max} – A_{min} = A_{c} + A_{m} – A_{c} +A_{m} = 2A_{m}

A_{m} = A_{max} – A_{min} /2

Therefore modulation index is now

**Bandwidth:**

**Bandwidth **is the difference between the highest and lowest frequencies of the signal.

BW = f_{max} – f_{min}

s(t) = A_{c }[1+ μ cos(2πf_{m}t)] cos(2πf_{c}t)

Therefore,

s(t) = A_{c} cos(2πf_{c}t) + Ac μ cos(2πf_{m}t) cos(2πf_{c}t)

s(t) = A_{c} cos(2πf_{c}t) + Ac μ/2 cos 2π (f_{c} + f_{m}) t + A_{c} μ/2 cos 2π (f_{c} – f_{m}) t

The main three frequencies in amplitude modulated wave are

- Carrier frequency f
_{c} - Upper sideband frequency f
_{c}+f_{m} - and lower sideband frequency f
_{c}−f_{m}

Where we can write

f_{max}=f_{c}+f_{m} and f_{min}=f_{c}−f_{m}

BW=f_{c}+f_{m}−(fc−f_{m})

BW=f_{c}+f_{m}−(f_{c}−f_{m})

BW= 2f_{m}

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