**Amplitude modulation (AM)** is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. AM was the first type of modulation used for communicating signals from one point to another and is still the simplest to understand.

## Amplitude modulation (AM) Operational Theory

Amplitude modulation is also defined in a more restrictive sense to mean modulation in which the amplitude factor of a sine-wave carrier is linearly proportional to the modulating wave. The signal can be written as:- **v = a _{c} (1 + m cos w_{m}t) cos w_{c}t ** This represents a signal at frequency w

_{c}whose amplitude is modulated by another frequency w

_{m}. m = a

_{m}/a

_{c}is the

**modulation index**. To find the frequency spectrum of the am signal the above expression can be rewritten as a sum of signals of constant amplitude:-

**v(t) = a**Above expression shows that the frequency spectrum consists of 3 components at frequencies w

_{c}{cos w_{c}t + m/2(cos(w_{c}+ w_{m})t + cos(w_{c}– w_{m})t)}_{c}, w

_{c}+ w

_{m}and w

_{c}– w

_{m}. The percent of the power transmitted which is in the carrier is given by Pc = 100/(1 + m * m/2) and varies from 100% for m = 0 to 66.66% for m = 1. This is considered to be one of the disadvantages of AM since the carrier is a sine wave and contains no information. If the modulating index becomes greater than 1 then the expression for the AM signal amplitude (1 + m cos w

_{m}t) can go negative. In practical AM systems The amplitude will be limited to zero and the modulating index to one. In AM, the modulated wave is composed of the transmitted carrier, which conveys no information, plus the upper and lower sidebands, which (assuming the carrier frequency exceeds twice the top audio frequency) convey identical and therefore mutually redundant information. Under these conditions and assuming adequate knowledge of the carrier, either sideband alone would uniquely define the message. This eventually led to the development of

**single-sideband (SSB)**and

**vestigial-sideband (VSB)**modulation. Apart from a scale factor, the spectrum of the upper sideband and lower sideband is the spectrum of the modulating wave displaced, respectively, without and with inversion by an amount equal to the carrier frequency.