Amplitude Modulation Derivation

Amplitude modulation is a modulation technique commonly used for transmission of information via a radio carrier wave. This is the earliest modulation used in radio to transmit voice. It was developed by Landell de Moura and Reginald Fessenden in the year 1900 with the experiments of a radiotelephone. It finds applications in two-way radios, computer modems in the form of QAM, VHF aircraft radio and citizens band radio. Let us learn the amplitude modulation derivation and modulation index derivation in this article.

Derivation of Amplitude Modulation

Mathematical representation of Amplitude Modulated waves in time domain�(�)=�����(2����)(modulating signal)�(�)=�����(2����)(carrier signal)�(�)=⌊��+�����(2����)⌋���(2����)(equation of Amplitude Modulated wave)

Where,

A_m: amplitude of modulating signal

A_c: amplitude of carrier signal

f_m: frequency of modulating signal

f_c: frequency of carrier signal

Modulation Index Derivation

Modulation index is also known as modulation depth is defined for the carrier wave to describe the modulated variable of the carrier signal varying with respect to its unmodulated level.

Consider maximum and minimum amplitudes of the wave as A_max and A_min

Depending upon cos(2𝜋f_mt) following two equations are derived with maximum and minimum amplitude of the modulated waves.

Therefore, this is the derivation of the modulation index.