In amplitude modulation (AM), the modulation refers to the process of varying the amplitude of the carrier wave in accordance with the modulating signal. The modulating signal is typically an audio waveform that contains the desired information to be transmitted, such as speech or music.
In double-sideband (DSB) amplitude modulation, the carrier wave is modulated by multiplying it with the modulating signal. This results in the creation of two sidebands, one above and one below the carrier frequency, each containing a copy of the modulating signal. The sidebands are mirror images of each other and carry the same information. The carrier itself does not contain any information, but it serves as a reference for demodulation at the receiver.
The modulation index, often denoted by m, is a parameter that describes the extent to which the carrier wave is modulated. It is defined as the ratio of the peak amplitude of the modulating signal to the peak amplitude of the carrier wave. Mathematically, the modulation index is given by:
m = (A_m / A_c)
where A_m is the peak amplitude of the modulating signal and A_c is the peak amplitude of the carrier wave.
The modulation index affects the level of modulation and determines the bandwidth occupied by the modulated signal. Higher values of modulation index result in stronger modulation and wider bandwidth. The optimum value of the modulation index for AM transmission is typically around 1, where the modulation is at 100% and provides good quality audio transmission without excessive bandwidth usage.
It's worth noting that in single-sideband (SSB) modulation, one of the sidebands and the carrier are suppressed to reduce the bandwidth requirements. However, the concept of modulation index still applies in SSB modulation.