# Amplitude Modulation, AM: Depth; Modulation Index

### Modulation Index and Modulation Depth are key issues for the effectiveness of amplitude modulated, AM signals.

It is possible to vary the level of modulation applied to an amplitude modulated signal.

If little modulation is applied then the audio (assuming it us an audio transmission) will be difficult to hear. However if too much is applied, distortion can result and signals will not be easy to listen to and interference will increase and could affect users on nearby frequencies or channels.

As a result of this it is necessary to have a way of defining the level of modulation applied to an amplitude modulated signal.Two figures are used for this, namely the amplitude modulation, AM modulation index, and the modulation depth. Both are related, but they have slightly different meanings.

## AM modulation index basics

The term, Modulation Index, is used for a number of forms of modulation, including AM.

For amplitude modulation, the modulation index is defined as the measure of extent of amplitude variation about an un-modulated carrier.

In other words it describes the amount by which the modulated carrier envelope varies about the static level.

$\mathrm{Modulation Index, m}=\frac{M}{A}$

Where:
A = the carrier amplitude.
M = the modulation amplitude and is the peak change in the RF amplitude from its un-modulated value.

Using the equation above it can be seen that a modulation index of 0.75 means that the signal will increase by a factor of 0.75 and decrease to 0.25 of its original level.

## AM modulation depth basics

The amplitude modulation AM modulation depth figure is complementary to the modulation index.

Typically the modulation depth is the amplitude modulation index expressed as a percentage.

In this way an AM modulation index of 0.75 would be expressed as a modulation depth of 75%.

In reality the terms AM modulation index and the AM modulation depth are often used interchangeably, so there are often no hard and fast rules regarding their use.

## AM modulation index examples

It is helpful to see some examples of amplitude modulated waveforms with different levels of modulation index.

The most widely seen modulation level is for a signal that has 100% modulation. Under these circumstances the signal level falls to zero and rises to twice the value with no modulation. In this case the voltage rises to a maximum of twice the normal level – this means that the power will be four times that of the quiescent value, i.e. 22 the value of the no modulation level.

If less than 100% modulation is applied, then the carrier will not fall to zero, no will it rise to twice the level, but the deviation will be less than this from the quiescent level. The diagram below shows a level of 50% modulation, but the principle holds good for any value between 0 and 100% modulation.

If the level of modulation is raised up above a modulation index of 1, i.e. more than 100% modulation this causes what is termed over-modulation. The carrier experiences 180° phase reversals where the carrier level would try to go below the zero point. These phase reversals give rise to additional sidebands resulting from the phase reversals (phase modulation). These sideband caused by the phase reversal extend out, in theory to infinity. This can cause serious interference to other users if not filtered.

Broadcast stations using amplitude modulation take measures to ensure that the carries of their transmissions never become over modulated. The transmitters incorporate limiters to prevent more than 100% modulation. They also normally incorporate automatic audio gain controls to keep the audio levels such that near 100% modulation levels are achieved for most of the time. In this way the signal sounds clearer and stronger when demodulated.