Amplitude Modulation Index & Depth

- amplitude modulation index and modulation depth are key parameters for any AM transmission as it is necessary to keep the index or depth within limits to reduce distortion and interference.

It is often necessary to define the level of modulation that is applied to a signal.

In order to have a standard method of achieving this a factor or index known as the modulation index is widely used for this. A complementary figure known as the amplitude modulation depth is also seen on many occasions.

As an indicator of the level of modulation on an amplitude modulated signal, the modulation index is important - too low a level of modulation and the modulation does not utilise the carrier efficiently - too high and the carrier can become over modulated causing sidebands to extend out beyond the allowed bandwidth causing interference to other users.

AM modulation index basics

Modulation indices are described for various forms of modulation. The amplitude modulation, AM, modulation index can be defined as the measure of extent of amplitude variation about an un-modulated carrier.

As with other modulation indices, the modulation index for amplitude modulation, AM, indicates the amount by which the modulated carrier varies around its static un-modulated level.

When expressed as a percentage it is the same as the depth of modulation. In other words it can be expressed as:

The formula for modulation index m = RMS value of modulating signal / RMS value of unmodulated signal

    A is the carrier amplitude.
    M is the modulation amplitude and is the peak change in the RF amplitude from its unmodulated value.

From this it can be seen that for an AM modulation index of 0.5, the modulation causes the signal to increase by a factor of 0.5 and decrease to 0.5 of its original level.

Amplitude modulation depth

A complementary figure to modulation index is also used for amplitude modulation signals. Known as the modulation depth, it is typically the modulation index expressed as a percentage.

Thus a modulation index of 0.5 would be expressed as a modulation depth of 50%, etc.

However often the two terms and figures are used interchangeably and figures for a modulation index of 50% are often seen where the index is 0.5.

Modulation index / modulation depth examples

Typically the modulation index of a signal will vary as the modulating signal intensity varies. However some static values enable the various levels to visualised more easily.

Diagram of a carrier with an amplitude modulation index of 0.5 showing how the modulation rises and falls within the carrier envelope
Amplitude modulated index of 0.5

When the modulation index reaches 1.0, i.e. a modulation depth of 100%, the carrier level falls to zero and rise to twice its non-modulated level.

Diagram of a carrier with an amplitude modulation index of 1 showing how the modulation falls so that the carrier level is zero and it rises to twice the static level
Amplitude modulated index of 1.0

Any increase of the modulation index above 1.0, i.e. 100% modulation depth causes 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) that extend out, in theory to infinity. This can cause serious interference to other users if not filtered.

Diagram showing a modulation index of greater than one showing how the modulation rises to more than twice the static carrier level and falls below the zero line where there is a phase reversal
Amplitude modulated index of more than 1.0
i.e. over-modulated

Broadcast stations in particular take measures to ensure that the carries of their transmissions never become over modulated. The transmitters incorporate limiters to prevent more than 100% modulation. Hover 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.

By Ian Poole

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