# Frequency Modulation, FM Modulation Index & Deviation Ratio

### FM Tutorial includes

In order to characterise frequency modulated signals there are figures used that are the equivalent of those used for AM.

The modulation index and deviation ratio for FM are two of the major ones used. These appear to be very similar to each other but they are subtly different.

In view of the slight differences between the definitions for FM modulation index and FM deviation ratio, there is often confusion between the two terms.

## FM modulation index

In terms of a definition: the FM modulation index is equal to the ratio of the frequency deviation to the modulating frequency.

Thus the formula for the modulation index for FM is simple given by that shown below:

## FM deviation ratio

The modulation index will vary according to the frequency that is modulating the transmitted carrier and the amount of deviation. However when designing a system it is important to know the maximum permissible values. This is given by the deviation ratio and is obtained by inserting the maximum values into the formula for the modulation index.

Thus the FM deviation ratio can be defined as: the ratio of the maximum carrier frequency deviation to the highest audio modulating frequency.

Where
D = Deviation ratio.

To give an example of how the deviation ratio may be calculated and used, take the example of an FM broadcast transmitter. For these the maximum deviation is ±75 kHz and the maximum modulation frequency is 15 kHz. This means that the deviation ratio is 75 / 15 = 5.

## Modulation index & FM bandwidth

It will often be seen that the terms narrowband or wideband FM are used when describing the form of FM being used.

• Narrowband FM:   Narrow band FM is defined as an FM transmission where the value of Β is small enough that the terms in the Bessel expansion, i.e. sidebands are negligible. For this to be the case the modulation index must be less than 0.5, although a figure of 0.2 is often used. Narrowband FM is often used for short distance communications using vehicle mount radios or hand carried equipment. Here the narrow band means that the audio or data bandwidth is small, but this is acceptable for this type of communication.
• Wideband FM:   Wideband FM is defined as the situation where the modulation index is above 0.5. Under these circumstances the sidebands beyond the first two terms are not insignificant. Broadcast FM stations use wideband FM, and using this mode they are able to take advantage of the wide bandwidth available to transmit high quality audio as well as other services like a stereo channel, and possibly other services as well on a single carrier.

The bandwidth of the FM transmission is a means of categorising the basic attributes for the signal, and as a result these terms are often seen in the technical literature associated with frequency modulation, and products using FM. This is one area where the figure for modulation index is used.

By Ian Poole

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