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Figure 34-5. Bessel functions

Example 1. A commercial FM broadcast transmitter has a deviation ratio of 5 and the
frequency of the modulating audio is 15kHz. Determine (a) the amount of frequency
deviation and (b) the occupied bandwidth (BW) of the transmission.

Answer: the deviation is 75kHz and the occupied bandwidth is 180kHz.

Explanation:

We learned that modulation index = deviation / frequency of the modulating audio. This
is more often written as µ =Δf/fs. This equation can be transposed to give:
Δf (deviation) µ x fs and for our problem this gives:-
Δf (deviation) = 5 x 15kHz = 75kHz.

The significant number of side frequencies present in the transmitted wave is given by:
significant side frequencies= 2 (µ+1) = 2(5+1) =12.

Since each of these 12 significant side frequencies are spaced apart by an amount
equal to the frequency of the modulating audio (15kHz), then the bandwidth is:

BW = 12 x 15kHz = 180kHz.

A slightly easier method for determining the bandwidth of an FM wave can be derived.
In the last example we found the bandwidth from:

BW = 2(µ+1) x fs

By multiplying each term within the brackets by fs we get:

BW = 2(µ x fs + 1 x fs).

Since µ x fs equals the devia�on, the equa�on can be simplified to:

BW= 2(Δf +fs).
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