# The standard FM broadcast band has a frequency range of 88 – 108 MHz. Stations are spaced every 200 kHz beginning at 88.1 MHz and up to 107.9 MHz. The maximum permitted deviation is 75 kHz, with modulating frequencies up to 15 kHz. Compute the bandwidth of an FM station using two methods and then discuss how the bandwidth compares with the channel spacing.

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The two methods to compute the bandwidth of an FM station are by using the modulation index and by using the Carson’s rule.

1) The formula for bandwidth calculation using modulation index is given as

where, N is the number of significant sidebands, and fm is the highest modulating frequency

Assuming a modulation index of 2, the number of significant sidebands will be 4. The highest modulating frequency fm is given as 15 kHz. Thus the bandwidth can be calculated as

2) The formula for calculating the bandwidth using Carson’s rule is given as

where fd is the maximum frequency deviation and fm is the maximum modulating frequency.

fd is given as 75 kHz and fm is given as 15 kHz. Thus substituting these values in the formula the bandwidth is calculated as

Discussion on bandwidth and channel spacing:

As mentioned the stations are spaced every 200 kHz. As per the calculation of the bandwidth using Carson’s rule there will be very narrow spacing between two channels. Whereas with the modulation index method the spacing will be larger compared to the Carson’s rule. However it should be noted that if a higher modulation index is taken the spacing between two channels will reduce as the number of sidebands will increase, thus increasing the bandwidth.