Unlike amplitude modulation, prediction of the frequency spectrum occupied by an FM signal requires calculus. The Bessel function table allows predicting the values of the frequency components without requiring calculus.
The left column represents the modulation index for a frequency modulated carrier.
Example:
A high frequency carrier is modulated by a signal frequency in the audio spectrum. We'll use a 99.1 MHz carrier (fc) frequency modulated by a signal (fs) of 2 KHz. The carrier frequency will be shifted by +/- 10 KHz. The modulation index is calculated as:
While the carrier moves at a 2 KHz rate from 99.1 MHz up to 99.11 MHz, anddown to 99.09 MHz, the frequency spectrum produced is complex. The frequency spectrum is not as simple as AM. There is not a single vector above and below the carrier frequency vector. There is a spread of frequency vectors produced that extend well beyond the AM spectrum.
The Bessel function chart tells us how many significant vectors exist. The higher the modulation index, the larger the number of vectors (J terms) produced above and below the carrier vector (Jo). The spacing of the vectors is equal to the lower signal frequency (fs).
The chart shows that for a modulation index (mi, left column) of 5, there are 8 significant side band vectors spaced 2 KHz (fs) apart. These appear as a mirror image above AND below the carrier vector (Jo).
We can sketch these vectors with Jo in the middle ( the carrier frequency ), and J1 through J8 on either side.The actual bandwidth used then is determined by counting the spaces (2 KHz each).
The Federal Communications Commission (FCC) mandates that the bandwidthfor an FM radio station not exceed +/- 75 KHz.While it may not be obvious at this point, this pretty much says that you have to keep your modulation index small. ( mi < .5) Otherwise, your signal will occupy too large a bandwidth and you would be subject to a fine ( $$$ ) !
Since the modulation index is determined by carrier swing and signal frequency,and since you may desire a significant signal frequency, ( audio goes to 15 KHz ),it is necessary to limit your carrier swing, delta fc.In reality, the signal consists of higher frequency components due to stereo and a sub carrier authorization channel sometimes known as Musak. This can extend the fs spectrum past 80 KHz. Subcarriers are used to hide the stereo information and other information that is used to improve the profit picture of the radio station.
This suggests a low amplitude on the signal (fs) to limit FM of the carrier. When you see this on the oscilloscope in the lab, the carrier is deviated a very small amount. This shows up as a small horizontal blur toward the right edge of the oscilloscope screen.