Frequency Modulation

FM is a so called angle modulation scheme, it was inspired by phase modulation but has proved to be more useful partly for its ease of generation and decoding. The main advantages of FM over AM are:

1. Improved signal to noise ratio (about 25dB) w.r.t. to man made interference.
2. Smaller geographical interference between neighboring stations.
3. Less radiated power.
4. Well defined service areas for given transmitter power.

1. Much more Bandwidth (as much as 20 times as much).
2. More complicated receiver and transmitter.

In this scheme the frequency of the modulating signal is changed in proportion to the message signal . Thus the signal that is transmitted is of the form

Here the signal

is assumed to be normalized so that the maximum of the integral is 1 and

is called the frequency deviation of the modulation scheme. The index of modulation of an FM signal of the form

is defined to be

Figures 3, 4, and 5 are examples of what FM signals look like in the time domain for a message signal of the form

  
Figure 3: FM modulation with modulating frequency 1, carrier frequency 10 and modulation index 2

In general the determination of the frequency content of an FM waveform is complicated, but when

is small, for a sinusoidal signal

, the bandwidth of the FM signal is

On the other hand when

is large, the bandwidth is determined (empirically) to be

Your FM dial goes from 88 MHz to 108 MHz (this range is in between the frequency ranges for the TV channels 1-6, and 7-12. For a typical radio station,

varies from about 150 at low frequencies like 50 Hz to 3.75 at high frequencies (20 KHz), and a very rough bandwidth figure is 200 KHz. Thus, KDFC 102.5 on your FM dial goes from 102.4 MHz to 102.6 MHz.

  
Figure 4: FM modulation with modulating frequency 2, carrier frequency 10 and modulation index 2

  
Figure 5: FM modulation with modulating frequency 1, carrier frequency 10 and modulation index 5

Try to puzzle over how you might try to demodulate FM (think differentiation!).