Frequency Modulation
Cuthbert Nyack
In frequency modulation the amplitude is kept constant and the
frequency is modulated by the amplitude of the modulating
signal. The modulation index for fm is
m = maximum frequency
deviation/modulating frequency.
FM signal can be represented
as:-
v = ac sin(wct
+ m sin wmt )
The frequency spectrum can be found by rewriting the above
expression as a sum of components of constant frequency using
the properties of the Bessel Functions. This gives:-
v = ac{Jo(m)
sin(wct)
+ J1(m)[sin(wc
+ wm)t - sin(
wc
- wm)t]
+ J2(m)[sin(wc
+ 2wm)t + sin(
wc
- 2wm)t]
+ J3(m)[sin(wc
+ 3wm)t - sin(
wc
- 3wm)t]
+ ...
This expression implies that the FM spectrum consists of a component at
wc and an infinite number
of lines at wc
± nwm
and that the amplitude of the components are given by the bessel
functions.
Applet below shows a modulating signal in orange, the FM signal in red,
the frequency spectrum in black and how they vary with the modulation
index and modulating frequency.
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COPYRIGHT © 1996 Cuthbert Nyack.