The applet above shows the spectrum of the PM signal(green) and FM signal(red). When the frequency of the modulating signal is changed, the bandwidth of the FM signal remains constant as lower frequencies produce higher modulation indexes. With PM the bandwidth increases with modulating frequency. A PM signal can only use the maximum allowed bandwidth at the highest modulating frequency. With FM the full bandwidth is used at all modulating frequencies and a more efficient transmission system results

A carrier can have its phase or frequency modulated. If the modulating signal is cos(2 fmt), the maximum phase deviation mp and the maximum frequency deviation mf. PM signal can be written as:-

f(t) = sin(2 fct + mp cos (2 fmt));

and an FM signal as:-

f(t) = sin(2 fct + mf/fm sin (2 fmt));