For FM, the modulating signal m (t) is defined as
And for PM
where is the signal frequency in Hz and is its amplitude. This definition for is used to simplify determining the spectra of the modulated carrier by the use of BesselJ functions.
With defined as above, the modulated carrier can now be defined as
where is the modulation index, is the carrier frequency in Hz and is the carrier amplitude.
For FM modulation,
where K is the deviation constant in Hz per volt, and for PM modulation,
where is in radians per volt. The above units for assumes that the unit of is volts.
The bandwidth of the modulated carrier is defined as approximately . This bandwidth contains small the modulated carrier spectra become a narrow band and for a large the spectra becomes wideband.
The parameters can be adjusted and the effect on the spectra of the modulated carrier can be observed.
The demonstration also calculates and plots the power content (normalized) of the modulated carrier as a function of the bandwidth. This is also called the power ratio, and defined as
where BesselJ is Bessel function of the first kind, and M is the number of sidebands on each side of the carrier frequency .
This plot is useful in the design of FM and PM modulators as it allows one to determine the size of the bandwidth needed for a given power ratio.