This Demonstration illustrates frequency modulation (FM) and phase modulation (PM) using one sinusoidal tone as the modulating signal.
For FM and PM, the modulating signals
are defined by
, respectively, where
is the signal frequency in Hz, and
is its amplitude. This definition for
is used to simplify the spectra of the modulated carrier
by using Bessel functions of the first kind (BesselJ
defined as above, the modulated carrier
can now be defined as
is the modulation index,
is the carrier frequency in Hz, and
is the carrier amplitude.
For FM modulation,
is the deviation constant in Hz per volt, and for PM modulation,
is in radians per volt. (The above units for
assumes that the unit of
The bandwidth of the modulated carrier
is defined as approximately
. This bandwidth contains 98% of the power. For very small
the modulated carrier spectra become a narrow band and for a large
the spectra becomes wideband.
can be adjusted and the effect on the spectra of the modulated carrier can be observed.
This Demonstration also calculates and plots the (normalized) power content of the modulated carrier as a function of the bandwidth. This is also called the power ratio, and is defined as
is a Bessel function of the first kind and
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.