December 24, 2016

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 ... and ... , 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 ( ... in Mathematica). 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 ... 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 98% of the power. For very 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. 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 ... , where ... 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.