Chapter Four: Angle ModulationIntroductionFrequency ModulationFrequency DeviationFrequency Modulation IndexPhase ModulationRelationship Between FM and Phase ModulationModulating Signal FrequencyConverting PM to FMThe Angle Modulation SpectrumBessel FunctionsBandwidthCarson’s RuleVariation of FM SignalNarrowband and Wideband FMNarrow- and Wideband SignalsFM and NoiseFM StereoFM Broadcasting SpectraFM MeasurementsChapter Four:Angle ModulationIntroduction•There are three parameters of a carrier that may carry information:–Amplitude–Frequency–Phase•Frequency and Phase modulation are closely related and grouped together as phase modulationFrequency Modulation•Power in an FM signal does not vary with modulation•FM signals do not have an envelope that reproduces the modulation•The figure below shows a simplified FM generatorFrequency Deviation•Frequency deviation of the carrier is proportional to the amplitude of the modulating signal as illustratedFrequency Modulation Index•Another term common to FM is the modulation index, as determined by the formula:mffmPhase Modulation•In phase modulation, the phase shift is proportional to the instantaneous amplitude of the modulating signal, according to the formula: mpekRelationship Between FM and Phase Modulation•Frequency is the derivative of phase, or, in other words, frequency is the rate of change of phase•The modulation index is proportional to frequency deviation and inversely proportional to modulating frequencyModulating Signal FrequencyConverting PM to FM•An integrator can be used as a means of converting phase modulation to frequency modulationThe Angle Modulation Spectrum•Angle modulation produces an infinite number of sidebands•These sidebands are separated from the carrier by multiples of fm•For practical purposes an angle-modulated signal can be considered to be band-limitedBessel Functions•FM and PM signals have similar equations regarding composition•Bessel functions represent normalized voltages for the various components of an AM or PM signalBandwidth•For FM, the bandwidth varies with both deviation and modulating frequency•Increasing modulating frequency reduces modulation index so it reduces the number of sidebands with significant amplitude•On the other hand, increasing modulating frequency increases the frequency separation between sidebands•Bandwidth increases with modulation frequency but is not directly proportional to itCarson’s Rule•Calculating the bandwidth of an FM signal is simple, but tedious using Bessel functions•Carson’s Rule provides an adequate approximation for determining FM signal bandwidth: (max)max2mfB Variation of FM SignalNarrowband and Wideband FM•There are no theoretical limits to the modulation index or the frequency deviation of an FM signal•The limits are a practical compromise between signal-to-noise ratio and bandwidth•Government regulations limit the bandwidth of FM transmissions in terms of maximum frequency deviation and the maximum modulation frequencyNarrow- and Wideband Signals•Narrowband FM (NBFM) is used for voice transmissions•Wideband FM (WBFM) is used for most other transmissions•Strict definition of the term narrowband FM refers to a signal with mf of less than 0.5FM and Noise•One of the original reasons for developing FM was to give improved performance in the presence of noise, which is still one of the major advantages over AM•One way to approach the problem of FM and noise is think of noise as a phasor of random amplitude and phase angleFM Stereo•The introduction of FM stereo in 1961 was accomplished in such a way so as to insure compatibility with existing FM monaural systems•The mono FM receivers must be able to capture the L+R signal of a stereo transmitterFM Broadcasting SpectraFM Measurements•The maximum frequency deviation of an FM transmitter is restricted by law, not by any physical constraint•Traditional oscilloscope displays are not useful in analyzing FM signals•A spectrum analyzer is much more useful in determining the qualities of an FM