chapter 5. angle modulation husheng li the university of tennessee
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Chapter 5. Angle ModulationHusheng LiThe University of Tennessee
Phase and Frequency Modulation
Consider the standard CW signal
We define the total instantaneous angle
Phase and Frequency ModulationPhase modulation (PM)
Frequency modulation (FM)
Characteristics of Angle Modulation The amplitude of an angle
modulated wave is constant.
The message resides in the zero crossings alone, providing the carrier frequency is large.
The modulated wave does not resemble the message waveform.
Narrowband PM and FM We can expand the signal (using Taylor’s expansion)
The spectrum is given by
Hence, the signal has a bandwidth of 2W.
Example of Narrow Band Angle Modulation
Both PM and FM have carrier component.
Tone ModulationWe can allow a 90 degree difference in the
modulating tones:
Βis called the modulation index for PM or FM with tone modulation.
Spectrum of Narrowband Tone ModulationWhen the modulation index is very small, we
have
The spectrum is given by
Spectrum of Arbitrary Modulation IndexFor a single tone signal with arbitrary
modulation index, the modulated signal can be written as
where j_n(β) is the Bessel function.
Bessel Functions
Characteristic of FM Spectrum
Homework 5Deadline Oct. 14, 2013
Spectrum with Different Modulation IndicesWe can either fix or fix
Multi-toneConsider the case of multiple tones, e.g.,
The modulated signal can be written as
Periodic ModulationWhen the signal is periodic, the Fourier series
are given by
The modulated signal can be written as
Transmission BandwidthThe generation and transmission of pure FM
requires infinite bandwidth. Hence, our questions is: how much of the modulated signal spectrum is significant?
The Bessel function falls off rapidly for
There are M significant sideband pairs and 2M+1 significant lines all told. The bandwidth can be given by
Illustration
Arbitrary Modulated Signal BandwidthFor arbitrary modulating signal, the required
bandwidth is given by
An approximation:
Carson’s rule
(deviation ratio)
Case of Phase ModulationWe can also define the phase deviation.
We have
Linear DistortionWe consider an angle-modulated bandpass
signal applied to a linear system:
The lowpass equivalent output spectrum is
Nonlinear DistortionThe output of signal through a nonlinear
system is given by
Example: ClipperA clipper has only two outputs
The output signal is given by
Procedure of Clipper
Direct FM In direct FM, we use VCO to generate the
frequency modulated by the signal.
Phase ModulatorAlthough we seldom transmit a PM wave, we
are still interested in phase modulators because (1) the implementation is relatively easy; (2) the carrier can be supplied by a stable frequency source; (3) integrating the input signal to a phase modulator produces an FM output.
Switching-circuit ModulatorLarger phase shifts can be achieved by the
switching-circuit modulator:
Indirect FM TransmitterThe integrator and phase modulator constitute
a narrowband frequency modulator that generates an initial NBFM signal with instantaneous frequency:
Triangular-Wave FMTriangular-wave FM is a modern and rather
novel method for frequency modulation that overcomes the inherent problems of conventional CVOs and indirect FM systems.
Frequency DetectionA frequency detector, often called a
discriminator, produces an output voltage that should vary linearly with the instantaneous frequency of the input.
Almost every circuit falls into one of the following four categories:
FM-to-AM conversion
Phase-shift discrimination
Zero-crossing detection
Frequency feedback
FM-to-AM ConversionAny device of circuit whose output equals the
time derivative of the input produces FM-to-AM conversion:
PHASE-SHIFT DiscriminatorsPhase-shift discriminators
involve circuits with linear phase response, in contrast to the linear amplitude response for slope detection:
Quadrature DetectorA phase-shift discriminator built with a network
having group delay and carrier delay:
Zero Crossing Detector
Interference Interference refers to the contamination of an
information-bearing signal by another similar signal, usually from a human source.
Interfering sinusoids: consider a receiver tuned to some carrier frequency. The total received signal is
Demodulated OutputConsider a weak interference. The
demodulated output is
DeemphasisThe fact that detected FM interference is most
severe at large values of |f_i| suggests a method for improving system performance with selective postdetection filtering, called deemphasis filtering.