Husheng Li The University of Tennessee Phase and Frequency Modulation Consider the standard CW signal We define the total instantaneous angle Phase and Frequency Modulation Phase modulation PM ID: 550111
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Slide1
Chapter 5. Angle Modulation
Husheng Li
The University of TennesseeSlide2
Phase and Frequency Modulation
Consider the standard CW signal
We define the total instantaneous angleSlide3
Phase and Frequency Modulation
Phase modulation (PM)
Frequency modulation (FM)Slide4
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.Slide5
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.Slide6
Example of Narrow Band Angle Modulation
Both PM and FM have carrier component.Slide7
Tone Modulation
We can allow a 90 degree difference in the modulating tones:
Β
is called the modulation index for PM or FM with tone modulation.Slide8
Spectrum of Narrowband Tone Modulation
When the modulation index is very small, we have
The spectrum is given bySlide9
Spectrum of Arbitrary Modulation Index
For a single tone signal with arbitrary modulation index, the modulated signal can be written as
w
here
j_n(β) is the Bessel function.Slide10
Bessel FunctionsSlide11
Characteristic of FM SpectrumSlide12
Homework 5
Deadline Oct. 14, 2013Slide13
Spectrum with Different Modulation Indices
We can either fix or fix Slide14
Multi-tone
Consider the case of multiple tones, e.g.,
The modulated signal can be written asSlide15
Periodic Modulation
When the signal is periodic, the Fourier series are given by
The modulated signal can be written asSlide16
Transmission Bandwidth
The 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 Slide17
IllustrationSlide18
Arbitrary Modulated Signal Bandwidth
For arbitrary modulating signal, the required bandwidth is given by
An approximation:
Carson’s rule
(deviation ratio)Slide19
Case of Phase Modulation
We can also define the phase deviation.
We haveSlide20
Linear Distortion
We consider an angle-modulated
bandpass
signal applied to a linear system:The
lowpass equivalent output spectrum is Slide21
Nonlinear Distortion
The output of signal through a nonlinear system is given bySlide22
Example: Clipper
A clipper has only two outputs
The output signal is given bySlide23
Procedure of ClipperSlide24
Direct FM
In direct FM, we use VCO to generate the frequency modulated by the signal.Slide25
Phase Modulator
Although 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.Slide26
Switching-circuit Modulator
Larger phase shifts can be achieved by the switching-circuit modulator:Slide27
Indirect FM Transmitter
The integrator and phase modulator constitute a narrowband frequency modulator that generates an initial NBFM signal with instantaneous frequency:Slide28
Triangular-Wave FM
Triangular-wave FM is a modern and rather novel method for frequency modulation that overcomes the inherent problems of conventional CVOs and indirect FM systems.Slide29
Frequency Detection
A 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 discriminationZero-crossing detectionFrequency feedbackSlide30
FM-to-AM Conversion
Any device of circuit whose output equals the time derivative of the input produces FM-to-AM conversion:Slide31
PHASE-SHIFT Discriminators
Phase-shift discriminators involve circuits with linear phase response, in contrast to the linear amplitude response for slope detection:Slide32
Quadrature Detector
A phase-shift discriminator built with a network having group delay and carrier delay:Slide33
Zero Crossing DetectorSlide34
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 isSlide35
Demodulated Output
Consider a weak interference. The demodulated output isSlide36
Deemphasis
The 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.