Chapter 5. Angle Modulation 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)  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 Modulation  We 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 Modulation  When the modulation index is very small, we have  The spectrum is given by

Spectrum of Arbitrary Modulation Index  For 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 5  Deadline Oct. 14, 2013

Spectrum with Different Modulation Indices We can either fix or fix

Multi-tone  Consider the case of multiple tones, e.g.,  The modulated signal can be written as

Periodic Modulation  When the signal is periodic, the Fourier series are given by  The modulated signal can be written as

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

Illustration

Arbitrary Modulated Signal Bandwidth  For arbitrary modulating signal, the required bandwidth is given by  An approximation: Carson’s rule (deviation ratio)

Case of Phase Modulation  We can also define the phase deviation.  We have

Linear Distortion  We consider an angle-modulated bandpass signal applied to a linear system:  The lowpass equivalent output spectrum is

Nonlinear Distortion  The output of signal through a nonlinear system is given by

Example: Clipper  A 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 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.

Switching-circuit Modulator  Larger phase shifts can be achieved by the switching-circuit modulator:

Indirect FM Transmitter  The integrator and phase modulator constitute a narrowband frequency modulator that generates an initial NBFM signal with instantaneous frequency:

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.

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 discrimination  Zero-crossing detection  Frequency feedback

FM-to-AM Conversion  Any device of circuit whose output equals the time derivative of the input produces FM-to-AM conversion:

PHASE-SHIFT Discriminators  Phase-shift discriminators involve circuits with linear phase response, in contrast to the linear amplitude response for slope detection:

Quadrature Detector  A 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 Output  Consider a weak interference. The demodulated output is

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.