Chapter 5. Angle ModulationHusheng LiThe University of Tennessee

Phase and Frequency ModulationConsider 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 forThere 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.