Ch. 4 Linear Modulation

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Mohammad Fathi

Department of Electrical Engineering, University of Kurdistan,Sanandaj, Iran

[email protected]

March 2011

Linear Modulation

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Introduction

Modulation is the systematic alteration of one waveform, calledcarrier, according to the characteristics of another waveform, themodulating signal.

Continuous wave modulation:

The carrier is a sinusoidal wave modulated by an analog signal. Linear modulation: Amplitude modulation: direct frequency

translation of the signal spectrum

Nonlinear modulation: Frequency modulation

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Outline

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Bandpass signals and systems

Double side band amplitude modulation

Standard amplitude modulation (AM)

suppressed-carrier double side band modulation (DSB)

Modulators and transmitters

Suppressed sideband amplitude modulation

Single side band modulation (SSB)

Vestigial sideband modulation (VSB)

Demodulation

Bandpass signals and systems

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Most transmission systems have a bandpass frequency response.


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Bandpass signal

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Consider a real energy signal vbp(t) with spectrum Vbp(f). This

spectrum exhibits hermitian property, i.e. Vbp* (-f).

Wandfc are arbitrary as long as W< fc

This signal is defined as bandpass if

Band pass signal: Envelope-Phase

description

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The corresponding bandpass signal looks like a sinusoid atfrequency fc with slowly changing amplitude and phase angle.

A(t): envelope

: phase


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Band pass signal: Quadrature-carrier

description

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Another way of writing vbp(t). Let

vi(t): In-phase element vq(t): Quadrature element

Frequency analysis

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In frequency domain, the quadrature-carrier description is usuallyused:

Where

In order to satisfy the bandpass condition, vi(t) and vq(t) should below pass signals, i.e.


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Lowpass equivalent spectrum

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The lowpass equivalent spectrum ofVbp(f) is defined as

Vlp(f) Simply equals the positive frequency portion ofVbp(f)translated down to the origin.

Lowpass equivalent signal:

Complex signal

Lowpass to bandpass

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Time domain:

Frequency domain:


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Bandpass transmission

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It is usually easier to work with low pass equivalent transferfunction.

After finding the low pass response, perform lowpass to bandpasstransformation

Amplitude modulation (AM)

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The envelope of the modulated carrier has the same shape as themessage.

Ac : unmodulated carrier amplitude

x(t): message signal

: modulation index

The envelope clearly reproduce the shpae of x(t) if

Otherwise, an envelope can not be visualized.


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AM spectrum

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AM requires twice the bandwidth needed to transmitsthe message at baseband without modulation.


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AM transmission power

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Average transmitted power

If Putting in the form

Pc: unmodulated carrier powerPsb: power per sideband

Since

At lest 50 percent of the total transmission power resides in a carrierterm that is independent of the message.

Double sideband suppressed-carreier

modulation (DSB)

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The wasted carrier power in AM can be eliminated by setting 1 and suppressing the carrier frequency. The DSB-SC spectrum looks likes AM spectrum without the

carrier impulse.


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DSB

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Full recovery of the message requires knowledge of the phasereversal and could not be accomplished by a envelope detector.

DSB-SC makes better use of the transmission power

Practical transmitters impose a limit on the peak envelope power:

with Amax=Ac for DSB and Amax=2Ac for AM, we have

With fixed envelope power, if other factors are equal, a DSB-SCtransmitter produces four times the sideband power of an AMtransmitter. This is a tradeoff between transmission power anddemodulation methods.

Example

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Modulators and transmitters

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Since AM and DSB-SC spectrum contains frequencies other thanthe message, the modulator must therefore be a time-varying ornonlinear system.

Modulators

Product modulators

Square-law modulators

Balanced modulators

Switching modulators

Product modulator

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Signal multiplication at higher frequencies can be accomplished by the square-law modulators.

A nonlinear element approximates the square-law transfer curvature.


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Iffc>3W, the AM wave can be separate by filtering with B=2Wcentered atfc.

We have a DSB wave if a1= 0 , corresponding to the perfect square law curve:


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Balanced modulators

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Perfect square-law devices are rare, so high frequency DSB isobtained in using two AM modulators arranged in a balancedconfiguration to cancel out the carrier, called balanced modulator.

Switching modulators

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Because of the required filtering, square-law modulators are primarily usedin low power modulation. The following RF power amplifier with requiredlinearity is of high problems.

Switching modulators are used when power ST is to be large.

The tank circuit is tuned toresonate at fc.


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Suppressed sideband AM

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Suppressing one sideband in DSB, in whole or part, reducestransmission bandwidth and leads to Single sideband modulation (SSB)


Conceptual approach of SSB

SSB analyze in time domain

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Input: output:

The output is obtained by applying equivalent low pass method:

Low pass input

USSB filter

LSSB filter

Both filters


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SSB analyze in time domain

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In-phase and quadrature components

Envelope

Low pass output

SSB generation (1)

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Conceptual SSB generation calls for the ideal filter with a perfectcutoff atfc, which is not realizable.

A real sideband filter will either pass a portion of the undesiredsideband or attenuate a portion of the desired sideband (Doing sois called vestigial sideband modulation) .


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SSB generation (1)

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SSB is suitable for signals with little or no low frequency content,which their spectra having holes at zero frequency, e.g audiosignal.

SSB generation (2)

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Rewriting the SSB output

Phase-shift SSB generation:

Bypasses the need of sideband filters

HQ(f) is an unrealizable network that can only be approximated.


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Signals with low frequency content such as television video haveproblems with SSB. The compromise modulation scheme is VSB.

VSB is derived by filtering DSB or AM in such a fashion that onesideband is passed almost completely with just a trace or vestige of theother sideband.

Taking upper sideband case


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Depending on the vestige width , VSB approximates SSB or DSBmodulation.

The transmission power is not easy to determine exactly, but isbounded by

If an AM wave is applied to a vestigial filter, the resultingmodulation is VSB plus carrier (VSB+C).

This modulation is used in television video transmission.

VSB+C allows envelope detection.


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Demodulation

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Demodulation implies downward frequency translation in order torecover the message from the modulated wave:

Synchronous detection (Synchronous product detection, Homodyne detection)

Envelope detectors

Frequency translation or conversion is performed withmultiplication by a sinusoid.

Devices that carry out this operationare called frequency convertors ormixers. The operation is termedheterodyning or mixing.

Synchronous product detection

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All types of linear modulation can be detected by theproductdemodulator.

It is assumed that local oscillator (LO) is exactly synchronizedwith the carrier in both frequency and phase (Synchronous orcoherent detection).

Let the input signal be the generalized form:

Then


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Synchronous product detection

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With low pass filtering, we have KD: detection constant

KD KC : DC term corresponds to the translated carrier if present. This canbe removed by a blocking capacitor or transformer.

VSB

Recalling the symmetryproperty of the vestigial filter,

we find that the portionremoved from upper sidebandis exactly restored by thecorresponding vestige of thelower sideband.

Homodyne detection

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Synchronizing an oscillator to a sinusoid is the difficulty ofproduct demodulators in practice.

Homodyne detector

To facilitate the matter, suppressed carrier systems may have a smallamount of carrier reinserted in the transmitted signal.

This pilot carrier is picked off at the receiver by a narrow bandpass filter, amplified and used in place of an LO.

The pilot carrier may also be used to synchronize a separateoscillator.


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Envelope detection

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The envelope of an AM wave has the same shape of the message.

Demodulation can be accomplished by extracting the envelopewith no worries about synchronization. Vis the half-rectified version of

the input Vin.

R1C1 : low pass filter

R2C2 acts as a dc block to removethe bias of the unmodulated

carrier component.

Envelope reconstruction in DSB and SSB

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The addition of a large, locally generated carrier to the incomingsignal reconstructs the envelope for recovery by an envelopedetector.

This method eliminates signal multiplication but does not get

around the synchronization problem.

Ch. 4 Linear Modulation

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