Notes on Modulation

8/12/2019 Notes on Modulation

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ELE444 Communication System Electronics

1

MODULATION

Necessity for modulation

The term modulation is generally defined as the alteration or modification of any electronic parameter by another. In radio transmission and propagation, modulation is a process by which

certain characteristics of a carrier wave are modified, or modulated, in accordance with acharacteristic of another wave known as the modulating signal or message (signal).

There are two important reasons for using modulation in radio transmission & propagation:

Most electronic message signals (e.g. speech converted to electronic form by a microphone)are outside the range of electromagnetic frequencies which propagate well and requiremodulation onto a radio-frequency carrier before transmission.

Various parts of the radio frequency spectrum are designated for particular applications andmessages for transmission must be shifted in frequency (modulated) to the correct radio-frequency band to avoid causing interference to other legitimate users, and to avoidinterference from other radio transmissions.

Certain types of modulation may sometimes be used to provide the modulated signal with adegree of immunity to degradation over long distances by electrical noise (described later).

Basic principles of amplitude & frequency modulation

Amplitude modulation

The process of varying the instantaneous amplitude of a radio-frequency carrier signal by amodulating signal is known as amplitude modulation (AM) and is illustrated in Figure 1.Amplitude modulation is part of the family of analogue modulation systems , in which ananalogue property of the carrier signal (in this case, the amplitude) is modulated by the messagesignal.

In order to simplify the analysis of amplitude modulation, the modulating signal, or message, isconsidered to be a simple, single-frequency sinusoidal signal. If the modulating signal isdescribed by the equation:

v V t m m m= sin

The amplitude modulated carrier varies in amplitude according to the equation:

( )v V V t t c c m m c= + sin sin

Thus, the amplitude of the modulated carrier varies between V c V m, as shown in the followingdiagram.

ECS606U Communication Systems Electronics


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Figure 1

Expanding out the right-hand side of the previous equation gives:

( ) ( )[ ]( ) ( )

v V t V t t

v V t mV t t

mV V

a b a b a b

v V t mV t mV t

c c c m m c

c c c c m c

m

c

c c c c c m c c m

= += +

=

= += + +

sin sin sin

sin sin sin

sin sin cos cos

sin cos cos

where is the modulation factor

remembering that:12

12

12

This equation shows that the AM carrier signal consists of three frequency components:

the unmodulated carrier V csin( ct )

a lower sideband mV ccos(( c - m)t )/2

an upper sideband mV ccos(( c + m)t )/2

t

t

V

V V c

V c + V m

V c - V m

V m

Modulating signal

Amplitude modulated carrier signal



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3

Figure 2 shows this in the frequency domain. Note that f c = c /2, etc.

Figure 2

In the case of more complex modulating signals containing several different frequencycomponents, the lower and upper sidebands extend to the width of the original modulating signalspectrum. This is illustrated in Figure 3.

Figure 3

It can be seen from Figure 3 that AM is inefficient in that the sidebands around the radio-frequency carrier duplicate the original message information. Not only is this wasteful onspectrum occupancy, but it is inefficient from a power point of view. Since signal power is

proportional to the square of the signal amplitude (voltage), the total power of an AM signal(measured across a 1 resistor) is:

( ) ( )V mV V mc c c2 12 2 2 12 22 1+ = +

And the ratio of sideband power to total power is:

( )( )

2

1 2

12

2

2 12

2

2

2mV

V mm

mc

c + =

+

frequency

amplitude

carrier

upper sidebandlower sideband

f c f c - f m f c + f m

frequency

carrier

upper sidebandlower sideband

amplitude

modulating signal

0 f c



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From which the transmission efficiency is defined as:

=+

mm

2

22100%

It can be seen that:

The maximum transmission efficiency is only 33% when the modulation factor m has itsmaximum value ( m = 1.0).

Although the sideband power is proportional to m2, practical limitations usually limit m to lessthan 0.8, considerably reducing the useful power transmitted.

The carrier and one sideband may be suppressed without any loss of information since theoriginal message information is present in each sideband - this will be described later.

A sinusoidal a.c. signal may be represented in phasor form and hence an AM signal can beconsidered in terms of phasors as shown in Figure 4 below. The full phasor representation on theleft of Figure 4 can be simplified by applying a clockwise rotation at an angular frequency of Cto the whole phasor diagram, having the effect of making the carrier appear stationery and, thesidebands rotating at m relative to the carrier.

Figure 4

As previously mentioned, the transmission efficiency of AM can be improved by removing someof the unnecessary frequency components. This results in Double Sideband Suppressed Carrier AM (DSBSC-AM) when the carrier component C is removed at the transmitter, and in Single

V c

c - m c + m

c

V c

m m

LSBUSB

USB LSB

Rotating carrier Stationery carrier



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Sideband Suppressed Carrier AM (SSBSC) when both the carrier and one sideband areremoved. These techniques will be discussed more fully in a later section which describesmodulators and demodulators.

Frequency modulation

The process of varying the instantaneous frequency of a radio-frequency carrier signal by amodulating signal is known as frequency modulation (FM) and is illustrated in Figure 5.

Figure 5

The mathematical expression for a modulated FM carrier is derived separately see Notes on theSpectrum of an FM Carrier with Sinusoidal Tone Modulation .

It can be seen that a unit amplitude fm signal can be described by:

( )t t v mc fm sincos +=where is the Modulation Index and is the ratio of frequency deviation to modulating frequency.

Note that although the modulating signal is of the form cos mt , the modulation-dependent phaseterm in the equation for v fm is of the form sin mt . This will be referred to again later.

The spectrum of an FM signal is also derived separately and is of the form:

( ) ( ) ( )[ ]mcmcn fm nf f f nf f f J f V ++= +

21)(

The expression for V fm(f) shows that the frequency spectrum of a modulated FM signal consistsof a carrier at frequency f = f c and an infinite series of sidebands at frequencies:

f = f c f m, f c 2 f m, f c 3 f m, f c 4 f m, etc.

t

t

amplitude

amplitude

Modulating signal

Frequency modulated carrier signal



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with diminishing amplitudes proportional to J 1( ), J 2( ), J 3( ), J 4( ), etc. The carrier termamplitude is proportional to J 0( ), and is therefore dependent on the modulation index . Thiscan be explained by noting that the amplitude of the modulated carrier in the time domainremains constant, and hence its power also remains constant. As increases and more sidebands

become significant, their power comes from the carrier which must, therefore, decrease in powerin the frequency-domain representation. Note that as in the AM case, a mirror-image spectrumof sidebands exists below the carrier frequency f c and is given by the ( f + f c - nf m) terms above.

Some Bessel functions are plotted below in Figure 6 from which it can be seen that for 2.4,5.25, 8.65 etc., J 0( ) = 0 and the carrier component disappears from the spectrum. For othervalues of the carrier component amplitude varies considerably. Note that the negative valuesof the Bessel functions of Figure 7 denote a 180 phase shift of the corresponding term in thetime domain, but in the frequency domain the existence of components at particular frequenciesis more important than their phase; thus sideband spectrum plots generally ignore phase, showingall components with a positive amplitude.

The extent of significant sidebands is given by Carson's Rule which states that the sidebands ofsignificant amplitude lie within a bandwidth of 2 f m(1 + ) Hz, located centrally about the carrierfrequency f c. This rule somewhat underestimates the bandwidth requirements of FM signals andthe expression 2 f m(2 + ) Hz is more accurate.

Figure 6 illustrates some sideband spectrum plots for a few values of Modulation Index .

Figure 6

Bessel functions of order n

-

-

-

0.000

0.200

0.400

0.600

0.800

1.000

1.200

0 0. 1. 2. 3. 4. 4. 5. 6. 7. 8. 8. 9. 10.4 11.2 12.0 12.8 13.6 14.4

Modulation Index

Amplitud

J 0

J 1 J 2 J 3



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Figure 7

From Figure 7 it can be seen that for > 1 the spectrum of an FM modulated carrier is generallymuch wider than that of an AM modulated carrier and this may appear as a disadvantage.However, the Hartley-Shannon Law in information theory shows that it is possible to obtain animproved signal-to-noise ratio by using a greater bandwidth, and FM is an example of amodulation system with good noise immunity.

Figure 8 shows a simple phasor diagram for a modulated FM carrier includng only frequencydeviations from the unmodulated carrier frequency c and, in the absence of modulation, thecarrier is assumed to be at rest as shown in the central position. The application of a modulatingsignal causes the position of the carrier phasor to oscillate at a frequency m between the limitsshown. Note that the peak angular velocity (and hence frequency) will occur as the phasor passesthrough the central position, and as it momentarily pauses at the two extremes its frequency will

be c. It may help to think of the motion of the phasor as similar to that of an inverted pendulum.

position of unmodulatedphasor

limits of maximumdeviation

= c / m = Figure 8

f c

= 1

= 3

= 5

f c

f c



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Narrowband FM

If the modulation index < 1 the sideband spectrum becomes similar to that of AM and themodulation is known as narrowband FM. Although narrowband FM requires a much lower

bandwidth than conventional FM, it does not exhibit such good noise immunity, and it can be

shown that the signal-to-noise improvement gained from FM increases with increasing frequencydeviation.

Phase Modulation (PM)

In the analysis of FM, it was evident that the modulation of the frequency of the carrier wasachieved by modulating its phase by the integral of the modulating signal; FM and PM are thusvery closely related and this relationship is illustrated in the block diagrams of Figure 9.

Figure 9

I Phase Modulator v m (t)

Frequency Modulator d dt

v m (t)

FM

PM

Frequency modulation using a phase modulator

Phase modulation using a frequency modulator



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Modulators & demodulators for amplitude & frequency modulation

Double sideband amplitude modulators

Linear modulators

Probably the most frequently used method of generating DSBAM in radio transmitters is to usean anode-modulated, or a collector-modulated, Class-C tuned radio-frequency amplifier. Theanode or collector current of a Class C amplifier is directly proportional to the anode or collectorsupply voltage, and hence if the grid or base is driven by a signal at the carrier frequency c, andthe anode or collector supply is varied by the modulating signal vm, a DSBAM signal is producedacross the tuned anode or collector load.

Non-linear modulators

DSBAM signals can be generated by applying the unmodulated carrier signal vc and the

modulating, or message, signal vm to the input of a non-linear amplifier. In the notes onRegulatory Aspects, the problem of intermodulation distortion was considered, and it was shownthat the application of two, simultaneous, sinusoidal signals at frequencies 1 and 2 producedoutputs at frequencies of ( 1 2) in addition to the components at frequencies 1 and 2.These sum and difference components are of a similar form to the two sidebands of a DSBAMsignal. Thus, if a carrier-frequency signal and the modulating signal are simultaneously applied toa non-linear amplifier with a tuned load acting as band-pass filter, the output will be a DSBAMsignal. The principle is illustrated in Figure 10.

Figure 10

+VCC

DSBAMoutput

Modulatingsignal input

Carrier signalinput

0V



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Balanced modulators & Double Sideband Suppressed Carrier (DSBSC) AM

Since the carrier component of a DSBAM signal has no information content, it can theoretically be removed at the transmitter with a considerable saving of power, resulting in a DSBSC system.The disadvantage of this is that it complicates receiver design, as the receiver has to re-insert acarrier before the signal can be demodulated, and there are stringent phase requirements on the

re-inserted carrier at the receiver. One way around this problem is to insert a low-level carrierinto the DSBSC signal which can be used by the receiver to regenerate the correct carriercomponent prior to demodulation. Modulators producing DSBSC signals are known as balancedmodulators since the symmetry of the two parts of the modulator circuit results in cancellation ofthe carrier component. The block diagram of Figure 11 illustrates the basic arrangement of a

balanced modulator which again uses non-linear transfer characteristics to produce the sum anddifference frequencies.

Figure 11

DSBSCAM can also be produced by balanced modulators of the switching type. These employdiodes which are driven into and out of conduction by a switching wave at the carrier frequency,either 'chopping' ( Cowan modulator) or reversing ( Ring modulator) the modulating or messagesignal at the carrier rate, leading to a pulsed message waveform containing the usual sum anddifference frequencies. A band-pass filter is required at the output to pass the required DSBSCcomponents and to suppress all other components, of which there are many. Figure 12 illustratesthe Ring or Diode balanced modulator and its waveforms are shown in Figure 13; the Cowanmodulator is described in a many of the radio textbooks.

Non-linear

device

Non-linear device

m

c

DSBSCoutput



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Figure 12

Figure 13

Single sideband amplitude modulators

Single sideband AM can be achieved in several ways, the simplest of which is to insert a bandpass filter at the output of a DSBSC modulator so that the filter passes only one sideband,thus producing a SSBSC signal. Another method involves phase-shifting both the modulatingand carrier signals by 90 before applying the unshifted signals to one balanced modulator, andthe phase-shifted signals to a second balanced modulator; finally the two balanced modulatoroutputs are combined to produce a SSBSC signal. In practice, it is difficult to design suitable 90

phase shift networks which will operate over the bandwidth of the modulating signal. Yetanother method (the Third method or Weaver method) uses two pairs of double balanced

m

c

DSBSCoutput

t

V m

Modulating (message) signal

t

V o

Modulator output signal

Carrier-frequency switching signal

V c



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modulators with one modulator of each pair driven by cos ct , and the other by sin ct . Many ofthe radio textbooks explain these in block diagram form.

Vestigial (VSB) sideband modulators

To overcome the unnecessarily wide bandwidth required by DSB AM systems a modified form

of DSB is sometimes used in which a vestige of one sideband is transmitted together with thewhole of the other sideband; modulation of this form is known as vestigial sideband (VSB) AM.The best known example of this is in television broadcasting where a 12MHz bandwidthrequirement for DSB modulation is reduced to 8MHz with VSB transmission. Modulator designis generally based on conventional DSB modulators with an appropriate filter to eliminate part ofone sideband, forming the vestigial sideband.

AM demodulators (detectors)

The techniques used to demodulate, or detect, a DSBAM signal consist of three main types:

non-coherent or envelope detection

coherent or synchronous detection

non-linear detection

Envelope detection

As its name implies, envelope detection recovers the envelope or amplitude variations ofDSBAM signals. Figure 1 shows that both the positive and negative envelopes of a DSBAMsignal are of exactly the same form as the original modulating signal. Thus demodulation simplyconsists of rectifying the DSBAM signal to remove the negative-going part, and then filtering toremove the remains of the carrier component. Figure 15 illustrates the processes involved inenvelope detection and Figure 14 shows the basic envelope detection circuit.

Figure 14

DSBAM inputdetected

(demodulated)output

rectification dc blocklow-pass filter



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Figure 15

Synchronous detection

The process of synchronous detection is somewhat similar to the original modulation process inthat the received DSBAM signal and an unmodulated carrier of the correct frequency and phaseare multiplied together in a non-linear device. The required demodulated signal is extracted fromthe other products present at the output by a low pass-filter. The equations below illustrate the

process where vr is the received DSBAM signal and vl is the local oscillator signal at the originalcarrier frequency.

( )

( )( ) ( )( )

v V m t t

v V t

v v V m t t

v v V m t t

v v V m t m t t

m t

r c m c

l c c

r l c m c

r l c m c

r l c m m c

m

= +=

= + = + = + +

1

1

1 1 2

1 2

2 2

2 12

12

2

sin sin

sin

sin sin

sin cos

sin sin cos

sin

then

from which the component can be recovered by filtering.

As noted previously, the provision of the correct carrier frequency signal at the receiver isdifficult, adding to the complexity and cost of the receiver. For these reasons, synchronousdetection is usually confined to SSBSC systems, where envelope detection cannot be used.

Non-linear (square-law) detection

If a DSBAM signal is applied to a non-linear device such as a diode, having a square-lawcharacteristic, the v2 term of the transfer characteristic will produce a component at the originalmodulating or message frequency. Assuming a DSBAM signal vr as above:

t

V

0

negative-going portionof DSBAM waveformremoved by rectification

carrier frequencycomponets removed

by filtering

original modulation(message) atdetector output



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( )( )( )

( )( )[ ]( )

V m t t

V m t t

V m t m t t

v V t m t t m t t

v V t m t t m t t

v V t m t t m t m

r c m c

r c m c

r c m m c

r c c m c m c

r c c m c m c

r c c m c m

= +

= += + +

= + += + +

= + +

1

1

1 2

2

2 1 2

2

2 2 2 2

2 2 2 2 2

2 22 2 2 2 2

2 2 2 2 2 2 12

2 2 2 2 2 2

sin sin

sin sin

sin sin sin

sin sin sin sin sin

sin sin sin sin cos

sin sin sin sin sin

( )

m c

m

t t

m t

cos

sin

2

from which the trem can be recovered by filtering.

As can be seen from the above analysis, there are many unwanted terms present and the sin 2mt term is particularly troublesome since, on expansion, it gives second-harmonic distortion and the

possibility of intermodulation distortion too. Non-linear detection of this type is best suited tovery low-level DSBAM signals, where the unwanted demodulation products will be small andless troublesome, or to systems such as radar where linearity is not particularly important, anddetection of very weak signals is the primary objective. In radar system which are essentiallyworking with pulse signals rather than speech etc., other non-linear processing techniques canthen be used to improve the signal-to-noise ratio.

Frequency modulators

Frequency modulators are of two main types:

direct frequency modulation in which the modulating signal directly varies the frequency of an

oscillator, usually by varying the reactance of part of a resonant circuit.

indirect frequency modulation in which the phase of an oscillator is varied by the modulatingsignal (see Figure 9).

Direct frequency modulators

Direct frequency modulators are normally of the reactance modulator type, or the varactor diodetype. In the reactance modulator the output of a transistor with a suitable R-C feedback networkcan be made to appear as a variable capacitance whose capacity is directly proportional to themutual conductance ( g m) of the transistor; this in turn can be controlled by the input to thetransistor. The transistor output is connected across the resonant circuit which determines thecarrier frequency of the modulator, and hence the frequency can be directly varied by applyingthe modulating signal to the input of the transistor-controlled reactance.

A varactor (voltage-variable) diode can be used instead of a transistor-controlled reactance toalter the capacitance across the modulator resonant circuit, and thus directly modulate thefrequency. Direct frequency modulation of this type is particularly simple, but care has to betaken to restrict operation to a relatively small frequency deviation in order to avoid non-linearities cause by the varactor diode characteristics. Sometimes it is necessary to modulate at asub-multiple of the carrier frequency, and then multiply up the FM signal in order to obtain

sufficient deviation with adequate linearity.



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Carrier frequency stability is a particular problem in direct frequency modulation since the needfor frequency stability of the unmodulated carrier and the need to be able to vary the carrierfrequency over a wide range by modulation, impose conflicting requirements on the design. It is

possible to incorporate very high Q-factor quartz crystals in the design of some varactor diodedirect modulators to improve the carrier frequency stability, but stability and wide deviation(' pullability ') are very much opposites, and a compromise still has to be achieved. Automatic

frequency control (AFC), through a low-bandwidth feedback control loop, can be employed tosignificantly improve the frequency stability of the carrier frequency, but this adds considerablyto the complexity and cost of direct frequency modulators. For these reasons, indirect modulationis often used.

Indirect frequency modulators

Indirect frequency modulation uses the principle of Figure 9, by which FM can be obtained byintegrating the modulating signal and then applying the integrated modulating signal to a phasemodulator. A PM signal can be generated in two basic ways:

using an AM balanced modulator and adding the balanced modulator output to a 90 phase-shifted carrier (the Armstrong modulator).

using a varactor diode, or any other suitable controlled reactance, in a phase-shifting circuitadded to the output of a crystal oscillator.

The Armstrong modulator.

Figure 16

Figure 17 shows the essential blocks of an Armstrong phase modulator used as an FM modulator.

The crystal oscillator gives frequency stability and the 90 phase shift network has to operateonly at the fixed frequency of the oscillator and thus design is relative easy. The operation of the

phase modulation part is summarized in the following.

Assume the balanced modulator output to be( ) ( )t t mV v mccbm sincos=

Adding the phase-shifted carrier gives the overall output as( ) ( ) ( )t t mV t V v cmccc cossinsin0 +=

Substituting ( ) ( )sintan t m m = into the above gives

( ) ( ) ( )( ) tancossin

0 t t V v ccc +=

Balanced modulator Adder

Crystal oscillator 90 phase shift

I

Modulatingsignal

FMoutput



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Next, multiply by ( ) ( )cos/cos to give( ) ( ) ( ) ( )( ) ( ) cos/sincoscossin0 t t V v ccc +=

Using the identity ( ) ( ) ( ) ( ) ( ) y x y x y x sincoscossinsin = gives

( ) ( )

( ) ( )( ) ( )

( ) ( )t mt V

t V t V

t V v

mcc

cc

cc

cc

22

2

0

sin1sin

tan1sinsecsin

cos/sin

++=

++=+=

+=

where the last three lines are included to show a number of representations are possible.

If m is small, will be small also, so that cos( ) 1and sin( ) 0. Thus,( )v V t m t c c m0 +sin sin , indicating phase modulation by sin( mt ); however, if sin( mt ) is the

output of the modulation signal integrator, the overall effect is that of frequency modulation. In

other words, the modulating or message signal at the integrator input must be cos( mt ).FM demodulators (detectors)

The demodulation of an FM signal requires detection of the changes in frequency of the receivedsignal, and these frequency changes have to be converted to the corresponding amplitude changesof the original modulating signal. Circuits used for FM demodulation are often referred to asdiscriminators and most rely on the amplitude/frequency dependence of R-C circuits. The most

popular such discriminators are the Foster-Seeley Discriminator and the Ratio detector . Theformer must be preceded by an amplitude limiter as it is sensitive to both amplitude andfrequency changes, but amplitude limitation is essential in FM receivers to take advantage of theinherent noise immunity of FM, and to prevent noise on the received signal from affecting thefrequency discrimination process. The Ratio Detector is somewhat less linear than the Foster-Seeley Discriminator, but has inherent amplitude limiting properties and is often used in low-quality domestic receivers and other FM systems where good linearity is not essential.

More complex FM demodulators are based on tracking loop systems such as the Phase-lockedloop (PLL) and Frequency-locked loop (FLL) in which an oscillator within a feedback loop is'locked' onto the received FM signal and follows the phase and/or frequency changes of thereceived signal; the oscillator phase/frequency control voltage within the loop then follows themodulation of the FM signal and can be used to provide a demodulated output. Such

demodulators are very complex and expensive and are only used where the performance andadditional costs can be justified.

The simplest and most linear of all FM demodulators is the pulse counting demodulator . Thisrecognises that the information content of an FM signal is contained within the zero-crossings ofthe modulated carrier, since these define the beginning and end of each cycle and hence enablethe instantaneous frequency to be determined. In the pulse counting demodulator the receivedFM signal is amplitude-limited or 'clipped' to remove noise effects before the resulting FMsquare wave is applied to a zero-crossing detector. Each positive-going zero-crossing is used totrigger a rectangular pulse generator which produces a fixed width, constant energy pulse forevery zero-crossing. Thus the spacing between adjacent pulses varies as the frequency of thereceived FM signal varies, and the frequency can be recovered by simply applying these pulses toa suitable low-pass filter. The pulse counting demodulator needs a much larger frequency



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deviation than that normally used in FM systems for good noise performance, and down-conversion of the received carrier to a much lower rate is normally used with this type ofdemodulation.

The Foster-Seeley Discriminator

Figure 17

Figure 17 shows the general arrangement of a Foster-Seeley Discriminator. The primary voltageV p of the transformer in the transistor collector is fed via a capacitor the centre-tap of thesecondary where the voltages V 1 and V 2 are in antiphase. The current in the primary is in phasewith V p at resonance which must coincide with the unmodulated frequency of the FM carrier.The induced secondary voltages V 1 and V 2 are in quadrature with V p since V 1 = -jMI p where I p isthe primary current and M is the mutual inductance between the windings of the transformer.The phasor diagrams of Figure 18 illustrate the operation of the discriminator.

Figure 18

V p

V 1

V 2

D1

D2

RF choke

V 3

V 4

R 1

R 2

C 1

C 2

V O

V p

V p

V p

V 1

V 2

V 1

V 1

V 2

V 2

Below resonance At resonance Above resonance



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The voltages ( V p + V 1) and ( V p + V 2) are applied to the diodes D1 and D2 respectively. These twodiodes and the R-C circuits R1C 1 and R2C 2 behave in a similar way to the AM envelope detector,rectifying the a.c voltages ( V p + V 1) and ( V p + V 2) to produce their d.c values across R1 and R2.The radio-frequency choke prevents any carrier signal components appearing at the demodulatedoutput. At resonance (i.e. at the unmodulated FM carrier frequency) the a.c voltages ( V p + V 1)and ( V p + V 2) are equal and opposite making V o is zero. Below resonance the primary circuit is

capacitative and the primary current leads V p by a small angle: V 4 will then be greater than V 3,resulting in a negative V o. Similarly above resonance the primary circuit is inductive and the

primary current lags V p by a small angle, making V 4 less than V 3, and V o positive.

Therefore as the FM carrier frequency varies with the applied modulation, V o will vary to followthe instantaneous frequency of the FM signal, thus reproducing the original modulating signal.The overall discriminator characteristic has an " S " shape as shown in Figure 19, and can be madevirtually linear over the centre region.

Figure 19

The actual demodulation process within the Foster-Seeley Discriminator is simultaneousenvelope detection of two derived a.c signals whose amplitudes are proportional to theinstantaneous frequency of the received FM signal. It is thus essential that the received FMsignal is of constant amplitude to prevent amplitude variations and noise from appearing at thedemodulated output, and for this reason the Foster-Seeley Discriminator must be preceded by anamplitude limiter.

Pre-emphasis and de-emphasis

The noise immunity of FM is frequency-dependent in such a way that most noise is received atthe upper end of the message frequency band. To further improve the noise performance of FM a

pre-emphasis circuit is often used before modulation to boost the high frequency components ofthe modulating signal, and a de-emphasis circuit is used after demodulation to remove the high-frequency boost. This process can improve the noise performance of FM by up to 5dB, givingFM some 20+dB signal-to-noise better performance than AM for similar applications. The pre-emphasis and de-emphasis circuits normally consist of simple R-C sections and are described inmost textbooks on radio.

V

0 0 +

0 -



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The Ratio detector

The Ratio detector is similar in many respects to the Foster-Seeley Discriminator, but uses atertiary winding on the input transformer to couple the FM reference signal into the detectornetwork. It also has an inherent amplitude-limiting characteristic making it attractive fordomestic receivers since a separate limiter is not required, saving on component count and

manufacturing cost. It is also possible to derive a d.c. signal proportional to the received carrieramplitude, and this can be used for automatic gain control (AGC) purposes without the need fora separate AGC detector. The linearity of the Ratio detector is, however, not as good as that ofthe Foster-Seeley Discriminator but is often adequate for mobile receivers where quality is not ofthe utmost importance.

PM demodulators

Phase demodulation may be achieved by the use of an FM demodulator followed by anintegrating network (the inverse of the process illustrated in Figure 10). Other types of PMdemodulation require the use of a phase-sensitive detector , frequently found in control systemsetc.

Figure 20

Figure 20 shows a simplified phase-sensitive detector. The operation of this circuit is verysimilar to that of the Foster-Seeley Discriminator and will not be described in detail. If the localoscillator is extremely stable, the phase sensitive detector output voltage V o follows the changesin phase of the phase-modulated input signal, and thus demodulates the PM signal.

The most important use of the phase sensitive detector is as part of a phase-locked-loop (PLL),extensively used in modern communication circuits. The PLL is capable of locking on to boththe phase and frequency of an incoming signal, and can be used as a sophisticated FM and PMdemodulator. The PLL is also often used in carrier signal generation as it can produce anextremely stable and noise-free carrier, and can easily be incorporated into a frequencysynthesiser where switchable frequency carriers are required. The basic principles of the PLL areshown in Figure 21.

D1

D2

V 3

V 4

R 1

R 2

C 1

C 2

V O

~ ~

PM inputsignal Local

oscillator



20/23


20

Figure 21

The operation of a PLL is very much determined by the loop filter characteristics. The phase-sensitive detector compares the phases of the input signal and the local signal form the VCO.The difference, after filtering, is amplified and fed back to the control input of the VCO. Oncethe PLL has locked onto the input signal it tracks both the frequency and phase of the inputsignal, but there will always be a small phase difference (phase error) between the input signal

phase and the phase of the VCO; this can be made very small if the amplification (and loop gain)is large.

If the input signal is an FM signal and the loop bandwidth is greater than the modulating signal bandwidth, the VCO control voltage will follow the frequency modulation on the input signaland act as a demodulator. Similarly, the phase-sensitive detector output will yield the messagecontent of a phase-modulated input signal. The detailed operation of PLLs is very complex and

beyond the scope of the course, but many simplified treatments can be found in most moderntextbooks on radio systems.

Multiplexing

Multiplexing is the term used to describe the simultaneous transmission of several signals in a single channel or path without loss of identity of an individual signal .

Figure 22

Phase-sensitivedetector

Loop filter Amplifier

Voltage-controlledoscillator (VCO)

OutputInput

Multiplexer (MUX)Demultiplexer

(DEMUX)

single communicationchannel (cable or

radio)

Multipleinput signals

Original inpusignals



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21

Figure 22 illustrates the basic principle of multiplexing of which there are two basic types, frequency division multiplexing (FDM) and time division multiplexing (TDM). FDM systems are best suited to analogue information signals, but require a high degree of linearity to preventcross-talk between individual channels due to inter-modulation distortion. TDM systems are

basically digital, and are ideally suited to digital information sources, but analogue-to-digitalconversion is now so widely used in electronic communication systems that TDM has superseded

FDM in many applications.

FDM consists essentially of modulating each input signal onto a different frequency carrier andcombining all the modulated carriers in an adder. The modulation may be AM or FM, but FM isgenerally preferred because of its superior signal-to-noise properties. The FDM DEMUX has a

parallel bank of band-pass filters, one for each signal channel, and after separation each signal isdemodulated in the appropriate way.

TDM requires the individual input channels to be available in digital format so that they can betime-interleaved or time-division-multiplexed as shown in Figure 23.

Figure 23

If the individual input signals to the MUX are already in digital form, the TDM operation iseasily implemented with digital logic circuits, and the DEMUX process is equally simple. Whenthe input signals are in analogue format, some form of analogue-to digital conversion (ADC) isrequired to yield digitally-modulated signals suitable for time-division multiplexing.

Digital modulation

The simplest form of ADC involves using the analogue signal to modulate a property (e.g.amplitude, width, position etc.) of a repetitive pulse train. Providing the repetition rate of the

pulse train is greater than twice the highest frequency component present in the analogue signal(Nyquist rate), all the information of the analogue signal is retained in this sampling process.The modulated pulse trains are then easily assembled in TDM format. Figure 24 illustrates the

basic pulse modulation processes.

Pulse Amplitude Modulation (PAM)

From Figure 24 it can be seen that the amplitude of each pulse in the modulated pulse traindirectly represent the modulating signal amplitude at the regular sampling instants of which theremust be at least two per cycle of the modulating signal. There are in fact two types of PAM. Inanalogue PAM, the top of each pulse follows the modulating signal amplitude exactly for theduration of the pulse. This is the simplest form of PAM since it simply requires an analogue'gate' to sample the modulating signal at regular intervals. The type of PAM illustrated in Figure24 is a flat-top waveform and requires a sample-and-hold operation prior to pulse modulation.Several such streams of PAM signals can readily be combined in TDM form if the samplingintervals of each channel are offset in time from each other.

Channel1

Channel2

Channel3

ChannelN

Channel1

Channel2

Channel3

ChannelN

Channel1

Channel2

Channel3

ChannelN



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22

Pulse Position Modulation (PPM)

This is also illustrated in Figure 24, where each pulse is displaced from its regular unmodulated position to a new position dependent on the modulating signal amplitude at the samplinginstants. Note that all pulses are of fixed amplitude and duration in PPM.

Pulse Width Modulation (PWM)

PWM is also illustrated in Figure 24 and can be seen to be closely related to PPM above. InPWM the leading edge of each pulse is fixed in position at the sampling instants but the trailingedge is modulated such that the width of each pulse is proportional to the modulating signalamplitude at each sampling point.

Figure 24



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23

Demodulation of PAM, PPM and PWM requires only a low-pass filter to extract message-frequency components, and to eliminate the pulse carrier frequency and its associated sidebands;these are similar in form to those of a DSB AM signal.

Pulse Time Modulation (PTM)

PPM and PWM are both examples of the more general class of Pulse Time Modulation (PTM) inwhich some time-related property of the pulse carrier waveform is modulated by the messageinformation. Many variants of PTM exist, including other versions of PPM and PWM, andtechniques such as Pulse Frequency Modulation (PFM), Pulse Interval Modulation (PIM), PulseRate Modulation (PRM) etc.

The pulse modulation techniques described above were first invented in the 1930s but saw littleuse, except in military applications, due to the circuit complexity required. The advent ofsemiconductors and integrated circuits has changed this, and pulse modulation is widely used onshort optical-fibre and other point-to-point systems where the inherent non-linearities of thetransmission system have negligible effect on the performance of modulated pulse carriers. PTMis also closely related to the asynchronous form of Delta Modulation (or more correctly Sigma-

Delta Modulation ) which forms the basis of many modern ADCs, especially in bandwidthcompression schemes.

Pulse Code Modulation (PCM)

PCM can be considered as an extension of PAM. In PCM each PAM pulse is quantized inamplitude: in other words the amplitude of each PAM pulse is compared with a 'ruler' (normallygraduated in a binary scale) and the nearest graduation on the 'ruler' is recorded as the quantized

pulse amplitude. The quantized amplitude of each pulse is converted into a block of binary digits

(byte) representing its measurement against the 'ruler'. For example, a simple PCM speechsystem may quantize message signals into 256 (= 2 8) separate amplitude levels. Each samplewould then require an 8 binary digit (8 bit) representation. If necessary, each such 8-bit byte can

be assembled with similar bytes from other message signals to form a TDM signal. Once themessages have been converted into digital form the TDM MUX and DEMUX operations becomesimple, digital logic operations. The basic process of converting an analogue message signal intoa series of digital bytes is known as Pulse Code Modulation (PCM). PCM is often used in TDMsystems, but can be used on its own where noise immunity, reproducibility and general'ruggedness' are needed. PCM is now widely used in both the public and private communicationsnetworks, and forms an essential part of modern secure communications systems where furtherdigital coding ('scrambling') and encryption of the basic PCM bytes is easily achieved withmodern VLSI (very large scale integration) processors. Perhaps one of the most frequently usedapplications of PCM techniques is in CD systems for audio reproduction etc.

Other digital modulation techniques.

Many other 'digital' modulation techniques exist, especially for data transmission. The word'digital' is used here more generally as many of the so-called digital modulation techniques are

based on digital modulation of analogue carrier syetems, e.g Quadrature Phase-Shift Keying(QPSK). These are too numerous to mention here and are well-described in many moderntextbooks on data transmission and digital communications.


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Notes on Modulation

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