Appendix comm. syss

7/29/2019 Appendix comm. syss

1/22

Appendix I

MODULATION SYSTEMS

I.1 AcknowledgmentThis appendix contains notes assembled from the Text Book by A. Bruce Carlson Com-munication systems, McGraw Hill, 1975. For the benefit of students who wish to extendtheir studies through the use of that text book, the notation of that book is adopted here.

I.2 Introduction and Objective

These notes provide an introduction to and analysis of the performance of some mod-ulation methods used in communication systems. The material provides a justification

for the use of modulation, give examples of circuits by means of which modulation andsubsequent detection can be achieved, and a compares the performance of communicationsystems using various forms of continuous wave modulation, i.e. systems in which theun-modulated carrier is a sinusoid.

I.3 Modulation Systems

I.3.1 Definition of modulation

Modulation may be defined as the systematic alteration of one waveform, called the

carrier, according to the characteristics of another waveform, which we call the modulatingsignal or the message. Normally the modulating signal or message is denoted by x(t),which is a dimensionless variable, and is subject to |x(t)| < 1. The message is assumedto be contained within a bandwidth W.

Sometimes the modulating signal is the single tone defined by

x(t) = Am cos2fmt with Am < 1 and fm < W. (I.1)

For such a tone, the double sided Fourier spectrum is given by

X(f) =Am

2 [(f+ fm) + (f fm)] (I.2)

and is illustrated in Figure I.1.

239


2/22

240 APPENDIX I. MODULATION SYSTEMS

Fourier spectrum for a single tone message.

For this figure you could consult Figure 7.3 ofPeter Cookes book

Figure I.1: Fourier spectrum for a single tone message.

I.3.2 Classes of modulation

We will recognise in our study the classes of linear modulation, in which the envelope ofthe carrier bears a simple and linear relation to the message, and so-called exponentialmodulation in which the phase or the frequency of the carrier is varied in response to themessage.

I.4 Bandpass Signals and Systems

A bandpass signal is one whose spectrum is concentrated in the vicinity of the carrierfrequency. It appears as a sinusoid at the carrier frequency with slowly changing amplitudeand phase, as shown in the equation below.

v(t) = R(t)[cos(ct + (t))] with R(t) 0 (I.3)Another way of writing this signal is in terms of slowly varying in-phase and quadrature

components as shown below.

v(t) = vi(t)cos ct vq(t)sin ct (I.4)This last description has the advantage is that it is more readily transformed into the

frequency domain than is the amplitude and phase description.

I.5 Linear modulation systemsWe study first the class oflinear modulation systems in which the envelope of the signal islinearly related to the message. The simplest of these is amplitude modulation as describedbelow.

I.5.1 Amplitude Modulation

In amplitude modulation, the modulated carrier wave takes the form

xc(t) = Ac(t)[1 +mx(t)] cos ct (I.5)

The envelope of the signal is therefore 1+mx(t). The envelope, relative to the carrier,follows the message signal x(t).


3/22

I.5. LINEAR MODULATION SYSTEMS 241

Normally m 1 to avoid envelope distortion and phase reversals in the carrier.The term linear modulation comes from the fact that an easily recognisable aspect of

the signal, namely the envelope, is a linear function of the message. An illustration of an

amplitude modulated signal is given in Figure ??.

Illustration of simple amplitude modulated signal.


Figure I.2: Illustration of a simple amplitude modulated signal.

For amplitude modulation with a single tone, the double sided Fourier spectrum isgiven by

X(f) =Am

2[(f+ fm) + (f fm)] (I.6)

and is illustrated in Figure I.3.

Fourier spectrum with amplitude modulation by a single tone.


Figure I.3: Fourier spectrum with amplitude modulation by a single tone.

It is clear that part of the single tone spectrum, and indeed the general amplitude

modulation spectrum, on the negative frequency axis is completely predictable from thepart on the positive frequency axis.

The transmission bandwidth of the general amplitude modulated signal BT = 2W,i.e. twice the bandwidth of the message signal. Amplitude modulation is sometimes saidto be wasteful of bandwidth in that the message could be sent at baseband (i.e. withoutmodulation) at half the transmission bandwidth.

The average power of an amplitude modulated signal is given by

ST = E{x2

c(t)} = (1 +m2x2)

A2c2

(I.7)

from which we see that at least half the transmitted power resides in the carrier. It canbe said that this part of the carrier power is wasted as it is independent of the message,and thus it carries no information.


4/22


I.5.2 AM circuits

A range of circuit arrangements can be used to accomplish amplitude modulation. One of

them, shown in the Figure I.4, uses a textitbalanced mixer to form a product betweena scaled version mx(t) of the message signal and the carrier wave Ac cos ct, the productthen being added to the carrier wave to produce the modulated carrier wave xc(t).

xc(t)mx(t) X

~

A cos tc cw

+

Figure I.4: Amplitude modulation using a balanced mixer.

Other ways of producing amplitude modulation exist. Some of them naturally producea modulation signal plus carrier without the carrier needing to be added.

The simplest way to recover the message from an amplitude modulated signal is toemploy the envelope detector shown Figure I.5.

+ +

_ _

vin voutR1 R2C1

C2

Figure I.5: Circuit for envelope detection.

Although other forms of demodulation circuits, which deal with a wider range ofmodulation methods, are available, this circuit is often preferred for simple amplitudemodulation because of its simplicity and its lack of dependence of knowledge of frequencyand phase of the original carrier signal.

I.5.3 Double sideband suppressed carrier modulation

In amplitude modulation the carrier signal is not considered to carry information, and, ashas been said before,, is said to cause the transmission of unnecessary power. Eliminatingthe carrier term and setting of the modulation index to unity produces double sidebandsuppressed carrier modulation as described in the equation below.

xc(t) = Acx(t)cos ct (I.8)

The spectrum bandwidth of double sideband suppressed carrier modulation is still2W.

There is the question of whether the envelope is still of the same shape as the message,

so that envelope detection may be employed. The simple example of tone modulationshown in Figure I.6 shows that it is not, so simple detection of the waveform of theenvelope which is possible in simple amplitude modulation will no longer recover the


5/22


Illustration of a double sideband suppressed carrier modulated signal.


Figure I.6: Illustration of a double sideband suppressed carrier modulated signal.

message. Instead, there is a need for special detectors e.g. the synchronous detector ofFigure I.10, which is discussed later.

I.5.4 Single sideband modulation

We have already eliminated some wasted power from amplitude modulation by eliminat-ing the carrier signal. Because both sidebands carry the same information, we can alsoeliminate some wasted bandwidth by eliminating either the upper or lower sideband ofthe signal. Such sideband suppression can be accomplished by means of a single sidebandfilter as shown in Figure I.7.

x(t)

~cos twc

DSBSSB

Balanced

mixer

Sidebandfilter

H(f)

Figure I.7: Single sideband modulation using sideband filter.

An alternative method of generation of a single sideband signal is shown in Figure I.8.This circuit can produce either the upper sideband or the lower sideband, depending

on whether we add or subtract the outputs of the two balanced modulators. There isagain the question of whether the envelope bears a simple relation to the message, so thatenvelope detection may be employed. We will not prove the result here, but it is may beshown that the envelope of the double sideband suppressed carrier signal is given by

RSSB(t) =Ac2

wx(t)2 + x(t)

2W

(I.9)

where x(t) is the Hilbert transform of x(t). As the Hilbert transform in generalproduces considerable change in shape of a signal, it is not surprising that the envelopeof a single sideband suppressed carrier signal is no longer similar to that of the original

message.Bearing in mind that changing the phase of all components of the message signal by90 degrees at baseband is equivalent to taking its Hilbert transform, we can see that the


6/22


0.5x(t)

modulator

Balanced

modulator

Balanced

+

90o

~ +

+_

SSB

A cos tc w

0.5x(t)A cos tc w

0.5x(t)A cos tc w>

Figure I.8: Phase shift single sideband modulator.

single sideband generation process may be interpreted as adding two double sidebandsignals having quadrature carriers, modulated respectively by the original message signaland by its Hilbert transform.

I.5.5 Vestigial sideband modulation

Practical single sideband systems have a poor low frequency response but good bandwidthefficiency. In addition, it is difficult to achieve the sharp cut-off required to completelysuppress one of the two sidebands.

The double sideband systems have good low frequency response but the message band-width is twice that of single sideband systems.

A compromise system which achieves some of the benefits of each of these two systemsis the vestigial sideband (VSB) modulation system in which the sideband filter is as shownin Figure I.9.

If vestigial sidebandfi

ltering is applied to double sideband suppressed carrier modula-tion, we produce pure vestigial sideband modulation in which a carrier is not present. Ifvestigial sideband filtering is applied to simple amplitude modulation, we produce vesti-gial sideband plus carrier (VSB+C) modulation in which a carrier is present. Sometimesadditional carrier amplitude is added for reasons that it may permit simpler, althoughapproximate, detection by an envelope detector.

A illustration of vestigial sideband generation and procesing is provided in Figure I.9

The vestigial sideband modulation system, with envelope detection, does produceappreciable signal distortion, but will transmit signals down to DC, and will transmithigh frequency signals with good bandwidth efficiency. This system is normally applied

in contexts, such as television picture transmission, is where the distortion is not readilynoticed by the uses of the system, and good picture sharpness (associated with good highfrequency response) is valued.


7/22


(a)

(b)

(c) f

X(f)

O2fc-2fc

f

X(f)

Ofc-fc f +Wc-f -Wc

f

X(f)

OW

W

-W

-W

Figure I.9: Illustration of vestigial sideband filtering.

I.5.6 Detection systems

Linear modulation can always be detected by the product detector of Figure I.10. Howeverthe Figure does require the availability of a local oscillator at the same frequency and phaseas the carrier frequency, which may not have been transmitted with the signal, or mayhave been transmitted only with low amplitude.

xc(t)

~ A cos tLO wc

y (t)DLPF

B=Wx

Figure I.10: Synchronous detection of a modulated signal.

Thus the carrier may need to be regenerated in some way which we will not discussin detail here. This fact makes the product detector more complicated than the envelopedetector shown in Figure I.5.

It is interesting to examine what happens in the detection process in the case ofvestigial sideband modulation. Figure I.9 has already provided an illustration.

This diagram pertains to pure vestigial sideband modulation and synchronous detec-tion, the latter as shown in Figure I.10. As the correct operation of the detector requires

a local oscillator which is synchronous and in phase with the transmitted carrier, and thatcarrier is absent in the case of pure vestigial sideband modulation, the system of vestigialsideband modulation with carrier is more often used. In that case it may be shown that


8/22


with an appropriate level of carrier, and tolerance of some distortion in the detectionprocess, an envelope detector, with its advantage of simplicity, may be used.

I.6 Receivers

In a receiver for modulated signal we need

Provision of frequency selectivity so that we receive the desired signal among manythat can enter the inputs to the receiver.

Amplification so that the received signal is at a suitable level for recovery of themessage. A suitable level is required because the recovery process often exploitsthe nonlinearity of some component, and the appropriate nonlinearity is usually

available only over a suitable range of signal levels. Usually, further amplification so that the output signal is increased from a level at

which the demodulation takes place, to the level desired at the destination.

The most common form of receiver is the superheterodyne receiver, described in thenext section. The principal benefit of the superheterodyne receiver is that it provides theappropriate degree of signal selectivity for us to be able to efficiently manage a crowdedcommunication spectrum.

I.6.1 AM superheterodyne receiver

A block diagram of a superheterodyne receiver for amplitude modulation is shown inFigure I.11.

Block diagram of a superheterodyne receiver.


Figure I.11: Block diagram of a superheterodyne receiver.

The way in which the frequency is the selectivity of the superheterodyne receiver isprovided is illustrated in Figure I.12.

I.7 Angle modulation

We now turn to consider angle modulation, sometimes called exponential modulation,

because of the connection between sinusoids and exponential functions. In angle modu-lation we may vary the phase or the frequency of the transmitted signal in accord withthe message.


9/22

I.7. ANGLE MODULATION 247

f

V0(f)

fIF

BT

O

2fIFf

V0(f)

fLOf -fLO IF f +fLO IF

BT BT

O

f

V0(f)

f -fLO IF

BT

O

f

V0(f)

f -fLO IFO

(a)

(b)

(c)

(d)

Figure I.12: Passbands in a superheterodyne receiver.


10/22


I.7.1 Phase modulation

In phase modulation with a message x(t) the modulated carrier is

xc(t) = Ac cos[t + x(t)] (I.10)

where is called the phase-deviation constant, and is the maximum phase deviationproduced byx(t), the message being still subject to the message restriction |x(t)| 1.In the above expression it is clear that the instantaneous phase of the modulated carrierrelative to the unmodulated carrier is x(t).

A method of producing phase modulation is shown in Figure I.13.

x(t)

+

_Balanced

mixer

fD

90o

NBPM

cos twc

sin twc

~

Figure I.13: Narrow band phase modulator using balanced mixer.

I.7.2 Frequency modulation

In frequency modulation it is the instantaneous frequency f of the modulating signalwhich is varied in accord with the message, that is

f= fx(t) (I.11)

where f is called the frequency deviation constant. Since frequency is the timederivative of phase, the modulated carrier in frequency modulation may be expressed as

xc(t) = Ac cos[ct + 2f8

t x()d (I.12)

This expression indicates the connection between frequency modulation and phasemodulation and that they are both cases of angle modulation.

So that the integral does not diverge, it is assumed that the message signal has nod.c. component. However, a message with a d.c. component can be made to make sensein the frequency modulation context, provided we do not attempt a description of it inphase modulation terms.

The appearance of the message term inside the argument of the cosine function pro-duces quite profound differences between angle modulation and amplitude modulation.

The most significant of these lies in the spectrum of the modulated carrier. In amplitudemodulation, when the message contains a number of tones, the sideband produced by themodulation process is the sum of the sidebands provided by each of the tones separately.


11/22


In angle modulation, this superposition behaviour does not occur. The sideband structureof the modulated carrier which is angle modulated by a multitone message is much morecomplex than the simple superposition would give. It is for this reason that our analysis

below will turn for a time to the study of single tone messages.

I.7.3 Spectral analysis

To provide a suitable basis for analysis, to be pursued later, of a frequency modulationspectrum, we will consider the case of a phase modulated signal in which the message is

x(t) = Am cos mt (I.13)

rather than a cosine wave. So the modulated carrier becomes

xc(t) = Ac cos[ct +

X2f

m

~Am sin mt] (I.14)

= Ac cos(ct+ sin mt) (I.15)

where is called the modulation index for phase modulation. It is the maximum phasedeviation for the tone of amplitude Am.

It may be shown that the Fourier spectrum of this signal is

xc(t) = Ac

3n=

Jn() cos(c + nmt) (I.16)

where Jn() is of the Bessel function of the first kind of order n and argument . TheBessel functions up to order seven are illustrated in Figure I.14.

The Bessel functions of negative order may be derived from those for positive orderby the relation

Jn() = (1)nJn() (I.17)

An illustration of the Fourier spectrum of this modulated signal is shown in Figure I.15.We note in this figure that in accord with equation above the even order sidebands

have the same signs above and below the carrier, while the odd order sidebands have

opposite signs above and below the carrier.An illustration of the magnitude of the spectrum such as shown in Figure I.16. This

figure does not show how the phases of the upper and lower sidebands are differentlyrelated for even and odd order sidebands, as was shown in Figure I.15.

In the case of a frequency modulated signal of the single tone and message x(t) =Am cos[mt we have by performing the integration in equation ?? the carrier signal

xc(t) = Ac cos

Xct +

2fm

sin mt

~. (I.18)

This is of the same form as was studied for phase modulation if we set

=2fAm

m=Amffm

(I.19)


12/22


~cos twc

0 1 2 3 4 5 6 7 8 9 10

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Figure I.14: Bessel functions of various orders.

ffc f fc m+ f 3fc m+

f 2fc m+

-J ( )1 b

J ( )1 b

J ( )2 b

-J ( )3 b

J ( )3 b

J ( )0 b

J ( )2 b

X(f)

O

Figure I.15: Amplitude spectrum of an angle modulated signal.

ffc f fc m+f fc m- f 3f c m+f 3fc m-

f 2fc m

+f -2fc m

J ( )1 b J ( )1 b

J ( )2 bJ ( )3 bJ ( )3 b

J ( )0 b

J ( )2 b

|X|(f)

O

Figure I.16: Magnitude spectrum of an angle modulated signal.


13/22


The Fourier spectrum of the FM signal is again

xc(t) = Ac

3n=

Jn() cos(c + nmt) (I.20)

which is of the same form as was obtained for phase modulation with modulationindex .

Note that the two forms of modulation share the property that is the maximumphase deviation for the tone of amplitude Am, but may be contrasted by the fact that inphase modulation

= Am (I.21)

and is independent of the modulating frequency fm, while in a frequency modulation

= 2fAm

m(I.22)

And depends on modulating frequency, and increases without limit as fm 0.

I.7.4 Bandwidth requirements

The above analysis of angle modulation spectra indicates that for transmission with com-plete fidelity, of even the single tone, an infinite number of sidebands occupying an infinitebandwidth is required.

However, as a study of Figure I.16 will show, for each modulation index, sidebands of

beyond a certain number are of negligible amplitude. The higher the modulation index,the more sidebands are required, but the above analysis shows that in the case of frequencymodulation, the combination of high sidebands order and amplitude is achieved only atthe lower modulation frequencies, so the actual bandwidth required for transmission withreasonable fidelity is not extreme.

1

2

5

10

20

50

0.1 0.2 0.5 1 2 5 10 20 50

Deviation ratio D

Average of values for = 0.01 and = 0.1e e

NumberM

ofsignificant

sidebands

Figure I.17: Number of significant sidebands in a frequency modulated signal.


14/22


This matter is illustrated in more detail in Figure I.17 wherein the number of significantsidebands required for transmission with reasonable fidelity is plotted as a function of thedeviation ratio

=ffm

(I.23)

which is also equal to the modulation index which applies at the maximum signalamplitudeAm = 1 and modulation frequency fm for a particular maximum frequencydeviationf.

If we make the approximation from this curve that

M() + 2 (I.24)We may derive the required transmission bandwidth BT for transmitting both upper

and lower sidebands is

BT = 2(f +W). (I.25)

I.7.5 Detectors of angle modulation

A number of circuits have been devised for the recovery of the message from a frequencymodulated signal. One of the simplest to comprehend is shown in Figure I.18.

x (t)c

+

_

Kx(t)

+

_

f >f0 c

f


15/22

I.8. PERFORMANCE OF MODULATION SYSTEMS 253

f

V0(f)

O

Top side

Bottom side

Sum

Figure I.19: Derivation of balanced FM discriminator transfer function.

I.8.1 A general communication systemThe system we consider is shown in Figure I.20.

x(t) x (t)c v(t) y (t)Dy(t)

x (t)cKR

H (f)R

BPFDet

LPF

WL

Channel+

ST

SRSTL

=

Trans

Noise and interference

Receiver

Figure I.20: A general CW communication system.

Although much of it has been defined before, for conveneince we summarise below thenotation used in Figure I.20.

x(t) The message signal.

ST The transmitted signal power.

L The channel power loss factor: 1/L is the channel power gain. It is not in dB.

W The bandwidth ofthe message signal.

xc(t) The modulated signal sent to the channel.

BT The transmisson bandwidth of the channel, assumed disortionless.

SR The channel output power after the loss L.

KR The channel amplitude gain associated with the power loss L. Thus KR = 1/L.

Ac The unmodulated carrier amplitude. The carrier amplitude to the detector inputis thus KRAc.


16/22


v(t) The modulated singal coming out of the channel. This will be KRxc(t).

HR(f) The response of the band pass pre-detection filter in the receiver.

Rv(t), v(t), vi(t), and vq(t), These are all descriptions of the signal v(t) presentedto the detector, either described in amplitude and phase terms, or in-phase (relativeto the unmodulated carrier) and quadrature component terms.

In phase modulation, phase deviation constant. It is the peak phase deviation,occurring when x(t) = 1.

f In frequency modulation, the frequency deviation constant. It is the peak fre-quency deviation, occurring when x(t) = 1.

The frequency modulation deviation ratio ffm

.

I.8.2 Illustration of modulation effects

A comparison of the effects of various system of modulation carrier wave, and of theintroduction of noise in the communications path, is shown in Figure I.21. As the figureis complex, it is best studied with the aid of the commentary below.

The figure shows an un-modulated carrier drawn, arbitrarily, upright. It is left tothe reader to imagine what happens to the carrier as it is amplitude modulated withpresumably 100 percent modulation. In such modulation, the vector OPc varies in lengthfrom zero size to double the size shown here.

Next in the figure we may pay attention to the effect of noise introduced either in phasewith or in quadrature with the carrier as shown by the vectors PcP1 and PcP2 respectively.In an amplitude detector the in phase noise will be present at the output while thequadrature noise will have practically no effect. The relative proportions of output noiseto output signal will depend upon the ratio of noise power to the unmodulated carrierpower.

Next in the figure we should give attention to the angle modulated carrier of whichthe instantaneous position in the modulation cycle is shown by the vector OP3. We notethat this is for the same carrier power as for the amplitude modulation case describedabove. When we come to consider the effect of noise in an angle modulated system we

see it is the quadrature noise component represented by the vector PcP2 that governs thenoise phase angle n.

To see the effect of this noise on the output signal-to-noise ratio products of anglemodulation system we must compare the distance PcP2 with the distance swept out bythe pointP3 during a modulation cycle.

For the case of phase modulation this distance can be up to half the circumference ofthe circle shown, as for phase modulation of phase angle must stay within the range to to avoid ambiguity in decoding. But this distance is considerably more than the radiusof the circle, so phase modulation is potentially able to produce signal-to-noise ratios atthe destination substantially better than those produced by amplitude modulation. Of

course if we mistakenly designed a phase modulation system so that the maximum ofphase angle deviation is only small, the noise performance of phase modulation system isinferior to that of a well-designed amplitude modulation system.


17/22


O

fn

fsUnmodulatedcarrier

Angle modulatedcarrier

Carrier within-phase noise

Carrier withquadrature

noiseP1

P2

Practical excursion of Pwith phase modulation

2

Practical excursion of Pwith frequency modulation

3

Unit circle

P3

Pc

Figure I.21: Signal and noise in various modulation systems.


18/22


Now we consider the possible excursion of the point P3 in a frequency modulationsystem. The phase deviation is no longer constrained to cover the range to , but canwind multiple times around the circle, roughly as shown by the outer spiral curve. It can

be seen that without any increase in the carrier power, but just by choice of a suitablylarge frequency deviation, with consequently large phase deviation, the detected signal-to-noise ratio can be made much greater than is possible with an amplitude modulationsystem. This is particularly so at the lower frequency is where the phase deviation canbecome very large.

This diagram indicates quite well how phase modulation and frequency modulationmay have, (depending on modulation index), noise performance both inferior to all su-perior to amplitude modulation systems, but does not show the extent to which noisegenerated over the transmission band manifests itself at the post detection output. Thesematters are considered in the next two sections.

I.8.3 PM post detection noise spectrum

For the evaluation of the noise spectrum at the output of the phase modulation detectora number of assumptions are made. One is that the band pass noise can be thought ofas a summation of random sinusoids distributed equally over 30 frequency band fc BT/2. Another is that, as already has been explained, only the quadrature componentcontributes to phase noise. A third is that the signal-to-noise ratio is reasonably high.With these assumptions, it can be shown that the power spectral density GPM(f) of thephase modulation detector output signal is given by

GPM(f) =

2SRRect

XfBT

~(I.26)

where 2

is the power spectral density (one side of a double sided spectrum] at theinput to the band pass filter HR(f), i.e. at the input to the receiver. This spectrum isillustrated in Figure I.22.

fBT2

BT2

__

W W

G (f)zPM

O

h

2SR

Figure I.22: PM post detection noise spectrum.

This diagram is of considerable interest because it shows us that although a transmis-sion bandwidth BT considerably in excess of the message bandwidth W was needed to


19/22


transmit the signal without distortion, not all of the noise in that transmission bandwidthfalls within the recovered signal bandwidth W. Thus from a noise point of view, we arenot paying an increased penalty for the additional transmission bandwidth.

I.8.4 FM post detection noise spectrum

We observe that for frequency modulation the signal recovered from the detector is afrequency, which is is the derivative of the phase. It can then be shown that the powerspectral density GFM(f) of the frequency modulation detector output signal is attainablefrom the above derived expression for the phase modulation detector by multiplication by|f|2, and is therefore given by

GFM(f) =f2

2SRRectX f

BT~ (I.27)

where the rectangular function Rect and are as defined above. This spectrum isillustrated in Figure I.23.

fBT2

BT2

__

W W

G (f)zFM

O

hf

2

2SR

Figure I.23: FM post detection noise spectrum.

This figure is of even greater interest in that it firstly reinforces the notation that

not all of the output detector noise will fall within the message detection bandwidth W,and also shows that the very low frequency noise components are suppressed by the factor|f|2. This observation is entirely in accord with the earlier observation that with frequencymodulation, at low frequencies, the phase deviation becomes very large, and the phasejitter introduced by quadrature noise becomes relatively unimportant.

I.8.5 Pre-emphasis and de-emphasis in frequency modulation

We have just observed that frequency modulation systems deal well with low frequencynoise, and less well with high frequency noise. It is also true that in broadcasting or pro-

gram material does not normally contain high frequency components of large amplitude.In addition, the high frequency components do not produce the large phase deviations ofthe low frequency components. For all of these reasons, it is expedient to apply, before


20/22


frequency modulation, a controlled amount of enhancement of the amplitude of high fre-quency signals, and after frequency the modulation a corresponding attenuation of thosehigh frequency components. This process is known as pre-emphasis and de-emphasis,

and further improves signal-to-noise ratio. It is assumed that the pre-emphasis does notsignificantly increase the transmission bandwidth.

I.8.6 Parameters for broadcast FM

In broadcast FM systems for the following the parameters are used.

Deviation f 75 kHz.

Message bandwidth W 15 kHz.

In consequence, the deviation ratio is 5.

Time constant of the emphasis filter 75 s.

I.9 Destination signal to noise ratios

At good signal-to-noise ratios, the calculation of the output signal-to-noise ratio from afrequency modulation detection system and its post-detection filter is a straightforwardmatter from the results previously obtained, but we will not present the details here.The results depend upon the variance of the message signal, the deviation ratio, and the

signal-to-noise ratio at the receiver input, and are presented in a later section.

I.9.1 FM threshold effect and mutilation

However, when the assumption of high signal-to-noise ratio is no longer valid, some of theformulae employed in the preceding calculation break down, and the high signal-to-noiseratio is no longer obtained. We have already seen in our qualitative discussion in relationto figure ??, that angle modulation systems can perform a with inappropriate parametersless well than amplitude modulation systems. The results to be presented are to a degreea reflection of this fact.

But more seriously, unless the signal-to-noise ratio is high, frequency and phase mod-ulation decoding can produce very serious signal distortion which is known as mutilation.The poor output signal-to-noise ratio performance at low input signal-to-noise ratios arerepresented in in Figure I.24 which emerges from a detailed analysis. But this figure doesnot tell the whole story about the utility of frequency modulation systems at all failuresof signal-to-noise ratio. It is a fact that below the knee of the curve, and in the regionwhere the signal-to-noise ratio at the destination still appears to be good, the mutilationeffect has rendered the signal unusable.

I.9.2 FM threshold extension (advanced topic to be omitted)

The limitations just discussed above provided serious constraint on the design of minimumpower frequency modulation systems. There is a technique, shown in Figure I.25, of using


21/22

I.10. COMPARISON OF CW MODULATION SYSTEMS 259

gO dB

(S/N) dBD

Baseband

D=2D=5

Figure I.24: FM noise performance as a function of gamma.

a frequency compressing feedback loop in the receiver, that will extend the range of usefuloperation of FM system to lower signal levels. The use of a phase lock loop receiver canproduce a similar improvement

v(t) y (t)Dv (t)RH (f)IFH (f)RF

detectorLPFX

Frequency

VCO

Receiverinput

Figure I.25: FMFB receiver block diagram.

I.10 Comparison of CW modulation systems

In the table below we compare the performance of eight signal transmission systems, inrespect of, in column order: transmission bandwidth to signal bandwidth ratio, destination


22/22


signal to noise ratio to channel signal to noise ratio, normally used channel signal to noiseratio, d.c. coupling, circuit complexity, type of detection, and common application.

Most of the entries in the table are readily derivable from theory presented in these

notes.

Type BT/W (S/N)D/ th DC Cmplxty Comment ApplicationBB 1 1 N Small No mod Short link

AM 2 m2x2

1+m2x220 N Small Env det Bcst Radio

DSB 2 1 Y Large Sync det Analog dataSSB 1 1 N Medium Sync det PP voiceVSB 1+ 1 Y Large Sync det Dig data

VSB+C 1+ m2x2

1+m2x220 Y Medium Env det TV

PM 2M() 2x2 10BT/W Y Medium Phase det Dig data

FM 2M() 32x2 10BT/W Y Medium Freq det FM Radio

Table I.1: Comparison of Continuous Wave Modulation Systems.

Documents

Appendix comm. syss