ch5-angle modulation updated

7/29/2019 Ch5-Angle Modulation Updated

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ap er

1EEEC383(201-2012)NITIN Sharma


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FM Illustration

The frequency ofthe carrier is varied

around c in

relation with the

messa e si nal.

i(t)= c + kfm(t)

2EEEC383(201-2012) NITINSharma


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Instantaneous Frequency

ons er genera ze

sinusoidal signal (t)=A

generalized angle

(instantaneous Phase)

For conventional

sinusoidal (t) is ct + 0is a straight line (if0 isconstant ) with slope can n ercep o

EEEC383(201-2012) NITINSharma

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ns an aneous requency

Over a small time interval t0 the si nal t =A

cos(t) and the sinusoid A cos (ct + o) are identical It is ustified to sa that over this small interval t, the

instantaneous frequency of(t) is c .

As (ct + o) is tangential to (t), the instamtaneousfrequency of(t) is the slope of its angle (t) over this

small interval t.

Generalizing above concept at every instant and say thatthe instantaneous frequency i at any instant t is the

s ope a .


4


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The instantaneous angular frequency (in rad/sec) is the

i (t) = d(t)/dt.

For cos(c t+), i (t)= c as expected.

.)()(

t

i dt


5


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.

The angle could be constant [cos(300)], or varying with

The instantaneous angular frequency (in rad/sec) is the

rate of change of the angle. That is:i (t) = d(t)/dt.

For cos(c t+), i (t)= c as expected.

.)()(

t

i dt



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Representation of Angle Modulation in Time Domain

or an s gna : i = c fm

.)()()( t

fc

t

iFM dmktdt

( ) cos ( )

t

FM c fg t A t k m d

For Phase Modulation PM , the hase of the carrier is

varied in relation to the message signal: (t) = kp m(t)

( ) cos ( )g t A t k m t



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Relation Between FM and PM

t t k m t

( )( ) ( ).i c p c pdm tt k k m t

dt

( )

t

d

( )

t

m t dFM Modulator

m(t)gFM(t)

m(t)PM Mo u ator gPM

( )d

dt

( )dm t

dt



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Which is Which?



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5 5 5 -1 -1

FM and PM Modulation

f

kp = 10 rad/Volt = 5 v-1fc = 100 MHz

FM:

fi =fc + kfm(t)

108 -105 < fi < 108 +105

99.9 < fi < 100.1 MHZ

PM:

fi =fc + kp dm(t)/dt

108 -105 < fi < 108 -105

99.9 < fi < 100.1 MHZ

Power (FM or PM) = A2/2



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Frequency Modulation

Theimagecannotbedisplayed.Your computer may nothaveenough memory to open theimage,or theimagemay havebeen corrupted.Restartyour computer,and then open thefileagain.Ifthered x stillappears,you may haveto deletetheimageand then insertitagain.

The equation

tf

f+tV=tv mm

cccs sincos may be expressed as Bessel

series (Bessel functions)Theimagecannotbedisplayed.Your computer may nothaveenough memory to open theimage,or theimagemay havebeen corrupted.Restartyour computer,and then open thefileagain.Ifthered x stillappears,you may haveto deletetheimageand then insertitagain.

=mcncs tn+JV=tv cos

where Jn() are Bessel functions of the first kind. Expanding theequation for a few terms we have:

tVtJV

tVtVtVtvmcmcc ff

mcc

ff

mcc

f

ccs

Amp

1

Amp

1

Amp

0

2cos2cos

)(cos)()(cos)()(cos)()(

mcmc ff

mcc

ff

mcc

2Amp2Amp



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FM Signal Spectrum.

The amplitudes drawn are completely arbitrary, since we have not foundn .



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Spectrum of FM/PM

,

to relate the spectrum of the FM/PM modulated signalto that of the modulating signal m(t). We can deal witht on a case- y-case as s.

We are, however, particularly interested in finding the.

For that purpose, we will make some assumptions andwork on simple modulating messages.

Because of the close relation between FM and PM, wewill do the analysis for FM and extend it to PM.



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FM Spectrum Bessel Coefficients.

The FM signal spectrum may be determined from

mcnc tnJVtv )cos()()( n

The values for the Bessel coefficients, Jn() may be

found from graphs or, preferably, tables of Besselfunctions of the first kind.



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FM Spectrum Bessel Coefficients.

n read off the graph and hence the component amplitudes (V

cJn()) may be

determined.A further way to interpret these curves is to imagine them in 3 dimensions



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Examples from the graph

= =0

= ,

other Jn(0) = 0, i .e .

= 2.4: From the graph (approximately)

J0(2.4) = 0, J1(2.4) = 0.5, J2(2.4) = 0.45 and J3(2.4) = 0.2



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gn cant e an s pectrum.

As ma be seen from the table of Bessel functions for values ofn above acertain value, the values ofJn() become progressively smaller. In FM thesidebands are considered to be significant ifJn() 0.01 (1%).

Although the bandwidth of an FM signal is infinite, components withamplitudes VcJn(), for which Jn() < 0.01 are deemed to be insignificantand may be ignored.

Example: A message signal with a frequency fm Hz modulates a carrier fcto produce FM with a modulation index = 1. Sketch the spectrum.

n Jn(1) Amplitude Frequency

0 0.7652 0.7652Vc fc. .

c c m

c-

m2 0.1149 0.1149Vc fc+2fm fc - 2fm

3 0.0196 0.0196Vc fc+3fm fc -3fm

4 0.0025 Insignificant

5 0.0002 Insignificant

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Significant Sidebands Spectrum.

As shown, the bandwidth of the spectrum containing

m, = .



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Significant Sidebands Spectrum.

modulation indices () and the associated spectral bandwidth.

No of sidebands 1% ofunmodulated carrier

Bandwidth

0.1 2 2fm

0.3 4 4fm

0.5 4 4fm

1.0 6 6fm

2.0 8 8fm5.0 16 16fm

10.0 28 28fm

e. . for = 5

16 sidebands(8 pairs).



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Carsons Rule for FM Bandwidth.

An approximation for the bandwidth of an FM signalis given by BW = 2(Maximum frequency deviation +

g es mo u a e requency

)(2Bandwidth mc ff Carsons Rule



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Narrowband and Wideband FM

From the graph/table of Bessel functions it may be seen that for small , ( 0.3) there is only the carrier and 2 significant sidebands, i.e. BW = 2fm.

FM with 0.3 is referred to as narrowband FM (NBFM) (Note, the

bandwidth is the same as DSBAM).

Wideband FM WBFM

or > . ere are more an s gn can s e an s. s ncreasesthe number of sidebands increases. This is referred to as wideband FM(WBFM).



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VHF/FM

= transmissions, in the band 88MHz to 108MHz have the followingparameters:Max frequency input (e.g. music) fm 15kHz

mc Vf Deviation 75kHz

Modulation Index 5 cfm

For = 5 there are 16 sidebands and the FM signal bandwidth is 16fm =16 x 15kHz= 240kHz. Applying Carsons Rule BW = 2(75+15) = 180kHz.



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Comments FM

of sidebands at frequencies fc nfm (n = 0, 1, 2, )

,

n

mcncs

In FM we refer to sideband pairs not upper and lower sidebands.arr er or o er componen s may no e suppresse n .

The relative amplitudes of components in FM depend on the values Jn(),

where thus the component at the carrier frequency depends on

m(t), as do all the other components and none may be suppressedm

m

f

.



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Comments FM

n . . .

only J0() and J1() are significant, i.e. only a carrier and 2 sidebands.Bandwidth is 2fm, similar to DSBAM in terms of bandwidth - called NBFM.

Large modulation indexm

c

f

f

The FM process is non-linear. The principle of superposition does notapply. When m(t) is a band of signals, e.g. speech or music the analysis

.

frequency equal to the maximum input frequency. E.g. m(t) band 20Hz 15kHz, fm = 15kHz is used.



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Power in FM Signals.

From the equation for FM

n mcncs tnJVtv )cos()()( we see that the peak value of the components is V J () for the nth

component.

Then the nth component Single normalised average power is=2

2

)( RMSpk

V

V

2

)(

2

)(22

ncnc JVJV

Hence, the total power in the infinite spectrum is

2

Total power

n

ncT



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calculations to find PT. But, considering the waveform, the peak value isV-c, which is constant.

V VSince we know that the RMS value of a sine wave is

2 2

c

and power = (VRMS)2 then we may deduce that

n

ncccT

JVVVP

2

)(

22

222

Hence, if we know Vc for the FM signal, we can find the total power PT for

the infinite spectrum with a simple calculation. 27EEEC383(201-2012) NITINSharma


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Power in FM Signals.Now consider if we generate an FM signal, it will contain an infinitenumber of sidebands. However, if we wish to transfer this signal, e.g. over a

radio or cable, this implies that we require an infinite bandwidth channel.Even if there was an infinite channel bandwidth it would not all be

.particular signal. Thus we have to make the signal spectrum fit into theavailable channel bandwidth. We can think of the signal spectrum as a

train and the channel bandwidth as a tunnel obviously we make thetrain slightly less wider than the tunnel if we can.



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However, many signals (e.g. FM, square waves, digital signals) contain aninfinite number of components. If we transfer such a signal via a limited

channel bandwidth, we will lose some of the components and the outputsignal will be distorted. If we put an infinitely wide train through a tunnel,

,can be tolerated?

Generally speaking, spectral components decrease in amplitude as wemove awa from the s ectrum centre.



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In general distortion may be defined as

spectrumdBandlimiteinPower-spectrumin totalPowerD

BLT PP

D

With reference to FM the minimum channel bandwidth required would be

just wide enough to pass the spectrum of significant components. For abandlimited FM s ectrum let a = the number of sideband airs e. . for

= 5, a = 8 pairs (16 components). Hence, power in the bandlimitedspectrum PBL is

a 2

an

ncBLP

2= carrier power + sideband powers.



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Since 2

c

T

V

P a

cc VV 222

a

an

n

c

an

n

JV

D 22

))((1

2

22Distortion

Also, it is easily seen that the ratio

a

an nTPD ))((spectrumin totalPower = 1 Distortion

a

i.e. proportion pfpower in bandlimited spectrum to total power = an

n ))((



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Example

Consider NBFM, with = 0.2. Let Vc = 10 volts. The total power in the infinite

2

cVspectrum = 50 Watts, i.e.a

nJ2))(( = 50 Watts.

an

From the table the significant components are

n . c n .Power =

2

mp

0 0.9900 9.90 49.005

1 0.0995 0.995 0.4950125

PBL = 49.5 Watts

5.49. . .

50



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Example

Distortion = 01.050

5.4950

T

BLT

P

PP

or 1%.

c ua y, we on nee o now c, .e. a erna ve y

Distortion = 1

2

))2.0((1 nJ (a = 1)n

D = 01.0)0995.0()99.0(122

Ratio 99.01))((1

2 DPBL

1nT



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What is NOT the bandwidth of FM!

ne may en o e eve a s nce e mo u a e

signal instantaneous frequency is varying between by around then the bandwidth of the FM si nal is2f. False!

In fact, the motivation behind introducing FM was toreduce the bandwidth compared to that of Amplitude

Modulation, which turns out to be wrong.

a was m ss ng rom e p c ure o an w



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FM Visualization

u y

generator, and wiggling it back and forth tom l h rri in r n mmessage.

There are two wi lin arameters: Howfaryou deviate from the center frequency (f) Howfastyou wiggle (related toBm)

The rate of change of the instantaneousfrequency was missing!



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Carsons Rule

FM mwhere f = frequency deviation = kf |m(t)|max

m = an w t o m t

Define the deviation ratio = f / Bm.BFM 2( +1)Bm

The same rule applies to PM bandwidth,

BPM 2(f+Bm) = 2(+1)Bmwhere (f)PM = kp |dm(t)/dt|max



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Narrow Band and Wide Band FM

en m or , e sc eme s

called Narrow Band (NBFM, NBPM).

NBFM m same or

Therefore, no matter how small we make theev at on aroun c , t e an w t o t e

modulated signal does not get smaller than 2Bm.



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EstimateBFMandBPM= 5 = 5f

Hz/Volt = 105 V-1sec-1

kp = 5 rad/Volt = 2.5 v-1

=c

First estimate theBm.Cn = 8/2n2 for n odd, 0 n even

The 5th harmonic onward canbe neglected.Bm = 15 kHz

For FM: FM

For PM:f= 50 kHz;BPM=130 KHz



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Repeat ifm(t) is Doubled

5 5f

Hz/Volt = 10

5

V

-1

sec

-1


2

-

40,000

-40,000

c = z

For FM:

f= 200 kHz;BFM= 430 KHz For PM:

f= 100 kHz;BFM= 230 KHz

Doubling the signal peak has

significant effect on both FMand PM bandwidth



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Repeat if the period ofm(t) is Doubled

5 5 -f

Hz/Volt = 105 V-1sec-1


10,000

-10,000

c = z

Bm = 7.5 kHz

For FM:f= 100 kHz;BFM= 215 KHz

For PM:

f= 25 kHz;BFM= 65 KHz

Expanding the signal varies itsspectrum. This has significant

effect on PM.



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Question

period of 1.001x10-8s and a minimum period of 0.999x10-8s. The modulatin si nal is a 20 KHz ure

tone.

Find the value of the frequency deviation and

.


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e max mum requency s t e nverse o

the minimum period which is MHzmax 81

100.10.999 10

f

and the minimum frequency is the inverse of the

maximum eriod which is MHz.min 8

1

99.9f

The carrier is the average of these two

.

.

(2) The frequency deviation is MHz,

c

max min 0.c cf f f f

w c means .EEEC383(201-2012) NITIN

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5


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Spectrum of NBFM (2/2)

, f

( ) ( ) cos( ) ( )sin( )FM Narrowband c f cg t A t k a t t

Bandwidth ofa(t) is equal to the bandwidth ofm(t),Bm.

NBFM m .

Similarly for PM (|kp m(t)|


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NBFM Modulator

( ) ( ) cos( ) ( )sin( )FM Narrowband c f ct A t k a t t

( )

t

d

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NBPM Modulator

( ) ( ) cos( ) ( )sin( )PM Narrowband c p cg t A t k m t t

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Immunity of FM to Non-linearities

2

1 2

3

3

( ) cos ( ) cos ( )

cos ( )

c f c f

c f

q t a A t k m d a A t k m d

a A t k m d

21 cos ( ) 1 cos 2 2 ( )

2c f c f

a Aa A t k m d t k m d

3 1 cos 2 2 (2

c f

a At k m

32 21

) cos ( )

3cos ( ) cos 2 2 ( )

c f

c f c f

d t k m d

a Aa A a Aa A t k m d t k m d

Around with Around 2 with 2c f f c f f DC k k k k

3 cos 3 3 ( )4

c f

a At k m d

Around 3 with 3c f fk k

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Frequency Multipliers

( )FMg t ( ) contains the followingq t

cos ( )c fA t k m d

cos ( )c ft k m d

( ) ( )

cos ( )

FM output

c f

g t

B P t Pk m d

cos 2 2 ( )c ft k m d

cos ( )c fP t Pk m d

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Generation of WBFM: Indirect Method

,interested in generating

an FM signal of certainbandwidth (orfor)c.

In the indirect method,we generate a NBFM

with smallthen use ascaleto the requiredvalue.

This way,fc will alsoe sca e y e same

factor. We may need afrequency mixer toadjustfc.

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Sharma


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Example: From NBFM to WBFM

mo u a or s mo u a ng a message s gna

m(t) with bandwidth 5 kHz and is producing an FMsi nal with the followin s ecifications

fc1 = 300 kHz, f1 = 35 Hz.

We would like to use this si nal to enerate a WBFMsignal with the following specifications

fc2 = 135 MHz, f2 = 77 kHz.

3

2

1

77*102200

35

f

f

62

3

1

135*10450

300*10

c

c

f

f

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From NBFM to WBFM: System 1

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From NBFM to WBFM: System 2

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Sharma


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e o ow ng oc agram s or an rmstrong

indirect FM transmitter. Find the missing five values

1, c2, , 2, c . w y u .


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Generation of WBFM: Direct Method

as poor requency sta ty. equ resfeedback to stabilize it.

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,and then, at the receiver, these variations in the amplitude were

detected and the info recovered. In FM, the info signal is used to control the freq of the carrier wave.

The freq of the carrier is made to increase as the voltage in the infosignal increase and to decrease in freq as it reduces. The larger theamplitude of the info signal, the further the freq of the carrier signal is

.

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56

combined in 1 circuit

Figure: FM Transmitter


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Very similar to the AM transmitter.

The audio oscillator supplies the information signal (egmicrophone and AF amplifier to provide speech and music

instead of the sinewave signals in ANACOM 2).

The only difference between AM and FM transmitters are the

modulators. Two types of FM Modulator function in much the same way.

Varactor Modulator

Reactance Modulator

57


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these oscillators employ a parallel tuned circuit to determine

the frequency of operation.Addin an additional

The fre uenc of

capacitor in parallel willcause the total capacitanceto increase and this will

result in a decrease in theresonancedepends on valueof L and C

resonance freq.

Recall,

Hzfo1

58

gure: ara e une rcu


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The tuned circuit is art of the oscillator used to enerate the

carrier freq so, if the capacitance changes, then so will the carrier

freq. This is demonstrated in Figure below. To produce a freq,

needed to find a way ofmaking the info signal

size of the capacitance andhence control the carrierfreq.

How to achieve? using adevice called Varactor Diodand then by using a

59

transistor.Figure: Frequency Modulated

Carrier


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behave as a voltage controlled capacitor.

When a semiconductor diode is reverse biased, no current flows

-

conducting region.

This is very similar to the construction of the capacitor.

A, d

60

A


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AC

d

-capacitance.

-

By increasing the reverse biased voltage, the width of the

insulating region can be increased and hence the capacitance

.

value decreased (more frequecy). Thus, if the info signal is applied to the varactor diode, the

capacitance will therefore be increased and decreased in

61

accordance with the incoming signal.

The Varactor Modulator Circuit


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The Varactor Modulator Circuit

cb

Figure: Thee

Note that tuned circuit sets the operating freq of the oscillator and the

Modulator Circuit

varactor, which is effectively in parallel with the tuned circuit.

C1 is a DC blocking capacitor to provide DC isolation between the

oscillator and the collector of the transistor.

62

L1 is an RF choke which allows the info signal through to the varactor but

blocks the RF signals.


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The Reactance Modulator Circuit


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Behave like avariable

Figure: The Reactance ModulatorCircuit

Solution making it generate a current that is leading an appliedvoltage by connecting C and R in series with the collector and the

64

.


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FM Demodulator

our pr mary me o s

Differentiator with envelope detector/Slope detectoro convers on

Phase-shift discriminator/Ratio detector

Zero-crossing detector

Phase lock loops (PLL)

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FM Demodulation: Signal Differentiation

( ) cos ( )FM c fg t A t k m d

( ) sin ( )FM c f c f g

A k m t t k m ddt

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FM Demodulation: Signal Differentiation

( )d ( ) sin ( )c f c f A k m t t k m d

dt

( )sin ( )

dm tk t k m t

t

( )dm t

dt

t( )d

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Frequency Discriminators

ny sys em w a

transfer function of theform = a+ b

over the band of the FM

signal can be used for

emo u a on

The differentiator is just

.

68EEEC383(201-2012) NITIN

Sharma


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Slope Detectors (Demodulators)

( ) cos ( )c f c f A Ck m t t k m d

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FM Slope Demodulator

frequency discriminator, which implements frequency

to voltage conversion (FVC)

frequency. Example: filters, differentiator

s t x t |H f |

X(f)

dt

H(f)=j2 fS(f)

X(f)

output

voltage

f

freqency in s(t) voltage in x(t)

10 20

20 40

Hz j

Hz j

range in S(f)

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FM Slope Demodulator cont. Block dia ram of direct method slo e detector = slo e

circuit + envelope detector)

slope envelopes(t)s1(t) so(t)

(AM demodulator)

circuit detector

(FM AM)(FVC)

0( ) cos 2 2 ( ) , where ( ) ( )

t

c c f i c f s t A f t k m d f t f k m t

Let the slope circuit be simply differentiator:

10

( ) 2 2 ( ) sin 2 2 ( )t

c c f c f s t A f k m t f t k m d o c c f s t m t so(t) linear with m(t)

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Slope Detector

Magnitude frequencyresponse of

.

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Limiter

eren a or wor s correc y on y ere are no

amplitude variations in s(t) i.e. Ac =constant.c = t t me-vary ng , t en enve ope o

ds/dt will include term A(t). To remove amplitude

var at ons use ar m ter an BPF e ore t e

differentiator

EEEC383(201-2012) NITIN

Sharma

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Limiter

filterthat suppresses the unwanted products (harmonics) of the

limiting process.

Input Signal

))(cos()()(cos)()( t

fci daamktwtAttAtv

utput o ar m ter

)(5cos5

1)(3cos

3

1)(cos

4)( ttttvo

Bandpass filter ))(cos(4)( t

fco daamktwte

Remove the amplitude variations74EEEC383(201-2012) NITIN

Sharma


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Ratio Detector-

uses a double-tuned transformer to convert the instantaneous frequency

variations of the FM input signal to instantaneous amplitude variations.These amplitude variations are rectified to provide a DC output voltagew c var es n amp tu e an po ar ty w t t e nput s gna requency.

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Zero Crossing Detector

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Phase comparator circuit is use to detect the changes in the phase

of the signal by comparing the phase of the original input signal with

the output of the phase shifting circuit.

It then produces a DC voltage level which depends on the result of

the comparison according to the following rules:

Phase shift = 90, no change in DC voltage level.

Phase shift > 90, result in increased DC voltage level.

Phase shift < 90, result in decreased DC voltage level.

As the phase change, the DC voltage level moves up and down and

re-creates the audio si nal.

A low pass filter is included to reduce the amplitude of any high-freqripple and also blocks the DC offset. Consequently the signal at the

out ut closel resembles the ori inal in ut si nal.

78`

-


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rrorVoltage

(Reference)

Tuned Voltageused to control

Figure: Block Diagram of PLL Detector

PLL is a closed loop feedback control system in which either the

79

requency or e p ase o e ee ac s gna s e parame er ointerest.

-


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When there is no external in ut si nal FM si nal f the VCO o erates atthe preset frequency (natural/free-running frequency, fn)

The VCOs natural freq is determined by external component. It is normallyset (locked) to IF center freq.

W en FM signa is app ie to t e PLL, t e p ase comparator compares t e iwith the VCO output freq.

Phase comparator produced error voltage that is proportional to the freq

= - After several cycles around the loop, the VCOs freq will be equal to FM

signal freq. And the loop is said to have acquired freq locked.

Once the loop is freq locked, the freq difference between the externalinput and the VCOs output is converted to a dc bias voltage.

The error voltage is filtered, amplified and applied back to the input of theVCO.

80

ere ore, e error vo a e s a so propor ona o e req ev a ondemodulated info signal

The Phase-Locked Loop (PLL) Detector


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A PLL o erate in three different modes: Free running Capture Tracking

,VCO frequency and the PLL runs at the free running frequency determinedby the tuning circuits of the VCO. The error voltage is outside the range ofthe VCO.

As the input frequency gets closer to the VCO frequency, the error voltagereaches a value at which it can begin to change the VCO frequency. This isthe capture mode. The error voltage will continue to decrease as the VCO

.

Finally, when the VCO is operating at the same frequency as the input, thePLL is in the tracking mode. The VCO will track changes in the inputfrequency as long as the input frequency remains in a range of frequencies

81

nown as t e o - n range.


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.

Most noise results in unwanted amplitude variation. FM/PM receiver

use amplitude limiter to remove the amplitude variation.

Figure: The Amplitude Limiter

AGC is not necessary in an FM receiver, because the limiter circuit.

The limiter clips all noise peaks from the IF signal and the output of thelimter has constant amplitude.

A limiter cannot be used for this ur ose in an AM receiver because

82

amplitude variations in the signal contain information as well as noise.


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.

In FM/PM, limiters reduce noise thus improve SNR ratio during demodulation.

In AM, once signal is contaminated with noise, it cannot be remove.

3. Capture Effect

FM/PM receiver can differentiate between 2 signals received with the same

frequency. The receiver will capture (locked on) the stronger signal andeliminates the weaker signal.

In AM, if signals are received at the same freq, all of them will bedemodulated and heard.

4. Power Utilization and efficiency In FM/PM, total power remains constant regardless of modulation index

83

, .

Disadvanta e of An le Modulation


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.

High quality angle modulation produces many side freq, thus it

require wider BW than AM.

.

Commercial FM radio band => 200kHz of BW

. Modulation and demodulation ckt required for FM/PM are complex

than those for AM i.e expensive.

, .

84


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Phased-Locked Loop (PLL)

e mu p er o owe

by the filter estimatesthe error bewteen theangle ofgFM(t) and

gVCO(t).LoopFilter

to adjust the angle.

When the angles are VCO

locked, the output of thePLL would be followingm t attern.

85EEEC383(201-2012) NITIN

Sharma


86/107

FM Demodulator PLL-

A closed-loop feedback control circuit, make a signal in fixed phase

(and frequency) relation to a reference signal

Or, change frequency (or phase) according to inputs

PLL can be used for both FM modulator and demodulator

modulations and demodulations



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PLL FM Remember the followin relations

Si=Acos(wct+1(t)), Sv=Avcos(wct+c(t))

Sp=0.5AAv[sin(2wct+1+c)+sin(1-c)]o= . vs n 1- c = v 1- c

Section 2.14

s(t)+

+

freqency

devided

LPFilterLoops(t) e(t) v(t)

y

Reference

Carrier

rVCO


S h d R i


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Superheterodyne Receiver Radio receivers main function Demodulation get message signal

Carrier frequency tuning select stationer ng remove no se n er erence

Amplification combat transmission power loss

Su erheterod ne receiver Heterodyne: mixing two signals for new frequency Superheterodyne receiver: heterodyne RF signals with local

tuner convert to common IF

Invented by E. Armstrong in 1918.

AM: RF 0.535MHz-1.605 MHz, Midband 0.455MHz

- , .


Ad f h d i


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Advantage of superheterodyne receiver,

quality, and power amplification

Superheterodyne receiver deals them with different blocksoc s: se ec v y on y

IF blocks: filter for high signal quality, and amplification, use circuitsthat work in only a constant IF, not a large band


FM B d ti


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FM Broadcasting The fre uenc of an FM broadcast station is usuall an

exact multiple of 100 kHz from 87.5 to 108.5 MHz . In

most of the Americas and Caribbean only oddmultiples are used.

fm=15KHz, f=75KHz, =5, B=2(fm+f)=180kHz

Pre-emphasis and de-emphasis

Random noise has a 'triangular' spectral distribution in an

,

at the highest frequencies within the baseband. This can beoffset, to a limited extent, by boosting the high frequencies

before transmission and reducing them by a corresponding

amount in the receiver. 90EEEC383(201-2012) NITINSharma

FM Stereo MultiplexingFM Stereo Multiplexing


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Fc=19KHz.

(a) Multiplexer in transmitter

of FM stereo.

(b) Demultiplexer in receiver

o FM stereo.

For non-stereo receiver


TV FM b d ti


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TV FM broadcasting

fm=15KHz, f=25KHz, =5/3, B=2(fm+f)=80kHz

Center fc+4.5MHz



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93


The Operation of the Reactance Modulator


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The Operation of the Reactance Modulator

The oscillator and tuned ckt rovides the unmodulated

carrier freq, and this freq is present on the collector of

the transistor.an prov e p ase s t etween t e co ector

voltage and current this makes the ckt appear as a

capacitance.

The changing info signal being applied to the base has

the same effect as changing the bias voltage applied to

.

decrease. As the ca acitance is effectivel in arallel with the

94

tuned ckt, the variations in value will cause the freq of

resonance to change and hence the carrier freq will be

FM Receiver


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Similar to AM superhet Rx. The most

significant different is that the FMemo u a or mus now ex rac e n o

signal from a freq modulated wave.

The basic requirement of any FM

changes into changes in voltage, with the

95

FM Receiver


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96Figure: FM Receiver


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Figure: Block Diagram of Quadrature Detector

e incoming signa is passe t roug a p ase-s i ting circuit.

The degree of phase shift that occurs is determined by the exact

freq of the signal at any particular instant.

The rules are:

If the carrier is unmodulated, the phase shift is 90.

If the carrier fre increase the hase shift is GREATER than 90.

97

If the carrier freq decreases, the phase shift is LESS than 90.


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Phase comparator circuit is use to detect the changes in the phase

of the signal by comparing the phase of the original input signal with

the output of the phase shifting circuit.

It then produces a DC voltage level which depends on the result of

the comparison according to the following rules:

Phase shift = 90, no change in DC voltage level.

Phase shift > 90, result in increased DC voltage level.

Phase shift < 90, result in decreased DC voltage level.

As the phase change, the DC voltage level moves up and down and

re-creates the audio si nal.

A low pass filter is included to reduce the amplitude of any high-freq

ripple and also blocks the DC offset. Consequently the signal at the

out ut closel resembles the ori inal in ut si nal.

98`

-


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rrorVoltage

(Reference)

Tuned Voltageused to control

Figure: Block Diagram of PLL Detector PLL is a closed loop feedback control system in which either the

99

requency or e p ase o e ee ac s gna s e parame er ointerest.

-


100/107

When there is no external in ut si nal FM si nal f the VCO o erates atthe preset frequency (natural/free-running frequency, fn)

The VCOs natural freq is determined by external component. It is normallyset (locked) to IF center freq.

W en FM signa is app ie to t e PLL, t e p ase comparator compares t e iwith the VCO output freq.

Phase comparator produced error voltage that is proportional to the freq

= - After several cycles around the loop, the VCOs freq will be equal to FM

signal freq. And the loop is said to have acquired freq locked.

Once the loop is freq locked, the freq difference between the externalinput and the VCOs output is converted to a dc bias voltage.

The error voltage is filtered, amplified and applied back to the input of theVCO.

100

ere ore, e error vo a e s a so propor ona o e req ev a ondemodulated info signal

The Phase-Locked Loop (PLL) Detector


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A PLL o erate in three different modes: Free running Capture

Tracking,

VCO frequency and the PLL runs at the free running frequency determinedby the tuning circuits of the VCO. The error voltage is outside the range ofthe VCO.

As the input frequency gets closer to the VCO frequency, the error voltagereaches a value at which it can begin to change the VCO frequency. This isthe capture mode. The error voltage will continue to decrease as the VCO

.

Finally, when the VCO is operating at the same frequency as the input, thePLL is in the tracking mode. The VCO will track changes in the inputfrequency as long as the input frequency remains in a range of frequencies

101

nown as t e o - n range.


102/107

.

Most noise results in unwanted amplitude variation. FM/PM receiver

use amplitude limiter to remove the amplitude variation.

Figure: The Amplitude Limiter

AGC is not necessary in an FM receiver, because the limiter circuit.

The limiter clips all noise peaks from the IF signal and the output of thelimter has constant amplitude.

A limiter cannot be used for this ur ose in an AM receiver because

102

amplitude variations in the signal contain information as well as noise.


103/107

.

In FM/PM, limiters reduce noise thus improve SNR ratio during demodulation.

In AM, once signal is contaminated with noise, it cannot be remove.

3. Capture Effect

FM/PM receiver can differentiate between 2 signals received with the samefrequency. The receiver will capture (locked on) the stronger signal and

eliminates the weaker signal.

In AM, if signals are received at the same freq, all of them will bedemodulated and heard.

4. Power Utilization and efficiency In FM/PM, total power remains constant regardless of modulation index

103

, .

Disadvanta e of An le Modulation


104/107

.

High quality angle modulation produces many side freq, thus it

require wider BW than AM. .

Commercial FM radio band => 200kHz of BW

. Modulation and demodulation ckt required for FM/PM are complex

than those for AM i.e expensive.

, .

104

Summary of FM spectrum:


105/107

Frequency spectrum consists ofcarrier component at fc

and also sideband at fcnfmwhere n is an integer(n=

1,2,3,)

The number of sideband depends on index modulation

value m.

Magnitude of carrier signal decreases as m increases.

Jn(m).

The bandwidth of modulated signal increases when index

modulation, mincreases. BW > 2fm is expected.

Revision

After modulation using an FM modulator, the modulated wave is passedthrough an ideal bandpass filter having a center frequency of 500Hz


106/107

through an ideal bandpass filter having a center frequency of 500Hzand a bandwidth of 200Hz.

AntennaMessageSignal

CarrierFMModulator Bandpass

Filter

TransmittedSignal

Signal

The unmodulated carrier signal is given by 10 cos(1000t) V and themessage signal is 8 cos(96t) V. The frequency deviation sensitivity is

12Hz/V.Assuming all devices have resistance of 10, calculate:a) Peak frequency deviation in Hertz

c) Carrier swing

d) Modulation indexe) Power at the bandpass filter input

106

raw e requency spec rum o e s gna a e er npu anoutput Label the amplitude and frequency of each spectralcomponent

Power at the band ass filter out ut

2. An angle modulated wave has the equation ,36

is applied to the antenna with a load resistance of 50.

FM


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m rms,a frequency deviation of 2 kHz. Determine:

i. The instantaneous frequency, fi(t)ii. The actual minimum bandwidth from the Bessel Function table [1

marks]iii. The approximate minimum bandwidth using Carsons rule [1 marks]iv. The modulating signal, Vm(t) equation [2 marks]

b) If the maximum frequency deviation has been increased until theamplitude of the second sideband pairs are 50% of the unmodulatedcarrier amplitude, determine:

v. e new mo u a e carr er power mar s

vi. If the signal from part (iv) is passes through the bandpass filter with acenter frequency of 100 MHz and a bandwidth of 6 kHz, draw thefre uenc s ectrum of the si nal at filter out ut. Label the am litude

107

and frequency of each spectral component. [3 marks]vii. The total modulated wave power after the bandpass filter in part (v).[1

marks]

ch5-angle modulation updated

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