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ANGLE MODULATION

In this modulation frequency or phase of carrier is

varied according to the message signal, carrier

amplitude is constant.

It can be classified in to

1.Frequency modulation2.Phase modulation


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Application of angle modulation

1.Radio broadcasting.

2.TV-sound transmission.

3.Cellular radio.4.Microwave communication.

5.Sattelite communication


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Phase Modulation


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When mod. signal goes positive, the amount ofphase lag increases with amplitude of

mod.signal.so carrier signal is stretched & or itsfreq. reduced.

When mod. Signal is negative,phase shiftbecomes leading. so carrier is compressed. Soits freq. increased.

Phase mod. wave is same as the FM.producedby dx(t)/dt i.e.the derivative of X(t) w.r.t.time


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Phase Modulation

We know ec =Ec Cosct -----------------------------1ec= Ec Cos(2fct+ct) -------------------2

Phase modulation is

S(t) = Ec.Cos[2fct+ Kp.Vm(t) ] --------------------3

Vm(t)=EmCos2fmt ,Kp = Phase sensitivity

S(t) = Ec.Cos[2fct+ Kp Em.Cos2fmt ]

Kp Em == Phasedeviation 180 degree

S(t) = Ec.Cos[2fct+ .Cos2fmt ] ----------------------4


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Frequency modulation


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The amount by which the carrier signal varies from itsunmodulated value is called as deviation.this deviationis proportional to the instantaneus value of modulating

signal.


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Derivation of FMFrom above fig.instantaneus freq. of FM is given by

F = fc[1+k.Vm.Cosmt] -----------------1Fc = carrier freq., k= proportionality constant

Max.deviation for this signal occures when cosine= 1,under

this condition.the inst.freq. is

f= fc[1 k.Vm ] ------------------2

Max.deviation = fc.k.Vm -------------------3

Inst.signal of FM-signal is v= Asin[ F(c, m) ]=Asin---------4

F(c, m) is function of carrier & modulating freq.it represents

angle & will be called as for convenience.


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is angle traced by the vector A in time t .

The angular velocity is from FM equn.

= c[1+k.Vm.Cosmt] --------------------------------------------5to find we have to integrate above eqn.

= .dt

= c[1+k.Vm.Cosmt] dt.

= c*1kVmCosmt] dt

= c(t+ kVmSinmt/m )

= ct+ c.kVmSinmt/m

= ct+ fc.kVmSinmt/fm

= ct /fm Sinmt --------------------------------------------------6

put in eqn.4 we get


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V =Asin= Asin[ct (/fm) Sinmt ) ---------------------------------7

V= A Sin[ct+ mf. Sinmt ] -----------------------------------------------8

Modulation index = mf.= /fm = unit is Radian

It is imp.to note that mod.freq. decreases & mod.voltage ()

remains constant,modulation index increases.


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Frequency Spectrum of FM-Wave

From eqn.8 it shows Sine of Sine.it is complex function ,to solveit we have to use Bessel function (J).eqn.8 can be expanded as

v =A{J0(mf)Sinct

+ J1(mf)[Sin(c + m)t - Sin(c- m)t ]

+ J2(mf)[Sin(c +2m)t - Sin(c- 2m)t ]

+ J3(mf)[Sin(c +3m)t - Sin(c-3m)t ]

+ J4(mf)[Sin(c +4m)t - Sin(c- 4m)t +}

It can be seen that o/p consist of carrier & n-number of pair ofsideband.each preceded by J-coefficient


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Formula for Bessel function is

Jn(mf) = (mf/2)[1/n!(mf/2)/1!(n+1) ! + (mf/2)4/2!(n+2) !

- (mf/2)6 /3!(n+ 1)!

To calculate carrier,pair of sideband it is necessary to know the

value of Bessel function.FM has infinite sideband,as well as

carrier.they are seperated from carrier by fm,2fm,3fm .


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Bessel function (J Vs modulation index )


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Amplitude of Carrier & USB-LSB


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Sr.no Modulation

index

Side bands

1 1 32 2 4

3 3 6

4 4 7

5 5 8 Max.


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The no.of sideband having significant amplitude will increase

with increase in the value of modulation index.

Bandwidth :Ideally B.W of FM is infinite.because infinite sideband

transmitted ideally.

Practically we have to consider those sideband whose

amplitude is greater than 5% of amplitude of unmodulatedcarrier.strength of spectral component depends on M.I.so B.W is

also depends on M.I

B.W = 2 fm x number of significant band ------------------------1

Carsons Rule:B.W = 2* fm .max.+ --------------------------------------------------2

it gives correct result if M.I is greater than 6


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Power in FM

P= Vc/R

= (Ec/2)/R

P = Ec/2R ----------------------------------------------a


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Relation between FM & PM

Eqn.for PM

S(t) = Ec.Cos[c + Kp.Vm(t)]-------------------1

Now for FM is

S(t) = Ec.Cos[c + 2Kf Vm(t)]---------------2

There is little diff.between FM &PM

In FM there is integration of modulating signal so if weintegrate the mod.signal & apply it to i/p of Phase modulatorwe will get FM o/p


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If we differentiate the mod.signal & apply it to FM-modulator we

get phase modulation


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Types of FM

1.Narrow Band FM (NBFM):The FM with small B.W is known as NBFM.modulation index is mf.Is small as compared to one radian.

Spectrum is consist of carrier,USB & LSB

Mathematically NBFM is expressed as

Efm =S(t) = EcSinct + mf.Ec/2Sin(c +m)t USB

carrier - mf.Ec/2Sin(c -m)t LSB

Permissible freq.deviation up to 5KHZ.

Used in Police wireless,ambulanceetc


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2.Wideband FM (WBFM)

For large value of mf, the FM wave contains carrier & infinite number

of sidebands located symmetrically around the carrier.

Such FM have infinite B.W & hence it is WBFM.

Modulation index of WBFM is greater than 1.max. permissible

deviation is 75 KHZ.

used in Broadcasting application such as FM-radio,TVetc

arame ers e an arrow an


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. arame ers e an arrow anFM

1 Modulation index Greater than 1 Less than or slightly

greater than 1

2 Max.deviation 75 KHZ 5 KHZ

3 Range of mod.freq. 30 HZ to 15 KHZ 30 HZ to 3KHZ

4 Max.mod.Index 5 to 2500 Slightly greater than

1

5 B.W Large,15 times more than B.W

of NBFM

Small same as AM

6 Application Entertainment broadcasting FM mobile commn.Police

wireless,Ambulance

..etc

7 Pre-emphasis &De-emphasis

Needed Needed


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Generation of FM1.Direct Method 2.Indirect method

Direct method:

a.Varactor Diode modulator

b.Reactance modulatori.Capacitive reactance FM-Mod.

ii.Inductive reactance modulator


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1.Varactor Diode FM-Modulator


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Reactance FM -Modulator

1.Capacitive Reactance modulator:

Ckt.should satisfy two condition 1. biasing c/n ib> R


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Zeq. = V/( Ib + Id) but Id >>> Ib, so

Zeq. = V/Id -------------------------------------------------------1

Transconductance gm = Id/Vg

Id = Vg x gm -------------------------2

Since gate source is reverse biase,no c/n flows through

gate.so c/n Ib flows through resistor R

Vg = Ib x .R --------------------------------------------------3

Ib = V/(R-JXc)

Vg = V.R/(R-JXc)Id = V.R/(R-JXc) x gm -------------------------------------4

put in eqn. 1


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Zeq. = V/[V.R.gm/(R-JXc) ] = R-JXc /R.gm

Zeq.= 1/gm x [1- j xc /R] since Xc/R >>>1Zeq.= - jXc/R.gm -----------------------------------------------------------5

This impedance is clearly capacitive reactance,which can be

writen as

Xc.eq.= Xc/gm.R1/2f.Ceq. = 1/2f.C.gm.R

Ceq. = C.gm.R -------------------------------------------------------------6

Equvalent capacitance across the pt-AA depends on thegm.transconductance of FET.


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gm. Depends on gate voltage of FET.

We can vary the gate voltage with modulating signal.

equvalent capacitance vary with modulating signal.

if this ckt. Is connected to the tank ckt. of LC-tank.

so the freq. of that tank ckt. vary with mod . Signal &FM generated


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Capacitive Reactance modulator:


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Inductive reactance FM-Modulator


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Zeq. = V/( Ib + Id) but Id >>> Ib, so

Zeq. = V/Id -------------------------------------------------1

Transconductance gm = Id/Vg

Id = Vg x gm -------------------------2Since gate source is reverse biase,no c/n flows through gate.so

c/n Ib flows through resistor R

Vg = Ib x .R --------------------------------------------------3

Ib = V/(R+JXL)Vg = V.R/(R+JXL)

Id = V.R/(R+JXL) x gm -------------------------------------4

put in eqn. 1

Ckt.should satisfy two condition 1. biasing c/n ib> R


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Zeq. = V/[V.R.gm/(R+JXL) ] = R+JXL /R.gm

Zeq.= 1/gm x [1+ j xL /R] since XL/R >>>1

Zeq.= jXL/R.gm ------------------------------------------------------5

This impedance is clearly inductive reactance,which canbe writen as

XL.eq.= XL/gm.R

2f.L.eq. = 2f.L/gm.R

L.eq. = L/gm.R --------------------------------------------------------6

Equvalent Inductance across the pt-AA depends on thegm.transconductance of FET.


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gm. Depends on gate voltage of FET.

We can vary the gate voltage with modulatingsignal.

equvalent inductance vary with modulating

signal.

if this ckt. Is connected to the tank ckt. of LC-tank.

so the freq. of that tank ckt. vary with mod .Signal & FM generated

Indirect method: FM GENERATOR USING


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Indirect method: FM.GENERATOR USING

ARMSTRONG METHOD


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From.phaser diag.phase of phasemodulated signal depends on amplitude

of DSB-SC signal i.e.amplitude of modulating signal because

tan= EDSB/Ec

= EDSB/Ec


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o/p of mixer is = nfc +nf(n-1)fc

= n f + fc

Carrier freq. is reduced to its original value & freq.deviation is

multiply by factor n which is suitable for transmission.

Then this signal is amplified by class-C power amplifier &transmitted through the antenna.


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Advantages of FM

Amplitude of the frequency modulated waveremains unaffected.

Large decrease in noise, hence increase in S/Nratio.

Noise may reduce by increasing deviation

Frequency allocation allows for a guard bandwhich reduces adjacent channel interference.

FM permits several independent transmitterson the same frequency with negligibleinterference.


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Disadvantages:

1.B.W is large

2.FM TX-RX are complex.

3. FM wave cant cover large area.

4.Transmitting & receiving equipments for FM

are costly.


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APPLICATION OF FM

1.Radio broadcasting

2.Sound broadcasting in TV

3.Sattellite commn.

4.Point to point commn.5.Police wireless

6.FM is used in many radio stations (FM Radio

Stations) all over the world. Normally thefrequency range of FM channels are between88.0 MHz - 108.0 MHz.


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Effect of noise in FM & PM


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EFFECT OF NOISE/NOISE TRIANGLE


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Consider a single noise voltage having a freq.which falls in the

passband of the reciever.

This noise voltage will mix with the carrier to produce interference.

Noise vector is superimposed on carrier vector & it is rotating at a

relative angular velocity (n-c).due to this the amplitude & phase

of the carrier will change.

The amplitude & phase angle of resultant shown in fig.will keep

changing due to the relative rotation of the noise vector.

Max.deviation in the amplitude = Vn

Max.deviation in phase = =Sin-1(Vn/Vc)

Amplitude & phase both change due to noise


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AM is affected by amplitude change in the carrier due to noise

FM is affected by phase change of carrier due to noise

Effect of modulating Frequency/FM-Noise


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1.In AM-the change in noise freq.or change in mod.freq. does

not effect the signal to noise ratio, hence we get a rectangular

distribution for AM.

2.In FM this effect is different:

The noise phase modulates the carrier.

3 The effect of modulating freq.

The phase modulation of carrier can be expressed

= tan-1[VnA/Vc] ----------------------------------------------------1

VnA =Perpendicular noise component

4.For phase modulated signal the inst.phase angle (t) isexpressed as

(t) = c + t -------------------------------------------------------2

c = Carrier phase angle


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c = Carrier phase angle

t = Inst.change in phase angle with time

Differentiate eqn.2 we getd (t) /dt = d c/dt + dt /dt ----------------------------------------3

Inst.angular freq. is i= d (t) /dt = d c/dt + dt /dt ---------4

c= d c/dt

pt= d t/dt =angular freq.deviation due to phase mod.i = c + pt ----------------------------------------------------------5

pt= d t/dt

2fpt = d t/dt

fp(t)= 1/2 x d t/dt ----------------------------------------------6Fp(t) = freq.deviation due to phase mod. produced by noise

FM-Reciever produces an o/p voltage is proportional to thisfreq.deviation.this is unwanted o/p voltage it is treated asnoise .


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The noise in the FM receiver is proportional to mod freq.

If mod freq. decreases the modulation index increases, noise

to signal ratio goes on decreasing.

Effect of noise in FM is higher at high mod.freq.

Effect of noise in FM is higher at lower mod.index.

At lower mod freq. M.I is higher so less noise effect in FM.

PRE EMPHASIS


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PRE-EMPHASIS

It has been proved that in FM ,the noise having greater effect on higher

modulating freq.This effect can be reduced by increasing modulation index.(mf).for

higher modulating freq.

This can be done by increasing the deviation & it can be


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This can be done by increasing the deviation & it can be

increased by increasing the amplitude of modulating signal.&

higher mod.freq.

If we boost the amplitude of high freq.mod freq.signal.artificially

Then it could be possible to improve the noise immunity at high freq.

The artificial boosting of higher modulating freq.

is called PRE-EMPHASIS.

When this High freq. mod. Signal passing through the high passfilter

as fm incraeses reactance Xc = 1/2fm of capacitor decrease so

modulating voltage increases. so M.I increases at high mod.freq.

It is shown in Pre-emphasis characteristic


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DE EMPHASIS


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DE-EMPHASIS

The artificially boosted high freq.signal are brought to their original

amplitude using the De-emphasis. It is low pass filter. RC=75sec

The demodulated FM is applied to the DE-EMPHASIS ckt.with increase

in fm the reactance of Cap.C decreases & o/p of De-emphasis will also

reduce.

Comparison of AM- Vs FM


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Modulating differences:

In AM, a radio wave known as

"carrier wave" is modulated in

amplitude by the signal that is to

be transmitted.

In FM, a radio wave known as the

"carrier" or "carrier wave" is

modulated in frequency by the

signal that is to be transmitted.

Importance:

It is used in both analog and

digital communication and

telemetry.

It is used in both analog and

digital communication and

telemetry.

Pros and cons:

AM has poorer sound quality

compared to FM, but is cheaper

and can be transmitted over long

distances. It has a smaller

bandwidth so it can have more

stations available in anyfrequency range.

FM is less prone to interference

than AM. However, FM signals

are impacted by physical barriers.

FM has greater sound quality due

to higher bandwidth.

Stands for:AM stands for Amplitude

Modulation

FM stands for Frequency

Modulation


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Range:

AM radio ranges from 535

to 1705 kilohertz (OR) Up

to 1200 Bits per second

FM radio ranges in a

higher spectrum from 88

to 108 megahertz. (OR)

1200 to 2400 bits per

second

Bandwidth Requirements:Twice the highestmodulating frequency.

Twice the sum of the

modulating signalfrequency and the

frequency deviation.

Zero crossing in modulated

signal:Equidistant not equidistant

Complexity:

transmitter and receiver

are simple but in case of

SSBSC AM carrier

syncronization is needed

transmitter and receiver

are more complex .

Comparison of AM- Vs FM


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