ANGLE MODULATIONportal.unimap.edu.my/portal/page/portal30/Lecture Notes/KEJURUTERAAN... · Frequency modulation (FM) Phase modulation (PM) Used for : Commercial radio broadcasting

ANGLE MODULATION

EKT358 – Communication System

Muzammil Jusoh

1

Introduction

Angle modulation is the process by

which the angle (frequency or phase) of

the carrier signal is changed in

accordance with the instantaneous

amplitude of modulating or message

signal.

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Muzammil Jusoh

Cont’d…

classified into two types such as ◦ Frequency modulation (FM) ◦ Phase modulation (PM)

Used for : ◦ Commercial radio broadcasting ◦ Television sound transmission ◦ Two way mobile radio ◦ Cellular radio ◦ Microwave and satellite communication system

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Muzammil Jusoh

Cont’d…

Advantages FM/PM over AM: Freedom from interference: all natural and

external noise consist of amplitude variations,

thus receiver usually cannot distinguish

between amplitude of noise or desired signal.

AM is noisy than FM.

Operate in very high frequency band (VHF):

88MHz-108MHz

Can transmit musical programs with higher

degree of fidelity.

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Muzammil Jusoh

Principles of FM A sine wave carrier can be modified for

the purpose of transmitting information

from one place to another by varying its

frequency. This is known as frequency

modulation (FM).

In FM, the carrier amplitude remains

constant and the carrier frequency is

changed by the modulating signal

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Muzammil Jusoh

Principles of FM

As the amplitude of the information signal

varies, the carrier frequency shifts

proportionately.

As the modulating signal amplitude

increases, the carrier frequency increases.

With no modulation the carrier is at its

normal center or resting frequency

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Muzammil Jusoh

Principles of FM Frequency deviation (fd) is the amount

of change in carrier frequency produced by the modulating signal.

The frequency deviation rate is how many times per second the carrier frequency deviates above or below its center frequency.

The frequency of the modulating signal determines the frequency deviation rate.


Muzammil Jusoh

Principles of FM

8

Carrier

Modulating

Signal

FM

signal


Muzammil Jusoh

Principles of Phase Modulation, PM

When the amount of phase shift of a constant-frequency carrier is varied in accordance with a modulating signal, the resulting output is a phase-modulation (PM) signal.

Phase modulators produce a phase shift which is a time separation between two sine waves of the same frequency.

The greater the amplitude of the modulating signal, the greater the phase shift.


Muzammil Jusoh

Principles of Phase Modulation

The maximum frequency deviation produced by a

phase modulator occurs during the time that the

modulating signal is changing at its most rapid rate.

A frequency shift occurs in PM only when the modulating signal amplitude varies.


Phase-Shift Keying

◦ The process of phase modulating a carrier

with binary data is called phase-shift keying

(PSK) or binary phase-shift keying

(BPSK).

◦ The PSK signal has a constant frequency, but

the phase of the signal from some reference

changes as the binary modulating signal

occurs.


Muzammil Jusoh


Figure: Phase modulation of a carrier by binary data produces PSK.


Muzammil Jusoh

Mathematical analysis of FM

Mathematical analysis:

Let message signal:

And carrier signal:

tVt mmm cos

]cos[ tVt ccc

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Muzammil Jusoh

Mathematical analysis of FM During the process of frequency modulations the

frequency of carrier signal is changed in accordance with the instantaneous amplitude of message signal. Therefore the frequency of carrier after modulation is written as

To find the instantaneous phase angle of modulated signal, integrate equation above w.r.t. t

tcosVKtvK mm1Cm1ci

tsinVK

tdttcosVKdt m

m

m1Cmm1Cii

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Thus, we get the FM wave as:

Where modulation index for FM is given

by

)tsinVK

tcos(VcosVc)t(v m

m

m1CC1FM

)sincos()( tmtVtv mfCCFM

15

m

m1f

VKm


Muzammil Jusoh


Therefore:

K1 – deviation sensitivities Hz/V

m

f

m

f

fm

VKf

;1

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Muzammil Jusoh

Example 1 (FM)

Determine the peak frequency

deviation (∆f) and modulation index

(m) for an FM modulator with a

deviation sensitivity K1 = 5 kHz/V and a

modulating signal,

Δf = 5k x 2 = 10 k Hz

)t20002cos(2)t(vm

17

m

f

m

f

fm

VKf

;1

52

10

k

km f


Muzammil Jusoh

Mathematical analysis of PM

The process by which changing the phase of carrier

signal in accordance with the instantaneous of message

signal. The amplitude remains constant after the

modulation process. Mathematical analysis:

Let message signal:

And carrier signal:

tVt mmm cos

]cos[ tVt ccc

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PM (cont’d)

Where = phase angle of carrier signal. It is changed in

accordance with the amplitude of the message signal;

i.e.

After phase modulation the instantaneous voltage will be

or

Where mp = Modulation index of phase modulation

K is a constant and called deviation sensitivities of the phase

tKVtKV mmm cos)(

)coscos()(

)coscos()(

tmtVtv

tKVtVtv

mpCCpm

mmCCpm

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Muzammil Jusoh

Example 2 (PM)

Determine the peak phase deviation (m)

for a PM modulator with a deviation

sensitivity K = 2.5 rad/V and a modulating

signal,

)20002cos(2)( ttvm

20

mp KVm

radxmp 525.2


Muzammil Jusoh

Summary of Mathematical

Equation for FM and PM

21

Tomasi

Electronic Communications Systems, 5e Copyright ©2004 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458

All rights reserved.


Muzammil Jusoh

Modulation Index

and Sidebands

Any modulation process produces sidebands.

When a constant-frequency sine wave modulates a carrier, two side frequencies are produced.

Side frequencies are the sum and difference of the carrier and modulating frequency.

The bandwidth of an FM signal is usually much wider than that of an AM signal with the same modulating signal.


Muzammil Jusoh

Modulation Index

and Sidebands Modulation Index ◦ The ratio of the frequency deviation to the

modulating frequency is known as the modulation index (mf).

◦ In most communication systems using FM, maximum limits are put on both the frequency deviation and the modulating frequency.

◦ In standard FM broadcasting, the maximum permitted frequency deviation is 75 kHz and the maximum permitted modulating frequency is 15 kHz.

◦ The modulation index for standard FM broadcasting is therefore 5.


Muzammil Jusoh

Modulation Index

and Sidebands

Bessel Functions

◦ The equation that expresses the phase angle

in terms of the sine wave modulating signal is

solved with a complex mathematical process

known as Bessel functions.

◦ Bessel coefficients are widely available and it is

not necessary to memorize or calculate them.


Muzammil Jusoh

FM&PM (Bessel function)

Thus, for general equation:

)coscos()( tmtVtv mfCCFM

2

nncos)m(J)cosmcos(

n

n

25

n

mcnC2

ntntcos)m(JV)t(m


Muzammil Jusoh

Bessel function

)...}(...)2(cos)(

)2(cos)(2

)(cos)(

2)(cos)(cos)({

2

21

10

fnmCf

mCfmCf

mCfCfCFM

mJtmJ

tmJtmJ

tmJtmJVtv

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Muzammil Jusoh

B.F. (cont’d)

It is seen that each pair of side band is preceded by J coefficients. The order of the coefficient is denoted by subscript m. The Bessel function can be written as

N = number of the side frequency Mf = modulation index

....

!2!2

2/

!1!1

2/1

2

42

n

m

n

m

n

mmJ

ff

n

f

fn

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Muzammil Jusoh

Modulation Index

and Sidebands

Bessel Functions

◦ The symbol ! means factorial. This tells you to multiply all integers from 1 through the number to which the symbol is attached. (e.g. 5! Means 1 × 2 × 3 × 4 × 5 = 120)

◦ Narrowband FM (NBFM) is any FM system in which the modulation index is less than π/2 = 1.57, or

mf < π /2.

◦ NBFM is widely used in communication. It conserves spectrum space at the expense of the signal-to-noise ratio.


Muzammil Jusoh

B.F. (cont’d)

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Muzammil Jusoh

Bessel Functions of the First Kind, Jn(m)

for some value of modulation index

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Muzammil Jusoh

Representation of frequency spectrum

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Muzammil Jusoh

Example 3

For an FM modulator with a modulation index m = 1, a modulating signal vm(t) = Vm sin(2π1000t), and an unmodulated carrier vc(t) = 10 sin(2π500kt). Determine the number of sets of significant side frequencies and their amplitudes. Then, draw the frequency spectrum showing their relative amplitudes.

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Muzammil Jusoh

Solution for Example 3

From the bessel table, m = 1,

◦ J0 = 0.77, J1= 0.44, J2= 0.11, J3 = 0.02

◦ So, n = 3

◦ Amplitudes for n =3,

◦ V0 = J0Vc = 0.77 x 10 = 7.7 V

◦ V1 = J1Vc = 0.44 x 10 = 4.4 V

◦ V2 = J2Vc = 0.11 x 10 = 1.1 V

◦ V3 = J3Vc = 0.02 x 10 = 0.2 V

EKT343 –Principle of Communication

Engineering 33

Comparison NBFM&WBFM

34

WBFM NBFM

Modulation index greater than 10 less than 1

Freq deviation 75 kHz 5 kHz

Modulation

frequency

30 Hz- 15 kHZ 3 kHz

Spectrum Infinite no of sidebands and

carrier

Two sidebands and carrier

Bandwidth 15 x NBFM

2(δ*fm (max))

2 fm

Noise More suppressed Less suppressed

Application Entertainment &

Broadcasting

Mobile communication


Muzammil Jusoh

FM Bandwidth

Theoretically, the generation and transmission of FM requires

infinite bandwidth. Practically, FM system have finite bandwidth and

they perform well.

The value of modulation index determine the number of

sidebands that have the significant relative amplitudes

If n is the number of sideband pairs, and line of frequency

spectrum are spaced by fm, thus, the bandwidth is:

For n≥1

mfm nfB 2

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Muzammil Jusoh

FM Bandwidth (cont’d)

Estimation of transmission b/w; Assume mf is large and n is approximate mf + 2; thus Bfm=2(mf + 2)fm

= (1) is called Carson’s rule

m

m

ff

f)2(2

36

)1)........((2 mfm ffB


Muzammil Jusoh

Example 4

For an FM modulator with a peak frequency deviation, Δf = 10 kHz, a modulating-signal frequency fm = 10 kHz,

Vc = 10 V and a 500 kHz carrier, determine ◦ Actual minimum bandwidth from the Bessel function

table.

◦ Approximate minimum bandwidth using Carson’s rule.

◦ Plot the output frequency spectrum for the Bessel approximation.

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Muzammil Jusoh


; n = 3

BW = 2 n fm

= 2 x 3 x 10 k = 60 kHz

BW (carson rule) =

= 2 (10k + 10 k)

= 40 kHz

38

m

ff

fm

1

10

10

k

km f

)(2 mff


Muzammil Jusoh

Deviation Ratio (DR)

The worse case modulation index which produces the widest

output frequency spectrum.

Where

◦ ∆f(max) = max. peak frequency deviation

◦ fm(max) = max. modulating signal frequency

(max)

(max)

mf

fDR

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Muzammil Jusoh

Example 5

Determine the deviation ratio and bandwidth for the worst-case (widest-bandwidth) modulation index for an FM broadcast-band transmitter with a maximum frequency deviation of 75 kHz and a maximum modulating-signal frequency of 15 kHz.

Determine the deviation ratio and maximum bandwidth for an equal modulation index with only half the peak frequency deviation and modulating-signal frequency.

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Muzammil Jusoh


For m = 5; n = 8

BW = 2n fm = 2 x 8 x 15k

= 240 kHz

Δf = 75k/2 = 37.5 kHz

fm = 15k/2 = 7.5 kHz

BW = 2n fm = 2 x 8 x 7.5k

= 120 kHz

41

(max)

(max)

mf

fDR

5

1575

kk

55.75.37 kkDR


Muzammil Jusoh

Angle Modulation

Part 2

Power distribution of FM

Generation & Demodulation of FM

Noise in FM

Application of FM

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Muzammil Jusoh

FM Power Distribution

As seen in Bessel function table, it shows that as the sideband relative amplitude increases, the carrier amplitude,J0 decreases.

This is because, in FM, the total transmitted power

is always constant and the total average power is equal to the unmodulated carrier power, that is the amplitude of the FM remains constant whether or not it is modulated.

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Muzammil Jusoh

FM Power Distribution (cont’d)

In effect, in FM, the total power that is originally in the

carrier is redistributed between all components of the

spectrum, in an amount determined by the modulation

index, mf, and the corresponding Bessel functions.

At certain value of modulation index, the carrier

component goes to zero, where in this condition, the

power is carried by the sidebands only.

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Muzammil Jusoh

Average Power

The average power in unmodulated carrier

The total instantaneous power in the angle modulated carrier.

The total modulated power

R2

VP

2

cc

R2

V)]t(2t2cos[

2

1

2

1

R

VP

)]t(t[cosR

V

R

)t(mP

2

cc

2

ct

c

22

c

2

t

45

R

V

R

V

R

V

R

VPPPPP no

nt2

)(2..

2

)(2

2

)(2

22..22

22

2

2

1

2

210


Muzammil Jusoh

Example 6

For an FM modulator with a modulation index m = 1, a modulating signal

vm(t) = Vmsin(2π1000t)

and an unmodulated carrier

vc(t) = 10sin(2π500kt)

Determine the unmodulated carrier power for the FM modulator given with a load resistance, RL = 50Ω. Determine also the total power in the angle-modulated wave.

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Muzammil Jusoh


47

0051.1)50(2

)2.0(2

)50(2

)1.1(2

)50(2

)4.4(2

)50(2

7.7 2222

tP

WPc 1)50(2

102


Muzammil Jusoh

Quiz For an FM modulator with modulation index,

m = 2, modulating signal,

vm(t) = Vmcos(2π2000t)

and an unmodulated carrier,

vc(t) = 10 cos(2π800kt)

Assume, RL=50Ω

a) Determine the number of sets of significant sidebands.

b) Determine their amplitudes.

c) Draw the frequency spectrum showing the relative amplitudes of

the side frequencies.

d) Determine the bandwidth.

e) Determine the total power of the modulated wave.

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Muzammil Jusoh

Solution for Quiz Vm = 1 V, Vc = 10 V, fm = 2 kHz, fc = 800 kHz, RL = 50 Ω

a) m = 2; n = 4 c)

b) V0 = 10 (0.22) = 2.2 V

V1 = 10 (0.58) = 5.8 V

V2 = 10 (0.35) = 3.5 V

V3 = 10 (0.13) = 1.3 V

V4 = 10 (0.03) = 0.3 V

d) BW = 2n fm

= 2 x 4 x 2k

=16 kHz

e) PT = P0 + 2P1 + 2P2 + 2P3 +2P4

=

49

W0018.1)50(2

2)3.0(2

)50(2

2)3.1(2

)50(2

2)5.3(2

)50(2

2)8.5(2

)50(2

22.2


Muzammil Jusoh

Generation of FM

Two major FM generation: i) Direct method:

i) straight forward, requires a VCO whose oscillation

frequency has linear dependence on applied voltage.

ii) Advantage: large frequency deviation

iii) Disadvantage: the carrier frequency tends to drift and

must be stabilized.

iv) Common methods: i) FM Reactance modulators

ii) Varactor diode modulators

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Muzammil Jusoh

Generation of FM (cont’d)

ii) Indirect method: i. Frequency-up conversion.

ii. Two ways: a. Heterodyne method

b. Multiplication method

iii. One most popular indirect method is the Armstrong

modulator

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Muzammil Jusoh

52

Wideband Armstrong Modulator


Muzammil Jusoh

A complete Armstrong modulator is supposed to

provide a 75kHz frequency deviation. It uses a

balanced modulator and 90o phase shifter to phase-

modulate a crystal oscillator. Required deviation is

obtained by combination of multipliers and mixing,

raise the signal from

suitable for broadcasting.

Armstrong Modulator

53

kHz75MHz2.90toHz47.14kHz400


Muzammil Jusoh

Generation of FM and PM

54

2 f

p

k

k

2

p

f

k

k


Muzammil Jusoh

FM Detection/Demodulation FM demodulation ◦ is a process of getting back or regenerate the

original modulating signal from the modulated FM signal.

◦ It can be achieved by converting the frequency

deviation of FM signal to the variation of equivalent voltage.

◦ The demodulator will produce an output where

its instantaneous amplitude is proportional to the instantaneous frequency of the input FM signal.

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Muzammil Jusoh

FM detection (cont’d)

To detect an FM signal, it is necessary to have a circuit whose output voltage varies linearly with the frequency of the input signal.

The most commonly used demodulator is the PLL

demodulator. Can be use to detect either NBFM or WBFM.

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Muzammil Jusoh

PLL Demodulator

57

Phase

detector

VCO

Low pass

filter Amplifier

FM input

Vc(t)

fvco

V0(t)

fi


Muzammil Jusoh

PLL Demodulator

The phase detector produces an average output voltage

that is linear function of the phase difference between

the two input signals. Then low frequency component is

pass through the LPF to get a small dc average voltage

to the amplifier.

After amplification, part of the signal is fed back through

VCO where it results in frequency modulation of the

VCO frequency. When the loop is in lock, the VCO

frequency follows or tracks the incoming frequency.

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Muzammil Jusoh

PLL Demodulator

Let instantaneous freq of FM Input,

fi(t)=fc +k1vm(t),

and the VCO output frequency,

f VCO(t)=f0 + k2Vc(t);

f0 is the free running frequency.

For the VCO frequency to track the

instantaneous incoming frequency,

fvco = fi;

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Muzammil Jusoh

PLL Demodulator

f0 + k2Vc(t)= fc +k1vm(t), so,

If VCO can be tuned so that fc=f0, then

Where Vc(t) is also taken as the output voltage, which therefore is the demodulated output

)()( 10 tvkfftV mcc

)()( 1 tvktV mc

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Muzammil Jusoh

Noise in FM Noise is interference generated by

lightning, motors, automotive ignition systems, and power line switching that produces transient signals.

Noise is typically narrow spikes of voltage with high frequencies.

Noise (voltage spikes) add to a signal and interfere with it.

Some noise completely obliterates signal information.

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Muzammil Jusoh

Noise in FM

In AM systems, noise easily distorts the

transmitted signal however, in FM systems

any added noise must create a frequency

deviation in order to be perceptible.

62

θ


Muzammil Jusoh

Noise in FM(Cont’d)

The maximum frequency deviation due to random noise occurs when the noise is at right angles to the resultant signal. In the worst case the signal frequency has been deviated by:

δ = θfm

This shows that the deviation due to noise increases as the modulation frequency increases. Since noise power is the square of the noise voltage, the signal to noise ratio can significantly degrade.

Noise occurs predominantly at the highest frequencies within the baseband

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Muzammil Jusoh

Noise-Suppression Effects of FM

FM signals have a constant modulated carrier amplitude.

FM receivers contain limiter circuits that deliberately restrict the amplitude of the received signal.

Any amplitude variations occurring on the FM signal are effectively clipped by limiter circuits.

This amplitude clipping does not affect the information content of the FM signal, since it is contained solely within the frequency variations of the carrier.

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Muzammil Jusoh


65

Figure 5-11: An FM signal with noise. EKT358 – Communication System

Muzammil Jusoh


Preemphasis ◦ Noise can interfere with an FM signal and

particularly with the high-frequency components of the modulating signal. ◦ Noise is primarily sharp spikes of energy and

contains a lot of harmonics and other high-frequency components. ◦ To overcome high-frequency noise, a

technique known as preemphasis is used. ◦ A simple high-pass filter can serve as a

transmitter’s pre-emphasis circuit. ◦ Pre-emphasis provides more amplification of

only high-frequency components.

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Muzammil Jusoh


67

Preemphasis circuit.


Muzammil Jusoh


Preemphasis ◦ A simple low-pass filter can operate as a

deemphasis circuit in a receiver. ◦ A deemphasis circuit returns the frequency

response to its normal flat level. ◦ The combined effect of preemphasis and

deemphasis is to increase the signal-to-noise ratio for the high-frequency components during transmission so that they will be stronger and not masked by noise.

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Muzammil Jusoh


69

Deemphasis circuit.


Muzammil Jusoh

Application of FM

FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (FM broadcasting). Normal (analog) TV sound is also broadcast using FM. The type of FM used in broadcast is generally called wide-FM, or W-FM

A narrowband form is used for voice communications in commercial and amateur radio settings. In two-way radio, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.

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Muzammil Jusoh

Frequency Modulation Versus Amplitude

Modulation

Major applications of AM and FM


Muzammil Jusoh

Advantages Wideband FM gives significant improvement in the SNR at the

output of the RX which proportional to the square of

modulation index.

Angle modulation is resistant to propagation-induced selective

fading since amplitude variations are unimportant and are

removed at the receiver using a limiting circuit.

Angle modulation is very effective in rejecting interference.

(minimizes the effect of noise).

Angle modulation allows the use of more efficient transmitter

power in information.

Angle modulation is capable of handing a greater dynamic range

of modulating signal without distortion than AM.

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Muzammil Jusoh

Disadvantages Angle modulation requires a transmission

bandwidth much larger than the message

signal bandwidth.

Angle modulation requires more complex

and expensive circuits than AM.

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Muzammil Jusoh

Summary of angle modulation -what you need to be familiar with

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Summary (cont’d)

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Muzammil Jusoh

Summary (cont’d)

Bandwidth:

a) Actual minimum bandwidth from

Bessel table:

b) Approximate minimum bandwidth

using Carson’s rule:

)(2 mfnB

)(2 mffB

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Muzammil Jusoh

Exercise 1

Determine the deviation ratio and worst-

case bandwidth for an FM signal with a

maximum frequency deviation 25 kHz and

maximum modulating signal 12.5 kHz.

77

25.12

25 kkDR

BW = 2n fm = 2 x 4 x 12.5k

= 100 kHz


Muzammil Jusoh

Exercise 2 For an FM modulator with 40-kHz frequency

deviation and a modulating-signal frequency 10 kHz, determine the bandwidth using both Carson’s rule and Bessel table.

; n = 7 Carson’s rule:

BW = 2 (40k + 10 k)

= 100 kHz

Bessel table:

BW = 2 n fm

= 2 x 7 x 10 k = 140 kHz

78

410

40

k

km f

Exercise 3

For an FM modulator with an

unmodulated carrier amplitude 20 V, a

modulation index, m = 1, and a load

resistance of 10-ohm, determine the

power in the modulated carrier and each

side frequency, and sketch the power

spectrum for the modulated wave.

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Muzammil Jusoh

Solution for Exercise 3

80

W

x

P 858.11)10(2

2)77.020(

0

Wx

PP 872.3)10(2

2)44.020(11

Wx

PP 242.0)10(2

2)11.020(22

Wx

PP 008.0)10(2

2)02.020(33


Muzammil Jusoh

Exercise 4 A frequency modulated signal (FM) has

the following expression:

The frequency deviation allowed in this

system is 75 kHz. Calculate the: ◦ Modulation index

◦ Bandwidth required, using Carson’s rule

)1010sin10400cos(38)( 36 tmttv ffm

81

155

75

k

km f

BW = 2 (75k + 5 k)

= 160 kHz EKT358 – Communication System

Muzammil Jusoh

END OF ANGLE

MODULATION

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Muzammil Jusoh

Documents

ANGLE MODULATIONportal.unimap.edu.my/portal/page/portal30/Lecture Notes/KEJURUTERAAN... · Frequency modulation (FM) Phase modulation (PM) Used for : Commercial radio broadcasting