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Frequency Modulation (FM)

The frequency of the carrier signal is varied with the amplitude of the

modulating (baseband) signal.

Frequency of FM signal

fsig ( t ) = fc ( 1 + k em )t

where fsig ( t ) = signal frequency as a function of timefc = un modulated carrier frequencyk = proportionality constant

em ( t ) = modulating voltage as a function of time

Substituting for em(t),

fsig ( t ) = fc ( 1 + k Em sin wm t)

http://www.google.com.om/imgres?imgurl=http://www.moz.ac.at/sem/lehre/lib/ks/lib/fm/frequency-modulation-Dateien/_FMMOD.GIF&imgrefurl=http://www.moz.ac.at/sem/lehre/lib/ks/lib/fm/frequency-modulation.h

Frequency Deviation (δδδδ)

Modulation will cause the signal frequency to vary, or deviate, from its

resting value. This deviation will be proportional to the amplitude of the

modulating signal.

Substituting for em(t),

fsig ( t ) = fc ( 1 + k Em sin wm t)

The peak frequency deviation is given by the symbol �,

� = k fc Em = kf Em

where � = peak frequency deviation in hertzEm =peak value of the modulating signal in voltskf = modulator sensitivity in hertz per volt

Thus,fsig ( t ) = fc + � sin �m t

carrier swing

Thus,fsig ( t ) = fc + � sin wm t

Lowest carrier frequency = fc - �

Highest carrier frequency = fc + �

Therefore, the carrier swing = fc + � – ( fc - �) = 2 �

Frequency Modulation Index

No theoretical limits on mf and it can exceed one.

Resting FrequencyIt is the frequency of FM signal when there is no modulation

Maximum Frequency DeviationIt is the maximum frequency shift of the FM signal from the resting frequency.

Carrier SwingIt is the difference between highest and lowest frequency of FM signal.

Modulation IndexIt is the amount by which the carrier signal is frequency modulated by the message signal.

FM signal

Equation for Instantaneous value of FM signal is

eFM(t) = Ec sin (ωct+ mf sin ωmt)Where mf=� �/fm

Frequency spectrum of FM (Solved by Bessel function)

eFM(t) = Ec sin (ωct+ mf sin ωmt)

eFM(t) = Ec{ Jo(mf) sin wct

+J1(mf) [sin (wc + wm)t - sin (wc - wm)t]

+ J2(mf) [sin (wc + 2wm)t- sin (wc – 2wm)t]

+J3(mf) [sin (wc + 3wm)t - sin (wc – 3wm)t]

+ J4(mf) [sin (wc + 4wm)t - sin (wc – 4wm)t] . . . }

http://web.sunybroome.edu/~eet_dept/252/bessell.htm

Plot of Bessel functions

http://www.efunda.com/math/bessel/besselJYPlot.cfm

…… fc- 2 fm fc – fm fc fc+fm fC +2fm …… ……… frequency

Frequency Spectrum of the FM wave

mf = 1

� The instantaneous value of the FM voltage is the sine of a sine, and

the solution for such expressions can be obtained only by using Bessel

Functions.

� The output consists of a carrier and an apparently infinite number of

pairs of sidebands, each preceded by J coefficients.� Theoretically the bandwidth of an FM signal is infinity.

Jo

J1

J2

Bandwidth of FM

Bandwidth for FM is theoretically infinity.

But an approximate bandwidth is given by Carson’s rule.

Carson’s Rule

The bandwidth required to pass an FM wave is twice the sum of the

maximum deviation and the highest modulating frequency.

BW = 2 (δ + fm )

)sinsin( tmtEe mfCCFM ωω +=

mf E

Kδ=

δ2. minmax =−= ffsc

δ+= Cffmax

δ−= Cffmin

Formula

mf = δ /fm

(BW )FM= 2 (δ + fm)

Advantages of FM over AM

FM AM

Amplitude is constant and is

independent of mf

All transmitted power is useful in

FM

Amplitude depends on modulation

index(m)

Transmitted power is wasted in

carrier in AM.

FM receivers have amplitude

limiters to remove noise

Noise cannot be removed

Reduce noise by increasing

deviation

Modulation index cannot be

increased above 100% without

causing distortion.

Disadvantages of FM over AM

FM AM

Bandwidth is large for FM, so

wider channel is required

Bandwidth is small

Transmitters and receivers are

complex

Circuits are not complicated

The area of reception is less,

limited to line of sight

The area of reception is more.

Pre-emphasis and De-emphasis

Need for Pre-emphasis and De-emphasis in FM

In FM, noise has a greater effect on the higher modulating frequencies

than on the lower ones. Thus, if the higher frequencies were artificially

boosted at the transmitter and correspondingly cut at the receiver, an

improvement in noise immunity could be expected.

Pre-emphasis

Boosting of higher modulating frequencies in accordance with a pre

arranged curve before modulation.

De-emphasis

Reducing the higher modulating frequency amplitudes, in accordance

with a pre arranged curve after modulation.

75-µs emphasis curves

emphasis curves

Pre-emphasis Circuit

Output signal amplitude depends on input signal frequency. As

frequency increases output voltage increases, which in turn increase

the gain. The time constant (L/R) of the circuit is 75-µs.

De-emphasis

Higher frequencies are attenuated by the low pass filter. So their

amplitude decreases which in turn decrease the gain. The time

constant (RC) of the circuit is 75-µs.