angle modulation (part 1)

7/31/2019 Angle Modulation (Part 1)

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ANGLE MODULTATION

(FM and PM)LECTURE NOTES BY:

ENGR. ANALENE MONTESINES-NAGAYO


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Angle ModulationI. FREQUENCY MODULATION (FM)

- Type of angle modulation wherein the frequency of the constant-amplitude

carrier signal is varied or changed according to the instantaneous amplitude

of the modulating signal.

- As the amplitude to the information varies, the carrier frequency varies

above and below its normal center frequency.

tf2sinV)( CC tVC

tf2sinV)( mm tVm

VFM(t)


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Angle Modulation

Frequency deviation, - The peak frequency shift that occurs in the carrier

- Is the amount by which the carrier frequency is varied from its unmodulated

value.

Carrier shift, CS- is the peak to peak frequency deviation.

- CS = 2

- FM was developed to cope with the undesirable noise, which

competed with the desired signal when it is amplitude modulated.


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Angle Modulation

MATHEMATICAL DESCRIPTION OF A FM SIGNAL

The instantaneous frequency of the FM signal is given by the equation

tf2sinV1mm

kff c

Where

fc= unmodulated carrier frequency, Hzk = proportionality constantVm sin 2 fmt = instantaneous modulating voltage, V

The instantaneous value of the FM signal is given by the equation,

tf2sinftf2sinV)(

m

m

cc

dtVFM

where

fc = unmodulated carrier frequency, Hzfm = modulating signal frequency, Hz

= Frequency deviation

Vc = peak amplitude of the carrier voltage, V


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Angle Modulation

butfm

is the modulation index, mf.

tf2sinmftf2sinV)( mcc tVFMIn expanded form ,

....t)3sin(-t)3sin()(J

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

t)sin(-t)sin()(J

tsin)(J

Vc)(

3

2

1

0

mcmc

mcmc

mcmc

c

FM

mf

mf

mf

mf

tV

FREQUENCY SPECTRUM OF A FM SIGNAL

The frequency spectrum of the FM signal can be obtained using the Bessel

function table.


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Angle Modulation


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Angle ModulationBANDWIDTH REQUIREMENT FOR AN FM SIGNAL

The exact bandwidth obtained using the Bessel function is given by the equation,

BW = 2 x n sideband pairs x fm

The approximate minimum bandwidth obtained using Carsons rule is given by theequation,

BW = 2 ( + fm(max))

For Narrow Band FM with low modulation index values, the minimum bandwidth is

given by the equation,

BW = 2 fm

For Wide Band FM with high modulation index values, the minimum bandwidth is

given by the equation,

BW = 2


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Angle ModulationPOWER CONTENT OF AN FM SIGNAL

where:

PT = total transmitted power or total modulated power in Watts

Pc = unmodulated carrier power in WattsP1 = power of the 1st sideband pair in Watts

P2 = power of the 2nd sideband pair in Watts

Pn = power of the nth sideband pair in Watts

RRRR 2

V2.....

2

)(V2

2

)(V2

2

)(VP

2

n

2

2

2

1

2

c

T

where:

R = load resistance in ohms

Vc = peak carrier voltage, Volts

V1 = peak voltage of the 1st sideband in Volts

V2 = peak voltage of the 2nd sideband in Volts

Vn = peak voltage of the nth sideband in Volts

n21CT P.......PPPP

angle modulation (part 1)

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