Fm Fsk Demodulation

7/30/2019 Fm Fsk Demodulation

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FM/FSK DEMODULATION

One form of FM/FSK demodulator is shown below

is a fixed time delay such that the output is delayed or phase shifted by a time

compared to the input, i.e.

LPF is a low pass filter which effectively determines the average value of Vx.

In general VIN (t) will be

tCosVtVINcIN =)(

Where IN is the input frequency (rad/sec) ( ININ f 2= )

IN will vary about a nominal frequency cf Hz as the carrier is frequency modulated.

Depending upon the type of modulation, i.e. analogue or digital, the input signal will be FM

or FSK respectively.

Analysing ,( ) ( )

( ) ( )[ ]

( )( ) ( )( )[ ]ttCosttCosV

V

BACosBACosCosBCosASince

tCosVtCosVV

tVtVV

ININININc

x

INcINcx

ININx

++++=

++=

+=+=

2

2

1

)(.

2

i.e

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( ) ( )[ ]

( ) ( )[ ]

INININc

x

ININININININ

c

x

CostCosV

V

ttCosttCosV

V

++=

++++=

22

22

2

Thus there are two components

( )( )[ ]

)2(2

)1(2

22

2

2

+

tCosV

and

tCosV

INc

INc

Component (1) is at frequency 2 fIN Hz and component (2) is effectively a DC voltage if

IN is constant.

The cut-off frequency for the LPF is designed so that component (1) is removed and

component (2) is passed to the output.

i.e. tCosV

V INc

OUT

2

2

=

The Delay

In order to determine the effect of the delay , the frequency modulator (V/F) is first

considered.

m(t) represents an analogue message signal

tCosVtmgemm =)(..

d(t) represents a digital data signal

i.e. d(t) = V1 in for 1s , d(t) = V0 in for 0s .

The V/F characteristics and inputs are shown below

Analogue FM

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c

cDCc

mmDCout

mmDCIN

DCIN

INout

mc

fTVf

ftCosVVfei

tCosVVV

tmVV

fVf

cxmy

Vf

1,

..

)(

0

0

==

++=

+=

+=

+=

+=

=

Modulation Indexm

m

m

c

f

V

f

f =

=

is the frequency conversion factor, KHz/volt , (i.e. gradient of the characteristics)

The spectrum of the analogue FM signal depends on and is given by

( )tnCosJVtVFM mcn

ncs +==

=1

)()(

Waveforms

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Digital FSK

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c

cDCc

DC

DC

DCIN

DCIN

DCIN

INout

fTVf

sforfVVf

sforfVVf

sforVVV

sforVVV

tmVV

fVf

cxmy

1,

'0

'1

'0

'1

)(

000

011

0

1

0

==

+=

++=

=

+=

+=

+=

+=

Normalized frequency Deviation ratio

01

01.. ffModulusei

R

ffh

b

=

The spectrum of FSK depends on h

Waveforms

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Consider again the output from the demodulator

IN

c

OUT CosV

V2

2

=

ININ f 2= and outIN ff = from the demodulator

i.e. INc

OUT fCosV

V 22

2

=

The delay is set to4

cT wherec

cf

T1

= and cf is the nominal carrier frequency, i.e.

delay is of the period of the nominal carrier frequency cf

Hence

42

2

2

c

IN

c

OUT

TfCos

VV =

Or

=

c

INc

OUTf

fCos

VV

4

2

2

2

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=

c

INcOUT

f

fCos

VV

22

2

Where INf is a frequency which varies around Cf . Note if INf is held constant, OUTV

is a constant DC voltage. If INf varies, OUTV varies.

Plotting OUTV as function of INf

INf OUTV

02

02

22

cc VCosV

=

2cf 707.0

422

1

22

22

cc CosV

CosV

=

=

cf ( ) 00222

22

==

cc VCosV

cf2

3

20707.0

4

3

2

22

cc VCosV

=

2 cf22

22

ccV

CosV

=

The curve shows the demodulator F/V characteristics which in this case is non linear.

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The slope of the characteristics, K, the voltage conversion factor (volts/Hz) is not constant; it

depends on the frequency input.

A practical realization of this process, using digital logic gates gives linear characteristics.

Practical Realization

This is form of delay and multiply circuit where the delay is set by C and R with

= CR

The comparator is LIMITER which is a zero crossing detector to give a digital input to

the first gate.

Considering the waveforms.

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The low pass filters determines the average value of waveform E, with average given by

c

OUTT

AEV

= (Peak x duty ratio)

{Assuming gain including LPF = A}

Consider now INf cf

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IN

OUTT

AEV

=

i.e. INOUT fEAV = wherec

c

f

T

4

1

4==

Hence we may also write

c

INOUT

f

fAEV

4=

In this case, outf is proportional to INf with the constant of proportionality

= AE =cf

AE

4

Plotting Vout versus INf (Assuming A=1)

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SYSTEM

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Fm Fsk Demodulation