Modulasi Sudut (2)

Levy Olivia MT

• Design an oscillator whose frequency changes with the input voltage.• Voltage-controlled oscillator

– Varactor diode - capacitance changed with the applied voltage.– A inductor with the varactor diode is used in the oscillator

circuit.

3.3.3 Implementation of Angle Modulators and Demodulators

0L

• Let the capacitance of the varactor diode is given by

• When m(t) = 0, the frequency of the tuned circuit is given by

• In general for nonzero m(t), we have

• Assuming that

• We have

)()( 00 tmkCtC

0021CL

fc

)(1

1

)(1

12

1))((2

1)(

0

0

0

000000 tmCk

ftm

CkCLtmkCL

tf ci

0

0

11 1 1 and 1 / 2( ) 2 1 / 2

kC m t

)(

21)(

0

0 tmCkftf ci

• Indirect method for generation of FM and PM signals– generate a narrow band angle-modulated signal– change the narrow band signal to wideband signal

• Generate wideband angle-modulated signals from narrow band angle-modulated signals– frequency multiplier– implemented by nonlinear device and bandpass filters

• Using down converter))()(2cos()( tntfnfAtu LOcc

Input: ( ) cos(2 ( )) Output: ( ) cos(2 ( ))n c c c cu t A f t t y t A nf t n t

• A nonlinear device followed by a bandpass filter tuned to the desired center frequency can be used as frequency multiplier.

• For example, assume a nonlinear device has the function

• The output signal will be

• The frequency is multiplied by a factor of 2.

2( ) ( )ny t u t

2 2

22

( ) cos (2 ( ))

1 cos(2 (2 ) 2 ( ))2 2

c c

cc c

y t A f t t

A A f t t

• FM demodulation– generate an AM signal– use AM demodulator to recover the message signal

• Pass the FM signal through a filter with response

• If the input to the system is

the output

• The above signal is an AM signal.

2for )()( 0

ccc

BffffkVfH

t

fcc dmktfAtu )(22cos)(

t

fcfc dmktftmkkVAtv )(22cos))(()( 00

FM Signal ( )u t

Output Signal ( )x t

R

L C

(a) (b)

Linear Region

fcf

Am

plit

ude

Res

pons

e

FM to AM converter: Tuned circuit implementation

But, usually the linear region of the frequency characteristic may not be wide enough.

• Balanced discriminator– use two tuned circuits– connect in series to form a li

near frequency response region.

R

R

1L 1C

2L 2C

( )u t ( )m t

Bandpass filter Envelope detector

(a)

f1f

Am

plitu

de R

espo

nse

2f

(b)

f1f

Am

plitu

de R

espo

nse

2f

(c)

Linear region

• FM demodulator with feedback

• FM demodulator with phase-locked loop (PLL)

Input : VCO output:

Phase Comparator: )(2cos)( ttfAtu cc dmkt

t

f )(2)(

)(2sin)( ttfAty vcvv dvktt

vv )(2)(

)()]()([)]()(sin[)( tttttAAte evvcv

• Linearized model of the PLL

or

dvkttt

ve 0

)(2)()(

)()()(2)(

)()(2)(

0t

dtddtgkt

dtd

tdtdtvkt

dtd

eve

ve

• By taking the Fourier transform

• Suppose that we design G(f) such that

)()(1

)()()()(

)()(1

1)(

)()2()()(2)()2(

ffG

jfkfGfGffV

ffG

jfk

f

ffjfGfkffj

ve

ve

eve

1)(

jffGkv )(

22)( fkfjfVv

)()(2

1)( tmkk

tdtd

ktv

v

f

v

v(t) is the demodulated signal