modulasi sudut (2)
DESCRIPTION
Modulasi Sudut (2). Levy Olivia MT. 3.3.3 Implementation of Angle Modulators and Demodulators. Design an oscillator whose frequency changes with the input voltage. Voltage-controlled oscillator Varactor diode - capacitance changed with the applied voltage. - PowerPoint PPT PresentationTRANSCRIPT
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