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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.
– A inductor
with the varactor diode is used in the oscillator
circuit.
L0
•
Let the capacitance of the varactor diode is given by
C (t )  C0  k0m(t )
•
When m(t) = 0, the frequency of the tuned circuit is given by
•
In general for nonzero m(t), we have
1
fc 
•
Assuming that
1
•
We have
2 L0C0
1
f i (t ) 

2 L0 (C0  k0m(t )) 2 L0C0
k0

 1
C0 m(t )

1
1
 fc
k
k
1  0 m(t )
1  0 m(t )
C0
C0
1   1



k0
f i(t )  f c 1 
m(t ) 
 2C0

2
and
1
1  / 2
1  / 2
•
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 anglemodulated signals
– frequency multiplier
– implemented by nonlinear device and bandpass filters
Input: un (t )  Ac cos(2 fct   (t ))
•
Using down converter
Output: y(t )  Ac cos(2 nf ct  n (t ))
u(t )  Ac cos( 2 (nf c  f LO )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
y (t )  un2 (t )
• The output signal will be
y (t )  Ac2 cos 2 (2 f ct   (t ))
Ac2 1 2

 Ac cos(2 (2 f c )t  2 (t ))
2 2
• The frequency is multiplied by a factor of 2.
•
FM demodulation
– generate an AM signal
– use AM demodulator to recover the message signal
•
Pass the FM signal through a filter with response
•
H (tof the
) system
V0  kis( f
If the input
the output
•
 fc )
for f  f c 
u(t )  Ac cos 2f ct  2k f

The above signal is an AM signal.
Bc
2
m( )d 



t
v0 (t )  Ac (V0  kk f m(t )) cos 2f ct  2k f

m( )d 



t
FM to AM converter: Tuned circuit implementation
But, usually the linear region of the frequency characteristic may not be wide
enough.
FM Signal
u (t )
L
C
Output Signal
Amplitude Response
R
Linear Region
x(t )
f
fc
(a)
(b)
•
Balanced discriminator
– use two tuned circuits
– connect in series to form a
linear frequency response
region.
R
L1
C1
m(t )
u (t )
L2
C2
R
Bandpass filter
Envelope detector
Amplitude Response
Amplitude Response
(a)
f1
f1
f2
f2
f
(b)
Linear region
(c)
f
•
FM demodulator with feedback
•
FM demodulator with phase-locked loop (PLL)
Input :
VCO output:
u(t )  Ac cos2f ct   (t )
Phase Comparator:
yv (t )  Av sin 2f ct  v (t )
t
 (t )  2k f  m( )d

t
v (t )  2kv  v ( )d

e(t )  Av Ac sin[  (t )  v (t )]  [ (t )  v (t )]  e (t )
•
Linearized model of the PLL
or
t
e (t )   (t )  2kv  v( )d
0
d
d
e (t )  2kv v (t )   (t )
dt
dt

d
d
e (t )  2kv e ( )g (t   )d   (t )
0
dt
dt

•
By taking the Fourier transform
( j 2f ) e ( f )  2kv  e ( f )G ( f )  ( j 2f ) ( f )
1
 e ( f ) 
( f )
 kv 
1   G ( f )
 jf 
•
G( f )
 V ( f )   e ( f )G ( f ) 
( f )
Suppose that we design G(f) such that
 kv 
1   G ( f )
 jf 
G( f )
kv
 1
jf
V( f ) 
kf
1 d
v (t ) 
 (t )  m(t )
2kv dt
kv
j 2f
( f )
2kv
v(t) is the demodulated
signal