Modulasi Sudut (2) - Indonesian Computer University
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Transcript Modulasi Sudut (2) - Indonesian Computer University
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 nfct n (t ))
u(t ) Ac cos(2 (nfc 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 2f ct 2k f
The above signal is an AM signal.
Bc
2
m( )d
t
v0 (t ) Ac (V0 kk f m(t )) cos 2f ct 2k 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 cos2f ct (t )
Phase Comparator:
yv (t ) Av sin2f ct v (t )
t
(t ) 2k f m( )d
t
v (t ) 2kv 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 ) 2kv v( )d
0
d
d
e (t ) 2kv v (t ) (t )
dt
dt
d
d
e (t ) 2kv e ( )g (t )d (t )
0
dt
dt
•
By taking the Fourier transform
( j 2f ) e ( f ) 2kv e ( f )G ( f ) ( j 2f ) ( 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 )
2kv dt
kv
j 2f
( f )
2kv
v(t) is the demodulated
signal