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EEE C364/INSTR C 364
Analog Electronics
Lecture 13
14-02-2012
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A triangular wave which goes from -12 V to +12 V is
applied to the inverting input of the opamp. Assume that
the output of the opamp swings from +15 V to -15 V. The
voltages at the input of the noninverting input switches
between .. and ..
-
+ +3
2
6
7
4
OP2 !OPAMP
10
k
10k
10k
V1 15
V2 15
Vi
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T
Time (s)
0.00 1.00m 2.00m 3.00m
Output
-20.00
-10.00
0.00
10.00
20.00
-
++3
2
6
7
4
OP2 !OPAMP
10k
10k
10k
V1 15
V2 15
Vi
30VVi
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Oscillators
Oscillation: an effect that repeatedly andregularly fluctuates about the mean value
Oscillator: circuit that produces oscillation
Characteristics: wave-shape, frequency,
amplitude, distortion, stability
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Application of Oscillators
Oscillators are used to generate signals:
Used as a local oscillator to transform the RF
signals to IF signals in a receiver;
Used to generate RF carrier in a transmitter
Used to generate clocks in digital systems;
Used as sweep circuits in TV sets and CRO.
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Linear Oscillators
1. Wien Bridge Oscillators
2. RC Phase-Shift Oscillators
3. LC Oscillators
Non-linear Oscillators
Multivibrators or Relaxation oscillators1. Astable 2. Bistable 3. Monostable
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Positive feedback
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How to generate a signal.
Regenerative
feedback
Amplifier
Oscillator
1v vA
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Effects of Avon oscillator operation.
Barkhausen criterion: Av=1
Av1
Av=1
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Properties of Linear Oscillators
For sinusoidal input is connected
Linear because the output is approximately sinusoidal
A linear oscillator contains:
- a frequency selection feedback network
- an amplifier to maintain the loop gain at unity
+
+ Amplifier (A)
Frequency-Selective
Feedback Network ()
Vf
Vs VoV
Positive
Feedback
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Basic Linear Oscillator
+
+
SelectiveNetwork
(f)Vf
Vs VoV A(f)
)( fso VVAAVV and of VV
A
A
V
V
s
o
1If V
s
= 0, the only way that Vo
can be nonzero
is that loop gain A=1 which implies that
0
1||
A
A (Barkhausen Criter ion)
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No input s ignal is needed. Noise at the desired oscillation frequencywill likely be present at the input and when picked up by the
oscillator when the DC power is turned on, it will start the oscillator
and the output will quickly buildup to an acceptable level.
Wien Bridge Oscillator
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Wien Bridge Oscillator
Frequency Selection Network
Let
11
1
CX
C and
111 CjXRZ 2
2
1
CX
C
22
22
1
22
2
11
C
C
C jXR
XjR
jXR
Z
Therefore, the feedback factor,
)/()(
)/(
222211
2222
21
2
CCC
CC
i
o
jXRXjRjXR
jXRXjR
ZZ
Z
V
V
222211
22
))(( CCC
C
XjRjXRjXR
XjR
Vi Vo
R1 C1
R2C2
Z1
Z2
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can be rewritten as:
)( 2121221221
22
CCCCC
C
XXRRjXRXRXR
XR
For Barkhausen Criter ion, imaginary part = 0, i.e.,
02121 CC XXRR
Supposing,
R1=R2=R and XC1= XC2=XC,
2121
21
21
/1
11or
CCRRCC
RR
f
f
R
XRjRX
RX
CC
C
0
0
C
C
22
f
fj3
1
X
X
Rj3
1
)(3
0.2
0.22
0.24
0.26
0.28
0.3
0.32
0.34
Feedb
ack
factor
-1
-0.5
0
0.5
1
Phase
Frequency
=1/3
Phase=0
f(R=Xc)
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Example
Rf
+
R
R
C
CZ1
Z2
R1
Vo
By setting , we get
Imaginary part = 0 and
RC
1
3
1
Due to Barkhausen Criter ion,
Loop gain Av=1
where
Av : Gain of the amplifier
1
131
R
RAA
f
vv
21
R
RfTherefore, Wien Bridge Oscillator
)(3 22 CC
C
XRjRX
RX