wein bridge oscillators - 1
TRANSCRIPT
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Wien-Bridge OscillatorCircuits
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Why Look At the Wien-
Bridge? It generates an
oscillatory output
signal withouthaving any input
source
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Basics About the Wien-
Bridge Uses two RC
networks
connected to thepositive terminal toform a frequencyselective feedbacknetwork
CausesOscillations toOccur
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Basics About the Wien-
Bridge Amplifies the
signal with the two
negative feedbackresistors
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Modification to Circuit
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Analysis The loop gain
can be found by
doing a voltagedivision
V o s( ) V 1 s( )Z 2 s( )
Z 1 s( ) Z 2 s( )+
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Analysis The two RC
Networks must
have equalresistors andcapacitors
Z1 s( ) R1
s C+
Z2 s( )
R1
s C
R1
s C
+
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Analysis
Operational amplifier gain
GV1 s( )
Vs s( )1
R2
R1+
V o s( ) V 1 s( )
Z 2 s( )
Z 1 s( ) Z 2 s( )+
Need to find the Gain over the whole Circuit:Vo/Vs
V o s( ) G V s s( )s R C
s2 R2 C2 3 s R C+ 1+
Solve G equation for V1 and substitute in for above eq
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Analysis
T s( ) V o s( )V s s( )
s R C G
s2
R2
C2
3 s R C+ 1+
We now have an equation for the overall circuitgain
T j( )j R C G
1 2
R2
C2
( ) 3 j R C+
Simplifying and substituting jw for s
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AnalysisIn order to have a phase shift of zero,
1 2
R2
C2
0
This happens at = 1/RC When =1/RC, T(j) simplifies to:
T j( )G
3
If G = 3, oscillations occur
If G < 3, oscillations attenuate
If G > 3, oscillation amplify
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Time
0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms
V(R5:2)
-4.0V
0V
4.0V
G = 3
Time
0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms
V(R5:2)
-4.0V
0V
4.0V
G = 2.9
Time
0s 100us 200us 300us 400us 500us 600us
V(R5:2)
-20V
0V
20V
G =3.05
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Ideal vs. Non-Ideal Op-
Amp Red is the ideal op-amp.
Green is the 741 op-amp.
Time
0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms
V(R1:2) V(R5:2)
-4.0V
0V
4.0V
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Making the Oscillations
Steady Add a diode
network tokeep circuitaround G =3
If G = 3,diodes areoff
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Making the Oscillations
Steady When output
voltage ispositive, D1turns on andR9 is switched
in parallelcausing G todrop
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Making the Oscillations
Steady When output
voltage isnegative, D2turns on andR9 is switched
in parallelcausing G todrop
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Results of Diode Network
Time
0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms
V(D2:2)
-4.0V
0V
4.0V
With the use of diodes, thenon-ideal op-amp can produce
steady oscillations.
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Frequency Analysis By changing the resistor and
capacitor values in the positive
feedback network, the outputfrequency can be changed.R 10k := C 1nF:=
1
R C:= 1 105
rad
sec=
f
2 := f 15.915kHz=
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Frequency Analysis
Frequency
0Hz 10KHz 20KHz 30KHz 40KHz
V(D2:2)
0V
2.0V
4.0V(15.000K,2.0539)
Fast Fourier Transform ofSimulation
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Frequency Analysis Due to limitations of the op-
amp, frequencies above 1MHz
are unachievable.
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Conclusions No Input Signal yet Produces
Output Oscillations
Can Output a Large Range ofFrequencies
With Proper Configuration,
Oscillations can go onindefinitely