Transcript Wein Bridge Oscillators

Wien-Bridge Oscillator Circuits
Why Look At the Wien-Bridge?

It generates an
oscillatory output
signal without
having any input
source
Basics About the Wien-Bridge


Uses two RC
networks
connected to the
positive terminal to
form a frequency
selective feedback
network
Causes
Oscillations to
Occur
Basics About the Wien-Bridge

Amplifies the
signal with the two
negative feedback
resistors
Modification to Circuit
Analysis

The loop gain can
be found by doing
a voltage division
V o( s )
V 1( s ) 
Z 2( s )
Z 1( s )  Z 2( s )
Analysis

The two RC
Networks must
have equal
resistors and
capacitors
Z 1( s )
R
R
Z 2( s )
R
1
sC
1
sC
1
sC
Analysis
Need to find the Gain over the whole Circuit: Vo/Vs
Operational amplifier gain
G
V1( s )
Vs( s )
V o( s )
1
R2
R1
V 1( s ) 
Z 2( s )
Z 1( s )  Z 2( s )
Solve G equation for V1 and substitute in for above equ.
V o( s )
G  V s( s ) 
sRC
2
2
2
s  R  C  3 s  R  C  1
Analysis
We now have an equation for the overall circuit gain
T( s )
V o( s )
s  R  C G
V s( s )
s  R  C  3 s  R  C  1
2
2
2
Simplifying and substituting jw for s
T j
j   R  C G
1  2  R2  C2  3  j    R  C
Analysis
In order to have a phase shift of zero,
2
2
2
1 R C
0
This happens at RC
T j
When RC, T(j) simplifies to:
G
3
If G = 3, oscillations occur
If G < 3, oscillations attenuate
If G > 3, oscillation amplify
4.0V
G=3
0V
-4.0V
0s
0.2ms
0.4ms
0.6ms
0.8ms
1.0ms
0.6ms
0.8ms
1.0ms
V(R5:2)
Time
4.0V
G = 2.9
0V
-4.0V
0s
0.2ms
0.4ms
V(R5:2)
Time
20V
G = 3.05
0V
-20V
0s
100us
V(R5:2)
200us
300us
Time
400us
500us
600us
Ideal vs. Non-Ideal Op-Amp


Red is the ideal op-amp.
Green is the 741 op-amp.
4.0V
0V
-4.0V
0s
V(R1:2)
0.2ms
V(R5:2)
0.4ms
0.6ms
Time
0.8ms
1.0ms
Making the Oscillations Steady


Add a diode
network to
keep circuit
around G = 3
If G = 3,
diodes are off
Making the Oscillations Steady

When output
voltage is
positive, D1
turns on and
R9 is switched
in parallel
causing G to
drop
Making the Oscillations Steady

When output
voltage is
negative, D2
turns on and
R9 is switched
in parallel
causing G to
drop
Results of Diode Network

With the use of diodes, the nonideal op-amp can produce steady
oscillations.
4.0V
0V
-4.0V
0s
0.2ms
0.4ms
0.6ms
V(D2:2)
Time
0.8ms
1.0ms
Frequency Analysis

By changing the resistor and
capacitor values in the positive
feedback network, the output
frequency can be changed.
R  10k
 
f 
1
RC

2 
C  1nF
5 rad
  1  10
sec
f  15.915 kHz
Frequency Analysis
Fast Fourier Transform of Simulation
4.0V
(15.000K,2.0539)
2.0V
0V
0Hz
10KHz
20KHz
V(D2:2)
Frequency
30KHz
40KHz
Frequency Analysis

Due to limitations of the op-amp,
frequencies above 1MHz are
unachievable.
Conclusions



No Input Signal yet Produces
Output Oscillations
Can Output a Large Range of
Frequencies
With Proper Configuration,
Oscillations can go on indefinitely