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

Vo s( ) V1 s( )Z 2 s( )

Z 1 s( ) Z 2 s( )

Analysis The two RC

Networks must have equal resistors and capacitors

Z1 s( ) R1

s C

Z2 s( )

R1

s C

R1

s C

Analysis

Operational amplifier gain

GV1 s( )

Vs s( )1

R2

R1

Vo s( ) V1 s( )Z 2 s( )

Z 1 s( ) Z 2 s( )

Need to find the Gain over the whole Circuit: Vo/Vs

Vo s( ) G V s s( )s R C

s2R2 C

2 3 s R C 1

Solve G equation for V1 and substitute in for above equ.

Analysis

T s( )Vo s( )

V s s( )

s R C G

s2R2 C

2 3 s R C 1

We now have an equation for the overall circuit gain

T j j R C G

1 2R2 C

2 3 j R C

Simplifying and substituting jw for s

Analysis

In order to have a phase shift of zero,

1 2R2 C

2 0

This happens at RC When RC, T(j) simplifies to:

T j G

3

If G = 3, oscillations occur

If G < 3, oscillations attenuate

If G > 3, oscillation amplify

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0msV(R5:2)

-4.0V

0V

4.0V

G = 3

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0msV(R5:2)

-4.0V

0V

4.0V

G = 2.9

Time

0s 100us 200us 300us 400us 500us 600usV(R5:2)

-20V

0V

20V

G = 3.05

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 1.0msV(R1:2) V(R5:2)

-4.0V

0V

4.0V

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

Time

0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0msV(D2:2)

-4.0V

0V

4.0V

With the use of diodes, the non-ideal op-amp can produce steady oscillations.

Frequency Analysis By changing the resistor and

capacitor values in the positive feedback network, the output frequency can be changed.

R 10k C 1nF

1

R C 1 10

5rad

sec

f

2 f 15.915kHz

Frequency Analysis

Frequency

0Hz 10KHz 20KHz 30KHz 40KHzV(D2:2)

0V

2.0V

4.0V(15.000K,2.0539)

Fast Fourier Transform of Simulation

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