1. Wien-Bridge Oscillator Circuits

2. Why Look At the Wien-Bridge?
It generates an oscillatory output signal without having any input source
The Wien-bridge oscillator is a unique circuit because it generates an oscillatory output signal without having a sinusoidal input source. Instead, it uses capacitors with initial voltages to create the output. This circuit can be especially useful if connected to a voltage follower to de-couple the load from the source.
As you can see, the Wien-bridge oscillator uses two RC networks connected to the positive terminal to form a frequency selective feedback network. It also amplifies the signal with the two negative feedback resistors.

3. 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
The Wien-bridge oscillator is a unique circuit because it generates an oscillatory output signal without having a sinusoidal input source. Instead, it uses capacitors with initial voltages to create the output. This circuit can be especially useful if connected to a voltage follower to de-couple the load from the source.
As you can see, the Wien-bridge oscillator uses two RC networks connected to the positive terminal to form a frequency selective feedback network. It also amplifies the signal with the two negative feedback resistors.

4. Basics About the Wien-Bridge
Amplifies the signal with the two negative feedback resistors

5. Modification to CircuitZ1 Z2

6. Analysis
The loop gain can be found by doing a voltage division Z1 Z2

7. Analysis
The two RC Networks must have equal resistors and capacitors Z1 Z2

8. Analysis Need to find the Gain over the whole Circuit: Vo/Vs
Solve G equation for V1 and substitute in for above equ.

9. Analysis We now have an equation for the overall circuit gain
Simplifying and substituting jw for s

10. Analysis If G = 3, oscillations occur
If the negative feedback resistors are set so G = 3, then T(jw) = 1 and oscillations will occur.
If G is less than three then oscillations attenuate. If G greater than 3 then oscillations amplify.
If G = 3, oscillations occur
If G < 3, oscillations attenuate
If G > 3, oscillation amplify