1. Wien-Bridge Oscillator Circuits

2. Why Look At the Wien-Bridge? It generates an oscillatory output signal without having any input source

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

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

5. Modification to Circuit

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

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

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 G < 3, oscillations attenuate If G > 3, oscillation amplify

11. G = 3 G = 2.9 G = 3.05

12. Ideal vs. Non-Ideal Op-Amp Red is the ideal op-amp. Green is the 741 op-amp.

13. Making the Oscillations Steady Add a diode network to keep circuit around G = 3 If G = 3, diodes are off

14. Making the Oscillations Steady When output voltage is positive, D1 turns on and R9 is switched in parallel causing G to drop

15. Making the Oscillations Steady When output voltage is negative, D2 turns on and R9 is switched in parallel causing G to drop

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

17. Frequency Analysis By changing the resistor and capacitor values in the positive feedback network, the output frequency can be changed.

18. Frequency Analysis Fast Fourier Transform of Simulation

19. Frequency Analysis Due to limitations of the op-amp, frequencies above 1MHz are unachievable.

20. Conclusions No Input Signal yet Produces Output Oscillations Can Output a Large Range of Frequencies With Proper Configuration, Oscillations can go on indefinitely