1. M2-3 Oscillators 1. Wein-Bridge Oscillator
2. Active-filter Tuned Oscillator

2. The basic structure of a sinusoidal oscillator
The basic structure of a sinusoidal oscillator. - A positive-feedback loop is formed by an amplifier A and a frequency-selective network β. - In an actual oscillator circuit, no input signal will be present; here an input signal xs is employed to help explain the principle of operation.

3. Dependence of the oscillator-frequency stability on the slope of the phase response. A steep phase response (i.e., large df/dw) results in a small Dw0 for a given change in phase Df (resulting from a change (due, for example, to temperature) in a circuit component).

4. Barkhausen stability criterion
The loop gain is equal to unity in absolute magnitude,
The phase shift around the loop is zero or an integer multiple of 2π:

5. 1. Wien-bridge oscillator without amplitude stabilization

6. A Wien-bridge oscillator with a limiter used for amplitude control

7. A Wien-bridge oscillator with an alternative method for amplitude stabilization.

8. - A Wien-bridge oscillator uses two RC networks connected to the positive terminal to form a frequency selective feedback network - Causes Oscillations to Occur

9. -Amplifies the signal with the two negative feedback resistors

10. -The loop gain can be found by doing a voltage divisionZ1 Z2
Analysis
-The loop gain can be found by doing a voltage division

11. -The two RC Networks must have equal resistors and capacitorsZ1 Z2
Analysis
-The two RC Networks must have equal resistors and capacitors

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

13. Simplifying and substituting jω for s
Analysis
An equation for the overall circuit gain
Simplifying and substituting jω for s

14. Analysis
- If G = 3, oscillations occur - If G < 3, oscillations attenuate - If G > 3, oscillation amplify

15. Capture schematic of a Wien-bridge oscillator.

16. Start-up transient behavior of the Wien-bridge oscillator for various values of loop gain.

17. (Continued)

18. (Continued)

19. 2. Active-filter-tuned oscillator

20. A practical implementation of the active-filter-tuned oscillator.

21. Capture schematic of an active-filter-tuned oscillator for which the Q of the filter is adjustable by changing R1.

22. Output waveforms of the active-filter-tuned oscillator for Q = 5 (R1 = 50 kW).

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

24. Memo