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

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.

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).

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:

1. Wien-bridge oscillator without amplitude stabilization

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

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

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

-Amplifies the signal with the two negative feedback resistors

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

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

- 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.

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

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

Capture schematic of a Wien-bridge oscillator.

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

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2. Active-filter-tuned oscillator

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

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

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

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

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