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6 March, 21:04

Consider a sinusoidal oscillator consisting of an amplifier having a frequency-independent gain A (where A is positive) and a second-order bandpass filter with a pole frequency ω0, a pole Q denoted Q, and a positive center-frequency gain K. a) Find the frequency of oscillation, and the condition that A and K must satisfy for sustained oscillation.

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  1. 6 March, 23:12
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    Sinusoidal oscillator frequency of oscillation is given below.

    Explanation:

    The criterion for a stable oscillator is given in the equation

    l A (jw) β (jw) l ≥ 1

    In this task A represents the gain of the amplifier, and

    β represents gain/attenuation of the second-order bandpass filter.

    This sinusoidal oscillation is a special edge case where the product is equal to one.

    So the condition is A-K=1

    to obtain the sustained oscillations at the desired frequency of oscillations, the product of the voltage gain A and the feedback gain β must be one or greater than one. In this case, the amplifier gain A must be 3. Hence, to satisfy the product condition, feedback gain β must be 1/3.
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