A bench rig uses a Wien-bridge oscillator with and to generate a reference tone

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Feedback, operational amplifiers and analogue signal processing

Electronics for Measurement, Ch Active filters, oscillators and timers

Problem

A bench rig uses a Wien-bridge oscillator with

R = 4.7\,\mathrm{k}\Omega

and

C = 22\,\mathrm{nF}

to generate a reference tone, and a separate comparator-based relaxation oscillator (astable, used as a slow clock) with

R = 10\,\mathrm{k}\Omega

C = 220\,\mathrm{nF}

and positive-feedback fraction

\beta = 0.6

. ((a)) Predict the Wien-bridge oscillator's frequency and the amplifier gain it requires, before any bench measurement. ((b)) Predict the relaxation oscillator's period, using

T_{\rm per} = 2RC\ln\!\left(\dfrac{1+\beta}{1-\beta}\right)

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