An ultrasonic rangefinder module carries a Sallen-Key envelope filter after its…

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

An ultrasonic rangefinder module carries a Sallen-Key envelope filter after its detector diode, and a relaxation oscillator that triggers each transmitted burst. Both circuits use an ideal operational amplifier or an ideal comparator, with gain-bandwidth and switching speed ample at these frequencies. ((a)) The equal-component Sallen-Key envelope filter is designed for

f_0 = 800\,\mathrm{Hz}

and damping

Q = 0.707

. Using

C = 33\,\mathrm{nF}

(E12), find the

R

the design equation asks for, round to the nearest E12 preferred value, and state the corner the filter will actually show. ((b)) Find the gain

K

that

Q = 0.707

requires, and choose a preferred-value feedback resistor pair from the E12 series that comes as close as the series allows to that

K

. State the

Q

this pair actually gives. ((c)) The trigger oscillator, built from an ideal comparator with positive-feedback fraction

\beta = 0.5

, is to repeat every

T_{\rm per} = 100\,\mathrm{\mu s}

, where

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

. Using

C = 1\,\mathrm{nF}

(E12), find the required

R

, round to the nearest E12 value, and state the period the oscillator will actually produce.

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