A strain-gauge conditioning board carries a Sallen-Key low-pass filter ahead of 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

A strain-gauge conditioning board carries a Sallen-Key low-pass filter ahead of its analogue-to-digital converter, and a monostable timer that produces a fixed-width gate for a pulse counter. 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 low-pass is designed for

f_0 = 2.0\,\mathrm{kHz}

and damping

Q = 1.00

. Using

C = 4.7\,\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 = 1.00

requires, and choose a preferred-value feedback resistor pair from the E12 series that realises it exactly. State the

Q

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

\beta = 0.5

and a diode that holds its capacitor at

0\,\mathrm{V}

between pulses, has output pulse width

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

. A pulse width of

2.00\,\mathrm{ms}

is wanted. Using

C = 100\,\mathrm{nF}

(E12), find the required

R

, round to the nearest E12 value, and state the pulse width the timer will actually produce.

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