An electromyography (EMG) amplifier board carries two active circuits built around an…

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 electromyography (EMG) amplifier board carries two active circuits built around an ideal operational amplifier and an ideal comparator (gain-bandwidth and switching speed are assumed ample at these frequencies). ((a)) A second-order low-pass filter is built as an equal-component Sallen-Key stage (both resistors equal

R

, both capacitors equal

C

) with Butterworth damping

Q = 0.707

and a design corner

f_0 = 1.5\,\mathrm{kHz}

. Using

C = 10\,\mathrm{nF}

(an E12 preferred value), find the

R

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

K

of the filter's amplifier sets

Q

through

Q = 1/(3-K)

. State the

K

that

Q = 0.707

requires, then choose a preferred-value feedback resistor pair

R_1

(to ground) and

R_2

(feedback) from the E12 series with

R_2/R_1

as close as the series allows to the ratio

K - 1

demands, and state the

Q

this pair actually gives. ((c)) The board's sampling clock is a relaxation oscillator built from the comparator, with positive-feedback fraction

\beta = 0.6

and period

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

. A period of

5.00\,\mathrm{ms}

is wanted. Using

C = 100\,\mathrm{nF}

(E12), find the required

R

, round to the nearest E12 value, and state the period the oscillator will actually produce. State every preferred value used and give the three predicted measured quantities.

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