Active Filters Questions and Answers

Q: Calculate the cut-off frequency of an OP-Amp based first order low pass filter for R = 2·5 kΩ and C = 0·05 μF.

The cut-off frequency is 1.273 kHz.For a first order RC low pass filter, active or passive, the cut-off frequency is\[ \begin{aligned} f_{c} &= \frac{1}{2\pi RC} \\ &= \frac{1}{2\pi (2.5 \times 10^{3})(0.05 \times 10^{-6})} \\ &= \frac{1}{2\pi \times 1.25 \times 10^{-4}} \\ &\approx 1273\ \text{Hz} = 1.273\ \text{kHz} \end{aligned} \]The other options are the same digits with the decimal point moved, the result of a slip with the powers of ten for kilo-ohms and microfarads: 12.73 kHz and 127.3 kHz are ten and a hundred times too high, and 127.3 Hz ten times too low.

Q: The roll-off of a first order low pass filter is :

The roll-off is -20 dB/decade.A first-order low pass filter has the response \(H(f) = 1/(1 + jf/f_{c})\). Well above the cut-off frequency its magnitude is about fc/f, so each tenfold increase in frequency divides the gain by 10, a fall of 20 dB, equal to -6 dB per octave.The positive slopes belong to high pass behaviour below cut-off, and -40 dB/decade is the roll-off of a second-order filter, which has two poles. Each additional pole adds a further -20 dB/decade.

Calculate the cut-off frequency of an OP-Amp based first order low pass filter for R = 2·5 kΩ and C = 0·05 μF.

A.1·273 kHz
B.12·73 kHz
C.127·3 kHz
D.127·3 Hz

Exam Year(s)

MH SET - 2018, SET Exam - 2018,

Answer: A

The cut-off frequency is 1.273 kHz.

For a first order RC low pass filter, active or passive, the cut-off frequency is

\[ \begin{aligned} f_{c} &= \frac{1}{2\pi RC} \\ &= \frac{1}{2\pi (2.5 \times 10^{3})(0.05 \times 10^{-6})} \\ &= \frac{1}{2\pi \times 1.25 \times 10^{-4}} \\ &\approx 1273\ \text{Hz} = 1.273\ \text{kHz} \end{aligned} \]

The other options are the same digits with the decimal point moved, the result of a slip with the powers of ten for kilo-ohms and microfarads: 12.73 kHz and 127.3 kHz are ten and a hundred times too high, and 127.3 Hz ten times too low.

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The roll-off of a first order low pass filter is :

A.+20 dB/decade
B.-20 dB/decade
C.+40 dB/decade
D.-40 dB/decade

Exam Year(s)

MH SET - 2021, SET Exam - 2021,

Answer: B

The roll-off is -20 dB/decade.

A first-order low pass filter has the response \(H(f) = 1/(1 + jf/f_{c})\). Well above the cut-off frequency its magnitude is about f_c/f, so each tenfold increase in frequency divides the gain by 10, a fall of 20 dB, equal to -6 dB per octave.

The positive slopes belong to high pass behaviour below cut-off, and -40 dB/decade is the roll-off of a second-order filter, which has two poles. Each additional pole adds a further -20 dB/decade.

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Assertion (A) : Active filters are better than passive filters in terms of price and performance.
Reason (R) : Integrated circuit technology has made available cheaper operational amplifiers.

A.Both (A) and (R) are true and (R) is the correct explanation of (A)
B.Both (A) and (R) are true but (R) is not the correct explanation of (A)
C.(A) is true but (R) is false
D.(A) is false but (R) is true

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: A

Both (A) and (R) are true and (R) is the correct explanation of (A).

Active filters use op-amps with resistors and capacitors instead of inductors. They give gain, have high input and low output impedance so stages do not load each other, avoid bulky and costly inductors at low frequencies, and are easy to tune. That makes them better in price and performance for most low-frequency work, so A is true.

Their cost advantage comes directly from integrated circuit technology, which made op-amps cheap and widely available, as R says. R therefore explains A, which rules out the other options.

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