This set of Analog Circuits Question Paper focuses on “Frequency Filters – 2”.

1. Find which one is a sallen-key topology.

a)

b)

c)

d)

View Answer

Explanation: Sallen-key topology is an electronic filter topology used to implement second-order active filters. It requires a single op-amp for gain control and 4 passive RC components to accomplish the tuning. These are also called positive feedback circuits since the output flows back into non-inverting terminal too.

2. A first-order Butterworth low pass filter is an interconnection of ____________ and ___________

a) Single low pass RC circuit, Voltage follower

b) Low pass RC circuit, Band-pass RC circuit

c) Low pass RC circuit, LC feedback

d) Single low pass RC circuit, Power amplifier

View Answer

Explanation: A first-order Butterworth LPF is an interconnection of a single low pass RC circuit and a voltage follower.

3. Considering a second-order Butterworth LPF using an op-amp, where damping factor = 1.414 find the value of R3, given the following circuit. (R2=5kΩ)

a) 6.71 kΩ

b) 4.22 kΩ

c) 2.93 kΩ

d) 5 kΩ

View Answer

Explanation: Maximum gain, A = 3 – α = 1.586

For the above circuit, the gain is 1 + R3/R2 = 1.586

R3/R2 = 0.586

R3 = 2.93 kΩ.

4. For the following circuit, R2=220kΩ, R1=10kΩ, find the maximum gain and the phase shift at the cutoff frequency.

a) Maximum gain = 22, Phase shift = 45°

b) Maximum gain = 23, Phase shift = 135°

c) Maximum gain = 22, Phase shift = 225°

d) Maximum gain = 23, Phase shift = 45°

View Answer

Explanation: Above is a high pass filter, with maximum gain = 1+R2/R1 = 23

Phase shift = tan

^{-1}(1) = 45°.

5. Find the cutoff frequency for the following circuit. (R1=R2=20kΩ)

a) 25 kHz

b) 3987 rad/sec

c) 2500 Hz

d) 25000 rad/sec

View Answer

Explanation: Cutoff frequency ω

_{C}= 1/RC

ω

_{C}= 1000000/20×2 = 25000 rad/s.

6. Given a second-order Butterworth HPF, find the maximum gain magnitude.

a) 1.586 dB

b) 4 dB

c) 2.66 dB

d) 1 dB

View Answer

Explanation: For a second-order Butterworth HPF, the maximum gain A

_{MAX}= 3 – α.

α is the damping factor = 1.414

A

_{MAX}= 1.586

In dB, the gain is 20 log(1.586) = 4dB.

7. Consider the following circuits.

If a band-pass filter is created by using the above two circuits in cascade, find the correct relation from the choices below.

a) R_{4}C_{2} >> R_{1}C_{1}

b) R_{4}C_{2} << R_{1}C_{1}

c) R_{6}R_{5} = R_{2}C_{3}

d) R_{4}C_{2} = R_{1}C_{1}

View Answer

Explanation: A band-pass filter can be created as an interconnection of an LPF and an HPF. For this to work, the LPF cut-off frequency should be much greater than the HPF cut-off frequency.

Thus, 1/2π R

_{1}C

_{1}>> 1/2π R

_{4}C

_{2}

Thus R

_{4}C

_{2}>> R

_{1}C

_{1}.

8. Which of these is incorrect for a band-stop filter?

a) An adder is required when designing it using LPF and HPF

b) LPF and HPF are connected in parallel

c) The HPF cut-off frequency should be much higher than LPF cut-off frequency

d) The LPF and HPF are connected in series

View Answer

Explanation: When designing a band-stop filter, a HPF and LPF are connected in parallel, and their output goes into the input of an adder to get the desired the output. For correct output, the cut-off frequency of HPF should be much higher than that of the LPF.

9. Which of these is wrong for an all-pass filter?

a) It is used for phase equalization in a communication system

b) It is used in landline communication

c) Its phase shift is -2tan^{-1}RC, between 0 to -180°

d) It can be made using a single op-amp

View Answer

Explanation: An all-pass filter passes all frequencies but provides a different phase shift to each frequency present in the circuit. It is used for phase equalization or delay equalization and is used in landline communication. Following is a circuit of an all-pass filter using a single op-amp.

However, its phase shift is -2tan

^{-1}(ωRC)

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