This set of Tricky Signals & Systems Questions and Answers focuses on “Ideal LPF, HPF, BPF and BSF Characteristics”.

1. In the circuit given below, C = C_{1} = C_{2}. The gain of the multiple-feedback band-pass filter is ___________

a) \(A_0 = \frac{R_2}{R_1}\)

b) \(A_0 = \frac{R_1}{R_2}\)

c) \(A_0 = \frac{R_2}{2R_1}\)

d) \(A_0 = \frac{R_1}{2R_2}\)

View Answer

Explanation: The total output C = C

_{INPUT}+ C

_{OUTPUT}that is the gain capacitor.

∴ The total Resistance is equal to the Resistance input and Resistance output.

Again, the total resistance gain = \(\frac{R_1 R_2}{R_1+ R_2}\)

Hence, the gain = \(A_0 = \frac{R_2}{2R_1}\).

2. Two network functions are given below.

H_{ } = \(\frac{1}{s^2 + \sqrt{2} s + 1}\), H_{2} = \(\frac{1}{s^3+2s^2+2s+1}\)

The frequency response indicates that the filter is ___________

a) Low-pass

b) Band-pass

c) High-pass

d) Band reject

View Answer

Explanation: | H

_{1}|

^{2}= \(\frac{1}{[(jω)^2 + \sqrt{2} jω + 1] [(jω)^2 + \sqrt{2} jω + 1]}\)

Similarly, | H

_{2}|

^{2}= \(\frac{1}{1+ ω^6}\)

Therefore at ω = 0, 1 and∞, we have | H |

^{2}= 1, \(\frac{1}{2}\) and 0 respectively.

Hence, the filter is a Low-pass filter.

3. A particular band-pass function has a network function as H(s) = \(\frac{3s}{s^2+4s+3}\) then, its quality factor Q is ___________

a) \(\frac{3}{4}\)

b) \(\frac{2}{\sqrt{3}}\)

c) \(\frac{\sqrt{3}}{2}\)

d) \(\frac{\sqrt{3}}{4}\)

View Answer

Explanation: H(s) = \(\frac{Ks}{s^2+as+b}\)

Then, quality factor is given as \(\frac{\sqrt{b}}{a}\)

Here, b = 3, a = 4

∴ Q = \(\frac{\sqrt{3}}{4}\).

4. The filter which passes all frequencies above f_{c} by attenuating significantly, all frequencies below f_{c} is _______________

a) Low-pass

b) High-pass

c) Band-pass

d) Band-stop

View Answer

Explanation: A high-pass filter is one which passes all frequencies above f

_{c}by attenuating significantly, all frequencies below f

_{c}.

5. For the circuit given below, the cut-off frequency of the filter is ________________

a) 5283 kHz

b) 5283 Hz

c) 2653.1 kHz

d) 2653.1 Hz

View Answer

Explanation: We know that, F = \(\frac{1}{2π×R×C}\)

Where, R = 1200 Ω, C

_{1}= 0.05 × 10

^{-6}F

∴ F = \(\frac{1}{2π×1200×C}\)

= \(\frac{1}{2π×60×10^{-6}}\)

= \(\frac{10^6}{2π×60}\) = 2653.1 Hz.

6. For a Band Pass Filter, the slope of the filter is given as 40dB/decade. The order of the Band Pass Filter is __________

a) 2

b) 3

c) 4

d) 6

View Answer

Explanation: The Bode plot is a logarithmic plot which helps in fitting a large scale of values into a small scale by the application of logarithm. Plotting the slope 40dB/decade on the Bode plot, we get n = 4. Hence the order of the Band Pass Filter is 4.

7. The circuit given below represents which type of filter circuit?

a) Low-pass Filter

b) High-pass Filter

c) Band-pass Filter

d) Band-stop Filter

View Answer

Explanation: We know that, the position of Resistance (R) and Capacitance (C) determines whether it is Low-pass Filter or High-Pass Filter. If R is connected directly to source and the capacitor connected in parallel to it, then it is a Low-pass Filter and if the position of R and C are inter change then high pass filter is formed.

Here since R and C are in series and also R is not connected directly to the power source, hence the filter is a High-pass Filter.

8. The circuit given below represents which type of filter circuit?

a) Low-pass Filter

b) High-pass Filter

c) Band-pass Filter

d) Band-stop Filter

View Answer

Explanation: The given circuit is a first order Band Pass Filter. Also, the Roll-off of the filter depends upon the order of the filter. For a first order it is 20dB/decade, for second order it is 40dB/decade, and so on.

9. For the circuit given below, the Roll-off value of the filter is _____________

a) 20 dB/decade

b) 40 dB/decade

c) 60 dB/decade

d) 80 dB/decade

View Answer

Explanation: The given filter is a first order Band Pass Filter. Also, the Roll-off of the filter is depends upon the order of the filter. For a first order it is 20dB/decade, for second order it is 40dB/decade, and so on. Therefore, the Roll-off of the filter = 20 dB/decade. Roll of first order low pass Butterworth filter is 20dB/decade. Now here two stages of second order Low-pass Butterworth filter are cascaded.

∴ Roll-off = 20*4 = 80 dB/decade.

10. The circuit given below, represents which filter?

a) Low-pass

b) High-pass

c) Band-pass

d) Band-stop

View Answer

Explanation: From the given circuit, we can infer that Roll off of the Filter circuit is 80dB/decade. This Roll-off value is obtained as second order high pass filter followed by another 2nd order HPF results in an HPF.

Therefore the circuit represents a High-pass Filter.

11. In the circuit given below, the Roll-off of the filter is _______________

a) 20 dB/decade

b) 40 dB/decade

c) 60 dB/decade

d) 80 dB/decade

View Answer

Explanation: The given filter is a first order Band Pass Filter. Also, the Roll-off of the filter depends upon the order of the filter. For a first order it is 20dB/decade, for second order it is 40dB/decade, and so on.

Therefore, the Roll-off of the filter = 20 dB/decade.

12. In which of the filter circuits given below, will the bandwidth be equal to the critical frequency?

a) Low-pass

b) High-pass

c) Band-pass

d) Band-stop

View Answer

Explanation: Bandwidth can be calculated by considering,

Largest positive value – Smallest Positive Value

Here, in case of the Low-pass filter only, the largest positive value will of course be the critical frequency, beyond which frequencies have to be blocked. Hence, the bandwidth in a Low-pass filter equals the critical frequency.

13. For the circuit given below, the cut-off frequency of the filter is ________________

a) 3225.8 Hz

b) 7226 Hz

c) 3225.8 kHz

d) 7226 kHz

View Answer

Explanation: We know that, F = \(\frac{1}{2π×(R_1×R_2)×(C_1×C_2)}\)

Where, R

_{1}= 4700 Ω, R

_{2}= 4700 Ω, C

_{1}= 0.047×10

^{-6}F, C

_{2}= 0.047 × 10

^{-6}F

∴ F = \(\frac{1}{2π×(4700×4700)×(C_1×C_2)}\)

= \(\frac{1}{2π×48796.81×10^{-12}}\)

= \(\frac{10^6}{2π×0.04879681}\)

= \(\frac{10^6}{0.30654156042}\) = 3225.8 kHz.

14. For providing a Roll-off greater than 20dB/decade/pole, filters with which characteristics are useful?

a) Butterworth

b) Chebyshev

c) Bessel

d) Butterworth & Bessel

View Answer

Explanation: Roll off is a term commonly refers to the steepness of the transmission function wrt to the frequency.

For a Chebyshev filter, the Roll-off value greater than 20. This characteristic feature is useful when a rapid roll-off is required because it provides a Roll-off rate is more than 20.

On the other hand, both Butterworth and Bessel have the Roll-off rate less than or equal to 20 dB/decade/pole.

15. A Low-pass filter circuit has a cut-off frequency of 1.23 kHz. The bandwidth of the filter is ______________

a) 2.46 kHz

b) 1.23 kHz

c) 0.615 kHz

d) 3.69 kHz

View Answer

Explanation: The bandwidth is defined as the highest cut-off frequency to the lowest cut-off frequency. Here the lowest cut-off frequency is Zero.

For a Low-pass filter, Cut-off Frequency = Bandwidth of the filter

∴ Bandwidth = 1.23 kHz.

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