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Test: Butterworth Filters Design - 1


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10 Questions MCQ Test Signals and Systems | Test: Butterworth Filters Design - 1

Test: Butterworth Filters Design - 1 for Electrical Engineering (EE) 2022 is part of Signals and Systems preparation. The Test: Butterworth Filters Design - 1 questions and answers have been prepared according to the Electrical Engineering (EE) exam syllabus.The Test: Butterworth Filters Design - 1 MCQs are made for Electrical Engineering (EE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Butterworth Filters Design - 1 below.
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Test: Butterworth Filters Design - 1 - Question 1

 The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies as found above.

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 1

The arithmetic mean of the two cutoff frequencies as found above is the final cutoff frequency of the low pass Butterworth filter.

Test: Butterworth Filters Design - 1 - Question 2

 Which of the following is a frequency domain specification?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 2
  • We are required to design a low pass Butterworth filter to meet the following frequency domain specifications.
  • KP ≤ 20 log|H(jΩ)| ≤ 0 and 20 log|H(jΩ)| ≤ KS.
Test: Butterworth Filters Design - 1 - Question 3

What is the value of gain at the pass band frequency, i.e., what is the value of KP?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 3

We know that the formula for gain is:

Test: Butterworth Filters Design - 1 - Question 4

 What is the value of gain at the stop band frequency, i.e., what is the value of KS?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 4

We know that the formula for gain is:

Test: Butterworth Filters Design - 1 - Question 5

 Which of the following equation is true?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 5

We know that,

Test: Butterworth Filters Design - 1 - Question 6

 Which of the following equation is true? 

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 6

We know that:

Test: Butterworth Filters Design - 1 - Question 7

What is the order N of the low pass Butterworth filter in terms of KP and KS?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 7

Explanation:

Test: Butterworth Filters Design - 1 - Question 8

What is the expression for cutoff frequency in terms of pass band gain?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 8

We know that:

Test: Butterworth Filters Design - 1 - Question 9

 What is the expression for cutoff frequency in terms of stop band gain?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 9

We know that:

Test: Butterworth Filters Design - 1 - Question 10

What is the lowest order of the Butterworth filter with a pass band gain KP= -1 dB at ΩP= 4 rad/sec and stop band attenuation greater than or equal to 20dB at ΩS= 8 rad/sec?

Detailed Solution for Test: Butterworth Filters Design - 1 - Question 10

We know that the equation for the order of the Butterworth filter is given as:

From the given question:
KP= -1 dB, ΩP= 4 rad/sec, KS= -20 dB and ΩS= 8 rad/sec
Upon substituting the values in the above equation, we get N = 4.289
Rounding off to the next largest integer, we get N=5.

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