GATE EC 2024 Set 1 — Question 12
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Control Systems → Frequency-Domain Analysis → Bode Plots
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Question
In the context of Bode magnitude plots, 40 dB/decade is the same as
Correct answer
(A) 12 dB/octave
Solution
In Bode plots, a 'decade' refers to a frequency ratio of 10, and an 'octave' refers to a frequency ratio of 2.We are given a slope of 40 dB/decade. This means that for every factor of 10 increase in frequency, the magnitude changes by 40 dB.Let be the gain in dB. The slope is given by:
dB/decade
dB/octaveWe know that .So,
And From these, we can relate the two slopes:
We are given dB/decade.
We need to find .Calculate :
Now, substitute this value:
dB/octaveRounding to the nearest integer, this is 12 dB/octave.Alternatively, a slope of 20 dB/decade corresponds to a first-order system. A first-order system has a slope of dB/octave.
Since 40 dB/decade is twice 20 dB/decade, it corresponds to a second-order system. Therefore, the slope in dB/octave would be dB/octave.The final answer is
dB/decade
dB/octaveWe know that .So,
And From these, we can relate the two slopes:
We are given dB/decade.
We need to find .Calculate :
Now, substitute this value:
dB/octaveRounding to the nearest integer, this is 12 dB/octave.Alternatively, a slope of 20 dB/decade corresponds to a first-order system. A first-order system has a slope of dB/octave.
Since 40 dB/decade is twice 20 dB/decade, it corresponds to a second-order system. Therefore, the slope in dB/octave would be dB/octave.The final answer is
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