GATE EC 2016 Set 1 — Question 42
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Control Systems → LTI Systems → First & Second-Order Response
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Question
A first-order low-pass filter of time constant is excited with different input signals (with zero initial conditions up to ). Match the excitation signals X, Y, Z with the corresponding time responses for :
| Excitation Signals | Time Responses |
|---|---|
| X: Impulse | P: |
| Y: Unit step | Q: |
| Z: Ramp | R: |
Correct answer
(C) X→R, Y→P, Z→Q
Solution
For a first-order low-pass filter with time constant , the transfer function is typically of the form .
.
Taking the inverse Laplace transform, .
This matches the functional form of R ().
.
Taking the inverse Laplace transform, .
This matches the form of P ().
.
Taking the inverse Laplace transform, .
This matches the form of Q ().Therefore, the correct matching is X→R, Y→P, Z→Q, which corresponds to option (C).
1.Impulse Response (X):
If , then . .
Taking the inverse Laplace transform, .
This matches the functional form of R ().
2.Unit Step Response (Y):
If , then . .
Taking the inverse Laplace transform, .
This matches the form of P ().
3.Ramp Response (Z):
If , then . .
Taking the inverse Laplace transform, .
This matches the form of Q ().Therefore, the correct matching is X→R, Y→P, Z→Q, which corresponds to option (C).
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