Previous Year Question
Which of the following transfer functions represents a zero-order hold system?
Correct answer: D
Explanation
A zero-order hold keeps each sampled value constant for one sampling period T. Its impulse response is a rectangular pulse of width T, whose Laplace transform is (1−e⁻ˢᵀ)/s.
Formula
GZOH(s)=(1−e⁻ˢᵀ)/s
Step-by-step solution
Correct Answer
D — (1 − e^(−sT))/s
Concept and Reasoning
A zero-order hold keeps each sampled value constant for one sampling period T. Its impulse response is a rectangular pulse of width T, whose Laplace transform is (1−e⁻ˢᵀ)/s.
Calculation / Key Relation
GZOH(s)=(1−e⁻ˢᵀ)/s
Exam Takeaway
Rectangular hold pulse → integrate e⁻ˢᵗ from 0 to T.
Common Mistake
Do not omit the division by s.
Common mistake
Do not omit the division by s.
Exam tip
Rectangular hold pulse → integrate e⁻ˢᵗ from 0 to T.
Quick method
Rectangular hold pulse → integrate e⁻ˢᵗ from 0 to T.