The bode plot of the delay transfer function e-3s has the following shape

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Question

This question was previously asked in

ISRO Scientist Electronics 2024 Official Paper

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Answer 1

Concept:

The transfer function represents a pure time delay of T seconds.

When analyzing this in the frequency domain for Bode plots, we substitute :

This is a complex exponential which affects only the phase of the frequency response, not the magnitude.

Magnitude:

So the magnitude plot is a horizontal straight line at 0 dB.

Phase:

Phase decreases linearly with frequency. Specifically, for T = 3 seconds:

radians

In degrees:

This is a straight line with a negative slope in the phase plot.

Given:

Transfer function: e-3s (pure delay of 3 seconds)

Conclusion:

Magnitude plot: Constant at 0 dB (flat line)
Phase plot: Straight line with a negative slope (due to the increasing delay with frequency)