This question was previously asked in

ESE Electronics 2012 Paper 2: Official Paper

Option 1 : 0.25

CT 3: Building Materials

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10 Questions
20 Marks
12 Mins

__Concept:__

__DC gain:__

The DC gain is the ratio of the magnitude of the steady-state step response to the magnitude of step input.

DC Gain of a system is the gain at the steady-state which is at t tending to infinity i.e., s tending to zero.

DC gain is nothing but the error coefficients.

For type 0 system:

\({K_P} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)\)

For type 1 system:

\({K_v} = \mathop {\lim }\limits_{s \to 0} sG\left( s \right)\)

For type 2 system:

\({K_a} = \mathop {\lim }\limits_{s \to 0} {s^2}G\left( s \right)\)

__High-frequency gain:__

The high-frequency gain of a system is the gain at the steady-state which is at t tending to 0 i.e., s tending to infinity.

__Calculation:__

Given:

\(G(s)=\frac{(2s+5)}{(s+5)(s+4)}\)

This is Type 0 system:

\({K_P} = \mathop {\lim }\limits_{s \to 0} G\left( s \right)\)

K_{P} = 0.25