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ESE Electronics 2016 Paper 2: Official Paper

Option 3 : dc gain 1 and high frequency gain 0

CT 1: Determinants and Matrices

2903

10 Questions
10 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:

\(G(s)=\frac{1}{2s+1}\)

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

\(DC \ Gain = \mathop {\lim }\limits_{s \to 0} \frac{1}{2s+1}\)

DC Gain = 1

High-frequency gain is calculated as:

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

\( = \mathop {\lim }\limits_{s \to ∞ } \frac{1}{2s+1}\)

High frequency gain = 0