A sensitivity of transfer function T = A_1 + kA_2A_3 + kA_4 with respect to parameter k is given by

k( A_2A_3 - A_1A_4 )( A_3 + kA_4 )( A_1 + kA_2 )

This question belongs to Electronics And Communications Engineering Control Systems

Control Systems

A sensitivity of transfer function $$T = \frac{{{A_1} + k{A_2}}}{{{A_3} + k{A_4}}}$$ with respect to parameter k is given by

A) $$\frac{{k\left( {{A_2}{A_3} - {A_1}{A_4}} \right)}}{{\left( {{A_3} + k{A_4}} \right)\left( {{A_1} + k{A_2}} \right)}}$$ B) $$\frac{{\left( {{A_2}{A_3} - {A_1}{A_4}} \right)}}{{{{\left( {{A_3} + k{A_4}} \right)}^2}}}$$ C) $$\frac{{k\left( {{A_2}{A_3} - {A_1}{A_4}} \right)}}{{{{\left( {{A_3} + k{A_4}} \right)}^2}}}$$ D) $$\frac{{\left( {{A_2}{A_3} - {A_1}{A_4}} \right)}}{{\left( {{A_3} + k{A_4}} \right)\left( {{A_1} + k{A_2}} \right)}}$$

Answer & Solution

Correct Answer: Option A

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A sensitivity of transfer function $$T = \frac{{{A_1} + k{A_2}}}{{{A_3} + k{A_4}}}$$ with respect to parameter k is given by

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