The price for improvement in sensitivity by the use of feedback is paid in terms of

Concept:

Sensitivity is the relative variation in one parameter with respect to the other parameters i.e.

\(S_k^A = \frac{{\partial A/A}}{{\partial K/K}}\)

\(S_k^A\) : the sensitivity of variable A with respect to parameter K.

It is preferable that the sensitivity function \(S_k^A\) to be minimum.

Analysis:

The closed-loop transfer function is given by:

\({T_1}\left( s \right) = \frac{{G\left( s \right)}}{{1 + G\left( s \right)H\left( s \right)}}\)

And the Open-loop transfer function T₂(s) = G(s)

Clearly, T₂(s) > T₁(s)

Hence, with the use of feedback, the overall Transfer function G(s) is reduced by \(\frac{1}{{1 + G\left( s \right)H\left( s \right)}}\) times.