Sensitivity analysis question

Question

I am trying to figure out how to calculate the sensitivity of a circuit, especially the sensitivity of a damping ratio (how much the damping ratio changes as each component value varies).

Expression for zeta is quite long and complicated, so I prefer not to take partial derivative. I would like to do something like:

calculate the value of zeta when R = 100 ohms.

calculate the value of zeta when R = 101 ohms.

then divide the change in zeta by the change in R.

In this case, how would I normalize this sensitivity value (x/y part)?

Answer 1

In this case your "y" is zeta and your "x" is R. So just subsitute the values in.

$$S_R^\zeta \approx \frac{R}{\zeta}\frac{\Delta \zeta}{\Delta R}$$