Sensitivity analysis of a filter

Question

I have a question about sensitivity calculations. I have a lowpass Sallen & Key filter. I calculated:

• the relative error of the pole frequency due to the relative error of passive components and the respective sensitivities
• the relative error of the pole frequency due to the finite gain-bandwidth product of the OPAMP
• the relative error of the pole frequency due to the relative error of the gain-bandwidth product of the OPAMP.

My question now is, to obtain the total relative error do I simply add up all these components? Or is there other operation to perform? Do I only add up the first and third components?

Answer 1

You have found the sensitivities. But, now you need to use the actual expected variation in the components and the GBW to compute the variation in the response. For each component that varies, multiply the variation of the component by the sensitivity. Add up the contribution of all the components in a square root of the sum of the squares fashion. Then you have an estimate of the output variation.