On the expected passband ripple of cascade RC active filters with random element variations

A lower bound has been derived on the expectation of passband ripple for cascade type active filters with random element variations. Without performing a detailed sensitivity analysis, it can indicate that a cascade connection of first-and second-order building blocks would fail to satisfy given tolerance requirements, and a more subtle design method should be used. So it may provide a shortcut in the filter design process. Some examples are given, in order to verify the tightness of the bound in some practical situations.