Parasitic pole approximation techniques for active filter design

A method of approximating the parasitic poles of active filters employing one, two, or three operational amplifier(s) is presented. These approximations are good for both a single-pole and two-pole model of the operational amplifier and are useful for determining filter stability. The approximation expressions are sufficiently simple that they may be included in the active filter design process. Stability criteria for active filters employing two-pole operational amplifiers are stated in terms of the parasitic pole approximations obtained using the simpler single-pole model of the operational amplifier. The necessity of including the more accurate two-pole model of an operational amplifier in some applications is discussed. Detailed comparisons of the actual and approximate parasitic poles in two examples are made.