Stability of a continuous-time state variable filter with op-amp and OTA-C integrators

Abstract

The stability of a continuous-time state variable filter is analyzed using the Routh-Hurwitz criterion. This criterion assesses stability by indicating the number of poles that lie in the right-half plane. The filter is examined separately with integrators implemented with an op-amp and an OTA-C. Both amplifier types are characterized by a dominant-pole frequency response, and the stability of each implementation is compared. HSPICE simulations confirm the theoretical analyses, which indicate that the gain-bandwidth product of the op-amps and the bandwidth of the OTAs must be much larger than the desired frequency of operation to ensure stability. Since the analyses assume a dominant-pole response, all higher-order poles of the actual amplifier must also be much greater than the unity-gain frequency to minimize excess phase.