An Improved Describing Function With Applications for OTA-Based Circuits

Electronic systems make extensive use of operational transconductance amplifiers (OTAs) to build filters and oscillators. Studying the effects of the saturation nonlinearity on these OTA-based circuits is difficult and often requires lengthy simulations to check the system's performance under large-signal operation. The describing function (DF) theory allows to circumvent these simulations by deriving a signal-dependent linearized gain, which predicts the effects of the nonlinearity. However, its use is limited since the state-of-the-art DFs deviate significantly from the real saturating behavior of OTAs. This paper proposes an improved DF, which can be directly derived from the static nonlinear characteristic of the transconductance amplifier. The performance of the proposed methodology is demonstrated for both an OTA-based filter and oscillator. It is shown that the proposed DF has a better nonlinear prediction capability than the state-of-the-art solutions.