Stability Considerations in Nonlinear Feedback Structures as Applied to Active Networks

Abstract

Active filters have recently acquired widespread use in the realization of frequency-selective networks. Unlike their passive counterparts, active filters have the potential of oscillating. Furthermore, it has been observed that the onset of oscillations in biquad active filters is dependent upon signal level. This led to the recognition that nonlinear stability theory would be necessary to comprehend this behavior. This paper develops a technique to analyze the stability of networks containing linear and nonlinear elements interconnected in multifeedback structures. This is accomplished by extending the concept of the “Describing Function” to include networks containing nonlinearities with frequency-dependent linear feedback. The technique is then applied to explain qualitatively and quantitatively nonlinear effects in op-amps and their relation to the stability of frequency-selective networks containing them (e.g., the Multiple Amplifier Biquad, MAB, and the Single Amplifier Biquad, SAB). The technique is also applied to explain frequency shifts in amplitude-limited oscillators. The most valuable result of this analysis is the discovery of nonlinear feedback circuits which circumvent the conditional stability of high-frequency biquads. This has allowed us to obtain Q's of 50 at 100 kHz in a MAB employing 709 op amps. Similarly, a MAB employing 702 op amps was made to operate at 2 MHz with a Q of 10.