Theory and Design of OTA-C Oscillators with Native Amplitude Limiting

Abstract

An analog sinusoidal oscillator usually involves some form of amplitude-limiting mechanism. We examine operationaltransconductance-amplifier (OTA) nonlinearity as a choice for amplitude limiting and develop a general theory for its use in OTA-capacitor (OTA-C) oscillators. We facilitate our theoretical discussion with an illustrative design example that we fabricated and tested.Index Terms-Nonlinear oscillators. I. OSCILLATOR DESIGN APPROACHEST HE SINUSOIDAL oscillator is a basic analog-circuit component in communication and instrumentation systems. High-quality oscillators usually involve inductor-capacitor networks and are used in RF systems. However, the inductance values required for low-and moderate-frequency oscillators cannot practically be realized in integrated circuits. Ring oscillators provide much better economy in terms of size, but they are limited to such uses as clock generation due to their high harmonic content. Operational transconductance amplifier-capacitor (OTA-C) oscillators, on the other hand, operate at low to moderate frequencies with fairly high spectral purity and are compact enough for integration. An OTA-C oscillator is typically designed as an unstable second-order system that is regulated by some nonlinear amplitude-limiting circuitry. Buonomo et al. [1] identified a set of conditions on the nonlinearity for the system to exhibit oscillation. The most common implementations of an amplitude limiter are a piecewise-linear resistor and an automatic gain control circuit [1]- [4]. A third possibility is to use the inherent nonlinear behavior of an OTA as an amplitude limiter.The success of using OTA nonlinearity, as reported in the literature, has been mixed. This approach is considered in [3], but the results are only poorly controlled distorted oscillations. The approach is also mentioned in [2] but is characterized as yielding only unpredictable oscillations. On the other hand, the results in [5], [6], and [7] show success in designing sinusoidal oscillators based on OTA nonlinearity. However, none of these papers, nor, to our knowledge, any other sources in the literature, provide a systematic and analytical presentation of how exactly to exploit OTA nonlinearity in a general second-order oscillator structure. This is a relevant lack, as an oscillator that Manuscript Fig. 1. OTA converts a differential voltage input into an output current. A differential pair of transistors is at the heart of the voltage-current conversion. An attenuating stage may exist between the voltage input and the differential pair. A current-subtraction network combines the drain currents of the differential-pair transistors into a single output.properly exploits OTA nonlinearity can easily confer power and area savings, since no external amplitude-limiting scheme is required. For instance, a slight redesign of the oscillator in [2] could have used one of the existing OTAs as an amplitude limiter, precluding the need for the extra piecewise-linear (PWL) circuit that its authors describe.This paper provides ...

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