INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS Int. J. Circ. Theor. Appl. 2010; 38:747–760 Published online 28 April 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/cta.592 LETTER TO THE EDITOR Sinusoidal oscillators with lower gain requirements at higher frequencies based on an explicit tanh( x ) nonlinearity A. S. Elwakil 1, ∗, † , S. Ozoguz 2 and K. N. Salama 3 1 Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah, Emirates 2 Faculty of Electrical-Electronics Engineering, Istanbul Technical University, 34469 Maslak, Istanbul, Turkey 3 Department of Electrical Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia SUMMARY Two novel sinusoidal oscillator structures with an explicit tanh(x ) nonlinearity are proposed. The oscillators have the attractive feature: the higher the operating frequency, the lower the necessary gain required to start oscillations. A nonlinear model for the two oscillators is derived and verified numerically. Spice simulations using AMS BiCMOS 0.35  model parameters and experimental results are shown. Copyright 2009 John Wiley & Sons, Ltd. Received 29 May 2008; Revised 25 January 2009; Accepted 21 February 2009 KEY WORDS: oscillators; RC circuits; LC circuits; nonlinear circuit design; nonlinear oscillators 1. INTRODUCTION Sinusoidal oscillators are key elements in various electronic systems. New designs with enhanced features such as low voltage operation [1], low phase noise [2], digital programmability [3] and low power consumption [4] continue to be introduced in the literature. Some of the proposed oscillators explore new topologies and design techniques [5–7]. However, a problem observed in many oscillator architectures is that the higher the oscillation frequency, the higher the necessary loop gain needed to start-up oscillations [8, 9]. This gain–frequency conflict arises from the implicit nonlinearity of the oscillators’ active building blocks (transistors, op amps, G m cells,..., etc.) and ∗ Correspondence to: A. S. Elwakil, Department of Electrical and Computer Engineering, University of Sharjah, P.O. Box 27272, Sharjah, Emirates. † E-mail: elwakil@sharjah.ac.ae, elwakil@ieee.org Copyright 2009 John Wiley & Sons, Ltd.