Antonio Buonomo,
Dipartimento di Ingegneria dell’Informazione, Seconda Universita degli Studi di Napoli, Napoli, Italy,

Alessandro Lo Schiavo,
Dipartimento di Ingegneria dell’Informazione, Seconda Universita degli Studi di Napoli, Napoli, Italy,

DOI: 10.36724/2664-066X-2021-7-5-7-11

SYNCHROINFO JOURNAL. Volume 7, Number 5 (2021). P. 7-11.


The purpose of this investigation is to develop a systematic nonlinear analysis of the circuit in Figure 1, as yet not available in the literature, obtaining an exact formula for the oscillation frequency. Then, we find the condition for the circuit to behave as a relaxation oscillator, or as a nearly sinusoidal oscillator, analyzing the circuit behavior around the equilibrium point through a circuit model accounting for the transistor intrinsic capacitances. A nonlinear analysis of the popular emitter-coupled multivibrator is performed, which is based on the classical discontinuity theory. Exact relationships for calculating its waveform are obtained. Then, we investigate the circuit dynamic behavior showing that at very high frequencies the circuit exhibits a completely different behavior, similar to an LC second-order nearly sinusoidal oscillator. Conditions allowing us to predict one or the other behavior are found.

KeywordsRelaxation oscillations, emitter-coupled multivibrator, nearly sinusoidal oscillators, differential VCOs.


[1] A.A. Abidi and R.G. Meyer. Noise in relaxation oscillators, IEEE J. Solid-State Circuits, vol. 18, pp. 794-802, Dec. 1983.
[2] I.M. Filanovsky. Remarks on design of emitter- coupled multivibrators, IEEE Trans. on Circuits and Syst., vol. 35, pp. 751-755, June 1988.
[3] B.J. Song, H. Kim, Y. Choi and W. Kim. A 50% power reduction scheme for Cmos relaxation oscillator, AP-ASIC ’99, pp. 154-157, 1999.
[4] J.R. Fernandes, M.H.L. Kouwehoven, C. van der Bos, K. van Hartingsveldt and C. Verhoeven. A 5.8 Ghz quadrature cross-coupled oscillator, Proc. IEEE ISCAS, vol. II, pp. 404-407, 2002.
[5] A.A. Andronov, A.A. Vitt and S.E. Khaikin, Theory of oscillators, Pergamon Press, 1966. 
[6] Buonomo and A. Lo Schiavo. Analyzing the Dynamic Behavior of RF Oscillators, IEEE Trans. on Circuits and Syst.-Part I, vol. 49, pp. 1525-1534, 2002.