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In this paper, a new expression of the equations describing the locked states of two van der Pol oscillators coupled through a broadband network and allowing an accurate prediction of the oscillators' amplitudes is presented. To do so, the York's theory is improved using a more accurate van der Pol model in order to obtain a new system of four equations with four unknowns describing the locked states of two van der Pol oscillators coupled through a resonant network. Then, the case of a resistive coupling circuit is deduced from this new system of equations. The theory regarding the prediction of the oscillators' amplitudes is verified using Agilent's ADS software for the practical case of an array made of two differential Voltage Controlled Oscillators (VCOs) coupled through a resistive network.

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New Formulation of the Equations Describing the Locked States of Two Van der Pol Oscillators Coupled through a Broadband Network – Application to the Design of Two Differential Coupled VCOs