Analysis and design of an array of two differential oscillators coupled through a resistive network

This paper considers the analysis and the design of an array of two NMOS differential oscillators coupled through a resistor. A new writing of the nonlinear equations proposed by R. York to describe the oscillators´ locked states but limited for the specific case of a resistive coupling is presented. The new system permits the calculation of the free-running frequencies of the oscillators when a specific phase shift is desired. This has led to the modeling of the two coupled NMOS differential oscillators as two coupled differential Van der Pol oscillators, with a resistive coupling network. A good agreement between the circuit, the model and the theory was found, giving some design considerations for a network of two differential oscillators coupled through one resistor.