Analysis of coupled oscillators through a two-port passive network

Voltage controlled microwave oscillators are used in digital communication systems. Pairs of coupled and synchronized voltage controlled oscillators are used to control the phase in microwave antenna arrays as an alternative to other methods. A particular phase shift can be obtained by choosing the free-running frequencies of the oscillators in the array. The aim of this paper is to analyze such a pair of coupled oscillators by targeting the phase shift between their output voltages, the coupling circuit being a passive two-port passive network. For this purpose, we use our computer-aided analysis tool ANCSYANP (Analog Circuit Symbolic Analysis Program) capable to build the symbolic expressions of desired network functions or global parameters (as input/output/transfer impedances and admittances, fundamental or hybrid parameters) and to find the resonant frequencies of any two-port network as function of global parameters. The analysis is performed both in time domain and in frequency domain. To prove the procedure, we include two relevant examples.