Mode stability of radiation-coupled interinjection-lockedoscillators for integrated phased arrays

An analysis is presented of a two-element, 10-GHz array consisting of two oscillators coupled solely by means of the free-space interaction between their respective antenna elements. The oscillators are modeled as energy-storing L-C tank circuits in parallel with voltage-dependent negative conductances. A simplified far-field slot antenna model is used to derive the mutual admittance of the two antennas. Even-odd mode analysis yields the normal modes of the system, and a theorem from averaged potential theory is used to determine which mode is stable. Two microstrip Gunn diode oscillators were built to verify the essential features of the model. Oscillator frequencies, relative phases, and radiation patterns were measured as functions of the interantenna distance, and the periodic alternation of modes with distance predicted by theory was confirmed quite well