Development of a symmetrically stabilized four‐phase oscillator and some implications

This paper treats the development of a non‐linearly stabilized oscillator model which generates four sine waves in quadrature. This system is dealt with in spite of the fact that quadrature signals can be generated by a simple two‐phase oscillator. the latter generates only two of the signals needed in a four‐phase system. the rest of the phases signals could nevertheless be obtained by inventing the originally existing signals. It appears, however, that for certain applications the generation of all four signals in a completely cyclic and symmetrical manner (the one described here) is preferable. It is envisaged that one such application is related to recent methods of actively feeding phased array antennas, where each element in the array is connected to an appropriate oscillator phase stage. Most of the paper deals with the development of an appropriate generator model. the non‐linear oscillator dynamics is treated comprehensively. the peculiar behaviour associated with the limit cycle dynamics and with other manifestations of the system dynamics is investigated. It appears from the detailed simulation work that there exist regions of initial conditions where the system solutions are expected to be relatively sensitive to initial conditions. As a result, it is believed that the system with certain additions may reveal chaotic dynamic behaviour. the realization of the system in electronic hardware is also discussed.