D. Yardeni

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.

Possible chaotic phenomenon in a three phase oscillator

A three-phase harmonic oscillator, which has been found useful in modeling compactly synchronous generator systems, is slightly modified to become a source of a supposedly chaotic signal. The apparently sustained chaotic behavior is attained by using a solution region where the dynamics are unusually sensitive to the position of the solution. The supposedly chaotic source is expected to assist in investigating multidimensional chaotic phenomena of predetermined complexity. >

Oscillators with partial conservativity and practical implications

The paper suggests an unconventional concept, ‘partial conservativity’. Oscillator models (three-phase oscillators of a certain type are chosen here to demonstrate the concept) which exemplify the property of partial conservativity are discussed. These models are also suggested for developing practical systems where an interfering bias level is avoided.

Development of a new three-phase triangular wave oscillator

Abstract The present paper is another one in a series of papers on the development of models of precisely stabilized three-phase ocillators. A new model of a three-phase triangular wave oscillator is developed by considering its expected analogy to previously suggested models of sinusoidal and triangular wave oscillators in two and three phases. The development is validated by solving the nonlinear model equations on a digital computer. The expected advantages of the new model and its envisaged applications are considered in the conclusion section. The paper possesses a further value in serving as a tutorial review in the field of precisely stabilized oscillators. The review is carried out with the aid of a relatively new concept of. ‘invariants’ associated with the damping stabilization forces in the oscillator systems.

Semi-conservative three-phase oscillators

Examples of systems which can be called semiconservative are described. Some of the dynamic models of such systems appear conservative (their related oscillations are maintained steady since the initiation of the system from initial conditions), while other modes are not conservative. The new approach assists in identifying three-phase oscillator models where the bias level associated with their steady oscillations decays gradually to zero when the system is initiated. This leads to the construction of practical three-phase oscillators of improved quality.<<ETX>>

Investigation of a suspected chaotic behavior in a three phase oscillator model by employing analog realization

A three-phase oscillator model was shown to exhibit chaotic behavior when feedback switching terms were added to the original oscillator signal. This behavior was demonstrated previously by solving the system equations on a digital computer. In the present work, an investigation of the suspected chaotic behavior of the system is performed by using an analog instrument built in accordance with the system equations. The results of the experimental work employing the analog model also suggest (like the results of the numerical simulations) that the dynamics of the model is most probably chaotic in certain regions of parameters.<<ETX>>

Development of a new stabilized four-phase oscillator based on partial conservativity

The paper treats the development of a non-linearly stabilized oscillator model for generating four sine waves in quadrature. the treatment appears important although quadrature signals can also be generated by a well-known twophase oscillator. the latter generates only two of the signals needed in a four-phase system, but the rest of the phases signals could nevertheless be generated by simply inverting the two existing signals. For certain applications, however, the generation of all four signals in a completely cyclic and symmetrical manner is preferable. This method of generation is dealt with in the present paper. A previous paper of ours has treated a system of a similar objective. the present system, however, is much simpler. This simplicity is manifested not only through the mathematical representation but also when an electronic realization of the system is considered. the present model realization appears considerably less expensive, since the number of necessarily non-linear operations is much reduced. This reduction is due to the fact that the non-linearly stabilized model imbeds a ‘partially conservative’ linear oscillator. the concept of ‘partial conservativity’ has been introduced recently. the present work treats comprehensively the advantages that are gained by imbedding a partially conservative oscillator.

Development of nonlinearly stabilized five-phase oscillator based on partial conservativity

The basic system imbedded in the model described is a partially conservative five-phase oscillator. The property of partial conservativity enables the initially linear oscillator system to possess only one oscillatory mode in steady-state, while another oscillatory mode and the bias mode both decay to zero. As a result, the related nonlinearly stabilized oscillator model is simple. It is shown that this simplicity should contribute to a tractable electronic realization. An analytical treatment of the model is presented and a proof is given to show that the system reaches a stable steady state (a multidimensional limit cycle phenomenon).<<ETX>>