Preface

This book is a compilation of research results obtained primarily over the past two decades in the application of groups of oscillators coupled in various configurations to the excitation of phased-array antennas. Much of the work was carried out at the Jet Propulsion Laboratory of the California Institute of Technology under contract with the National Aeronautics and Space Administration (NASA) building on the early work at the University of Massachusetts, Cornell University, and the University of California, Santa Barbara. More recent work at several institutions in Spain and especially at the Centre Tecnologic de Telecomunicacions de Catalunya (CTTC), as well as at a variety of institutions across Europe and Asia, is also described. A motivation for much of this work was the promise of a method of providing beam agility at electronic speed that is simpler than the conventional method of using a phase shifter at each element or module and controlling these phase shifters in a coordinated manner. More generally, however, the effort has focused on the integration of transmitter, receiver, and antenna including the beam-steering function in a single planar package.

The intended audience for the book comprises primarily designers of phased-array antennas and the associated electronics, but the book may also be of interest to those who may, through understanding the principles presented, envision other innovative applications of oscillator arrays such as distribution of timing signals and phase locking in general. In the same way, graduate students may find inspiration for research work leading to theses or dissertations based on extending the work described here.

With regard to the references, as a general rule we have used peer-reviewed archival journal articles and not conference presentations in the interest of ease of access. We have, however, made a few exceptions in this regard in cases of very recent work that, as far as we know, has not yet appeared in the peer-reviewed literature and in one case for the use of figures with proper attribution. We have endeavored to present a comprehensive treatment of the work in this field to date but recognize that we cannot be sure that we are aware of everyone in the world with interest in and contributions to this fascinating area of research. We, therefore, extend apologies to any who feel their work has been slighted in any way. Be assured it was unintentional.

The book begins with a note concerning the early use of coupled oscillators in the field of mathematical biology wherein researchers used them as an artifice in representing the behavior of neurons in what is known as a central pattern generator in a manner amenable to mathematical analysis. The application to phased-array antennas owes its origin primarily to Karl Stephan at the University of Massachusetts [1–3] and to Richard C. Compton at Cornell and his student, Robert A. York [4–7]. However, the modern emphasis on the study of the dynamics of such arrays was inspired by the interest of James W. Mink of the U. S. Army Research Office [8] in spatial power combining at millimeter wave frequencies. Thus, the presentation continues with a discussion of the utility of oscillator arrays in phased-array antennas and a detailed discussion of the mathematical analysis of the dynamic behavior of such arrays. The mathematics is at a level that should be easily accessible to graduate students in the physical sciences. Advanced calculus, linear algebra, complex variables, and Laplace transforms are the primary tools.

The treatment is arranged in two passes. On the first pass in Part I, we formulate the analysis in the simplest possible manner while retaining the essence of the dynamic behavior, the so-called phase model. Most of the results are based on a linearization of the equations valid for small inter-oscillator phase differences. This permits introduction of the key features of array behavior with a minimum of complexity. We then describe a number of experimental demonstrations of this approach to phased-array beam agility and validation of the approximate theoretical results in Part II. In Part III, we return for a second pass at the analysis, this time including a more sophisticated theoretical description of the oscillators permitting detailed study of the impact of their nonlinear properties. Much of the contemporary research in this area is focused on these properties and their potential utility in modern physical array implementations with many and varied applications. In Part III the presentation of experimental work is integrated with the theoretical as appropriate.

In preparing material for this book, a number of sign errors, typographical errors, and, in rare cases, errors of substance were uncovered in the references. Every effort has been made to correct these so that where the book differs from the literature, it is the book version that is correct.

Ronald J. Pogorzelski and Apostolos Georgiadis
Pasadena, California and Castelldefels, Barcelona, Spain
June 2011