Preface

The purpose of this book is to present the analysis and design of phased array antennas and systems in a comprehensive manner. Starting with the basic theory of electromagnetism and antenna radiation, the book covers the fundamental principles of phased array antennas and systematically develops advanced methods for analyzing phased array antennas and passive array structures. Detailed derivations of theorems and concepts are included to make the book as self-contained as possible. Several design examples and design guidelines for practical arrays are also presented. The book should be useful for antenna engineers and researchers, especially for those pursuing a career in antenna engineering. The reader is assumed to have a basic knowledge of engineering mathematics and antenna theory. This book can be used either as a text for an advanced graduate-level course or as a reference book for antenna professionals.

The book contains 15 chapters, which are broadly divided into three sections. The first section, which includes Chapters 1 through 6, is mostly devoted to developing a "Floquet modal-based approach" for infinite and finite phased arrays, starting with an introduction to the traditional approach. The second section, Chapters 7 through 11, presents applications of the Floquet modal analysis to important phased array structures. The third section, including Chapters 12 through 15, is not directly related to the Floquet modal analysis; however, it covers several important aspects of phased array design. This section includes shaped beam array synthesis, array beam forming networks, active phased array systems, and an uncertainty analysis of phased array patterns due to manufacturing tolerances of the antenna components. To provide the reader with an interactive experience, several exercise problems are included at the end of each chapter. Information on the solution manual and selective software may be available upon request.

Chapter 1 presents an overview of phased array fundamentals, with two main goals. First, it illustrates the basic radiation characteristics of phased array antennas. Second, it spells out the limitations of conventional first-order analysis. This approach allows the reader to comprehend the traditional method's limitations and appreciate the need for higher-order analysis, which is developed in later chapters.

The chapter begins by defining the element pattern, followed by the array pattern and array factor. Next, the maximum gain theorem of a general array antenna is presented. The scan characteristics of a pencil beam array are discussed, considering gain, beam width, grating lobes, and beam squint. A performance comparison between a phase shifter and a time delay unit with regard to beam squint is also presented. This is followed by a detailed discussion of a two-level beam forming network designed to mitigate the beam squint issue. Prevalent array synthesis procedures for pencil beam arrays are then illustrated. Analyses of phased array-fed reflector technology, including array-fed confocal reflectors, are also presented. The scope and limitations of this first-order approach are outlined at the end.

Chapter 2 initiates the development of Floquet modal analysis for array antennas - the book's main objective. Using simple analytical methods, it is shown that the Floquet modal expansion evolves from the well-known Fourier expansion. The relationship between a Floquet mode and observable antenna parameters, such as radiation direction, is then established. The derivation of Floquet modal functions for arbitrary array grids is presented next. Finally, the coupling of a Floquet mode with a guided mode is considered, and the resulting consequences are discussed.

In Chapter 3, expressions for normalized Floquet modal functions are deduced. The Floquet modal expansion method is illustrated through an example of an infinite array of electric current sources. Two array antenna parameters, the Floquet impedance and the active element pattern, are defined, and their significance is discussed in the context of array performance. A detailed discussion on array blindness is also presented. The chapter concludes with a scattering matrix formulation for an infinite array of rectangular horn apertures.

Chapter 4 demonstrates how the results of an infinite array analysis can be used to analyze a finite array with an arbitrary excitation. The first part presents important theorems and concepts relevant to developing a finite array analysis. As is well known, mutual coupling is the most important factor in a finite array analysis. It is demonstrated that this mutual coupling between elements can be determined using infinite array data obtained through Floquet modal analysis. Next, the active impedances and the radiation pattern of the elements for a finite array with an arbitrary amplitude taper are obtained. The active return loss for an element of a "real finite array" is analyzed, and a comparison between the Floquet model and the Method of Moments is shown. Radiation pattern analysis of a real finite array, including edge effects, is also presented. Finally, an alternate approach for finite array analysis, based on the convolution theorem, is described and shown to converge with the Floquet model developed herein.

It is often beneficial to divide the entire array into a number of identical groups. Such a group, called a subarray, consists of a few elements that are excited by a single feed. In Chapter 5, a systematic procedure is presented for analyzing an array of subarrays. Using matrix theory, it is demonstrated analytically that a subarray impedance matrix can be constructed from the Floquet impedance of an array of individually excited elements, ignoring the subarray grouping. The chapter concludes with important characteristic features of an array of subarrays and a discussion of subarrays with sequentially rotated elements, typically used for obtaining circularly polarized radiation.

Chapter 6 presents the Generalized Scattering Matrix (GSM) approach for analyzing multilayer array structures. The chapter begins with the definition of a GSM, followed by the cascading rule for multiple GSMs. Advantages of the GSM approach over a transmission matrix approach are discussed from a numerical stability standpoint. Using the method of moments and modal matching, the GSMs of several important "building blocks" are deduced. The stationary character of the GSM approach is established, and the convergence of the solution is discussed in detail. The chapter concludes with a discussion of the advantages and disadvantages of the GSM approach.

Chapter 7 applies the GSM approach to analyze probe-fed and slot-fed multilayer patch arrays. The radiation and impedance characteristics of patch arrays are presented. Bandwidth improvement and bandwidth limits of patch arrays are discussed. The analysis of an electromagnetically coupled (EMC) patch array, stripline-fed patch array with mode-suppressing vias, and a ring-slot array for wide-angle scanning are presented. The results for finite patch arrays are also shown.

Chapter 8 focuses primarily on horn radiators as array elements. It begins with linearly flared rectangular horns, showing that, under certain conditions, a horn array structure may support surface and leaky waves. The dips and nulls in active element patterns are explained via surface and leaky wave coupling. The chapter also discusses the wide-angle impedance matching aspect of horn arrays. Characteristics of step and multi-flared horns, which can be used for enhanced radiation efficiency, are presented, along with the scan characteristics of circular horn arrays. Various excitation methods for horn elements are also discussed, and their typical performance characteristics are illustrated.

In Chapter 9, the analysis of three important passive printed array structures is undertaken: frequency-selective surfaces (FSS), screen polarizers, and printed reflect arrays. The first part of the chapter presents the features of single- and two-layer FSS in terms of return loss, co-polar, and cross-polar characteristics. It also considers the analysis of a horn antenna loaded with an FSS. In the second part, the analysis of a meander-line polarizer screen is presented. The chapter concludes with an analysis of a printed reflect-array antenna for linear and circular polarization, and it also discusses the gain enhancement method and contour beam reflect arrays.

In Chapter 10, an analytical model of metamaterial constructed with a multilayer array of conducting obstacles is presented. The modification of the constitutive parameters of the composite medium is examined from a Maxwellian point of view. This is followed by a step-by-step development of a Floquet eigenmodal approach for constitutive parameter retrieval. The Floquet model shows that the inclusion of PEC obstacles in a host medium modifies the permittivity but not the permeability of the composite medium. Consequently, the realization of a "double-negative (DNG)" medium using PEC obstacles is impossible. The Lorentz model, on the other hand, shows a change in permeability with PEC obstacle inclusion. It is found that the fictitious magnetic dipole moment invoked in the Lorentz model is the root cause for the difference in permeability. The simulated results of a metamaterial slab obtained from independent full-wave...