Phased Array Antennas

Arun K. Bhattacharyya retired from RF Center of Excellence group of Lockheed Martin Space Systems in 2024. He also worked for Hughes Space and Communication (now Boeing) and Northrop space systems. He was an associate professor at the University of Saskatchewan, Canada and a visiting professor at Seoul National University, South Korea. He has authored over 100 technical papers and five book-chapters and has 25 issued patents. He is an IEEE fellow since 2002 and has received numerous awards including Hughes Technical Excellence award, Distinguished Engineer award at Northrop Grumman and the 2020 Extraordinary Engineering and Technology Award at Lockheed Martin Space.

• About the Author xixForeword xxiPreface xxiiiAcknowledgments xxixAbout the Companion Websitexxxi1 Phased Array Fundamentals: Pattern Analysis and Synthesis 11.1 Introduction 11.2 Array Fundamentals 11.3 Pencil Beam Array 131.4 Linear Array Synthesis 331.5 Planar Aperture Synthesis 541.6 Discretization of Continuous Source 611.7 Array-Fed Reflector 641.8 Confocal Array-Fed Reflector 701.9 Summary 762 Introduction to Floquet Modes in Infinite Arrays 832.1 Introduction 832.2 Fourier Spectrum and Floquet Series 842.3 Floquet Excitation and Floquet Modes 942.4 Two-Dimensional Floquet Excitation 972.5 Grating Beams from Geometrical Optics 1032.6 Floquet Mode and Guided Mode 1042.7 Summary 1083 Floquet Modal Functions 1153.1 Introduction 1153.2 TEz and TMz Floquet Vector Modal Functions 1153.3 Infinite Array of Electric Surface Current on Dielectric Coated Ground Plane 1213.4 Determination of Blind Angles 1293.5 Active Element Pattern 1333.6 Array of Rectangular Horn Apertures 1414 Finite Array Analysis 1614.1 Introduction 1614.2 Symmetry Property of Floquet Admittance 1624.3 Mutual Coupling 1694.4 Array of Multimodal Sources 1724.5 Mutual Coupling in Two-Dimensional Arrays 1734.6 Active Input Impedance of Finite Array 1764.7 Active Reflection Coefficient of Open-Ended Waveguide Array 1784.8 Radiation Patterns of Finite Array 1824.9 Radiation Patterns of Open-Ended Waveguide Array 1854.10 Active Element Patterns of Real Finite Array 1874.11 Array with Nonuniform Spacing 1974.12 Finite Array Analysis Using Convolution 1985 Array of Subarrays 2075.1 Introduction 2075.2 Subarray Analysis 2085.3 Subarray with Rectangular Grid 2135.4 Subarrays with Arbitrary Grid 2145.5 Subarray and Grating Lobes 2165.6 Active Subarray Pattern 2185.7 Four-element Subarray Fed by a Power Divider 2235.8 Subarray Blindness 2275.9 Subarray with Sequentially Rotating Elements 2285.10 Concluding Remarks 2346 The GSM Approach for Multilayer Array Structures 2436.1 Introduction 2436.2 Generalized Scattering Matrix Approach 2446.3 GSM Cascading Rule 2456.4 Transmission Matrix Representation 2496.5 Building Blocks for GSM Analysis 2506.6 Equivalent Impedance Matrix of Patch Layer 2616.7 Stationary Character of MoM Solutions 2656.8 Convergence of MoM Solutions 2726.9 Advantages of GSM Approach 2806.10 Other Numerical Methods 2817 Analysis of Microstrip Patch Arrays 2877.1 Introduction 2877.2 Probe-Fed Patch Array 2887.3 Electromagnetically Coupled Patch Array 3027.4 Slot-Fed Patch Array 3037.5 Stripline-Fed Slot-Coupled Array 3147.6 Finite Patch Array 3157.7 Ring-slot Element 3178 Array of Waveguide Horns 3278.1 Introduction 3278.2 Linearly Flared Horn Array 3288.3 Grazing Lobes and Pattern Nulls 3348.4 Surface and Leaky Waves in Array 3408.5 Wide-Angle Impedance Matching (WAIM) 3518.6 Multimodal Rectangular/Square Horn Elements 3578.7 Multimodal Step-Circular Horn 3608.8 Muti-flared High-efficiency Horns 3618.9 Excitation of Waveguide Horn 3629 FSS, Polarizer, and Reflect-array Analysis 3719.1 Introduction 3719.2 Frequency-Selective Surface 3719.3 Screen Polarizer 3829.4 Printed Reflect Array 38910 Metamaterial Analysis and Fundamental Properties 40710.1 Introduction 40710.2 Origin of Constitutive Parameters: Maxwellian Point of View 40910.3 Solutions of Maxwell's Equation in a Periodic Array Medium 41110.4 Constitutive Parameters for 2D Obstacles 41810.5 Constitutive Parameters for 3D Obstacles 42710.6 On the Uniqueness and Structure of [ε] Tensor 43010.7 The Lorentz Model Versus Floquet Model 43410.8 Floquet Versus Lorentz: Test on Metamaterial Slab 43610.9 Floquet Versus Lorentz: Nonresonant Obstacles 44110.10 Mode Degeneracy and Non-Maxwellian Medium 44310.11 Concluding Remarks 45111 Multilayer Array Analysis with Different Periodicities and Cell Orientations 45911.1 Introduction 45911.2 Layers with Different Periodicities: Rectangular Lattice 46011.3 Nonparallel Cell Orientations: Rectangular Lattice 46511.4 Layers with Arbitrary Lattice Structures 47311.5 Summary 47512 Shaped Beam Array Design: Optimization Algorithms 47912.1 Introduction 47912.2 Array Size: Linear Array 48012.3 Element Size 48312.4 Pattern Synthesis (Woodward–Lawson's Method) 48612.5 Gradient Search Algorithm 48912.6 Conjugate Field Matching Algorithm 50012.7 Successive Projection Algorithm 50512.8 Projection Matrix Algorithm 50912.9 Other Optimization Algorithms 51412.10 Design Guidelines of Shaped Beam 51512.11 Pattern Null Algorithms 51613 Beam Forming Networks in Multiple-Beam Arrays 53313.1 Introduction 53313.2 BFN Using Power Dividers/Combiners 53413.3 Butler Matrix Beam Former 53413.4 Blass Matrix BFN 54813.5 Rotman Lens 55013.6 Digital Beam Former 56613.7 Optical Beam Formers 56914 Active Phased Array Antenna 57514.1 Introduction 57514.2 Active Array Block Diagrams 57614.3 Aperture Design of Array Antenna 57814.4 Solid State Power Amplifier (SSPA) 58214.5 Phase Shifter 58714.6 Time Delay Unit 58814.7 Intermodulation Product 59014.8 Noise Temperature and Noise Figure of Antenna Subsystems 59714.9 Active Array System Analysis 60714.10 Active Array Calibration 61114.11 Concluding Remarks 61515 Statistical Analysis of Phased Array Antenna 62115.1 Introduction 62115.2 Array Pattern 62215.3 Statistics of R and I 62415.4 Probability Density Function of |F(u)| 62915.5 Confidence Limits 63815.6 Element Failure Analysis 64415.7 Concluding Remarks 648References 650Bibliography 650Problems 650Appendix A1 Shannon's Sampling Theorem 653Appendix A 2 A Proof of the Identity 655Index 657