Introduction to Active Phased Arrays

Introduction to
Active Phased Arrays
	Contents
	Chapter 1
Introduction to Phased Arrays
		1.1	Phased Array History and Perspective
		1.2	Fundamentals of Wave Propagation: The Wave Equation
			1.2.1 Boundary Condition Cases
		1.3	Array Antennas
		1.4	Aperture State Fundamentals
			1.4.1 General Aperture State Relationships
			1.4.2 Radiation Integrals for Circular Apertures
		1.5	Array Far-Field Fundamentals
		1.6	Frequency-Time Domains
			1.6.1 Frequency-Time Domain: Fast Fourier Transform
		References
	Chapter 2
Array Theory
		2.1	Array Far-Field Radiation
		2.2	Array Far-Field Fundamental Observations
		2.3	General Array Theory
		2.4	Two-Element Arrays
		2.5	Linear Arrays
			2.5.1 Linear Arrays in Sine Space
			2.5.2 Linear Array Aperture Projection
		2.6	Planar Arrays
			2.6.1 Planar Arrays with No Real-Space Grating Lobes
			2.6.2 Planar Arrays with Real-Space Grating Lobes
		2.7	Conformal Arrays
			2.7.1 Radius of Curvature Embedded Element Geometry
			2.7.2 Conformal Array Phase Alignment
			2.7.3 Eclipsed Elements in Conformal Arrays
		References
	Chapter 3
Lattice Theory
		3.1	Introduction
		3.2	Floquet’s Theorem
			3.2.1 Phased Array Surface Wave Condition
			3.2.2 Phased Array Scan Volume
		3.3	Lattice Theory
			3.3.1 Rectangular Lattice
			3.3.2 Equilateral Triangular Lattice
			3.3.3 Isosceles Triangular Lattice
		3.4	Reordered Lattice Theory
			3.4.1 Ring Lattice Arrays
			3.4.2 Spiral Lattice Arrays
		3.5	Finite Array and Surface Wave Effects
		References
	Chapter 4
Array Fundamentals: Supporting Theories, Part I
		4.1	Introduction
		4.2	Radiating Aperture Fundamentals: Three Domains
		4.3	Array Architecture
			4.3.1 Case 1: Hybrid Beamformed, Single Polarization
			4.3.2 Case 2: Analog Beamformed, Dual Simultaneous Polarization
		4.4	Practical Limits
			4.4.1 Theorem of Reciprocity
			4.4.2 Conservation of Energy
			4.4.3 Superposition
			4.4.4 Duality Theorem
		4.5	Near and Far Fields
			4.5.1 The Far-Field Criterion
			4.5.2 Array Reactive and Near Fields
		4.6	Rotational Transforms
			4.6.1 Coordinate Frames
			4.6.2 Sine Space
			4.6.3 Rotated Coordinate Frames
			4.6.4 Inverted Rotated Coordinate Frames
		References
	Chapter 5
Array Fundamentals: Supporting Theories, Part II
		5.1	Introduction
		5.2	Radiated Gain
		5.3	Polarization Domain
			5.3.1 Polarization Transforms
			5.3.2 Stokes Parameters
			5.3.3 Polarization Isolation
			5.3.4 Cross-Polarization
			5.3.5 Scan-Dependent Polarization Properties
			5.3.6 Polarization Compensation
		5.4	Phased Array Noise Temperature
			5.4.1 Antenna Noise Sources
			5.4.2 Noise Wave Theory
		References
	Chapter 6
Phased Array Radiating Elements
		6.1	Introduction
		6.2	Single-Element Dipole over Ground Plane Radiators
			6.2.1 Dipole Boundary Conditions
			6.2.2 Dipole Radiation
		6.3	Single-Element Waveguide Radiators
			6.3.1 Rectangular Waveguide
			6.3.2 Circular Waveguide
			6.3.3 Circular Waveguide Radiator
		6.4	Single-Element Patch Radiators
			6.4.1 Square Patch Boundary Conditions
			6.4.2 Square Patch Design Methods
			6.4.3 Square Patch Radiation
			6.4.4 Circular Patch Boundary Conditions
			6.4.5 Circular Patch Radiation
		References
	Chapter 7
Active Radiating Elements
		7.1	Introduction
		7.2	Mutual Coupling and Embedded Elements in Arrays
			7.2.1 Active Impedance, Reflection Coefficient, and Embedded Element Gain
			7.2.2 WAIM
			7.2.3 Real-Space Grating Lobes
			7.2.4 Surface Impedance Effects
		7.3	Active Radiating Element Cases
		7.4	Active Dipole over Ground Plane Radiators
			7.4.1 Linear Dipole Array
			7.4.2 Vee Dipole Array
			7.4.3 PUMA Array
		7.5	Active Patch Radiators
			7.5.1 Balanced Patch Radiator Array
			7.5.2 Unbalanced Patch Radiator Array
			7.5.3 Balanced Stacked Patch Radiator in a Rectangular Lattice Array
		References
	Chapter 8
Far-Field Synthesis, Part I
		8.1	Introduction
		8.2	Fourier Transform Method for Linear Arrays
		8.3	Schelkunoff’s Form
		8.4	Canonic Forms
		8.5	Truncated Complex Gaussian Forms
			8.5.1 Truncated Gaussian Magnitude Aperture Taper
			8.5.2 Truncated Gaussian Phase Aperture Taper
		8.6	Modified sin(x)/x Distribution
		References
	Chapter 9 Far-Field Array Synthesis, Part II
		9.1	Introduction
		9.2	Woodward-Lawson Method
			9.2.1 Nonorthogonal Woodward-Lawson Method
			9.2.2 Difference Patterns by the Woodward-Lawson Method
			9.2.3 Woodward-Lawson Synthesis Method with Controlled Sidelobes
		9.3	Dolph-Chebyshev Synthesis
		9.4	Taylor Line Source Synthesis
		9.5	Planar 2-D Array Distributions
		9.6	Circular Aperture Distributions
			9.6.1 Taylor Circular Array Sources
		9.7	Iterative Synthesis Methods
		9.8	MLE
		References
	Chapter 10
Stochastic Aperture Errors in Phased Arrays
		10.1	Introduction
			10.1.1 Stochastic (Random) Errors in Arrays
			10.1.2 Average (rms) Far-Field Characteristics
			10.1.3 Beam-Pointing Error
			10.1.4 Peak and rms Sidelobes
			10.1.5 Dispersion and Its Impact on Instantaneous Bandwidth
			10.1.6 Polarization Isolation
		10.2	Stochastic Error Budgets
		10.3	Periodic (Correlated) Array Errors
			10.3.1 Element-Level Phase Quantization
			10.3.2 Subarray Spatial Effects
			10.3.3 Subarray Frequency-Domain Effects
			10.3.4 Aperture Blockage
		References
	About the Author
	Index