Planar Circuits for Microwaves and Lightwaves (Springer Series in Electronics and Photonics)

Until recently, three principal classes had been known in the electrical cir­ cuitry. They were as follows: 1) The lumped-constant circuit, which should be called a zero-dimensional circuit, in the sense that the circuit elements are much smaller in size as compared with the wavelength in all three spatial directions. 2) The distributed-constant circuit, which should be called a one-dimensional circuit, in the sense that the circuit elements are much smaller than the wavelength in two directions but comparable to the wavelength in one di­ rection. 3) The waveguide circuit, which should be called a three-dimensional circuit, in the sense that the circuit elements are comparable to the wavelength in all three directions. The principal subject of this book is the analysis and design (synthesis) theories for another circuit class which appeared in the late 1960s and became common in the 1970s. This new circuit class is 4) the planar circuit, which should be called a two-dimensional circuit, in the sense that the circuit elements are much smaller in size as compared with the wavelength in one direction, but comparable to the wavelength in the other two directions.

1. Introduction.- 1.1 Seven Ranks in Electrical and Optical Circuitry.- 1.1.1 Conventional Four Ranks.- 1.1.2 Comparison of Circuit Dimensions.- 1.1.3 Nonconventional Three Ranks.- 1.1.4 Planar Circuits.- 1.1.5 Optical Planar Circuits.- 1.1.6 Long-Waveguide Circuit.- 1.2 Classification and Technical Significance of Planar Circuits.- 1.2.1 Three Basic Structures.- 1.2.2 The Neumann and Dirichlet Problems.- 1.2.3 Technical Significance of the Planar Circuit Concept.- 1.3 History of Planar Circuit Research.- 1.3.1 History of the Earliest Stage.- 1.3.2 History After 1972.- 1.4 History of Optical Planar Circuit Research.- 1.5 Purpose and Organization of This Book.- 2. Analysis of Planar Circuits Having Simple Shapes.- 2.1 Background.- 2.2 Basic Equations.- 2.2.1 Wave Equation.- 2.2.2 Boundary Conditions for Cases when External Ports Are Absent.- 2.2.3 Eigenfunction Expansion.- 2.2.4 A Simple Example of the Solution.- 2.2.5 Boundary Condition at Ports.- 2.3 Derivation of Circuit Characteristics.- 2.3.1 Definition of Terminal Voltage and Current.- 2.3.2 Circuit Characteristics Expressed in Terms of Green’s Function.- 2.3.3 Expansion of Green’s Function by Eigenfunctions.- 2.4 Examples of Analysis Based on Green’s Function.- 2.4.1 Rectangular Circuit.- 2.4.2 Circular Circuit.- 2.4.3 Triangular Circuit.- 2.4.4 Annular Circuit.- 2.4.5 Circular and Annular Sectors.- 2.4.6 Open-Ended Stripline (Comparison with Distributed-Constant Line Theory).- 2.5 Determination of Equivalent Circuit Parameters Based on Energy Consideration.- 2.6 Equivalent Circuit of a Multiport Planar Circuit.- 2.7 Validity of the Open-Boundary Assumption.- 2.8 Examples of Planar Circuits Having Simple Shapes.- 2.8.1 Circular Resonator.- 2.8.2 Coupled-Mode Filter Using a Single Circular Resonator.- 2.8.3 Planar 3-dB Hybrid Using a Circular Resonator.- 2.9 Summary.- 3. Analysis of Planar Circuits Having Arbitrary Shapes.- 3.1 Background.- 3.2 Basic Formulation of the Contour-Integral Method.- 3.3 Circuit Parameters of an Equivalents N Port.- 3.4 Transfer Parameters of a Two-Port Circuit.- 3.5 Numerical Computation Procedure.- 3.5.1 Description of Circuit Pattern.- 3.5.2 Computation of rij and ?ij.- 3.5.3 Computation of Matrix Elements uij and hij.- 3.5.4 Computation of Transfer Parameters.- 3.5.5 Computation of Input Admittance and S12.- 3.5.6 RF Voltage Along the Circuit Periphery.- 3.6 Examples of Computer Analysis by the Contour-Integral Method.- 3.6.1 One-Port Circular Circuit.- 3.6.2 Two-Port Circular Circuit.- 3.6.3 Two-Port Square Circuit.- 3.6.4 Irregularly Shaped Circuit.- 3.6.5 Computer Time.- 3.7 Analyses Based on Eigenfunction Expansion.- 3.7.1 Advantages and Disadvantages of Eigenfunction-Expansion Approaches.- 3.7.2 Methods for Solving Eigenvalue Problems.- 3.7.3 Silvester’s Theory.- 3.7.4 Solution of an Eigenvalue Problem by Variational Method.- 3.7.5 Rayleigh-Ritz Method.- 3.7.6 Finite-Element Method.- 3.8 Summary.- 4. Short-Boundary Planar Circuits.- 4.1 Background.- 4.2 Principle of Analysis.- 4.3 Short-Boundary Planar Circuit Having Two Coaxial Coupling Ports.- 4.3.1 Basic Equation.- 4.3.2 Simplification of the Basic Equation.- 4.3.3 Derivation of Admittance Parameters.- 4.3.4 Derivation of Transfer Parameters.- 4.4 Short-Boundary Planar Circuit Having Two Waveguide Coupling Ports.- 4.4.1 Basic Equation.- 4.4.2 Simplification of the Basic Equation.- 4.5 Examples of Numerical Analysis.- 4.5.1 Short-Circuited Radial Line.- 4.5.2 Uniform Waveguide Section.- 4.5.3 Waveguide Section Including a Thick Inductive Window.- 4.5.4 Waveguide Sections Including Corners.- 4.5.5 Waveguide Section Including Post.- 4.6 Higher-Order Mode Consideration at Reference Planes.- 4.7 Summary.- 5. Segmentation Method.- 5.1 Background.- 5.2 Theory of Segmentation Method Using S Matrices.- 5.2.1 Basic Concepts.- 5.2.2 Interface Network.- 5.2.3 Computation of the S Matrix.- 5.2.4 Reduction of Computer Time in S Matrix Computation.- 5.3 Theory of Segmentation Method Using Z Matrices.- 5.3.1 Basic Equations.- 5.3.2 Computation of the Z Matrix.- 5.3.3 Reduction of Computer Time in Z Matrix Computation.- 5.4 Summary.- 6. Trial-and-Error Synthesis of Optimum Planar Circuit Pattern.- 6.1 Background.- 6.2 Method of Synthesis.- 6.2.1 Principle of the Method.- 6.2.2 Computer Analysis.- 6.2.3 Starting Circuit Pattern.- 6.2.4 Figure of Merit.- 6.2.5 Variation of Characteristics by Modification of Circuit Pattern.- 6.2.6 Optimum Circuit Pattern.- 6.3 Comparison with Experiment.- 6.4 Computer Time.- 6.5 Summary.- 7. Fully Computer-Oriented Synthesis of Optimum Planar Circuit Pattern.- 7.1 Background.- 7.2 Method of Synthesis.- 7.2.1 Outline of Synthesis Process.- 7.2.2 Analysis of Frequency Characteristics.- 7.2.3 Pattern Variables.- 7.2.4 Evaluation Function.- 7.2.5 Algorithm for Optimization of Circuit Pattern.- 7.3 Parameters and Computational Techniques in an Actual Example of Synthesis.- 7.3.1 Number of Pattern Variables.- 7.3.2 Reduction of Computer Time Taking Advantage of Double Symmetry.- 7.3.3 Number of Sampling Points Along Periphery.- 7.3.4 Parameters in Evaluation Function.- 7.3.5 Relative Widths of External Striplines.- 7.3.6 Assumption of Uniform Current at Ports.- 7.4 Results of Synthesis.- 7.4.1 Process of Optimization.- 7.4.2 Optimized Circuit Patterns.- 7.5 Experimental Verification.- 7.5.1 Circuit Design and Structure.- 7.5.2 Result of Measurement.- 7.6 Further Improvement of Frequency Characteristics by Addition of External Circuits.- 7.6.1 Types of External Circuits.- 7.6.2 Optimization of Parameters.- 7.6.3 Result of Optimization.- 7.6.4 Obtained Frequency Characteristics.- 7.7 Evaluation of the Synthesized Circuit Patterns.- 7.7.1 Comparison of Theory and Experiment.- 7.7.2 Comparison with Other Characteristics.- 7.7.3 Comparison with Other Trials for Synthesizing Planar Circuits.- 7.8 Summary.- 8. Planar Circuits with Anisotropic Spacing Media.- 8.1 Background.- 8.2 Theories of Analysis.- 8.2.1 Basic Equations.- 8.2.2 Analysis Based on Eigenfunction Expansion.- 8.2.3 Analysis Based on a Contour-Integral Equation.- 8.3 Formulations for Numerical Computation and Examples of Calculation.- 8.3.1 Formulation for the Eigenfunction-Expansion Method.- 8.3.2 Examples of Calculation.- 8.3.3 Formulation for the Contour-Integral Method.- 8.3.4 Examples of Calculation.- 8.4 Comparison of the Eigenfunction-Expansion and Contour-Integral Methods.- 8.5 Optimum Design of Ferrite Planar Circuits.- 8.5.1 Technical and Historical Backgrounds.- 8.5.2 Method of Numerical Analysis.- 8.5.3 Optimum Design of a Disk-Shaped Circulator.- 8.5.4 Optimum Design of a Triangular Circulator.- 8.5.5 Modified Triangular Circulators Having Curved Sides.- 8.6 Summary.- 9. Optical Planar Circuits.- 9.1 Background.- 9.2 Wave-Optics Approach to Optical Planar Circuits.- 9.2.1 Basic Equations.- 9.2.2 TE Modes.- 9.2.3 TM Modes.- 9.2.4 Vertical Field Distributions.- 9.3 Geometrical Optics Approach to Optical Planar Circuits.- 9.3.1 Concepts of Geometrical Optics and Ray.- 9.3.2 Eikonal and Eikonal Equation.- 9.3.3 Ray Equation.- 9.4 Optical Planar Circuits Having Uniform Slab Structure.- 9.4.1 Model to be Considered.- 9.4.2 TE-Mode Waves.- 9.4.3 TM-Mode Waves.- 9.5 Optical Planar Circuits Having Periodic Structures.- 9.5.1 Mathematical Expression of Optical Bloch Waves.- 9.5.2 Dispersion Relation and Group Velocity of Optical Bloch Waves.- 9.5.3 Excitation of Optical Bloch Waves.- 9.5.4 Example of Measured ?z??x Relations.- 9.6 Planar Lenses.- 9.7 Summary.- 10. Optical Planar Circuits Having Stripelike Waveguiding Structures.- 10.1 Background.- 10.2 Model to be Considered.- 10.3 Geometrical Optics Approach.- 10.3.1 Limitation of Geometrical Optics.- 10.3.2 Propagating Condition.- 10.4 Wave-Optics Approaches.- 10.5 Beam-Propagation Method.- 10.5.1 Principle.- 10.5.2 Numerical Calculations.- 10.5.3 Examples of Calculation Results.- 10.6 Summary.- A2.1 Derivation of (2.5).- A2.2 Some Characteristics of Eigenvalues and Eigenfunctions.- A3.1 Weber’s Solution Using Cylindrical Waves.- A3.2 Derivation of (3.1).- A3.3 Choice of the Green’s Function Used in Contour-Integral Analysis.- A4.1 Proof of (4.1) for a Multiply Connected Circuit Pattern.- A8.1 Derivation of (8.5, 8).- A8.2 Derivation of (8.18, 19).- A9.1 Derivation of (9.27).- A9.2 Derivation of (9.32, 33).- References.