Foundations for Microwave Circuits, Softcover reprint of the original 1st ed. 1989

While many articles have been written on microwave devices, a great majority of them are prepared for specialists dealing in specific aspects of microwave engineering. At the same time, material at a fundamental level in tutorial form is extremely limited, especially for stu­ dents who need to acquire basic knowledge in the field. Individuals seeking to gain a prelim­ inary understanding of microwave circuits are usually relegated with little success to the end­ less search from one reference source to another. For non-experts, sequential derivations of basic relations are rarely available and extremely difficult to locate. The purpose of this volume is to collect in one place the essential fundamental principles for a group of microwave devices. The chosen devices are those which form the basic modules found in practical microwave systems. Thus, these devices provide the crucial build­ ing blocks in common microwave systems, and their inherent characteristics are also the basis of some of the fundamental concepts in more complex devices. The material is presented in a continuous, self-contained manner. With the appropriate background, readers should be able to follow and understand the contents without the need for additional references.

I Review of Transmission Line Theory.- 1. Transmission Line Equations.- 2. Wave Parameters and Characteristic Impedance.- 2.1. Example: Determination of Propagation Constant — General Case.- 3. Interpretation of the Solution.- 4. Terminated Line.- 5. The Crank Diagram.- 6. The Short-Circuited Line.- 7. Quarter-Wave Transformer.- 8. Power Calculation — Complex Notation.- 9. Problems.- II Review on Waveguides.- 1. Maxwell’s Equations.- 2. Guided Waves.- 3. Transverse Electromagnetic (TEM) Waves.- 4. Transverse Electric (TE) Waves.- 5. Transverse Magnetic (TM) Waves.- 6. General Case.- 7. Group Velocity.- 8. Propagation Constant.- 9. Electromagnetic Energy.- 10. Poynting Theorem.- 11. Method of Separation of Variables.- 11.1. Laplace Equation in Cylindrical Coordinates.- 12. Rectangular Waveguide.- 13. Circular Waveguide.- 13.1. Field Distribution — TM01 Mode in Circular Guide.- 13.2. TE Field Distribution — Circular Guide.- 14. Problems.- III The Scattering Matrix.- 1. Introduction.- 2. The Scattering Matrix.- 2.1. Scattering Matrix of a Series Impedance.- 3. Definition of Scattering Coefficients.- 3.1. Appendix.- 3.2. Example: Scattering Matrix for a Two-Port Device.- 3.3. Example: Scattering Matrix for a Two-Port Network — Alternate Approach.- 4. Characteristic Equation of the Scattering Matrix.- 5. Eigenvalues and Eigenvectors.- 5.1. Example: Eigenvalues and Eigenvectors.- 6. Some Properties of Eigenvalues.- 6.1 Example: Show validity of Eq. (6.13).- 7. Multiple Eigenvalues.- 7.1. Example: Eigenvectors for Repeated Roots.- 8. Cayley-Hamilton Theorem.- 9. Eigenvectors and Eigenvalues of a Two-Port Device.- 9.1. Example: Scattering Matrix of a Shunt Admittance.- 10. Diagonalization of a Scattering Matrix — Distinct Eigenvalues.- 11. Diagonalization of a Symmetric Matrix.- 11.1. Example: Diagonalization.- 11.2. Inverse of a Matrix.- 12. Diagonalization — Multiple Eigenvalues.- 13. Unitary Property.- 14. Dissipation Matrix.- 15. Problems.- IV Immittance Matrices.- 1. Introduction.- 2. Impedance Matrix.- 3. Admittance Matrix.- 3.1. Example: Admittance of a Line Terminated by Reactances.- 4. Eigen-network.- 4.1. Example: Scattering Matrix of a Shunt Impedance.- 4.2. Example: Scattering Matrix of a Section of Uniform Transmission Line.- 5. Relations Between [S], [Z], and [Y].- 5.1. Example: Scattering Matrix of a Two-Port Device.- 6. Problems.- V Symmetrical Devices.- 1. Introduction.- 2. Reflection Operation.- 3. Symmetry Operations.- 4. Symmetry Matrix.- 5. Commutable Matrices.- 5.1. Determination of a Commutable Matrix.- 6. Properties of Commutable Matrices.- 7. Symmetrical Two-Port Junction.- 8. H-Plane T-Junction.- 8.1. Shifting reference Planes in a Scattering Matrix.- 8.2. E-Plane T-Junction.- 9. Symmetrical Y-Junction.- 10. Problems.- VI Directional Couplers.- 1. Introduction.- 2. Directional Couplers.- 3. Even- and Odd-Mode Theory.- 4. Lorentz Reciprocity Theorem.- 5. Probe Coupling in a Waveguide.- 6. Radiation from Linear Current Elements.- 7. Radiation from a Current Loop.- 8. Waveguide Coupling by an Aperture.- 9. Aperture in a Transverse Wall of a Waveguide.- 10. Side-wall Coupler — Even-Odd Mode Theory.- 11. Eigenvalue Theory.- 12. Problems.- VII Impedance and Mode Transformers.- 1. Quarter-Wave Transformer.- 2. Small-Reflection Theory.- 3. Multistep Impedance Transformer.- 4. Maximally Flat Transformer.- 4.1. Expansion of cos m?.- 5. Chebycheff Transformer.- 5.1. Chebycheff Polynomials.- 5.2. Example: Chebycheff Transformer.- 6. Perturbation in a Cavity.- 7. Perturbation in Waveguides.- 8. Dielectric Phase Shifter.- 9. Strip Attenuator.- 10. Polarization of Plane Waves.- 11. Quarter-Wave Plate.- 12. Problems.- VIII Ferrite Devices.- 1. Propagation in Ferrite.- 1.1. Magnetic Moment and Angular Momentum of Atomic Models.- 1.2. Angular Momentum.- 2. Permeability Tensor.- 2.1. Components of Susceptance Elements.- 3. Scalar Susceptibility.- 4. Faraday Rotation.- 4.1. Traveling Wave in the Negative z?-Direction.- 4.2. Verification of Equation (4–7).- 4.3 Frequency Response of the Propagation Constant.- 5. Isolator.- 6. Gyrator.- 7. Polarization of Guided Wave.- 8. Resonance Isolator.- 9. Problems.- IX Review on Resonators.- 1. Q Factor.- 2. Waveguide Resonant Circuits.- 3. Rectangular Cavity Resonators.- 4. Scattering Matrix of a Lossless Resonator.- 5. Resonator with Damping.- 6. Cavity with Shunt Elements.- 7. Transformer-Coupled Resonator.- 7.1. Mutual Coupling.- 7.2. Transformer.- 8. Problems.- X Review on System Functions.- 1. Linear System.- 1.1. Natural Frequencies.- 2. System Function.- 2.1 Properties of Network Function — One-terminal Pair Network.- 3. Properties of System Functions.- 3.1. Definition of Postive-Real Function.- 3.2. Some Properties of Poles and Zeros Located on the j?-Axis.- 4. Positive-Real Function.- 5. Properties of the Driving-Point System Function.- 6. Driving-Point Function of an LC Network.- 7. Realization by Partial Fraction Expansion.- 8. Realization by Continued Fraction.- 9. Magnitude and Frequency Normalization.- 9.1. Normalization.- 10. Frequency Transformation.- 11. Frequency Scaling.- 12. Low-Pass to High-Pass Transformation.- 13. Low-Pass to Band-Pass Transformation.- 14. Low-Pass to Band-Stop Transformation.- 15. Problems.- XI Normal Modes of a Waveguide.- 1. Orthogonality of Guided Waves.- 1.1. Green’s Theorem.- 2. Guided Wave Theory.- 3. Normal Modes.- 4. Orthogonal Functions for Electromagnetic Fields.- 5. Expansion of Fields in Normal Modes.- 6. Power and Energy Relations.- 7. Attenuation in Lossy Dielectric.- 8. Relation Between Energy Densities.- 9. Velocity of Energy Transport.- 10. Complex Frequency.- 11. Propagation with Complex Frequency.- 11.1. Example: Determination of Attenuation Coefficient — Real Frequency Case.- 12. Losses in the Guide Wall.- 13. Problems.- XII Resonant Cavity.- 1. Introduction.- 2. Normal-Mode Functions for the Cavity.- 2.1. Example: Equivalence of Eqs. (2–11b) and (2–12).- 3. Free Oscillations of a Cavity.- 3.1. Impedance of a Resonant Line Section.- 4. Input Impedance of a Cavity.- 5. Multi-Port Cavity.- 6. Electronic Discharge Within a Cavity.- 7. Problems.- XIII Resonant Cavity — 2.- 1. Single-Port Cavity — Traveling Wave Approach.- 2. Equivalent Circuit Representation.- 3. Single-Port Resonator — Equivalent Circuit.- 4. Unloaded Q.- 5. External Q.- 6. Loaded Q.- 7. Power Absorbed by a Cavity.- 8. Experimental Determination of Q’s.- 9. Frequency Scale.- 9.1. Example: Single-Port Resonator.- 10. Two-Port Cavity.- 11. Transmission Cavity.- 12. Problems.- XIV Filters.- 1. Introduction.- 2. Insertion Loss.- 3. Darlington’s Filter Synthesis.- 4. Analytic Continuation.- 5. Butterworth Low-Pass Response.- 5.1. Example: Design of a Maximally Flat Low-Pass Filter.- 6. Chebycheff Low-Pass Approximation.- 6.1. Example: Determination of s21(p?) for Chebycheff Low-Pass Approximation.- 6.2. Example: Determination of n and Tolerance ?.- 6.3. Example: Design of Chebycheff Filter.- 6.4. Verification of Eq. (6–23).- 7. Low-Pass to Periodic Band-Pass Transformation.- 8. Resonators in Cascade —General.- 9. Coincidental Cascaded Resonators.- 10. Quarter-Wavelength Coupled Resonators.- 10.1. Example: Quarter-Wavelength Coupled Nonsymmetrical Resonators.- 10.2. Example: Scattering Matrix for Quarter-Wavelength Coupling.- 11. Synthesis of Resonators in Cascade.- 12. Immittance Inverters.- 13. Multi-resonators in Cascade.- 13.1. Example: Resonators in Cascade.- 14. Problems.