Principles of RF and Microwave Design

This comprehensive resource provides a thorough introduction to the principles of electronic circuits operating in the radio, microwave, and millimeter-wave frequency ranges. The book highlights the fundamental physical laws of classical electromagnetics using a foundation of Maxwell's equations to give insight into the operating principles of circuit elements of all kinds, from lumped elements to transmission lines, waveguides, optical fibers, and quasi-optical structures. Standard passive system components like filters, splitters, couplers, hybrids, baluns, and antennas are explained to acclimate the reader to considering multiple technological solutions for common design problems. A basic overview of active circuit designs, such as amplifiers, mixers, and multipliers is also provided, along with discussion of the performance characteristics of electronic systems, including noise and linearity. Emphasis is placed on visualization and understanding of how and why electronic circuits of all frequencies are built and operate the way they do. Readers learn how to match an amplifier for optimum noise performance over the broadest bandwidth with the fewest number of elements and how to visualize the coupling of various modes in a mixed waveguide-type structure and avoid resonances due to trapped, higher-order modes. The book provides the tools needed to design and optimize a launcher from microstrip into waveguide, and whether the best characteristics can be achieved by incorporating matching elements in the microstrip section, the waveguide section, or both. Packed with references and examples, readers learn not only how to do the math but what the math means. Principles of RF and Microwave Design Preface Contents Acknowledgments Fields and Waves Maxwell's Equations Large-Scale Form and Constitutive Relations Physical Interpretation The Continuity Equation Boundary Conditions on a Perfect Conductor Boundary Conditions at a Dielectric Interface Differential Form Differential Boundary Conditions Static Fields Electrostatics Magnetostatics Static Fields in a Coaxial Geometry Wave Solutions Spectral Analysis Maxwell's Equations in the Frequency Domain Phasor Notation Wave-Boundary Interactions Reflection from a Conducting Boundary Reflection and Refraction from a Dielectric Boundary Lossy Materials Dielectric Polarization Magnetic Polarization Conduction The Skin Effect Lorentz Reciprocity From Fields to Circuits Problems References Lumped Elements Voltage, Current, and Kirchhoff's Laws Kirchhoff's Voltage Law Kirchhoff's Current Law Lumped-Element Devices Resistors Reactive Elements Capacitors Inductors Transformers Energy and Power Power Dissipation in Resistors Energy Storage in a Capacitor Energy Storage in an Inductor Energy Transfer in a Transformer Terminal Parameters in the Frequency Domain Impedance and Admittance Complex Power Resonators Series RLC Resonator Parallel RLC Resonator Loaded Q Sources Tellegen's Theorem and Its Implications Network Reciprocity Parasitics Realistic Capacitors Realistic Inductors Realistic Transformers Problems References Transmission Lines Construction from Lumped Elements Distributed Inductance and Resistance Distributed Capacitance and Conductance The Telegrapher's Equations Construction from Field Equations Separation of Variables Relating Terminal Parameters to Field Quantities Transmission Lines in Circuits The Terminated Transmission Line Stubs and Quarter-Wave Transformers Infinite T-Lines and the Characteristic Impedance Signal Transmission with Transmission Lines Loss in Transmission Lines The 50 ohm Standard Transmission-Line Resonators Half-Wave Resonators Quarter-Wave Resonators Coupling to a Transmission-Line Resonator Printed Circuit Technologies Microstrip Design Equations Planar Junctions and Discontinuities Radial Stubs Coupled Lines Problems References Network Parameters Immittance Network Parameters Impedance Parameters Admittance Parameters ABCD-Parameters Hybrid and Inverse-Hybrid Parameters Wave Network Parameters Scattering Parameters Scattering Transfer Parameters Properties of Networks Reciprocity Symmetry Antimetry Losslessness Passivity A Constraint on Three-Port Networks Signal-Flow Graphs Principles of Signal-Flow Graphs Decomposition Rules Mason's Rule Equivalent Matrix Form Even and Odd-Mode Analysis Two-Port Example Coupled Lines Normalization of the Scattering Parameters Generalized Scattering Parameters Renormalization Parameter-Defined Networks Gyrators Impedance Inverters Problems References Transformations and Identities Transformations Impedance Scaling Frequency Scaling Frequency Inversion (High-Pass Transformation) Band-Pass Transformation Band-Stop Transformation Richard's Transformation Immittance Inversion (Duality Transformation) Identities Delta-Wye Identity Star-Mesh Identity Inverter-Dual Identity Equivalent Impedance Groups Transformer Identities Kuroda's Identities Coupled-Line Identities A Three-Port Transmission-Line Identity Problems References Impedance Matching Single Frequency Matching Voltage Standing-Wave Ratio (VSWR) The Smith Chart Movements on the Smith Chart Two-Parameter Matching Networks Two Transmission-Line Matching Networks Broadband Impedance Matching Comparison of Two-Parameter Matching Networks Carter Chart Immittance Folding The Bode-Fano Criteria Resistance Matching Multisection Transformers Maximally Flat (Binomial) Matching Transformers Equiripple (Chebyshev) Matching Transformers Tapered Transformers Exponential Taper Klopfenstein Taper Problems References Waveguides Waveguide Modes Cutoff Frequencies Transverse Fields Backward-Traveling Waves Power Flow in Waveguide Modes TE and TM Modes Rectangular Waveguide TM Modes TE Modes Charge and Current Distributions Mode Plots Dispersion Diagrams Phase Velocity and Group Velocity Losses Modal Discontinuity Analysis Waveguide Discontinuity Equivalent Circuits Circular Waveguide TM Modes TE Modes Modes, Dispersion, and Shielding Losses Waveguide Cavity Resonators Rectangular Cavity Resonators Cylindrical Cavity Resonators Stored Energy in a Cavity Quality Factors of Cavity Resonators Other Cavity and Resonator Types Ridged Waveguide Double-Ridged Waveguide Quad-Ridged and Triple-Ridged Waveguides Coaxial Waveguide Periodic Waveguide and Floquet Modes Surface Impedance Approximation Hybrid Modes The Balanced Hybrid Condition Fast, Slow, Forward, Backward, and Complex Waves Dielectric Waveguides Confinement by Total Internal Reflection Fiber Cladding LP Modes in Optical Fiber Problems References Launchers and Transitions Microstrip-to-Coax and CPW-to-Coax Transitions End-Launch Transition Right-Angle Transition All-Planar Transitions Microstrip to CPW and GCPW Microstrip to Slotline CPW to Slotline Balanced to Unbalanced Coax to Waveguide Coax to Rectangular Waveguide Coax to Double-Ridged Waveguide Microstrip to Waveguide Longitudinal Probes Vertical Probes Waveguide Tapers Trapped Mode Resonances Hybrid-Mode Launcher Beam Coupling to Optical Fibers Numerical Aperture Beam Generation Problems References Antennas and Quasioptics Parallel-Plate Waveguide TEM Modes TE Modes TM Modes Fourier Optics Planar Fourier Optics Rotman Lens Fourier Optics in Free Space Gaussian Beams The Paraxial Helmholtz Equation The Gaussian Mode Solution Terms of the Gaussian Beam Equation Complex Beam Parameter Ray Transfer Matrices Rays in Gaussian Beams Matrices for Common Optical Elements Application to Gaussian Beams Field Equations for Antennas Potential Formulation of Maxwell's Equations Retarded Potentials Wire Antennas Short Dipoles Half-Wave Dipoles Gain and Directivity Radiation Resistance Other Wire Antennas Complementary Antennas Half-Wave Slot Planar Antennas Microstrip Patch Antenna Planar Inverted-F Antenna (PIFA) Horn Antennas Pyramidal Horn Conical Horn Potter Horn Conical Corrugated Feedhorn Metrics for Directive Beams Beam Area Beam Efficiency and Stray Factor Effective Area Friis Transmission Equation Problems References Flat-Frequency Components Terminations Printed-Circuit Terminations Waveguide Terminations Absorber Attenuators Splitters Tee Junctions Resistive Splitters Wilkinson Power Dividers Gysel Power Divider Rectangular Waveguide Combiners Phase Shifters Lumped-Element High-Pass and Low-Pass Schiffman Phase Shifters Corrugated Phase Shifters Directional Couplers Coupled-Line Coupler Multisection Couplers Codirectional Couplers Multi-Aperture Waveguide Couplers Beam Splitters Quadrature Hybrids Branchline Hybrids Lange Couplers and Tandem Couplers 180-Degree Hybrids Rat-Race Hybrids Waveguide Magic Tee Lumped-Element 180-Degree Hybrids Nonreciprocal Components Physical Mechanism of Nonreciprocity Faraday Rotation Devices Resonant Absorption Isolators Stripline Circulators and Isolators Problems References Frequency-Selective Components Equalizers Lumped-Element Equalizers Transmission-Line Equalizers Foundations of Electronic Filters Periodic Networks Canonical Filter Responses Lumped-Element Ladders Reflectionless Filters Topological Basis of Reflectionless Filters Mitigation of Negative Elements All-Pole Reflectionless Filters Distributed Filters Stepped-Impedance Filters Coupled Resonators Susceptance Slope and Band-Pass Scaling Edge-Coupled Band-Pass Filters General Coupling-Routing Topologies Empirical Extraction of Couplings Waveguide Filters Half-Wave Resonator Waveguide Filters Stepped-Height Waveguide Filter Waffle-Iron Low-Pass Filter Frequency-Selective Surfaces Time-Domain or Pulse-Shaping Filters Gaussian Filters Bessel-Thomson Filters Multiplexers Problems References Amplifiers Gain and Stability Power Gain Factors Oscillations Stability Circles Rollet Stability Factor Geometric Stability Factors Maximum Gains Balanced Amplifiers Low-Noise Amplifiers Noise Temperature and Power Noise Models of Two-Port Networks Noise Parameters and Matching Power Amplifiers Saturated Power Linearity Efficiency Multistage Amplifiers Problems References Frequency Conversion General Nonlinearity Multipliers Single-Element Multipliers Selective Harmonic Suppression Mixers Single-Diode Mixers Single-Balanced Double-Balanced Triple-Balanced Sideband-Separating Subharmonic Fundamental Limits Upon Conversion Efficiency Problems References Appendix A: Mathematical Identities Trigonometric Identities Pythagorean Identities Sum-Angle Formulas Double-Angle and Triple-Angle Formulas Half-Angle Formulas Power Reduction Product-to-Sum Formulas (Prosthaphaeresis) Sum-to-Product Formulas Composite-Angle Formulas Outphase Summation Trigonometric Products Exponential Forms (Euler's Formula) Hyperbolic Functions and Identities Relationships to Standard Trigonometric Functions Pythagorean Identities Sum-Argument Formulas Double-Argument Formulas Half-Argument Formulas Sum-to-Product Formulas Exponential Forms Other Theorems Binomial Theorem Law of Sines and Cosines Integrals Trigonometric Integrals Other Useful Integrals Appendix B: Integral Theorems The Divergence Theorem Stokes' Theorem Appendix C Vector Identities Appendix D: Vector Operator Forms Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates Appendix E: Delta-Wye Identities Appendix F: Transmission-Line Identities References Appendix G: Special Functions Chebyshev Polynomials Bessel Functions Recurrence Formulas Zeros and Extrema Asymptotic Approximations Modified Bessel Functions References About the Author Index