Advanced Signal Integrity for High-Speed Digital Designs

2

ELECTROMAGNETIC FUNDAMENTALS FOR SIGNAL INTEGRITY

2.1 Maxwell’s Equations

2.2 Common Vector Operators

2.2.1 Vector

2.2.2 Dot Product

2.2.3 Cross Product

2.2.4 Vector and Scalar Fields

2.2.5 Flux

2.2.6 Gradient

2.2.7 Divergence

2.2.8 Curl

2.3 Wave Propagation

2.3.1 Wave Equation

2.3.2 Relation Between E and H and the Transverse Electromagnetic Mode

2.3.3 Time-Harmonic Fields

2.3.4 Propagation of Time-Harmonic Plane Waves

2.4 Electrostatics

2.4.1 Electrostatic Scalar Potential in Terms of an Electric Field

2.4.2 Energy in an Electric Field

2.4.3 Capacitance

2.4.4 Energy Stored in a Capacitor

2.5 Magnetostatics

2.5.1 Magnetic Vector Potential

2.5.2 Inductance

2.5.3 Energy in a Magnetic Field

2.6 Power Flow and the Poynting Vector

2.6.1 Time-Averaged Values

2.7 Reflections of Electromagnetic Waves

2.7.1 Plane Wave Incident on a Perfect Conductor

2.7.2 Plane Wave Incident on a Lossless Dielectric

References

Problems

Much of signal integrity is based heavily in electromagnetic theory. Various aspects of this theory are found in numerous books on a variety of topics, such as microwaves, electromagnetics, optics, and mathematics. To rely on these books to form a basis of the fundamental understanding of signal integrity would result in a confusing disarray of conflicting assumptions, notations, and conventions. Although it is assumed that readers have a basic understanding of electromagnetics, the presentation of Maxwell’s equations and subsequent solutions in the form most often used ...