**Catalog Description:** Review of static electric and magnetic fields and applications; Maxwell's equations; transmission lines; propagation and reflection of plane waves; introduction to guided waves, microwave networks, and radiation and antennas. Minilabs on statics, transmission lines, and waves. Explanation of cellphone antennas, WiFi communication, and other wireless technologies.

**Units:** 4.0

**Prerequisites:** Electrical Engineering 16B, Mathematics 53, 54, Physics 7B, or equivalent that covers AC circuits and electromagnetics up to Maxwell's equations.

**Formats:**

Fall: 3.0 hours of lecture, 1.0 hours of discussion, and 2.0 hours of laboratory per week

Spring: 3.0 hours of lecture, 1.0 hours of discussion, and 2.0 hours of laboratory per week

**Grading basis:** letter

**Final exam status:** Written final exam conducted during the scheduled final exam period

**Also listed as:** EL ENG 117

**Class Schedule (Spring 2019):**

WeFr 2:00PM - 3:29PM, Cory 299 –
Eli Yablonovitch

Spring 2018 class homepage on bCourses

**Department Notes:**

Course objectives: To provide the basic skills required to understand, develop, and design various engineering applications involving electromagnetic fields. To lay the foundations of electromagnetism and its practice in modern communications such as wireless, guided wave principles such as fiber optics and electronic electromagnetic structures including those on the sub-micron scale. To provide basic laboratory exposure to electromagnetic principles and applications.

Topics Covered (Course Outline)

- Basic Electro-magnetic Relationships ¿ Introduction to wave motion, phase speed, basic forms of the wave equation, the electromagnetic spectrum, complex phasor notation, transverse waves on a string
- Transmission lines ¿ Circuit models of transmission lines and the coaxial line; the relationship of the coaxial transmission line to Ampere¿s and Gauss¿ Laws; basic derivations of L and C; transmission and reflection coefficients, pulses and transients; the capacitively loaded line and implications for high speed-digital systems; sinusoidal waves; standing wave ratio; expressions for impedance, transmission, and reflection coefficient and power flow; Smith chart relating complex reflection coefficient and impedance; scattering parameters and the Smith chart; single and double stub tuning; quarter wave tuning; lossy transmission lines; basic concept of resonance on transmission lines; Gaussian pulse propagation: group and energy velocity
- Introduction to Maxwell¿s Equations ¿ Review of vector analysis and coordinate systems; gradient, perpendicularity, and wave phase fronts; surface and volume integrals; Gauss¿ law; Gauss¿ law for magnetism; line integrals, currents and Ampere¿s law; divergence of a vector and Gauss¿ law in differential form; the divergence theorem; curl of a vector field and Ampere¿s law in differential form; Stoke¿s theorem; the Laplacian operator; Maxwell¿s equations; displacement current, continuity and Maxwell¿s equations; charges, conduction, convection, and diffusion currents; introduction to magnetic and electric potentials; Faraday¿s law
- Intermediate Aspects of Maxwell¿s Equations; Dynamics ¿ Scalar and vector potentials; generalizations of the potentials to include retardation; boundary conditions; capacitance and inductance; Poynting¿s theorem, power flow, and stored energy; Maxwell¿s equations for the sinusoidal steady-state (phasors); polarization; the steady-state Poynting vector and theorem; propagation in lossy media; forces, torque, and work
- Reflection and Transmission at Interfaces ¿ EM waves at boundaries and the transmission line analog; Snell¿s "laws" and the critical angle; oblique incidence; Brewster¿s angle; TEM modes and the coaxial cable; ray model of guided waves: TE and TM waves, cutoff, and phase velocity; general formulation of wave-guide fields; hollow metallic wave guides with guiding in one dimension; planar transmission lines; general properties two dimensional-rectangular guides; power transfer; dielectric, conical, slab-wave guides; periodic structures; optical fibers; loss and dispersion; resonators
- Antennas, Radiation, Diffraction, and Wireless Systems ¿ Basic antenna parameters for single and arrays of antennas; directivity and gain; effective area; Friis formula and its relation to uncertainty; signal to noise and the Friis equation; basic radar equation as extension of Friis equation; review of potentials and the Hertzian dipole; long-wire antenna; radiation resistance; arrays; far field, near field and the Fourier transform; circuit approach to arrays; Yagi-Uda arrays; integrated antennas; imaging, geometrical optics, and Gaussian beams
- Electromagnetic Properties of Materials (as time permits) ¿ Linear isotropic media; anisotropic media; introduction to electro-optics

A series of laboratory exercises is used to provide a hands-on illustration of many of the class topics.

**Related Areas:**