Courses 2024-25

Required for EE graduates and undergraduates. Weekly seminar given by successful entrepreneurs and EE faculty, broadly describing their path to success and introducing different areas of research in electrical engineering: circuits and VLSI, communications, control, devices, images and vision, information theory, learning and pattern recognition, MEMS and micromachining, networks, electromagnetics and opto-electronics, RF and microwave circuits and antennas, robotics and signal processing, specifically, research going on at Caltech and in the industry.

Mechatronics is the multi-disciplinary design of electro-mechanical systems. This course is intended to give the student a basic introduction to such systems. The course will focus on the implementations of sensor and actuator systems, the mechanical devices involved and the electrical circuits needed to interface with them. The class will consist of lectures and short labs where the student will be able to investigate the concepts discussed in lecture. Topics covered include motors, piezoelectric devices, light sensors, ultrasonic transducers, and navigational sensors such as accelerometers and gyroscopes. Graded pass/fail.

This course is intended to give the student a basic understanding of the major hardware and software principles involved in the specification and design of embedded systems. The course will cover basic digital logic, programmable logic devices, CPU and embedded system architecture, and embedded systems programming principles (interfacing to hardware, events, user interfaces, and multi-tasking).

This course is intended to introduce the student to the technologies and techniques used to fabricate electronic systems. The course will cover the skills needed to use standard CAD tools for circuit prototyping. This includes schematic capture and printed circuit board design. Additionally, soldering techniques will be covered for circuit fabrication as well as some basic debugging skills. Each student will construct a system from schematic to PCB to soldering the final prototype.

This course focuses on basic concepts needed for understanding classical and quantum optical phenomena and their applications to modern optical components and systems. Classical optical phenomena including interference, dispersion, birefringence, diffraction, laser oscillation, and the applications of these phenomena in optical systems employing multiple-beam interferometry, Fourier-transform image processing, holography, electro-optic modulation, optical detection and heterodyning will be covered. Quantum optical phenomena like single photon emission will be discussed. Examples and demonstrations will be selected from optical communications, lidar, adaptive optical systems, nano-photonic devices and quantum communications. Visits to research laboratories in optics are expected at the end of the course. This class is optimal for sophomores/juniors/seniors who want to get their first serious exposure to optics but also might work for well-prepared and motivated First-Year students.

Laboratory experiments to acquaint students with the basic aspects of Optics and Photonics Research and Technology. This course offers hands-on experience and teaches students how to handle major optical and electronic equipment and conduct experiments. It is useful for those who are thinking about a career utilizing both optical and electronic tools. Experiments encompass some of the topics and concepts covered in APh 23.

This course provides an introduction to the fundamental physics of modern device technologies in electrical engineering used for sensing, communications, computing, imaging, and displays. The course overviews topics including semiconductor physics, quantum mechanics, electromagnetics, and optics with emphasis on physical operation principles of devices. Example technologies include integrated circuits, optical and wireless communications, micromechanical systems, lasers, high-resolution displays, LED lighting, and imaging.

Modeling of physical systems by conversion to mathematical abstractions with an emphasis on electrical systems. Introduction to deterministic methods of system analysis, including matrix representations, time-domain analysis using impulse and step responses, signal superposition and convolution, Heaviside operator solutions to systems of linear differential equations, transfer functions, Laplace and Fourier transforms. The course emphasizes examples from the electrical circuits (e.g., energy and data converters, wired and wireless communication channels, instrumentation, and sensing) , while providing some exposure to other selected applications of the deterministic analysis tool (e.g., public opinion, acoustic cancellation, financial markets, traffic, drug delivery, mechanical systems, news cycles, and heat exchange).

Fundamentals of electronic circuits and systems. Lectures on diodes, transistors, small-signal analysis, frequency- domain analysis, application of Laplace transform, gain stages, differential signaling, operational amplifiers, introduction to radio and analog communication systems. Laboratory sessions on transient response, steady-state sinusoidal response and phasors, diodes, transistors, amplifiers.

Linear algebra and probability are fundamental to many areas of study in electrical engineering. This class provides the mathematical foundations of these topics with a view to their utility to electrical engineers. Topics include vector spaces, matrices and linear transformations, the singular value decomposition, elementary probability and random variables, common distributions that arise in electrical engineering, and data-fitting. Connections to signal processing, systems, communications, optimization, and machine learning are highlighted.

Individual research project, carried out under the supervision of a member of the electrical engineering faculty. Project must include significant design effort. A written thesis must be submitted to the department. Open only to senior electrical engineering majors. Not offered on a pass/fail basis.

A structured laboratory course that gives the student the opportunity to design and build a simple analog electronics project. The goal is to gain familiarity with circuit design and construction, component selection, CAD support, and debugging techniques.

Special problems relating to electrical engineering will be arranged. For undergraduates; students should consult with their advisers. Graded pass/fail.

All candidates for the M.S. degree in electrical engineering are required to attend any graduate seminar in any division each week of each term. Graded pass/fail.

The sequence covers the introductory methods in both theory and implementation of numerical linear algebra, approximation theory, ordinary differential equations, and partial differential equations. The linear algebra parts cover basic methods such as direct and iterative solution of large linear systems, including LU decomposition, splitting method (Jacobi iteration, Gauss-Seidel iteration); eigenvalue and vector computations including the power method, QR iteration and Lanczos iteration; nonlinear algebraic solvers. The approximation theory includes data fitting; interpolation using Fourier transform, orthogonal polynomials and splines; least square method, and numerical quadrature. The ODE parts include initial and boundary value problems. The PDE parts include finite difference and finite element for elliptic/parabolic/hyperbolic equations. Study of numerical PDE will include stability analysis. Programming is a significant part of the course.

Introduction to techniques of micro-and nanofabrication, including solid-state, optical, and microfluidic devices. Students will be trained to use fabrication and characterization equipment available in the applied physics micro- and nanofabrication lab. Topics include Schottky diodes, MOS capacitors, light-emitting diodes, microlenses, microfluidic valves and pumps, atomic force microscopy, scanning electron microscopy, and electron-beam writing.

An introduction to continuous and discrete time signals and systems with emphasis on digital signal processing systems. Study of the Fourier transform, Fourier series, z-transforms, and the fast Fourier transform as applied in electrical engineering. Sampling theorems for continuous to discrete-time conversion. Difference equations for digital signal processing systems, digital system realizations with block diagrams, analysis of transient and steady state responses, and connections to other areas in science and engineering.

This course introduces students to the fundamental concepts, methods, and models of applied probability and stochastic processes. The course is application oriented and focuses on the development of probabilistic thinking and intuitive feel of the subject rather than on a more traditional formal approach based on measure theory. The main goal is to equip science and engineering students with necessary probabilistic tools they can use in future studies and research. Topics covered include sample spaces, events, probabilities of events, discrete and continuous random variables, expectation, variance, correlation, joint and marginal distributions, independence, moment generating functions, law of large numbers, central limit theorem, random vectors and matrices, random graphs, Gaussian vectors, branching, Poisson, and counting processes, general discrete- and continuous-timed processes, auto- and cross-correlation functions, stationary processes, power spectral densities.

Energy technologies and the impact of government policy. Fossil fuels, nuclear power, and renewables for electricity production and transportation. Resource models and climate change policies. New and emerging technologies.

This course explores the fundamental underpinnings of experimental measurements from the perspectives of information, noise, coupling, responsivity, and backaction. Its overarching goal is to enable students to develop intuition about a diversity of real measurement systems and the means to critically evaluate them. This involves developing a standard framework for estimating the ultimate and practical limits to information that can be extracted from a real measurement system. Topics will include the fundamental nature of information and signals, physical signal transduction and responsivity, the physical origin of noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential underpinnings, while second-term topics will vary year-by-year according to interest. Among possible Ph 118 b topics are: high frequency, microwave, and fast time-domain measurements; biological interfaces and biosensing; the physics of functional brain imaging; and quantum measurement. Part b not offered 2024-25.

Advanced digital design as it applies to the design of systems using PLDs and ASICs (in particular, gate arrays and standard cells). The course covers both design and implementation details of various systems and logic device technologies. The emphasis is on the practical aspects of ASIC design, such as timing, testing, and fault grading. Topics include synchronous design, state machine design, arithmetic circuit design, application-specific parallel computer design, design for testability, CPLDs, FPGAs, VHDL, standard cells, timing analysis, fault vectors, and fault grading. Students are expected to design and implement both systems discussed in the class as well as self-proposed systems using a variety of technologies and tools. Given in alternate years;offered 2024-25.

This course focuses on hands-on experience with advanced techniques related to lasers, optics, and photonics. Students have the opportunity to build and run several experiments and analyze data. Covered topics include laser-based microscopy, spectroscopy, nonlinear optics, quantum optics, ultrafast optics, adaptive optics, and integrated photonics. Limited enrollment.

Study of programmable logic devices (FPGAs). Detailed study of the VHDL language, accompanied by tutorials of popular synthesis and simulation tools. Review of combinational circuits (both logic and arithmetic), followed by VHDL code for combinational circuits and corresponding FPGA-implemented designs. Review of sequential circuits, followed by VHDL code for sequential circuits and corresponding FPGA-implemented designs. Review of finite state machines, followed by VHDL code for state machines and corresponding FPGA-implemented designs. Final project. The course includes a wide selection of real-world projects, implemented and tested using FPGA boards. Not offered 2024-25.

This class treats Shannon's mathematical theory of communication and the tools used to derive and understand it. The class is organized around fundamental questions and their solutions, leading to central results such as Shannon's source coding, channel coding, and rate-distortion theorems. Quantities that arise en route to these solutions include entropy, relative entropy, and mutual information for discrete and continuous random variables. The course explores the calculation of fundamental communication limits like entropy rate, capacity, and rate-distortion functions under a variety of source and communication channel models (e.g., memoryless, Markov, ergodic, and Gaussian). The course begins with a foundational discussion of the simplest communication scenarios and then expands to include topics like universal source coding, the role of side information in source coding and communications, and the generalization of earlier results to network systems. Network information theory topics include multiuser data compression and communication over multiple access channels, broadcast channels, and multiterminal networks. Philosophical and practical implications of the theory are also explored. This course, when combined with EE 112, EE/Ma/CS/IDS 127, EE/CS 161, and EE/CS/IDS 167, should prepare the student for research in information theory, coding theory, wireless communications, and/or data compression. Part b not offered 2024-25

The course develops the core concepts of robotics. The first quarter focuses on classical robotic manipulation, including topics in rigid body kinematics and dynamics. It develops planar and 3D kinematic formulations and algorithms for forward and inverse computations, Jacobians, and manipulability. The second quarter transitions to planning, navigation, and perception. Topics include configuration space, sample-based planners, A* and D* algorithms, to achieve collision-free motions. Course work transitions from homework and programming assignments to more open-ended team-based projects.

This course builds up, and brings to practice, the elements of robotic systems at the intersection of hardware, kinematics and control, computer vision, and autonomous behaviors. It presents selected topics from these domains, focusing on their integration into a full sense-think-act robot. The lectures will drive team-based projects, progressing from building custom robotic arms (5 to 7 degrees of freedom) to writing all necessary software (utilizing the Robotics Operating system, ROS). Teams are required to implement and customize general concepts for their selected tasks. Working systems will autonomously operate and demonstrate their capabilities during final presentations.

We are at the beginning of a historic transformation to decarbonize our energy system. This course introduces the basics of power systems analysis: phasor representation, 3-phase transmission system, transmission line models, transformer models, per-unit analysis, network matrix, power flow equations, power flow algorithms, optimal powerflow (OPF) problems, unbalanced power flow analysis and optimization,swing dynamics and stability.

This class introduces information measures such as entropy, information divergence, mutual information, information density, and establishes the fundamental importance of those measures in data compression, statistical inference, and error control. The course does not require a prior exposure to information theory; it is complementary to EE 126a.

Social networks, the web, and the internet are essential parts of our lives, and we depend on them every day. CS/EE/IDS 143 and CMS/CS/EE/IDS 144 study how they work and the "big" ideas behind our networked lives. In this course, the questions explored include: Why is an hourglass architecture crucial for the design of the Internet? Why doesn't the Internet collapse under congestion? How are cloud services so scalable? How do algorithms for wireless and wired networks differ? For all these questions and more, the course will provide a mixture of both mathematical analysis and hands-on labs. The course expects students to be comfortable with graph theory, probability, and basic programming.

Students are expected to execute a substantial project in networking, write up a report describing their work, and make a presentation.

This is a research-oriented course meant for undergraduates and beginning graduate students who want to learn about current research topics in networks such as the Internet, power networks, social networks, etc. The topics covered in the course will vary, but will be pulled from current research in the design, analysis, control, and optimization of networks.

Content will vary from year to year, at a level suitable for advanced undergraduate or beginning graduate students. Topics will be chosen according to the interests of students and staff. Visiting faculty may present all or portions of this course from time to time.

Foundations of circuit theory-electric fields, magnetic fields, transmission lines, and Maxwell's equations, with engineering applications.

Part a: Subsystem Design: Students will be exposed to design for subsystem electronics in the space environment, including an understanding of the space environment, common approaches for low cost spacecraft, atmospheric / analogue testing, and discussions of risk. Emphasis on a practical exposure to early subsystem design for a TRL 3-4 effort. Part b: Subsystems to System Interfacing: Builds upon the first term by extending subsystems to be compatible with "spacecraft", including a near-space "flight" of prototype subsystems on a high-altitude balloon flight. Focus on qualification for the flight environment appropriate to a TRL 4-5 effort. Not offered 2024-25.

Introduction to the theory, algorithms, and applications of automated learning. How much information is needed to learn a task, how much computation is involved, and how it can be accomplished. Special emphasis will be given to unifying the different approaches to the subject coming from statistics, function approximation, optimization, pattern recognition, and neural networks.

This course focuses on current topics in machine learning research. This is a paper reading course, and students are expected to understand material directly from research articles. Students are also expected to present in class, and to do a final project.

Basics of information theory: entropy, mutual information, source and channel coding theorems. Basics of coding theory: error-correcting codes for information transmission and storage, block codes, algebraic codes, sparse graph codes. Basics of digital communications: sampling, quantization, digital modulation, matched filters, equalization.

Fundamentals of linear estimation theory are studied, with applications to stochastic and adaptive signal processing. Topics include deterministic and stochastic least-squares estimation, the innovations process, Wiener filtering and spectral factorization, state-space structure and Kalman filters, array and fast array algorithms, displacement structure and fast algorithms, robust estimation theory and LMS and RLS adaptive fields. Given in alternate years; offered 2024-25.

The course assumes students are comfortable with analysis, probability, statistics, and basic programming. This course will cover core concepts in machine learning and statistical inference. The ML concepts covered are spectral methods (matrices and tensors), non-convex optimization, probabilistic models, neural networks, representation theory, and generalization. In statistical inference, the topics covered are detection and estimation, sufficient statistics, Cramer-Rao bounds, Rao-Blackwell theory, variational inference, and multiple testing. In addition to covering the core concepts, the course encourages students to ask critical questions such as: How relevant is theory in the age of deep learning? What are the outstanding open problems? Assignments will include exploring failure modes of popular algorithms, in addition to traditional problem-solving type questions.

Part a covers the principles of optical photon transport in biological tissue. Topics include a brief introduction to biomedical optics, single-scatterer theories, Monte Carlo modeling of photon transport, convolution for broad-beam responses, radiative transfer equation and diffusion theory, hybrid Monte Carlo method and diffusion theory, and sensing of optical properties and spectroscopy, (absorption, elastic scattering, Raman scattering, and fluorescence). Part b covers established optical imaging technologies. Topics include ballistic imaging (confocal microscopy, two-photon microscopy, super-resolution microscopy, etc.), optical coherence tomography, Mueller optical coherence tomography, and diffuse optical tomography. Part c covers emerging optical imaging technologies. Topics include photoacoustic tomography, ultrasound-modulated optical tomography, optical time reversal (wavefront shaping/engineering), and ultrafast imaging. MedE/EE/BE 168 bc not offered 2024-2025. Part a offered 2024-2025.

Mobile robots need to perceive their environment and localize themselves with respect to maps thereof. They further require planners to move along collision-free paths. This course builds up mobile robots in team-based projects. Teams will write all necessary software from low-level hardware I/O to high level algorithms, using the robotic operating system (ROS). The final systems will autonomously maneuver to reach their goals or track various objectives.

Climate change has already begun to impact life on the planet, and will continue in the coming decades. This class will explore particular causes and impacts of climate change, technologies to mitigate or adapt to those impacts, and the economic and social costs associated with them - particular focus will be paid to distributional issues, environmental and racial justice and equity intersections. The course will consist of 3-4 topical modules, each focused on a specific impact or sector (e.g. the electricity or transportation sector, climate impacts of food and agriculture, increasing fires and floods). Each module will contain lectures/content on the associated climate science background, engineering/technological developments to combat the issue, and an exploration of the economics and the inequities that exacerbate the situation, followed by group discussion and synthesis of the different perspectives.

This course will explore the techniques and applications of nanofabrication and miniaturization of devices to the smallest scale. It will be focused on the understanding of the technology of miniaturization, its history and present trends towards building devices and structures on the nanometer scale. Technology and instrumentation for nanofabrication as well as future trends will be described. Examples of applications of nanotechnology in the electronics, communications, data storage, sensing and biotechnology will be analyzed. Students will understand the underlying physics and technology, as well as limitations of miniaturization.

Principles of semiconductor electronic structure, carrier transport properties, and optoelectronic properties relevant to semiconductor device physics. Fundamental performance aspects of basic and advanced semiconductor electronic and optoelectronic devices. Topics include energy band theory, carrier generation and recombination mechanisms, quasi-Fermi levels, carrier drift and diffusion transport, quantum transport.

The course focuses on the design and implementation of modern CPUs and microcontrollers. The topics covered in addition to basic CPU architecture include caching and cache controllers, memory management and virtual memory, pipelining CPU operations, VLIW CPUs, branch prediction, and hardware multi-threading. The emphasis is on the practical aspects of CPU design such as timing, testing, and power use. There is significant laboratory work in which the students are expected to design and implement the systems discussed in the class.

Students will learn to use an Arduino microcontroller to interface sensing and actuation hardware with the computer. Students will learn and practice engineering design principles through a set of projects. In part a, students will design and implement biosensing systems; examples include a pulse monitor, a pulse oximeter, and a real-time polymerase-chain-reaction incubator. Part b is a student-initiated design project requiring instructor's permission for enrollment. Enrollment is limited based on laboratory capacity.

Generation, manipulations, propagation, and applications of coherent radiation. The basic theory of the interaction of electromagnetic radiation with resonant atomic transitions. Laser oscillation, important laser media, Gaussian beam modes, the electro-optic effect, nonlinear-optics theory, second harmonic generation, parametric oscillation, stimulated Brillouin and Raman scattering. Other topics include light modulation, diffraction of light by sound, integrated optics, phase conjugate optics, and quantum noise theory. Part c not offered 2024-25.

Advanced topics in robotic motion planning and navigation, including inertial navigation, simultaneous localization and mapping, Markov Decision Processes, Stochastic Receding Horizon Control, Risk-Aware planning, robotic coverage planning, and multi-robot coordination. Course work will consist of homework, programming projects, and labs. Given in alternate years.

Special problems relating to electrical engineering. Primarily for graduate students; students should consult with their advisers.