Qualifying Examination
Introduction
The qualifying examination is designed to assess a PhD student’s readiness to undertake dissertation research in electrical and computer engineering.
This page is designed to provide specific information about the qualifying exam for current ECE doctoral students. If you have any questions about the exam that are not answered by the content on this page, please contact your faculty advisor or the student affairs office.
About the Qualifying Examination
PhD students must pass two topic areas on the qualifying examination to complete this requirement. (See the accordions below for information on each topic area.) Students have two hours to complete each area of the exam, which are based on material from upper-level undergraduate and beginning graduate coursework. The area-specific questions on the exam are based on a publicly announced list of required topics and suggested reading materials, rather than on specific ECE courses.
Requirements and Registration for the Qualifying Exam
Students seeking to take the qualifying examination must have full-standing status with the UIC Graduate College in the ECE master’s or doctoral program. They must be registered for coursework during the semester in which the exam is taken.
Students who are pursuing a PhD full-time must make their first attempt at the qualifying examination in the first April after their initial semester of enrollment.
Students who are pursuing a PhD part-time are required to take the qualifying exam in the semester following registration for a total of 24 PhD semester credit hours, including independent-study courses and ECE 599. In other words, they will take the exam after completing the equivalent of two semesters of full-time coursework.
Master’s students in ECE may petition to take the qualifying examination if they have completed at least one calendar year of residence and have a GPA of 3.5 or higher.
Students must register for the examination in Room 1020 SEO by the registration deadline, which is communicated in each semester by the student affairs office.
When students register for the exam, they must specify the areas in which they plan to take the exam.
First and Second Attempts
Students may sit for the qualifying exam a maximum of two times. Second attempts must be made at the time of the next consecutive offering of the examination. Students who pass any area of the examination during the first attempt are not required to re-take that area in the subsequent examination.
Students may elect to take one or two area examinations during the first attempt. Students who require a second attempt are not allowed to register for extra areas beyond the number required. (In other words, students who pass one area and fail one area on the first attempt may only take one area on the second attempt.)
Students who fail to pass two areas after their second attempt at the qualifying exam will be expelled from the graduate program. Full-time PhD students who fail to appear for the exam in the first May after their initial semester of enrollment will be expelled from the program.
Examination Procedure and Rules
Each student is assigned a code number for the qualifying examination. Students must not write their names or social security numbers anywhere on the examination papers, answer books, or other papers used in the examination. The code number is the only form of identification that should appear on any testing materials.
Students must remain in the examination room during the 15-minute intervals between examination periods. Before the start of the examination, students must leave their notes and other reading material in a place in the examination room designated by the proctor. Students will not have access to this material during breaks. Any student who leaves the examination room unescorted will not be allowed to return and complete the remainder of the examination.
Qualifying examinations are closed-book. Students may bring a scientific calculator, but no programmable calculators are allowed. Cell phone use in the examination room is not allowed.
Students are required to return their examination papers, answer books, and scratch paper at the end of each examination period.
Appeals related to the grading or results of the exam should be made by the student’s advisor to the director of graduate studies. The director of graduate studies will present the appeal to the Graduate Committee for reconsideration and possible re-evaluation.
Qualifying Examination Topic Areas
Algorithms and data structures
Note: All chapter/section pointers below refer to the Cormen at al. (4th edition) textbook given below. If someone has a different edition, the actual topics referenced below via Chap./Sec. numbers can be found in the Table of Contents of the textbook given in the appendix following this description, and then found in the edition one has.
Major topics:
Algorithms analysis techniques: Correctness and complexity, proving techniques (Chaps. 1-3).
Algorithm design approaches: Recursion, divide-and-conquer (Secs 4.1-4.6), dynamic programming (Chap. 14), greedy methods (Chap. 15).
Applied algorithms: Sorting (Chaps. 6-8), searching (Secs 9.1 and 9.3), graph computations (Chaps. 20-22).
Complex data structures: Lists, stacks, queues, sets, hash tables, trees, heaps, and graphs (Chaps. 10-13).
Typical references:
- Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, McGraw-Hill, 4th Edition, 2022.
- Weiss, Data Structures & Algorithm Analysis in C , 2nd Edition, Addison Wesley, 1999.
Courses helpful in this exam area:
- CS 401: Computer Algorithms I
- ECE 565: Physical Design Automation (aka VLSI CAD Algorithms) (discusses many basic algorithms, inculcates algorithmic thinking)
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as CS 151 and CS 251.
Please see appendix from the Table of Contents of the Cormen, et al. 4th Edition Textbook
Communications
Major topics:
Probability and Random Processes: discrete and continuous random variables, discrete and continuous random vectors, expectations, conditional expectations, conditional distributions, moment-generating functions, transformations of random variables, law of large numbers, central limit theorem, random processes, Gaussian random process, stationarity (wide-sense, strictly, and cyclo- stationary processes), correlation, independence, power spectral density, representation of bandpass processes, ergodicity, MMSE (Wiener) filtering, hypothesis testing, MMSE estimation, random processes through linear time-invariant systems, convergence (in distribution, probability, almost surely, in mean square).
Fourier Analysis and Analog Communications: Fourier series, Fourier transforms in continuous and discrete time, DFT and FFT, sampling and reconstruction of bandlimited signals, amplitude modulation, frequency modulation, single-sideband modulation (SSB), double-sideband modulation (DSB), reception in noise in analog communication systems.
Digital Communications: sampling, quantization, signal space representation, baseband representation, MAP and ML signal detection, probability of error calculation, M-ary ASK, PSK, FSK, QAM modulations, optimal receiver design, matched filter.
Basic Information Theory: Quantization, Huffman coding, entropy of discrete sources, differential entropy of continuous sources, mutual information, capacity of discrete channels, capacity of Gaussian channels.
Typical references:
- Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th Edition, McGraw-Hill, 2002. All, except Markov Chains.
- Random Processes for Engineers 1st Edition, by Bruce Hajek. All, except Markov processes and martingales.
- Proakis and M. Salehi, Communication Systems Engineering, 2nd Edition, Prentice Hall, 2002. All, except Wireless Communications.
- Cover and J. Thomas, Elements of Information Theory, 2nd Edition, Wiley, 2005. Chapter 2 (entropy, mutual information definitions 2.1-2.5), Chapter 5 (Huffman coding 5.6, 5.7), Chapter 7 (discrete channel mutual information and capacity, 7.1-7.7), Chapter 9 (Gaussian channel capacity, 9.1).
Courses helpful in the exam area:
- ECE 432: Digital Communications
- ECE 530: Random Signal Analysis
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 310 (signals & systems), ECE 311 (introduction to communications), and ECE 341 (probability & basics of random processes).
Computer architecture
Major topics:
Instruction set designs: Study the classification of Instruction Set Architectures (ISA), such as RISC, CISC, VLIW, and EPIC. Understand the different addressing modes (immediate, direct, indirect, register, base+offset, etc.) and how they affect instruction flexibility and performance. Learn the types of operands (registers, memory locations, constants) and operations (arithmetic, logical, control flow, data movement) supported by various ISAs. Analyze the trade-offs between instruction encoding complexity, code density, and execution efficiency.
Pipelining and superscalar designs: Understand the principles of pipelining, including pipeline hazards, and techniques for resolving them (forwarding, stalling, hazard detection). Study superscalar processor design, which involves issuing multiple instructions per cycle, and dynamic scheduling methods such as scoreboarding and Tomasulo’s algorithm for out-of-order execution. Examine branch prediction techniques (static and dynamic), including one-bit/two-bit predictors, and hybrid predictors.
Memory Hierarchy Designs: Dive into the structure and behavior of multi-level cache hierarchies, including direct-mapped, set-associative, and fully-associative caches. Learn how cache performance is influenced by block size, associativity, replacement policies, and write policies. Understand virtual memory concepts such as page tables, etc.
Performance Evaluation Metrics: Learn how to analyze and compare computer performance using metrics such as execution time, cycles per instruction (CPI), throughput, and speedup. Understand the impact of instruction mix, memory access latency, and pipeline efficiency on overall performance. Be able to apply Amdahl’s Law for theoretical performance analysis and scalability prediction.
Multiprocessor architecture: architecture of multicore and multi-threaded processors, logic organization of parallel platforms, shared memory multiprocessors, scalable multiprocessors, cache coherence and memory consistency.
Interconnection networks: communication models of multiprocessors, static and dynamic interconnection networks, bus-based and crossbar networks.
Typical references:
- Hennessy and D. Patterson, Computer Architecture: A Quantitative Approach, 3rd Edition, Morgan Kaufmann, 2002.
- Culler, J. P. Singh, and A. Gupta, Parallel Computer Architecture: A Hardware/Software Approach, Morgan Kaufmann, 1998.
Courses helpful in the exam area:
- ECE 466: Advanced Computer Architecture
- ECE 569: High Performance Processors and Systems
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 266, ECE 267, and ECE 366.
Controls
Major topics:
Frequency-domain methods: Laplace transform; transfer function; block diagrams; impulse response; frequency response; steady-state response; transient response; convolution; BIBO stability; Routh-Hurwitz criterion; Nyquist criterion; root-locus methods; Bode plots; feedback control.
Digital control: z-transform; z-transform analysis of discrete-time control systems; sampled-data systems; zero-order hold and first-order hold; z-domain control design; digital implementation of analog controllers.
Linear systems: causality; time invariance; linearity; state variable description of continuous and discrete time systems; linearization; impulse response matrix; time domain solution of linear matrix differential and difference equations; internal and BIBO stability; controllability and observability; reducible and irreducible realizations; state feedback; state observers and output feedback.
Typical references:
Frequency-domain methods:
- (Main reference) C. Dorf and R. H. Bishop, Modern Control Systems, 13th Edition, Pearson, 2016.
- Kuo and F. Golnaraghi, Automatic Control Systems, 8th Edition, John Wiley, 2002.
Digital control:
- (Main reference) B. Samanta, Introduction to Digital Control: An Integrated Approach, Springer, 2024. (Available online.) Chapters 1–12.
- Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, 3rd Edition, Ellis-Kagle Press, 1998. Chapters 1–7.
Linear systems:
- (Main reference) J. P. Hespanha, Linear Systems Theory, 2nd Edition, Princeton University Press, 2018. Chapters 1–9 and Chapters 11–17.
- Chen, Linear System Theory and Design, 3rd Edition, Oxford University Press, 1998. Chapters 1–8.
- S. Bay, Fundamentals of Linear State Space Systems, WCB/McGraw-Hill, 1999. (Available online.) Chapters 1–8, Chapter 9.1–9.3, and Chapter 10.
Courses helpful in this exam area:
- ECE 451: Control Engineering
- ECE 550: Linear Systems Theory and Design
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as MATH 310, ECE 310, and ECE 350.
data science
Major topics:
Pattern Recognition: Generative modeling using probability density functions, naïve-Bayesian methods, logistic regression, Gaussian-mixture modelling and K-means clustering (or vector quantization), dimensionally reduction and Principal Component Analysis (PCA).
Statistical inference: hypothesis testing, maximum likelihood estimation, Bayesian inference, least squares, Fisher information, Cramer-Rao bound, central limit theorem
Information: entropy, Kraft’s inequality, compression, KL divergence, cross-entropy, universal compression, mutual information, Fano’s inequality
Learning: Chernoff bound, concentration of the empirical distribution, PAC learning, classification, clustering, uniform concentration and generalization, complexity and VC dimension, bias-variance dilemma, regularization
Neural networks: mathematical models of a neuron, perceptrons, optimization, the backpropagation algorithm, associative memory, Hopfield networks, support vector machines, convolutional networks, deep learning
Typical references:
- Information Theory, Inference and Learning Algorithms, by MacKay
- Elements of Information Theory, by Cover and Thomas
- Understanding Machine Learning: From Theory to Algorithms, by Shalev-Shwartz and Ben-David
- Foundations of Data Science by Blum, Hopcroft, and Kannan
- All of Statistics, by Wasserman
- Deep Learning, by Goodfellow, Bengio, and Courville
- Introduction to Pattern Recognition, Sergios Theodoridis
Courses helpful in this exam area:
- ECE 407 Pattern Recognition I
- ECE 491 Information and Learning
- ECE 559 Neural Networks
Other courses such as ECE 418 Statistical Digital Signal Processing, or ECE 534 Elements of Information Theory also can be useful.
Students are expected to be proficient in the prerequisite areas, in particular probability and statistics (ECE 341), calculus (MATH 210), and linear algebra (MATH 310).
Digital systems and VLSI design
Major topics:
Combinational logic minimization techniques.
Finite state machine (FSM) synthesis (Moore, Mealy).
Synthesis and analysis of synchronous and asynchronous sequential circuits.
State minimization and state assignment techniques.
Logic design using MUXs, decoders, registers, shift registers, and PLAs.
Clocking issues: Clock methods, period determination, skew and jitter, and types of timing – edge triggered, two phase timing, and pulsed timing.
Introduction to IC building blocks: Semiconductor devices, and CMOS inverter.
Static and dynamic circuit implementation techniques.
VLSI circuit design issues of latches, flip-flops, and registers.
Basic concepts of integrated circuits implementation strategies: Custom, semi-custom, cell-based, and array-based design approaches.
Typical references:
- Digital Logic Circuit Analysis and Design, by Victor P. Nelson, H. Troy Nagle, Bill D. Carroll, David Irwin, Prentice Hall, 1995 (ISBN-10: 0134638948; ISBN-13: 978-134638942).
- Basic gates, minimization, K-Maps etc. (Chapters 1.1, 1.3-1.4, 2.1-2.2, 2.5, 3.1-3.8)
- Advanced Combinational Optimization (QM + Petrick) (Chapters 3.9-3.10)
- Component-Based Combinational Circuit Synthesis (Logic design using MUXs, decoders, registers, shift registers, and PLAs) (Chapters 4.2, 4.4, 5.1-5.5)
- Synchronous Sequential Circuits (FSM, Mealy, Moore FSMs, Synthesis and Analysis of Sync. Seq. Machines, State Minimization and State Assignment Techniques) (Chapters 8.1-8.4, 9.1-9.4)
- Asynchronous Sequential Circuits (Chapters 10.1 – 10.6)
- Digital Design: Principles and Practices, Fourth Edition, Prentice Hall, 2006, (ISBN-10: 0-13-1863894, ISBN-13: 978-0131863897)
- Basic gates, minimization, K-Maps etc.(Chapter 4)
- Component-Based Combinational Circuit Synthesis (Logic design using MUXs, decoders, registers, shift registers, and PLAs) (Chapters 6.1, 6.2, 6.4, 6.5, 6.7, 6.8, 6.9, 6.10)
- Synchronous Sequential Circuits (FSM, Mealy, Moore FSMs, Synthesis and Analysis of Sync. Seq. Machines, State Minimization and State Assignment Techniques) (Chapters 7.3, 7.4, 7.5 — 7.9)
- Nelson, H. T. Nagle, B. D. Carroll, and J. D. Irwin, Digital Logic Circuit Analysis and Design, Prentice Hall, 1995.
- Wakerly, Digital Design: Principles and Practices, 4th Edition, Prentice Hall, 2006.
- Rabaey, A. Chandrakasan, and B. Nikolic, Digital Integrated Circuits: A Design Perspective, 2nd Edition, Prentice Hall, 2003.
- E. Weste and D. Harris, CMOS VLSI Design: A Circuits and Systems Perspective, 3rd Edition, Addison Wesley, 2005.
Courses helpful in this exam area:
- ECE 465: Digital Systems Design
- ECE 467: Introduction to VLSI Design
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 265.
Electromagnetics
Major topics:
- Electromagnetic field problems in time and frequency domains
- Vector potentials for Helmholtz equations
- Electromagnetic wave propagation in Cartesian, cylindrical, and spherical coordinates
- Electromagnetic energy and the Poynting vector
- Scattering and diffraction from cylindrical and spherical objects
- Transmission lines; rectangular and circular waveguides; characteristic and wave impedances
- Basic antenna theory and fundamental antenna parameters
- Wire antennas: electric dipole/monopole antenna, loop antenna, helical antenna, and Yagi antenna
- Planar antennas: microstrip patch antenna and slot antenna
- Antenna array
- Reciprocity theorem; equivalence theorems; Huygens principle; duality and Babinet’s principles
- Friis equation
Typical references:
- A. Balanis, Antenna Theory: Analysis and Design, Wiley, 2016.
- L. Stutzman, Antenna Theory and Design, 2nd Edition, Wiley, 1997.
- A. Balanis, Advanced Engineering Electromagnetics, Wiley, 1989.
- F. Harrington, Time-Harmonic Electromagnetic Fields, Wiley, 2001.
- Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering, Prentice Hall, 1991.
Courses helpful in this exam area:
- ECE 421: Introduction to Antenna Engineering
- ECE 520: Electromagnetic Field Theory
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 322.
Power electronics and electronic circuits
Major topics:
Power Electronic Topologies: Basic isolated and non-isolated dc-dc converters
Power-converter dynamics and control: averaged modeling, stability analysis, voltage- and current-model controls, feedback-control realizations, modulation
Power Electronic Devices
Magnetics: basic high-frequency inductors and transformers, basic magnetics theory for inductor and transformer leading to modeling and equivalent circuit realizations, and design
Power semiconductor switches: switch realizations, device structure and operating principles of power diodes, power MOSFETs, and IGBTs, switching-loss calculations, and snubber design and safe operating area
Electrical Circuit Characterization and Synthesis: Characterization of active networks in frequency and time domains, fundamentals of network synthesis, S-domain transfer functions, frequency response, and elementary filter mathematics.
Filter Synthesis: Filtering; filter types and specifications – ideal filters, magnitude-phase representation, low-pass filters, band-pass filters, high-pass filters, etc.
Filter approximation: Passive and active filter designs
Active amplifier: Fundamentals of operational and differential amplifiers, different types of transistor amplifiers
Typical references:
- W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, Springer Nature, 2020.
- G. Kassakian, D. J. Perreault, G. C. Verghese, and M. F. Sclecht, Principles of Power Electronics, Cambridge University Press, 2023.
- T. Krein, Elements of Power Electronics, Oxford University Press, 2014.
- J. Baliga, Power Semiconductor Devices, PWS Publishing Company, 1995.
- K. Chen, Active Network Analysis, Teaneck, N.J.: World Scientific, 1991.
- Van Valkenburg, Analog Filter Design, New York: Holt, Rinehart and Winston, 1982.
- K. Chen, Passive and Active Filters: Theory and Implementations, New York: John Wiley, 1986.
- S. Sedra, K. C. Smith, T. C. Carusone, and V. Gaudet, “Microelectronic Circuits,” 8th Edition
- Razavi, “Design of Analog CMOS Integrated Circuits,” 2nd Edition.
Courses helpful in this exam area:
- ECE 412: Introduction to Filter Synthesis
- ECE 445: Analysis and Design of Power Electronic Circuits
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 310 and ECE 342.
Quantum
Major topics:
Part I — Core Fundamentals
Quantum Mechanics [1] Solution of the Schrödinger equation for standard potentials, including infinite and finite wells and barriers. Postulates of quantum mechanics — states, observables, measurement, and time evolution. Linear algebra and Hilbert-space formulation: Dirac notation, operators, eigenstates, unitary time-evolution operators. Perturbation theory — time-independent and time-dependent formulations. Angular momentum and spin — addition of angular momentum, spin-½ systems, and Pauli matrices. Identical particles — bosons and fermions.
Condensed Matter Physics [2] Crystal structures and Bravais lattices; reciprocal lattices and Brillouin zones. Phonons and lattice vibrations — dispersion relations and electron–phonon coupling. Band theory: Bloch’s theorem, formation of energy bands and band gaps, and classification of solids as metals, semiconductors, or insulators. Fermi surfaces — definition, properties, and relation to electronic transport and magnetism. Introduction to many-body theory — second quantization, Green’s functions, quasiparticles, and collective excitations such as magnetism and superconductivity.
Atomic, Molecular, and Optical (AMO) Physics and Quantum Optics [3,6] The hydrogen atom and its fine and hyperfine structure. Interaction of atoms with electromagnetic radiation; selection rules and transition probabilities. Rydberg atoms and ions; trapping and cooling mechanisms; optical and magnetic trapping potentials. Classical and quantum descriptions of light — coherent and incoherent states, stimulated emission, and interference.
Part II — Advanced and Specialized Topics
Quantum Algorithms and Information Processing [4] Qubits and quantum states; unitary transformations and quantum gates; density matrices and measurements. Quantum entanglement and its role in computation and communication. Basic quantum algorithms and an introduction to quantum error correction and information theory. Open quantum systems — Choi, Kraus, and Stinespring representations of quantum channels and environmental interactions. Physical error processes, including photon loss, amplitude damping, and dephasing.
Quantum Materials [5] Quantum-mechanical description of the electronic, magnetic, and optical properties of quantum confined materials at the nanoscale. Correlated electron systems, superconductors, magnets, topological materials. Fundamental mechanisms underlying applications in optoelectronics and sensing devices. Overview of synthesis, growth, and nanofabrication techniques for quantum materials.
Quantum Computing, Communication and Networks [6] Single-photon sources and detection. Quantum information protocols implemented via photonic systems, including electron-on-helium, transmon superconducting qubits, and photonic qubits. Bell-state measurements, quantum repeaters, and multipartite entanglement. Applications to clock synchronization and hybrid quantum–classical systems.
Typical references:
- Sakurai, J. J., & Napolitano, J. (2020). Modern Quantum Mechanics (3rd ed.). Cambridge: Cambridge University Press.
- Ashcroft, Neil W., and N. David Mermin. “Solid state physics holt.” Rinehart and Winston, New York 19761 (1976):12.
- Bransden, B.H. and Joachain, C.J. (1983) Physics of Atoms and Molecules. 2nd Edition, Pearson Education, New York.
- Nielsen, M. A., & Chuang, I. L. (2011). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.; Kaye, P., Laflamme, R., & Mosca, M. (2006). An introduction to quantum computing. OUP Oxford; Wong, Thomas G. “Introduction to classical and quantum computing.” E-book (2022).
- “Electronic Properties of Materials.” Part II-IV; Paglione, Butch, Rodriguez. “Fundamentals of Quantum Materials”. Ch. 6, 9, 11; Henini and Rodrigues. “Quantum Materials, Devices, and Applications.” Ch. 2, 5, 6
- Gerry, C., & Knight, P. (2004). Introductory Quantum Optics. Cambridge: Cambridge University Press.; Kono, J. (2022). Quantum Mechanics for Tomorrow’s Engineers. Cambridge: Cambridge University Press.Hajdušek, Michal, and Rodney Van Meter. “Quantum Communications.” arXiv preprint arXiv:2311.02367 (2023).
Courses helpful in this exam area:
- ECE 491 – Quantum Materials and Devices
- ECE 594 Special Topics – Introduction to Quantum Information Science and Engineering
- ECE 594 Special Topics – Quantum Engineering: Quantum Optics and Devices
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 346 and PHYS 421.
Signal processing
Major topics:
Signals and systems: Continuous-time and discrete-time signals and systems, linearity, time-invariance, stability, causality, frequency domain description, continuous-time and discrete-time Fourier transform (CTFT and DTFT), discrete Fourier transform (DFT) and its applications, fast Fourier transform (FFT), linear and circular convolution, sampling of continuous-time signals, sampling theorem and relation between CTFT and DTFT, sampling rate conversion – interpolation and decimation.
z-transform and filter design: z-transform and properties, system function, stability analysis, digital filter design and realization, infinite-duration and finite-duration impulse response (IIR and FIR) filter properties and design, linear convolution using DFT in FIR filter implementation.
Random signals: Random variables, expectations, random vectors, discrete-time random signals (random sequences) and application to discrete-time systems, stationarity of random sequences, autocorrelation and power spectral density of random sequences, spectral factorization.
Optimum processing of signals: Optimum signal estimation, minimum mean squared error estimation, discrete-time Wiener filters, linear prediction and algorithms.
Typical references:
- Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd Edition, Prentice Hall, 1999.
- Proakis and D. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, Prentice Hall, 1996.
- Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd Edition, Prentice Hall, 1997.
- Graupe, Time Series Analysis, Identification and Adaptive Filtering, 2nd Edition, Kreiger Publishing, 1989.
- Kay, Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory, Prentice Hall, 1993.
- Mitra, Digital Signal Processing: A Computer-Based Approach, 3rd Edition, McGraw-Hill, 2006.
Courses helpful in this exam area:
- ECE 417: Digital Signal Processing II
- ECE 418: Statistical Digital Signal Processing
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 310, ECE 317, and ECE 341.
Solid-state electronics
Major topics:
Quantum Mechanics: Schrodinger’s equation; Heisenberg’s principle; solving Schrodinger’s equation in quantum wells with finite and infinite barrier heights (1-dimensional solution); Fermi distribution; typical bandstructures for direct and indirect bandgap materials.
Semiconductors: Crystal structures; lattice parameter; bandgap; density of states; effective density of states; carrier distribution; resistivity; conductance; Hall effect; mobility; intrinsic and extrinsic carrier concentration; Fermi level; equilibrium and non-equilibrium; generation-recombination processes; continuity equation; Poisson’s equation; optical processes in semiconductors; radiative and non-radiative recombination; steady state and transient; drift current; diffusion current.
P-N Junctions: Step junctions; band profile; depletion width; depletion approximation; built in potential; forward and reverse bias; diffusion length; lifetime; diffusion coefficient; drift and diffusion currents; current-voltage relationship; quasi Fermi levels; depletion and diffusion capacitance.
Bipolar Junction Transistors: Concept of emitter, base and collector; band profile; uniform and graded doping in base region; base transit time; emitter injection efficiency; base transport factor; DC current gain (common emitter mode); device configurations (common base, common emitter, common collector); Ebers-Moll model; current-voltage relationship; active, cut-off, reverse active and saturation regions of operation; small signal model.
MOSFETs: Fundamentals of MOS capacitor; accumulation, depletion and inversion regions; capacitance-voltage characteristics (C-V); high frequency and low frequency C-V characteristics; threshold voltage; effects of oxide charges (fixed, interface, mobile) on MOS characteristics, MOSFET, current-voltage relationship, saturation and linear regions of operation; transconductance gain; small signal model; short channel effects.
Typical references:
- Streetman and S. Banerjee, Solid State Electronic Devices, 7th Edition, Prentice Hall, 2014.
- Pierret, Semiconductor Device Fundamentals, Prentice Hall, 1996.
- M. Sze, Physics of Semiconductor Devices, 3rd Edition, Wiley, 2007.
- Kittel, Introduction to Solid State Physics 8th Edition, Wiley, 2005
Courses helpful in this exam area:
- ECE 448: Transistors
- ECE 540: Semiconductor Device Physics
In addition, students are expected to be familiar with basic material covered in prerequisite courses such as ECE 346.