**This page is about the PhD qualifying exam.**

Class registration is required to take the qualifying examination.

Students must be admitted to the ECE graduate (PhD or Master) program on a full standing status with the Graduate College in order to appear for the qualifying examination.

Students who pursue a PhD degree part-time are required to appear for the qualifying exam in the semester following registration of 24 PhD semester credit hours (including independent study courses and ECE 599). This requirement is equivalent to two semesters of full time course work.

Master’s students in ECE may petition to appear in the qualifying examination if they have completed at least one calendar year of residence and have a GPA of 3.5 or higher.

Students are required to pass area examinations in two areas.

Students may sit for the qualifying exam a maximum of two times. Second attempts must be made in 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 are not allowed to register for extra areas other than the number required during the second attempt.

Students must register for the examination in Room 1020 SEO by the registration deadline. You must specify the areas at the time of registration.

Students must make their first attempt in the first April after their first semester of enrollment. If a second attempt is needed, it must be made at the next consecutive exam date. Students who fail to pass two areas after their second sitting will be expelled from the graduate program. Students who fail to appear for the exam in the first April after their first semester of enrollment will be expelled from the graduate program.

Each area of the examination lasts two hours.

Areas of the examination are based on upper-level undergraduate and beginning graduate level materials.

Exam questions are based on a publicly announced list of required topics and suggested reading materials, rather than specific ECE courses.

Students are to remain in the examination room during the 15 minute intervals between examination periods.

Students are to leave their notes and other reading material at a designated place in the examination room before the start of the examination. Students will not have access to this material during breaks.

All examinations are closed book. Students are permitted to bring a scientific calculator and no programmable calculators are allowed. Cell phone use in the examination room is not allowed.

The order of the papers is determined by the Director of Graduate Studies prior to the exam date. It will be revealed on the exam date by the faculty and staff supervising the examination.

Students are required to return their examination paper, answer book, and scratch paper at the end of each examination period.

Any student who leaves the examination room unescorted will not be allowed to return and complete the remainder of the examination.

Each student is assigned a code number for the qualifying examination. She or he must not write his/her name or social security number anywhere on the examination paper, answer book, or other papers used in the examination. The code number is the only form of identification that should appear on any testing materials.

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 DGS will present the appeal to the Graduate Committee for reconsideration and possible re-evaluation.

#### QUALIFYING EXAMINATION AREA

**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.

**Courses helpful in the 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.

**Typical references:**

- A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing, 2nd Edition, Prentice Hall, 1999.
- J. G. Proakis and D. Manolakis, Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, Prentice Hall, 1996.
- A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems, 2nd Edition, Prentice Hall, 1997.
- D. Graupe, Time Series Analysis, Identification and Adaptive Filtering, 2nd Edition, Kreiger Publishing, 1989.
- S. Kay, Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory, Prentice Hall, 1993.
- S. K. Mitra, Digital Signal Processing: A Computer-Based Approach, 3rd Edition, McGraw-Hill, 2006.

**Major topics:**

- Probability and random processes: Basic probability, random variables, expectations, moment-generating functions, transformation of random variables, random processes, Gaussian random process, stationarity (wide-sense, strictly, and cyclo- stationary processes), correlation, power spectral density, representation of bandpass processes, ergodicity, MMSE (Wiener) filtering.
- Fourier analysis and analog communication: Fourier series, Fourier transforms, time averages, amplitude modulation, frequency modulation, reception in noise in analog communication systems.
- Digital communication systems: Sampling, pulse code modulation, binary and M-ary modulation, signal space representations, optimum reception of signals, probability of error calculation.
- Source coding and basic information theory: Quantization, Huffman coding, entropy of discrete sources, discrete channel mutual information, channel capacity.

**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 311 and ECE 341.

**Typical references:**

- J. G. Proakis, Digital Communications, 4th Edition, McGraw-Hill, 2001.
- A. Papoulis and S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th Edition, McGraw-Hill, 2002.
- B. P. Lathi, Modern Digital and Analog Communications, 3rd Edition, Oxford University Press, 1998.
- S. Haykin, Communication Systems, 4th Edition, Wiley, 2000.
- J. G. Proakis and M. Salehi, Communication Systems Engineering, 2nd Edition, Prentice Hall, 2002.

**Major topics:**

- Causality; time invariance; linearity; superposition principle; 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.
- z-transform; z-transform analysis of discrete-time control systems; sampled-data systems; zero-order hold and first-order hold.
- Stability analysis; state variable description of continuous and discrete time systems; matrix algebra; state-space representation of systems; state variable description; linear operators; impulse response matrix; time domain solution of linear matrix differential and difference equations.
- Controllability; observability; reducible and irreducible realizations; state feedback; state observers; Lyapunov stability.

**Courses helpful in the 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 ECE 310 and ECE 350.

**Typical references:**

- B. C. Kuo and F. Golnaraghi, Automatic Control Systems, 8th Edition, John Wiley, 2002.
- R. C. Dorf and R. H. Bishop, Modern Control Systems, 10th Edition, Prentice Hall, 2005.
- G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, 3rd Edition, Prentice Hall, 1998.
- P. J. Antsaklis and A. N. Michel, Linear Systems, McGraw-Hill, 1997.
- C. T. Chen, Linear System Theory and Design, 3rd Edition, Oxford University Press, 1998.
- K. Ogata, Discrete Time Control Systems, 2nd Edition, Prentice Hall, 1995.

**Major topics:**

- Static and dynamic fields, Poisson’s and Laplace equations, Maxwell’s equations in time and frequency domains, potentials, and solutions to Helmholtz equation.
- Waves and wave propagation, scattering and diffraction, power and energy.
- Microwave circuits, transmission lines, simple waveguide structures, impedance matching, and microwave circuit elements.
- Antennas radiation, antenna parameters, simple antennas and radiating elements, and antenna arrays.

**Courses helpful in the 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.

**Typical references:**

- W. L. Stutzman, Antenna Theory and Design, 2nd Edition, Wiley, 1997.
- C. A. Balanis, Advanced Engineering Electromagnetics, Wiley, 1989.
- A. Ishimaru, Electromagnetic Wave Propagation, Radiation and Scattering, Prentice Hall, 1991.
- R. F. Harrington, Time-Harmonic Electromagnetic Fields, Wiley, 2001.
- R. E. Collin, Foundations of Microwave Engineering, 2nd Edition, Wiley-IEEE, 2000.
- P. A. Rizzi, Microwave Engineering: Passive Circuits, Prentice Hall, 1988.

**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; graded 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.

**Courses helpful in the 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.

**Typical references:**

- B. Streetman and S. Banerjee, Solid State Electronic Devices, 7th Edition, Prentice Hall, 2014.
- R. Pierret, Semiconductor Device Fundamentals, Prentice Hall, 1996.
- S. M. Sze, Physics of Semiconductor Devices, 3rd Edition, Wiley, 2007.

**Major topics:**

- Instruction set designs: ISA classification, addressing modes, operands and operations.
- Pipelining and superscalar designs: Basic issues in pipelining, out-of-order execution techniques including scoreboarding and Tomasulo algorithms, branch prediction techniques, and multi-threading techniques.
- Memory hierarchy designs: Cache organizations, cache performance, DRAM memory, and virtual memory systems.
- Multiprocessor architecture: Taxonomy of parallel architectures, cache coherence.
- Interconnection networks.
- I/O devices and peripherals: Basic I/O issues such as DMA and interrupts, RAID systems.
- Performance evaluation metrics: Execution time, CPI, throughput, and speedup.

**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 267 and ECE 366.

**Typical references:**

- J. Hennessy and D. Patterson, Computer Architecture: A Quantitative Approach, 3rd Edition, Morgan Kaufmann, 2002.
- D. Culler, J. P. Singh, and A. Gupta, Parallel Computer Architecture: A Hardware/Software Approach, Morgan Kaufmann, 1998.

**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.

**Courses helpful in the 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.

**Typical references:**

- V. P. Nelson, H. T. Nagle, B. D. Carroll, and J. D. Irwin, Digital Logic Circuit Analysis and Design, Prentice Hall, 1995.
- J. Wakerly, Digital Design: Principles and Practices, 4th Edition, Prentice Hall, 2006.
- J. M. Rabaey, A. Chandrakasan, and B. Nikolic, Digital Integrated Circuits: A Design Perspective, 2nd Edition, Prentice Hall, 2003.
- N. H. E. Weste and D. Harris, CMOS VLSI Design: A Circuits and Systems Perspective, 3rd Edition, Addison Wesley, 2005.

**Major topics:**

- Algorithms analysis techniques: Correctness and complexity, proving techniques, NP-completeness.
- Algorithm design approaches: Recursion, divide-and-conquer, dynamic programming, greedy methods, and solution searching methods.
- Applied algorithms: Sorting, searching, graph computations, and string matching.
- Complex data structures: Lists, stacks, queues, sets, hash tables, trees, heaps, and graphs.

**Courses helpful in the exam area:**

- CS 401: Computer Algorithms I
- ECE 566: Parallel Processing

- In addition students are expected to be familiar with basic material covered in prerequisite courses such as CS 201 and CS 202.

**Typical references:**

- T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to Algorithms, McGraw-Hill, 1990.
- M. A. Weiss, Data Structures & Algorithm Analysis in C++, 2nd Edition, Addison Wesley, 1999.
- A. Grama, G. Karypis, V. Kumar, and A. Gupta, Introduction to Parallel Computing, 2nd Edition, Addison Wesley, 2003.

**Major topics:**

- 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

- 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

**Courses helpful in the exam area:**

- ECE 412: Introduction to Filter Synthesis
- ECE 445: Analysis and Design of Power Electronic Circuits

**Typical references:**

- W.K. Chen, Active Network Analysis, Teaneck, N.J.: World Scientific, 1991.
- W.K. Chen, Passive and Active Filters: Theory and Implementations, New York: John Wiley, 1986.
- M. E. Van Valkenburg, Analog Filter Design, New York: Holt, Rinehart and Winston, 1982.
- R.W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, Kluwer Academic Publishers, 2001.
- P.T. Krein, Elements of Power Electronics, Oxford University Press, 1998.
- B.J. Baliga, Power Semiconductor Devices, PWS Publishing Company, 1995.