# Doctoral Qualifying Examination (DQE)

NOTE: In the topics listed below, the emphasis is meant to be on FUNDAMENTAL PRINCIPLES, and not on dry facts. Proper understanding of these principles, in the familiar context outlined below, should enable one to apply them to less familiar situations.

## Area 1: Circuits and Electronics

- Resistors, capacitors, inductors, ideal transformers, independent sources, dependent sources and operational amplifiers
- Charge, current, voltage, and power
- Kirchhoff's voltage and current laws
- Node and mesh analysis
- Analysis of RL, RC and RLC circuits (up to second order) using differential equations
- Natural and forced response
- Linearity and superposition; Thevenin and Norton equivalents
- Phasor analysis
- Transfer functions, the complex plane, poles and zeros
- Frequency response and Bode plots
- Resonant circuits
- Diodes and diode circuits
- MOS and bipolar transistor characteristics
- Basic logic gate circuits (CMOS, TTL, ECL)
- Noise margins, logic delay, rise and fall times, fanin and fanout
- Circuits for latches and flip-flops
- Transient response of logic gate circuits
- Small-signal equivalent circuits for diodes and transistors
- Single-transistor amplifiers and differential pairs, and their dc bias analysis, large-signal analysis, small-signal analysis and frequency response
- Circuits using operational amplifiers

## Area 2: Signals, Systems, and Communications

- Continuous-time and discrete-time systems
- Linear time-invariant systems
- Convolution
- Fourier series
- Continuous-time Fourier transform
- Discrete-time Fourier transform
- Filters and difference and differential equations
- One-sided and two-sided Laplace transforms (including the handling of initial conditions)
- One-sided and two-sided z-transforms (including the handling of initial conditions)
- Time and frequency characteristics of linear time-invariant systems
- Frequency domain analysis
- Transfer function
- Sampling theorem
- Frequency response, Bode plots
- Filtering, allpass, minimum-phase, linear phase systems
- Linear feedback systems
- Stability
- Gain and phase margin
- State-space analysis of continuous-time and discrete-time systems
- Analysis of basic communication systems
- Amplitude modulation
- Pulse amplitude modulations (PAM), pulse code modulation (PCM)
- Demodulation/detection
- Multiplexing signals: time division multiplexing (TDM), frequency division multiplexing (FDM)
- Elementary probability, sample spaces
- Discrete and continuous random variables
- Distribution functions (Bernoulli, Poisson, geometric, binomial, normal, exponential)
- Conditional probability and Bayes's formula
- Independent events and random variables
- Expectation, conditional expectation
- Covariance, variance, correlation

## Area 3: Solid-State Devices and Electromagnetics

- Electronic classification of solids: metals, semiconductors, insulators
- Density-of-states, Fermi-Dirac distribution function, quasi-Fermi levels
- Donors and acceptors, electrons and holes, majority and minority carrier
- Drift and diffusion, fundamental transport equations
- Recombination and generation
- P-N junctions: I-V characteristics and small-signal models, breakdown
- Bipolar junction transistors: Basic structure and operation, I-V characteristics and small-signal models
- MOS devices: C-V characteristics of MOS capacitors, accumulation, depletion, inversion, threshold voltage, I-V characteristics, and small-signal models
- Fundamental fabrication processes: photolithography, oxidation, epitaxy, diffusion, ion implantation
- Electric and magnetic fields
- Gauss, Coulomb, Ampere, Biot-Savart laws
- Electromotive force; magnetomotive force
- Current, current density, conservation of charge
- Current element; dipole
- Ohm's law, conductivity, electric power density
- Faraday's law, Maxwell's equations
- Transmission lines; wave propagation
- Standing waves; impedance matching
- Poynting theorem: real, complex
- Plane waves; polarization: linear, circular
- Snell's laws

## Area 4: Digital Computing Systems

- Elementary logic design
- Digital coding, parity, error correction
- Switching functions, truth tables, boolean algebra.
- Logic gates, canonical forms, K-maps and 2-level logic minimization
- Digital building blocks
- Decoders, multiplexers, encoders, logic arrays, read-only memory
- Latches, flip-flops, setup and hold times
- Registers, shift registers, counters, register files, read-write memories
- State machine design
- Synchronous and asynchronous systems, sequential systems
- State transition diagrams, finite-state machines, state minimization
- Computer architecture
- Data paths and control, busses, bit slices, register transfer language
- Microcode, microprogrammed controllers, hardwired controllers
- Instruction set architecture, assembly language, CPU, main memory, cache, I/O, interrupts
- Fundamental data structures and algorithms
- Arrays, linked lists, stacks, hash tables, queues, trees
- Sorting, searching, storage management
- Software engineering and operating systems concepts
- Basic programming and use of compilers/interpreters; operator precedence, naming, control structures, nesting and scope, definition of new data structures; subroutines, iteration, recursion, exception handling; virtual memory, processor scheduling, process management, interprocess communication, device management, file systems

## Area 5: Networking

- Basic probability and combinatorics
- Bernoulli and Poisson processes
- Binomial, geometric, exponential distributions
- Error detecting and correcting codes
- 1D and 2D parity check codes
- CRC check codes
- Hamming codes
- Multiple access resolution protocols
- ALOHA
- Slotted ALOHA / round-based methods
- Carrier sensing MAC protocols
- CDMA
- Routing and spanning tree algorithms
- Minimum spanning tree
- Dijkstra's algorithm
- Bellman-Ford / distance-vector algorithms
- Reliable transfer protocols
- Alternating-bit protocol
- Selective repeat
- Go-back-n
- Finite state methods
- Congestion and flow control
- Fluid models of congestion collapse
- Flow control (application of Little's law)
- AIMD adaptive congestion control
- Queueing and fairness
- FIFO queuing (M/M/k/n queueing systems)
- Round-robin
- Virtual clock
- (Weighted) fair queueing
- Markov model representations of queueing systems
- Max-min fairness
- Network analysis
- Little's law
- Kleinrock's independence approximation

## Area 6: Systems Biology and Neuroengineering

- Biomolecular sequence alignment
- Building of phylogenetic trees
- Gene prediction
- Biomolecular structure prediction
- Analysis of microarray data
- Modeling of biomolecular networks
- Hodgkin-Huxley neuron
- Reduced Hodgkin-Huxley models
- Integrate-and-fire neuron
- Stimulus representation and the neural code
- Algorithms for stimulus recovery
- Synaptic plasticity and learning algorithms
- Computation by excitatory and inhibitory networks