ME or MEng Master of Engineering Master of Electrical Engineering 4 — Questions and Answers
Question 1: In digital communication, what is the Nyquist intersymbol interference (ISI)-free condition for a pulse shaping filter?
- The filter bandwidth equals the symbol rate
- The Fourier transform of the pulse satisfies the Nyquist criterion: Σ H(f - k/T) = T for all f
- The pulse has zero crossings only at multiples of the symbol period T (Correct answer)
- The filter has a brick-wall (rectangular) frequency response
Correct answer: The pulse has zero crossings only at multiples of the symbol period T
A pulse is ISI-free if it equals 1 at t=0 and 0 at all other sampling instants t=nT, which requires zero crossings at all nonzero multiples of T.
Question 2: A PID controller with derivative kick can be avoided by applying the derivative action to:
- The error signal e(t) = r(t) - y(t)
- The process output y(t) only, not the reference r(t) (Correct answer)
- The setpoint r(t) only
- The integral of the error
Correct answer: The process output y(t) only, not the reference r(t)
Applying derivative to y(t) instead of e(t) eliminates the 'derivative kick' that occurs when a step change in setpoint is introduced.
Question 3: In electromagnetic compatibility (EMC), the concept of 'ground loops' causes interference primarily through:
- Capacitive coupling between power and signal planes
- Magnetically induced voltages in loops formed by multiple ground paths (Correct answer)
- Resistive voltage drops in the PCB ground plane
- Radiation from impedance mismatches at connectors
Correct answer: Magnetically induced voltages in loops formed by multiple ground paths
Ground loops act as antenna loops that pick up time-varying magnetic flux, inducing a voltage V = -dΦ/dt = -jωBA in the loop.
Question 4: For a first-order phase-locked loop (PLL), the closed-loop transfer function H(s) = ω_n/(s + ω_n) implies that the PLL:
- Tracks frequency ramp inputs with zero steady-state phase error
- Acts as a low-pass filter for phase deviations with bandwidth ω_n (Correct answer)
- Has a second-order response with defined damping ratio
- Rejects input phase noise at all frequencies
Correct answer: Acts as a low-pass filter for phase deviations with bandwidth ω_n
H(s) = ω_n/(s+ω_n) is a low-pass transfer function; the PLL tracks slow phase changes (below ω_n) and attenuates fast phase noise.
Question 5: Which semiconductor device structure is used in insulated-gate bipolar transistors (IGBTs) to combine high input impedance with low on-state voltage drop?
- MOSFET channel in series with a PNP BJT collector-emitter path (Correct answer)
- Back-to-back thyristor structure with MOS gate control
- Cascoded JFET and bipolar transistor with shared gate
- Dual-gate MOSFET with floating body
Correct answer: MOSFET channel in series with a PNP BJT collector-emitter path
An IGBT uses a MOSFET input stage (high impedance gate) to drive a PNP bipolar transistor output stage, combining MOS controllability with BJT low saturation voltage.
Question 6: In signal processing, the short-time Fourier transform (STFT) is limited by the Heisenberg-Gabor uncertainty principle, which states:
- Time resolution and frequency resolution can both be made arbitrarily small
- Better time resolution requires worse frequency resolution and vice versa (Correct answer)
- The STFT is only applicable to stationary signals
- Increasing window length improves both time and frequency resolution
Correct answer: Better time resolution requires worse frequency resolution and vice versa
The uncertainty principle Δt·Δf ≥ 1/(4π) means a shorter analysis window (better time resolution) broadens the frequency resolution and vice versa.
Question 7: In the design of a microstrip antenna, what is the primary factor that determines the resonant frequency?
- Substrate dielectric constant only
- The patch width and feed location
- The patch length, which must be approximately λ_eff/2 (Correct answer)
- The ground plane size relative to the wavelength
Correct answer: The patch length, which must be approximately λ_eff/2
A rectangular microstrip patch resonates when its length equals approximately half the effective wavelength λ_eff/2, where λ_eff accounts for the effective permittivity.
ME or MEng Master of Engineering Master of Electrical Engineering 4
In digital communication, what is the Nyquist intersymbol interference (ISI)-free condition for a pulse shaping filter?