ME or MEng Master of Engineering Master of Electrical Engineering 5 — Questions and Answers
Question 1: In a switched-mode power supply, the 'right-half-plane (RHP) zero' in the boost converter transfer function is problematic because it:
- Adds 90° phase lead, making the system conditionally stable
- Adds 90° phase lag while increasing gain, limiting achievable control bandwidth (Correct answer)
- Causes output voltage to decrease when duty cycle increases
- Only appears under discontinuous conduction mode (DCM)
Correct answer: Adds 90° phase lag while increasing gain, limiting achievable control bandwidth
An RHP zero increases gain at +20 dB/decade but simultaneously adds phase lag like a pole, constraining the control loop bandwidth to well below the RHP zero frequency.
Question 2: For a linear time-invariant system, the condition for BIBO (bounded-input bounded-output) stability is:
- All poles of the transfer function lie on the imaginary axis
- All poles of the transfer function lie in the open left-half s-plane (Correct answer)
- The impulse response has finite energy (is square-integrable)
- The gain margin is greater than 6 dB
Correct answer: All poles of the transfer function lie in the open left-half s-plane
A continuous-time LTI system is BIBO stable if and only if all poles of H(s) have negative real parts (lie strictly in the left-half plane).
Question 3: In power electronics, what is the purpose of 'dead time' inserted between gate signals of complementary switches in a half-bridge converter?
- To increase switching frequency without increasing losses
- To prevent shoot-through (cross-conduction) where both switches conduct simultaneously (Correct answer)
- To allow soft-switching (ZVS) by providing time for resonance
- To reduce electromagnetic interference by slowing gate transitions
Correct answer: To prevent shoot-through (cross-conduction) where both switches conduct simultaneously
Dead time ensures both high-side and low-side switches are off simultaneously before the complementary switch turns on, preventing a low-impedance short-circuit path.
Question 4: A digital FIR filter has linear phase if and only if its impulse response h[n] satisfies:
- h[n] = -h[N-1-n] (antisymmetric) or h[n] = h[N-1-n] (symmetric) (Correct answer)
- All filter coefficients are equal in magnitude
- The filter order is odd
- The z-transform poles lie on the unit circle
Correct answer: h[n] = -h[N-1-n] (antisymmetric) or h[n] = h[N-1-n] (symmetric)
Linear phase in FIR filters requires the impulse response to be either symmetric (Type I/II) or antisymmetric (Type III/IV) about its midpoint.
Question 5: In optical fiber communications, 'chromatic dispersion' causes pulse broadening because:
- Different wavelength components travel at different group velocities in the fiber (Correct answer)
- The fiber core absorbs power proportional to the square of the optical frequency
- Polarization-mode coupling randomizes pulse arrival times
- Nonlinear Kerr effect creates new frequency components
Correct answer: Different wavelength components travel at different group velocities in the fiber
Chromatic dispersion arises because the fiber's refractive index (and thus group velocity) varies with wavelength, spreading out spectrally diverse pulses.
Question 6: In the design of a phase-shifted full-bridge DC-DC converter, what enables zero-voltage switching (ZVS) for the primary switches?
- Resonance between transformer leakage inductance and switch output capacitance (Correct answer)
- Hard switching with optimized gate drive rise time
- Addition of a series capacitor on the transformer primary
- Operating at a frequency above the resonant frequency of the output LC filter
Correct answer: Resonance between transformer leakage inductance and switch output capacitance
ZVS is achieved when the energy stored in the transformer leakage inductance is sufficient to fully charge/discharge the switch output capacitances before turn-on, allowing switching at zero voltage.
Question 7: The Bode gain-phase relationship (Bode's integral theorem) for a minimum-phase system states that:
- Phase response is uniquely determined by the gain (magnitude) response (Correct answer)
- Gain and phase are independent for all LTI systems
- The phase is the Hilbert transform of the log-magnitude response
- Gain margin and phase margin are always equal in minimum-phase systems
Correct answer: Phase response is uniquely determined by the gain (magnitude) response
For minimum-phase systems, the phase response is uniquely determined by the magnitude response via the Hilbert transform relationship, so specifying gain fully determines phase.
ME or MEng Master of Engineering Master of Electrical Engineering 5
In a switched-mode power supply, the 'right-half-plane (RHP) zero' in the boost converter transfer function is problematic because it: