ME or MEng Master of Engineering Master of Electrical Engineering 3 — Questions and Answers
Question 1: An op-amp integrator with R = 10 kΩ and C = 1 µF receives a 1 V DC step at t = 0. What is the output voltage after 10 ms (assuming ideal op-amp, starting from 0 V)?
- -1 V (Correct answer)
- -0.1 V
- -10 V
- -0.01 V
Correct answer: -1 V
V_out = -(1/RC)∫V_in dt = -(1/0.01)·1·0.01 = -1 V.
Question 2: In the Z-transform, what is the Z-transform of the unit step sequence u[n]?
- 1/(1-z⁻¹), |z|>1 (Correct answer)
- z/(z+1), |z|>1
- 1/(1+z⁻¹), |z|<1
- z⁻¹/(1-z⁻¹), |z|>1
Correct answer: 1/(1-z⁻¹), |z|>1
The Z-transform of u[n] is Σz⁻ⁿ for n≥0, which converges to 1/(1-z⁻¹) for |z|>1.
Question 3: What is the primary advantage of using a synchronous rectifier over a diode rectifier in a DC-DC converter output stage?
- Higher output voltage ripple
- Lower conduction losses due to MOSFET R_DS(on) vs diode forward voltage (Correct answer)
- Simpler gate drive circuitry
- Better surge current handling
Correct answer: Lower conduction losses due to MOSFET R_DS(on) vs diode forward voltage
MOSFET R_DS(on) voltage drop (mΩ range) is much smaller than a diode's ~0.5-1 V forward drop, significantly reducing conduction losses.
Question 4: Maxwell's equation ∇ × H = J + ∂D/∂t includes the displacement current term ∂D/∂t, which was added by Maxwell to:
- Account for magnetic monopoles
- Ensure conservation of charge and allow electromagnetic wave propagation (Correct answer)
- Correct Faraday's law for moving media
- Describe magnetostatic boundary conditions
Correct answer: Ensure conservation of charge and allow electromagnetic wave propagation
Maxwell added ∂D/∂t to make Ampère's law consistent with charge continuity (∇·J + ∂ρ/∂t = 0) and this addition predicts electromagnetic wave propagation.
Question 5: In a BJT common-emitter amplifier, the Early effect causes:
- Increased transconductance at high frequencies
- A finite output resistance due to base-width modulation (Correct answer)
- Increased input impedance with collector voltage
- Reduced current gain at low temperatures
Correct answer: A finite output resistance due to base-width modulation
The Early effect (base-width modulation) causes I_C to increase slightly with V_CE, modeled as finite output resistance r_o = V_A/I_C.
Question 6: Which filter topology is best suited for implementing a maximally flat (Butterworth) low-pass response with minimal sensitivity to component tolerances?
- Passive LC ladder filter
- Active Sallen-Key topology
- Multiple-feedback (MFB) topology
- State-variable (biquad) topology (Correct answer)
Correct answer: State-variable (biquad) topology
The state-variable biquad topology independently controls Q and ω₀, giving low sensitivity to component variations for high-order Butterworth designs.
Question 7: In a power system, a 'bus impedance matrix' (Z_bus) is used to compute fault currents. For a bolted three-phase fault at bus k, the fault current is:
- V_k(pre-fault) / Z_kk (Correct answer)
- V_k(pre-fault) × Z_kk
- V_k(pre-fault) / Z_kj (j≠k)
- Sum of all Z_bus entries in row k
Correct answer: V_k(pre-fault) / Z_kk
For a bolted fault at bus k, I_fault = V_k(pre-fault) / Z_kk, where Z_kk is the Thevenin impedance seen at bus k.
ME or MEng Master of Engineering Master of Electrical Engineering 3
An op-amp integrator with R = 10 kΩ and C = 1 µF receives a 1 V DC step at t = 0.
What is the output voltage after 10 ms (assuming ideal op-amp, starting from 0 V)?