ME or MEng Master of Engineering Master of Electrical Engineering 3

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)?

Accepted Answer

-1 V

Answer

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]?

Accepted Answer

1/(1-z⁻¹), |z|>1

Answer

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?

Accepted Answer

Lower conduction losses due to MOSFET R_DS(on) vs diode forward voltage

Answer

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:

Accepted Answer

Ensure conservation of charge and allow electromagnetic wave propagation

Answer

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:

Accepted Answer

A finite output resistance due to base-width modulation

Answer

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.

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Practice Test

ME or MEng Master of Engineering Master of Electrical Engineering 3