Question 1: Consider the stepped voltage waveform shown in Figure 1 below.

Calculate the total harmonic distortion (THD) of the waveform for D=0.35 and compare your result to the THD of a square wave.

v_in (t) = (3 +2cos(5,000 Πt +30⁰ ) +2cos(15,000 Πt) V

Question 2:

a) The input and output voltages of a filter operating under sinusoidal steadystate conditions are observed on an oscilloscope. The peak amplitude of the input is 5V and the output is 15V. The period of both signals is 0.4ms. The input reaches a positive peak at t=0.1ms and the output reaches its positive peak at t=0.15ms. Determine the frequency and the corresponding value of the transfer function.

b) The transfer function of a filter is shown in Figure 1 below. The input signal is given by:

Find an expression (as a function of time) for the steady state output of the filter.

Question 3 A single-phase diode rectifier is shown in Figure 3 below. The rms value of the grid voltage is Vs = 240V. Assume the grid to be ideal (with no commutating inductance) and the load is represented by a constant dc current, Id = 10A. The grid frequency is equal to 50 Hz. Assume ideal diodes.

(a) Sketch the grid voltage vs(t) and the dc voltage vd(t).

(b) Calculate the average dc voltage Vd,ave.

(c) Sketch the grid current is(t), and indicate which diodes are conducting during specific periods of the line cycle.

(d) Calculate the rms value of the grid current, Is.

(e) Show that the rms value of the fundamental frequency component of the grid current is given by:

I_sI  = (4/√2Π) I_d

(f) Show that the power factor PF for this single-phase diode rectifier is 0.9.

(g) Provide expressions for the input (real) power and the output power of the rectifier.

(h) Why is the apparent power larger than the real power, even when the first harmonic current is in phase with the grid voltage?

Question 4 Consider the half wave rectified circuit with inductive load in Figure 4 below. Assume the diode is ideal and iL(0)=0

While the diode is conducting the circuit is described by the following differential equation:

a) Solve this equation for iL and plot iL for R=240Ω, L=800mH, f=50Hz and VM=340V using a program of your choice for the interval 0

b) From your graph determine the time t1 when the diode stops conducting.

c) Simulate the circuit using ICAP and provide a graph showing vin, vs and iL. Also include the ICAP schematic.

d) Discuss and compare your ICAP results with the results of part a) and b).

Question 5

a) Draw a circuit diagram showing the AC power supply, the power diode, the capacitor C1 and the resistor R1 and specify the component values used in your experiment for C1 and R1.

b) Calculate the voltage ripple in the voltage across C1. List your assumptions.

c) Simulate the circuit using ICAP and present simulation results for the voltage ripple in the voltage across C1 and the capacitor current.

d) Compare the calculated voltage ripple from b) and your results from c) with your observations from the experiments.