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Three hours

Special instructions:
 Mathematical formulae tables supplied by the Examinations Office

THE UNIVERSITY OF MANCHESTER

Faculty of Science and Engineering
School of Electrical and Electronic Engineering

Power Electronics

17 January 2019
09:45 – 12:45

Electronic calculators may be used in accordance with the University regulations.

© The University of Manchester, 2019
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Question 1
An H-bridge converter is fed by a 400 V DC link. Pulse width modulation (PWM) with
a 20 kHz triangle wave frequency is used.
a) Consider that the H-bridge is connected to a DC load with an average load voltage
of 15 V. Labelling voltage values and time instants when the voltage output
changes, draw the voltage applied to the load over a switching period for:
(i) Bipolar PWM
(ii) Unipolar PWM
[5, 5 marks]
b) Now consider the case where the H-bridge converter is connected to a DC motor
load. The motor load can be modelled as a 35 V back-emf in series with a 9 mH
inductance and a 35 mΩ resistance.
Making reasonable assumptions, calculate the current ripple (peak-to-peak) in the
motor current for:

(iii) Bipolar PWM
(iv) Unipolar PWM
[5, 5 marks]

c) The system in (b) has a PI current control loop applied to it. This is tuned to give a
step response with a damping ratio of 0.75 and a bandwidth of 200 Hz for the
motor-converter system.

Using the transfer function given below:

calculate the values of the proportional and integral gains, Kp and Ki (Note: these
will be the same for bipolar and unipolar PWM).
[6 marks]

d) The H-bridge converter is now connected to an AC load. A 50 Hz voltage
waveform reference is provided to the converter. Sketch the frequency spectrum
of the output voltage for 20 kHz bipolar PWM. Your x-axis scale should go up to
45 kHz. Label points of interest on the frequency axis.
[7 marks]

Total [33 marks]

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Question 2
(a) Figure Q2.1 shows the equivalent circuit of the secondary side of an isolated
DC/DC converter. A square-wave source voltage of magnitude (the waveform
is shown in Figure Q2.2) drives a rectifier via a small series inductance .
Assume all diodes are ideal, and the load inductance is sufficiently large that
is almost constant DC ( ≈ ).

Figure Q2.1

Figure Q2.2

(i) If the series inductance = 0, sketch the waveform of the rectified voltage
() and source current (). Mark the voltage and current levels and
time intervals on the waveform using circuit parameters , and .
(ii) If the series inductance = 0, write down an expression for the DC output
voltage in terms of the circuit parameters.
(iii) Practically is not zero and significantly affects the operation of the
rectifier as shown in Figure Q2.3. Based on the waveforms in Figure Q2.3,
give an expression for the commutation time 1 in terms of , , and .
(iv) Based on the assumptions in (iii), identify the states ON(conducting) or
OFF(blocking) of the four diodes in time intervals , , , and
marked on Figure Q2.3. Copy and complete Table Q2.1 into your answer
sheet.
(v) Derive an expression for the new average voltage at the output , in terms
of , , , and .

Question 2 continued over the page

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Question 2 continued

Figure Q2.3
1 2 3 4

Table Q2.1

[3, 3, 4, 4, 3 marks]

(b) The DC/DC converter in Figure Q2.4 has "common-positive" connection of the
input and output. The switches 1 and 2 operate complementarily and the duty
ratio of 2 is . Assume that 1 and 2 are positive values, and the capacitor is
big enough so that the output voltage has almost no ripple.

Figure Q2.4
Question 2 continued over the page
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Question 2 continued
(i) What type of converter is this? (Buck/Boost/Buck-boost)
(ii) Is it a direct type or indirect type converter?
(iii) Give an expression for the voltage gain (
2
1
) of this converter in continuous
conduction mode (CCM) as a function of .
(iv) Derive an expression for the average output current in discontinuous
conduction mode (DCM) (which means = 0 for a period of time) as a
function of , , , 1, and 2.
(v) The converter has the following parameters:
1 = 48 V, = 3.9 μH, = 8 Ω and = 300 kHz
At what value of duty ratio does the transition between continuous and
discontinuous conduction modes occur?
(vi) Select suitable switch devices for 1 and 2 from the options in Figure
Q2.5. One of them must be a diode. Draw the complete schematic
showing how you have connected the two switches into the circuit.

Figure Q2.5
[1, 1, 3, 4, 4, 4 marks]
Total [34 marks]

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Question 3
(a) For the three-phase inverter in Figure Q3.1, fundamental frequency modulation
with 180⁰ conduction is employed. The three-phase load uses 20 Ω resistors
connected in delta. VDC is 540V.

For parts (i) and (ii), show one complete cycle, and mark values of the voltage
levels on the waveforms.

(i) Sketch the switch s1 and s4 control signals, using the labelling in Figure
Q3.1.
(ii) Sketch the voltage at points VR and VY with respect to the converter 0 V.
Also show VRY.
(iii) Calculate the rms current in one phase of the delta-connected load.
(iv) Explain how the load current harmonics will change if the load resistors are
changed to inductors.
[2, 4, 4, 2 marks]

Figure Q3.1
Question 3 continued over the page
0V
s5 s1 s3
s4 s6 s2
.
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Question 3 continued
(b) A DC/DC converter output stage is shown in Figure Q3.2. Diode D1 has a
rectangular current waveform with a peak of 16 A, a duty cycle of 25%, and a
switching frequency of 20 kHz. The load current I_dc is constant at 4 A. The
capacitor C1 has a capacitance of 1 mF and an equivalent series resistance R1
of 0.13 Ω.
(i) Sketch the capacitor current IC, identifying maximum and minimum values,
(ii) Calculate the power loss in R1,
(iii) Calculate the peak-peak ripple voltage at the output VO.
[3, 5, 4 marks]

Figure Q3.2
(c) A diode has a worst-case loss of 26 W. The diode is placed on a heatsink with
RJunction-case = 2.4 KW
-1, Rcase-heatsink = 0.5 KW
-1. The maximum ambient
temperature is 40⁰C.
(i) Sketch the thermal circuit
(ii) Find the thermal resistance of the heatsink that will limit the junction
temperature to 130⁰C.
[2, 3 marks]
(d) For the inverter circuit in (a),
(i) What is ‘blanking time’? Explain why it is required.
(ii) What is ‘galvanic isolation’? Identify where it is used.
[2, 2 marks]
Total [33 marks]

END OF EXAMINATION PAPER
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