ECE533F test tut2 - Skuleexams.skule.ca/exams/custom/20109/ECE533_2010...ECE533F – Power...

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ECE533F – Power Electronics

Test

Lecturer - O. Trescases

Date – Wednesday, Oct. 27, 2010

Duration: 90 minutes

1. Answers should be written in pen. Warning: answers written in pencil are acceptable but

may be considered ineligible for remarking.

2. The marks for each question are indicated within brackets [ ]. Show your work: answers

without justification will not receive full marks! Write your numerical answers in the

boxes.

3. Use back side of sheets if necessary. Extra sheets are also provided at the end.

4. Aids: calculator only. (Any calculators including programmable are allowed).

5. Unless otherwise stated, you may use the small-ripple approximation

Question Mark

1 /25

2 /25

3 /25

4 /25

BONUS

Total /100

Last Name: ________________________

First Name: ________________________

Student #: ________________________

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Last Name: _________________

Question 1:

[25 marks] Consider the dc-dc converter shown below. Assume the MOSFET and diode to be ideal.

Vg = 12 V, L1 = 15 μH, L2 = 10 μH, fs = 1/Ts = 750 kHz, R = 1

(a) Using the standard method, find the steady-state dc conversion ratio M(D) = V2/Vg.

M (D) =

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(b) Find the average value of iL1 and iL2 for V2 = 5 V, as well as the peak ripple current iL1 and

iL2. Sketch, iL1, iL2 and iD on the axis provided below.

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(c) Find the maximum value of R to maintain continuous conduction mode (CCM) .

Rcrit =

IL1 = A

iL1= A

IL2 = A

iL2 = A

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Last Name: _________________

Question 2:

[25 marks] Consider the converter shown below. Vg = 24 V, fs = 500 kHz, 0.5 A < Iout < 15 A,

V = 100 V

(a) For this part only, you may assume that the semiconductor switches are ideal. Find the inductance

L such that the peak ripple current iL is 10% of the average IL at the maximum load current Iout. Find

the steady-state duty ratio D in CCM for V = 100 V. Does the converter stay in CCM for the full

current range (justify your answer)?

(b) Now assume that the MOSFET has a finite on-resistance Ron, the inductor has a series resistance Rl

and the diode has a forward voltage drop of Vd in the on-state. Derive an equivalent steady-state model

for the converter (you must include a dc transformer model in your result for full marks).

L = μH D = CCM?

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Last Name: _________________

(c) Calculate the efficiency at Iout = 10 A using the partial datasheets for M1 and D1 provided on the

following page. You must consider the conduction losses, gate-drive losses and switching losses. You

can ignore the reverse recovery loss in D1. Assume Rl = 100 m , Tj = 125 oC, ton = 75 ns, toff = 100 ns.

Efficiency = %

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Last Name: _________________

Bonus [5 marks] Find an expression for the conversion ratio M(D) in DCM mode with the same

assumptions as part (b).

MOSFET M1:

DIODE D1:

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Last Name: _________________

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Last Name: _________________

Question 3:

[25 marks]

a) Draw the device cross-section for an n-channel vertical UMOS power MOSFET and show the

channel region. What is the main benefit of this device structure?

b) The measured efficiency for a commercial synchronous buck converter is shown below. Based on

your knowledge of the losses in SMPS, explain the variation of the efficiency versus (1) the load

current and (2) the output voltage.

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Last Name: _________________

d) The following datasheet refers to a standard silicon-based MOSFET:

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Last Name: _________________

The device has active area of 2 cm2. Draw an “ ” corresponding to this device on the plot below. What

is the theoretical Ron for a device of this size if silicon carbide was used instead of Si?

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Last Name: _________________

BONUS [5 marks]:

The experimental UIS waveforms for two devices designed at UofT are shown below. Sketch the

simple circuit used for this standard test, including the component values used in this case. Estimate

the avalanche energy for these devices.

Eav = mJ

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Last Name: _________________

Question 4:

[25 marks] Consider the automotive battery charger shown below, which is designed to allow bi-

directional power flow. The MOSFETs have an on-resistance of Ron1 = 25 m for M1 and Ron2 = 50

m for M2. The inductor is ideal.

Vg = 42 V, Vbatt = 100 V

(a) Find an expression for the steady-state conversion ratio M(D). Hint: You can consider the

effective load resistance to be R = Vbatt/Ibatt.

M(D) =

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Last Name: _________________

(b) Given that the input and output voltages are fixed in this application (M is constant), the duty ratio

is used to control the power flow in the circuit. Plot the average power Pbatt = Vbatt Ibatt versus D

for 0.5 < D < 0.7 in the axis provided below.

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Last Name: _________________

ECE533F test tut2 - Skuleexams.skule.ca/exams/custom/20109/ECE533_2010...ECE533F – Power...

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