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Electronics (EO330)
s
School of Environment and Technology
Division of Engineering and Product Design
Semester-Two Examinations, May-June 2010
B.ENG. HONOURS DEGREE COURSE
ELECTRONICS (EO330)
EXAMINERS: Dr. S.S. Singh and Dr. B. Baha
Instructions to Candidates:
 The time allowed is THREE hours
 Attempt any FOUR questions only – at least ONE question from each section
 The total number of questions is SIX
 Each question carries 25 marks
 This is a CLOSED-BOOK examination
Special Requirements:
 Appendix 1 - Table of Laplace transforms (attached)
May-June 2010
Page 1 of 11
Electronics (EO330)
SECTION A
Question 1
(a) Semiconductor switches are an integral part of any power electronic system.
Discuss the main functions of such devices in a typical power electronics
system.
(3 marks)
(b) The power processor part of a switched-mode power supply is basically a DCDC converter circuit. Design a step-up DC-DC converter for a nominal 30 V
input and 120 V output. In reality the input voltage may vary between 15 V and
40 V and the inductor used is 10 H and the load power range is 120 kW.
(i)
Calculate the switching frequency (Fsw) in such a way to ensure that the
inductor current is continuous under all operating conditions.
(14 marks)
(ii) Determine the minimum value of the filter capacitor if the allowable ripple
voltage is 50 mV.
(4 marks)
(iii) Explain the relationship between the load current and the ripple voltage,
highlighting how the ripple voltage can be reduced.
(4 marks)
Page 2 of 11
Electronics (EO330)
Question 2
(a) Discuss the main differences between bipolar-junction transistors and metaloxide semiconductor field-effect transistors (MOSFETs). Suggest suitable
power electronics applications for each of these devices.
(6 marks)
(b) An input voltage of 15 V is connected to the circuit shown in Figure Q2. Assume
that the circuit is in the steady-state condition and that the value of L is 5 H and
the output power is Pload = 250 W.
L
Vo
iL
+
S
vL
_
iC
i
R
+
Vs
D
C
R
-
Figure Q2
(i)
Calculate the average input and output voltage V o(t) when the on time of
the switch is 6 s and the switching frequency is approximately 167 kHz.
(4 marks)
(ii) Assume that C has a large value so that Vo(t) = Vo. Calculate the load
current and the R.M.S. value of the capacitor current ic.
(8 marks)
(iii) Plot the voltage across the inductor (vL) and the current through the
inductor (iL) as indicated in Figure Q2.
(4 marks)
(iv) Explain the differences between the theoretical and practical results that
you will obtain from this power electronic circuit.
(3 marks)
Page 3 of 11
Electronics (EO330)
Question 3
(a) Discuss the main objective of the control circuit in a switched-mode power
supply (SMPS) and hence identify the primary desirable features of such a
control circuit.
(2 marks)
(b) With the aid of a circuit diagram, explain briefly the operation of the current
mode control as applied to an SMPS.
(5 marks)
(c) Describe the reasons why a compensation network is needed in the controller
for an SMPS.
(3 marks)
(d) Calculate the values of the compensation network shown in Figure Q3 below.
C3
R4
R3
-
Vf
C4
Voa
+
Vr
Figure Q3
(10 marks)
(e) What is the maximum limit of the bandwidth for the control loop of an SMPS?
Hence discuss the optimum limit of bandwidth for such a controller.
(5 marks)
Page 4 of 11
Electronics (EO330)
Question 4
(a) Discuss the disadvantages of PWM DC-DC converters operating at higher
frequencies and suggest possible solutions to overcome the shortcomings of
PWM converters at high frequencies.
(3 marks)
(b) Draw the topological circuit diagram of a PWM step-down DC-DC converter
operating in discontinuous conduction mode (DCM) and sketch the important
voltage and current waveforms. Derive the following relationship for the DC
gain:
Vo
2D

Vi
D  D 2  8L RT
where:
Vo is the output voltage
Vi is the input voltage
D is the duty cycle of the active switch
T is the switching period
L is the inductance
R is the load resistance
(13 marks)
(c) The input voltage Vs to the circuit shown in Figure Q4 is a step of 350 V DC
having a series resistor R = 5  to limit the maximum current through the
capacitor to 500 A. Determine the values of snubber inductance if the maximum
permitted vales of di dt and dV dt are 350A/s and 350 V/s respectively.
Ignore the switching time.
L
Vs
Cs
T
Rs
R
Figure Q4
(6 marks)
(d) Determine the snubber losses and the power dissipated in the snubber resistor
if the frequency of Vs is 3 kHz.
(3 marks)
Page 5 of 11
Electronics (EO330)
SECTION B
Question 5
The circuit in Figure Q5 is made up of three distinct stages, with each stage using
one of the operational amplifiers labelled A1, A2 and A3. The stages are linked in a
feedback manner.
R
R
r
Ir
A2
Vc
C
I
R
R
If
A1
V-
A3
V1 V2 Vd
V+
Vo
R
R
Vfb
Vin
0V
Vin input voltage
Vo output voltage
Vd difference voltage
Vfb feedback voltage
R, r resistors
A1,A2, A3 Op Amps
C capacitor
Vc capacitor voltage
V- op amp A3 inverting input voltage
V+ op amp A3 noninverting input voltage
Ir current in resistor r.
V1,V2 circuit voltages
I,If circuit currents
Figure Q5
QUESTION FIVE CONTINUES ON THE NEXT PAGE
Page 6 of 11
Electronics (EO330)
Question 5 (continued)
(a) State which of the operational amplifiers A1, A2 or A3 are used to perform each
of the three following functions: differential amplification, integration and
inversion.
(3 marks)
(b) The output voltage from this circuit is equal to the output voltage of the
operational amplifier A2, that is V2 = Vo . The circuit is initially in a stable state
with the input voltage Vin equal to zero and the capacitor voltage VC also equal
to zero.
When a negative input step voltage is applied to the circuit, in response, the
voltage Vd is initially non-zero but eventually is driven to zero as is the voltage
V fb . Also in response to the negative input step, the voltage V1 initially is at zero,
but settles some time later to the same voltage as the input voltage Vin .
(i)
The functional block associated with the operational amplifier A2 has an
effective input voltage V fb and an effective output voltage V2 . Derive a
relationship between the voltage V fb and the voltage V2 by considering only
that stage of the circuit whose function is dependent on the role of the
operational amplifier A2.
(4 marks)
(ii) The functional block associated with the operational amplifier A1 has an
effective input voltage V2 and an effective output voltage V1 . Including all
the mathematical steps, show that the relationship between the voltage V1
1
and V2 for this stage is given by V1  
V 2 dt . Ensure that you refer to
rC 
the resistor current I r and the capacitor voltage VC in your derivation.
(8 marks)
(iii) Referring to Figure Q5, the ‘difference voltage’ Vd is equal to the voltage
difference between V1 and Vin . Using mathematical analysis, show that Vd
and V fb are directly related. Refer to the circuit currents I and I f in your
analysis.
(5 marks)
(iv) If the voltage Vin was a positive voltage step with the same initial circuit
conditions, then sketch a diagram of the input voltage, the voltage V1 and
the difference voltage Vd on a single graph of voltage against time by
considering the response of all the stages of the circuit in Figure Q5.
(5 marks)
Page 7 of 11
Electronics (EO330)
Question 6
The function of the circuit in Figure Q6 is that of an input current integrator which
also has a separate input voltage. That is, the circuit has a current input I in which is
derived from the supply voltage V S and an input voltage Vin . The output voltage VO
is dependent on the size of the input current source as well as the size of the input
voltage. The feedback capacitor C has some leakage resistance which is
represented by the feedback resistor r .
Vs
r
Vc
Iin
C
ic
VA
V+
R
Vo
R
Vin
0V
A op amp
Iin controlled input current source
Vs supply voltage
Vin input voltage
Vo output voltage
R resistors
C capacitor
r leakage resistance of capacitor C
Vc capacitor voltage
V+ op amp positive input voltage
V- op amp negative input voltage
Ic Capacitor Current
Figure Q6
(a) Initially it may be assumed that the input current source is set to zero. Analyse
the circuit and show that the relationship between the Laplace transform of the
output voltage VO (s) and the Laplace transform of the input voltage Vin (s) , is
V ( s)
given by VO ( s)  VC ( s)  in
in which VC (s) is the Laplace transform of the
2
capacitor feedback voltage. Include all mathematical steps in your analysis.
(6 marks)
QUESTION SIX CONTINUES ON THE NEXT PAGE
Page 8 of 11
Electronics (EO330)
Question 6 (continued)
(b) Assume initially that both the input current source and input voltage are set to
zero. Analyse the operational amplifier circuit in Figure Q6 and show that the
circuit output voltage is fully determined by the following relationship:
VO (t )  VC (t )  rC
dVC
dt
(5 marks)
(c) Assume that the input current source is set to zero. Also assume an initial
voltage VC (t  0)  0 across the capacitor feedback. Using the relationship for
VO (s) in part (a) together with the capacitor voltage relationship in part (b), show
that the circuit in Figure Q6 has the following relationship:
VO ( s)  
VC (t  0)
sVin ( s)

1
1
(s 
)
2( s 
)
rC
rC
Note: the Laplace transform of
dx
is  x(t  0)  sX ( s)
dt
(6 marks)
(d) Using the following expression:
VO ( s)  
VC (t  0)
V ( s)
 in
1
2
dt ( s 
)
rC
determine the expression for the output voltage VO (t ) as a function of time if the
input voltage is a step input of size 2 volts.
Note: the Laplace transform of a unity step input Vin (t )  1 is Vin ( s ) 
inverse Laplace transform of
1
and the
s
1
is e  at .
( s  a)
(4 marks)
(e) Sketch a graph of the output voltage of the circuit in Figure Q6 against time for
the step input voltage discussed in part (d) with an initial voltage VC (t  0)  2
volts across the feedback capacitor.
(4 marks)
Page 9 of 11
Electronics (EO330)
APPENDIX 1 – TABLE OF LAPLACE TRANSFORMS

_
x( s)   e st x(t )dt
x(t )
0
1
1
s
1 or H(t)
2
1
s a
eat
3
1
s2
t
4
1
2
s  a




5

6

7







1
s  as  b
1
ss  a


1
2
s  a2
8
1
2
s  a2
9
1
2
s  a  b 2
10
1
2
s  a  b 2
11
s
2
s  a
12
s b
2
s  a





teat
eat  ebt
ba
1
1 eat 

a
1
sin( at)
a
1
sinh( at)
a
1 at
e sin( bt)
b
1 (ba )t (b a )t
e  e 
2b
1 at eat
(b  a)t 1eat


Page 10 of 11
Electronics (EO330)
13
s  as  b
aeat  bebt
ab

14
s c
s  as  b
(c  a)eat  (c  b)ebt
ba

15


s
(s  b)
ss  a



1
b  (a  b)e at
a
16
s
s  a2
cos(at)
17
s b
s  a2
1 2
b  a 2 sin at  tan 1 a
b
a
2

2

 24
1
s3
t2
2
1
3
s  a
1 2 at
te 

2
25
b
2

26
1
2
ss  a

30
1
2
s s  a

33
1
ss  a 2 


1
1  (1  at )e at
2
a


1
1 cos(at)
a2
2
Y(s)  x(t  0)  sX(s)



1 at t 1
e   2
a2
a a

34

1
a 2  b 2 e at sin bt  tan 1 b
a
b
s  a
2
 

s
 20


y(t) 
dx
dt


Page 11 of 11