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EO212 1 / 14
SCHOOL OF ENGINEERING
MODULAR HONOURS DEGREE COURSE
LEVEL 2
SEMESTER 2
2005/2006
ANALOGUE ELECTRONICS
Examiners: Dr.S.S.Singh
Attempt FOUR questions only.
Time allowed: 2 hours
Total number of questions = 6
All questions carry equal marks.
The figures in brackets indicate the relative weightings
of parts of a question.
Special requirements: None
EO212 2 /14
1) a) In the equation V = Ldi/dt, which of the parameters are vector quantities?
Explain how the direction of the vector parameters can be deduced or are
related. Explain how the magnitudes of the vector parameters are related.
(3)
b) In the equation i = Cdv/dt, which of the parameters are vector quantities?
Explain how the direction of the vector parameters can be deduced or are
related. Explain how the magnitudes of the vector parameters are related.
(3)
c) Write down the relationship between the input difference voltage, the output
voltage and the open-loop gain of an operational amplifier.
(2)
d) Explain the difference between the open-loop gain and closed-loop gain of an
operational amplifier.
(2)
e) What is meant by the input-offset voltage of an operational amplifier?
(2)
f) What is meant by the input-offset current of an operational amplifier?
(2)
g) What is meant by the common rejection-mode ratio of an operational amplifier?
(2)
h) With reference to Ohm’s law, explain why a resistance which has a negative
temperature coefficient will result in a voltage fall with rising temperature.
(2)
i) With reference to Ohm’s law, explain why an ammeter inserted into a circuit
will result in a disturbance to the circuit such that the current being measured is
in fact in error.
(2)
j) What voltage profile is required across an inductor to cause the inductor current
to ramp positively? Explain your answer with reference to an appropriate
equation.
(2)
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k) What current profile is required to flow in a capacitor to cause the capacitor
voltage to ramp positively? Explain your answer with reference to an
appropriate equation.
(2)
2) The circuit in Figure Q2 (shown overleaf) is a simple switched inductive load. The
switches are initially open. At the time t = 0 both switches operate together,
allowing current and magnetic field to build up in the inductor. After a time interval
t1 both switches are operated a second time to ‘break’ the current path in the circuit.
a) Describe what happens to the current and the magnetic energy in the circuit
from the instant the switches are operated at time t = 0. Ensure that your
explanation includes justification with reference to the equations V = Ldi/dt and
E = 0.5 L i2, in which the circuit current is ‘i’ and the inductor energy is ‘E’.
Pay particular attention to the directions of voltage and current flow.
(8)
b) Illustrate your explanation by sketching a graph of inductor current against time
‘t’ from the instant that t = 0 to the instant that t = t1 . Include on your graph a
clear indication of the times at which the switch is operated. Indicate the value
of any significant gradients on the graph.
(5)
c) Describe in detail what happens to the current in the circuit from the time t1
when both switches are operated a second time to ‘break’ the current loop in the
circuit. You may assume that each switch has a small but significant stray
capacitance ‘C’.
Ensure that your explanation is justified by including a
reference to the equation E = 0.5 L i2. Draw the equivalent circuit for this
circuit configuration and write down important voltage and current equations
for the circuit components and the circuit as a whole.
d) Illustrate your explanation by sketching a graph of inductor current against time
‘t’ from the instant that t = t1 to some time after, when the current has a value
lower than the value at time t = t1. Include on your graph a clear indication of
the times at which the switches are operated. Explain why the graph of inductor
(7)
EO212 4 /14
current is the shape you have drawn. Refer to appropriate portions of the graph
to support your explanation.
(5)
QUESTION 2 CONTINUED ON PAGE 4/12
Switched Inductive Load
Vs
S
L
Vs
S
L
S
Figure Q2
Switches
Inductor
Battery voltage
EO212 5 /14
3) The circuit in figure Q3 (overleaf) shows two simple PNP transistors in a circuit, in
which both transistors are forward biased. One transistor (T1) has a minimum
current gain (hFE) of 200 and the other has a minimum current gain of 10. The
supply voltage to the circuit is -12.0V and the transistor base and collector resistors
are 100 k and 1 k as shown. Throughout this question, you should take account
of the polarity of both the voltages and currents with respect to the voltage and
current arrow directions at all times.
a) Calculate the size of the input voltage that will guarantee to bias the transistor
‘T1’ into saturation. Take into account the finite base-emitter voltage drop of
0.6 V for both transistors as well as the finite collector-emitter voltage drop of
0.4 V transistor T1 when in saturation. Show all mathematical steps in your
derivation.
(14)
b) Evaluate the input voltage to the circuit that will cause the output voltage to be
-6.0 V at minimum hFE. Take into account the finite base-emitter voltage drop of
0.6 V and show all mathematical steps in you calculations.
(7)
c) Sketch a graph of input voltage versus output voltage for the circuit, indicating
at which value of input voltage, transistor saturation occurs. Also indicate on the
graph the input voltage at which the transistor begins to turn on. Ensure that the
sign of both voltages are represented correctly on the graph.
(4)
EO212 6 /14
QUESTION 3 CONTINUED ON PAGE 6/12
PNP Darlington Transistor Circuit
0V
Vin
Vout
T2
100k
T1
Vin
input voltage
Vout output voltage
T1, T2 transistors
I
transistor collector current
I
1k
-12.0V
Figure Q3
EO212 7 /14
4) Operational
amplifiers are known to have certain limitations that an
ideal operational amplifier does not have. For example an ideal operational
amplifier has zero input-offset voltage compared to a real operational amplifier. The
inverting amplifier circuit in figure Q4 has both finite input-offset voltage and finite
input-bias current.
a) Write down an expression for the voltage across the resistor R3 taking full
account of vector polarity.
(2)
b) Using the above expression for the voltage drop across resistor R3, derive an
expression for the voltage drop across the resistor R1 to include the input
voltage and the offset voltage.
(4)
c) Write down an expression for the current in the resistor R1 assuming the voltage
drop across R1, previously derived in part (b).
(3)
EO212 8 /14
d) Derive an expression for the current flow around the feedback path of the
operational amplifier using Ohm’s Law. Ensure that it includes the output
voltage, the offset voltage and the voltage across the resistor R2.
(6)
e) By equating the currents in the resistors R1 and R2 derived above, develop an
expression for the relationship between the input and output voltage of the
circuit.
(10)
QUESTION 4 CONTINUED ON PAGE 8/12
Inverter with finite input-offset voltage and finite input bias current
R2
VR2
I
R1
Z
Ib
Vos
Vin
Vout
R3
EO212 9 /14
Figure Q4
Vin
Vout
Vos
VR2
Ib, I
R1, R2, R3
Z
input voltage
output voltage
input offset voltage
feedback resistor voltage
input bias current
resistors
input impedance
5) Examine the circuit in figure Q5 (shown overleaf) which is a dc-to-dc power
converter.
a) Identify the power converter in figure Q5 and write down which type of
converter it is and what the purpose of this type of converter is?
(2)
b) Write down the expression for the voltage and current relationship for the
inductor from the time that the switch S is operated, allowing current to flow
through it. Using this relationship, derive an expression for the actual current
flow through the inductor.
(7)
EO212 10 /14
c) If the inductor has a value of 1 mH and the battery voltage is 24 V, at what time
after the switch is operated (i.e.closed) will the current achieve a value of
500 mA if the switch has a current of 260 mA flowing through it the instant it is
operated? Ensure that your answer is supported by a full explanation and
description of the behaviour as well as a full mathematical analysis of the circuit
during this time.
(6)
d) If the output voltage is assumed to be constant with a nominal voltage
Vo = 48 V, what is the voltage across the diode for the duration that the switch
is carrying current?
(2)
e) When the switch is opened, explain how the previously reverse-biased diode
becomes forward-biased. What are the conditions that determine the voltage at
which the diode begins to conduct?
Using this information, state what the
voltage across the inductor will be when the diode is forward-biased.
(5)
f) Determine what the inductor’s current gradient will be while the diode is
forward biased.
QUESTION 5 CONTINUED ON PAGE 9/12
(3)
EO212 11 /14
Power Converter
L
D
Vb
S
C
Figure Q5
R
Vb battery voltage
L power inductor
S power switch
D power diode
C charge storage capacitor
R load resistor
EO212 12 /14
6) Figure Q6 shows an inverting amplifier circuit. Assume that the op amp has infinite
input impedance, a finite input-error voltage  and that the open-loop gain may be
approximated by a multi-pole open-loop gain Bode plot. The open-loop Bode plot
has a ‘flat’ gain of 160 dB from low frequencies to frequency fp1. Above the pole
frequency fp1, the open-loop gain falls at –20 dB for every decade change in
frequency. At the higher pole frequency fp>fp1, the gain is 100 dB and above this
pole frequency the open-loop gain of the op amp falls at –40dB/decade.
a) Sketch the open-loop multi-pole gain-magnitude Bode approximation for the op
amp. Indicate the frequencies fp1 and fp2 with corresponding gains, together
with significant gradients. What is the relationship between the frequencies fp1
and fp2? Justify your answer.
(6)
b) If the closed-loop gain for the circuit in Figure Q6 is –1000, indicate on your
sketch the gain in dB and the bandwidth at this frequency and label it as
frequency ‘f’.
(3)
c) The inverting amplifier circuit in figure Q6 has an input difference voltage: .
Give a detailed explanation of what the relationship is between the current I1 in
the resistor R1 in terms of the input voltage Vin, difference voltage  and
resistor value R1.
(2)
d) What is the relationship between the current I2 in the feedback resistor R2 and
the current I1 in the resistor R1? Explain why they have the relationship you
have proposed.
QUESTION 6 CONTINUED ON PAGE 12/12
(3)
EO212 13 /14
e) Derive an expression for the voltage relationship between the input voltage Vin
and the output voltage Vout for the inverting amplifier circuit in figure Q6,
taking into account the input difference voltage . Show all mathematical steps
in your derivation.
(6)
f) Develop an equation for the closed loop gain of -1000 in terms of the open-loop
gain of 160 dB the frequency ‘f’ indicated in part (b) and the pole frequency
fp1. Assume the frequency fp2 is 1000 times higher than the pole frequency
fp1.
(5)
EO212 14 /14
Inverting amplifier circuit
I2
I1
R2
R1

Vin
Vout
R
Figure Q6
Vin
Vout
R, R1,R2

I1
I2
input voltage
output voltage
resistors
input difference voltage
current in resistor R1
feedback current