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EO319
SCHOOL OF ENGINEERING
MODULAR HONOURS DEGREE COURSE
LEVEL 3
SEMESTER 2
2003/2004
ELECTRONICS AND EMC
Examiner: Dr S Singh
Attempt THREE questions only
Time allowed: 2 hours
Total number of questions = 5
All questions carry equal marks.
The figures in brackets indicate the relative weightings
of parts of a question
Special requirements: Laplace Transform tables
Mathematical Formulae (B&C)
1/11
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1) A 10 V positive voltage pulse is applied as the input voltage Vin to the circuit in figure Q1
in which the operational amplifier is ideal. The transistor has a nominal gain of 100 and
the zener voltage is 5.6 V. Initially the capacitor has no charge on it.
a) Comment on the voltage waveform at the positive input of the operational amplifier
and explain how it is affected by any adjustment of the variable resistor RV. Explain
what effect the role of the resistor R2 has in stabilising the circuit against the effects of
any drift of the reference voltages +Vref and –Vref with respect to the 0V rail.
(2)
b) Explain how the base current into the transistor T is controlled by the presence of the
zener diode, if, as in this case, the input voltage Vin is larger than the zener voltage of
5.6V. Derive an expression for the current into the base of the transistor T and write
down the relationship it has to the transistor collector current.
(4)
c) Derive from first principles, including all mathematical steps the expression for the
voltage at the output Vo, during the time that the input voltage pulse is applied. Ensure
that the output voltage is related to the voltage set by the variable resistor RV as well
as the time for which the input pulse Vin is applied.
Note: Laplace Transform of dx/dt is -x(t=0) + sx(s)
Inverse Laplace Transform of 1/s
is 1 or unit step.
Inverse Laplace Transform of 1/s2 is t
QUESTION 1 CONTINUES ON THE NEXT PAGE
(14)
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d) Plot a graph showing the form of the output voltage Vo in relation to the input voltage
Vin and comment on any particular features that can be attributed to the expression
derived above.
(5)
+Vref
R3
R1

RV

R2
-Vref
ic
Rin
C
Vc
R
Vo
T
iZ
Vin
A1
Z
0V
Figure Q1
A1
op amp
Vin input
Vo
output voltage
+Vref, -Vref reference voltages
C
capacitor
Vc
capacitor voltage
Ic
capacitor current
R, R1, R2, R3, Rin resistors
RV variable resistor
T
transistor
Z
zener
IZ
zener current
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2) Figure Q2 is a voltage to current converter. All the current flowing through the resistor
Ro is forced to flow into or out of the bases of the transistors T1 and T2. The transistors
have closely matched current gains of 100 which enable the load inductive L to be
current driven.
a) Derive an expression that relates the input voltage Vin to the voltage Vo across the
resistor Ro. Assume that the transistors T1 and T2 have negligible base-emitter
voltage drops. Show that the relationship is independent of the voltage VL across the
inductive load and clearly show all mathematical steps in your solution.
(10)
b) What is the input voltage to the circuit that will ensure that the voltage across the
inductor L is constant? Show all mathematical steps in your solution.
(12)
c) What is the relationship between the input voltage and the voltage developed across
the inductive load if the transistors have a current gain of 100? Show all
mathematical steps in your solution and explanation.
QUESTION 2 CONTINUES ON THE NEXT PAGE
(3)
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+Vcc
T1
R
i
Ib
R
T2
B
I
R0
V+
+
V-
-
V0
A
L
-Vcc
R
R
Vin
0V
Vin input voltage
R resistors
A operational amplifier
B buffer
L Inductive load
i current in resistor R
Ib transistor base current
I Inductor current
Vo voltage across resistor Ro
VL voltage across inductive load L
V- inverting input operational amplifier input voltage
V+ non-inverting operational amplifier input voltage
T1 & T2 matched gain transistors
-Vcc negative transistor supply voltage
+Vcc positive transistor supply voltage
Figure Q2
VL
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3) The circuit in figure Q3 is part of an analogue voltage hold circuit and is assumed to
have ideal operational amplifiers. The capacitor is charged by the current source S and
the analogue voltage stored by the capacitor is held the instant that the current from the
current source is zero. The output voltage is also held, and its voltage value, is equal the
voltage on the capacitor C. The voltage stored on capacitor C is determined by the input
current source.
The capacitor has some leakage resistance. In order to compensate for the effects of the
capacitor leakage resistance additional circuitry is present. The compensation current
level is controlled by the wiper position of the potentiometer.
a) What is the relationship between the capacitor leakage current Ilk and the voltage if
the leakage resistance is 5 M? What is the value of the capacitor leakage current if
the capacitor voltage is 5.0 V?
(4)
b) The capacitor leakage compensation circuit uses the operational amplifier B. Derive
an expression for the relationship between the input voltage V1 to the amplifier and
its output voltage V2.
(3)
c) Derive the relationship between the voltage V4 in the circuit of figure Q3 and the
capacitor voltage Vc. Show all mathematical steps in your derivation.
(6)
d) As part of the capacitor leakage compensation circuit, the stabilising resistor R is
added to the circuit. The exact value of the resistor R is arrived through experimental
means by first ‘measuring’ the capacitor leakage current Ilk. Write down the
current/voltage relationship for the stabilising resistor R and how this relates to the
capacitor leakage current Ilk.
(4)
e) Using the resistor symbols shown in figure Q3 and a capacitor leakage resistance of
5 M find the value of the capacitor leakage compensation resistor R that must be
used if voltage stability is to be achieved with the potentiometer set to the centre
position.
(8)
QUESTION 3 CONTINUES ON THE NEXT PAGE
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i
R
Vc
C
R2
Ilk
r
VA-
VBR1
A
VA+
+
VB+
S
B
R39
RV
V1
Vo
V2
R4
0V
S input current source
A operational amplifier
B operational amplifier
C analogue voltage storage capacitor
r capacitor leakage resistance
Vc capacitor voltage
Ilk capacitor leakage current
R1,R2,R3,R4 resistors
R capacitor leakage compensation resistor
i current in capacitor leakage compensation resistor
Vo output voltage
VA- inverting input voltage, operational amplifier A
VA+ non-inverting input voltage, operational amplifier A
VB- inverting input voltage, operational amplifier B
VB+ non-inverting input voltage, operational amplifier B
V1, V2, V4 voltages
RV variable resistor or potentiometer
Figure Q3
V4
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4) The circuit in figure Q4 is subjected to a positive ramp input voltage, which starts at zero
voltage. The output stage of the circuit is an integrator.
a) Describe the operation of the circuit to such an input signal explaining what the input
voltage waveform Vbi will be to the buffer and how the corresponding buffer output
voltage Vbo will affect the current i into the integrator input resistance R.
Sketch the buffer input and output waveforms to illustrate your explanation as well
as the current in the resistor R. Ensure that the sketches have clearly labelled axis.
Make reference to the role of both the zener diodes which are a matched to have the
same zener breakdown voltage. Assume that before the ramp input voltage to the
circuit is applied, the integrator feedback capacitor has zero voltage across it.
Sketch the circuit output voltage and explain its shape with reference and
justification to the form of the current flowing in the integrator input resistance.
(15)
b) Using Laplace transforms derive a relationship for the circuit output voltage as a
function of time. Assume that the current in the integrator input resistance as a
function of time t has the following form i(t) = -Gt +Vz/R, in which –G is the current
gradiant, Vz is the zener breakdown voltage and R is the integrator input resistance.
Sketch a plot of the circuit output voltage expression you have derived and indicate
on the sketch how it relates to the expression you have derived.
Note: Laplace Transform of dx/dt is -x(t=0) + sx(s)
Inverse Laplace Transform of 1/s2 is t
Inverse Laplace Transform of 1/s3 is t2/2
QUESTION 4 CONTINUES ON THE NEXT PAGE
(10)
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Vss
Vc
Rz
I
Rin
iR
R
V-
B
C
A
+
V+
Vin
Vb i
Z
Vbo
Vo
Z
0V
Vin ramp input voltage
B buffer
A operational amplifier
Z zener diodes
C feedback capacitor
Vc capacitor voltage
Vbi buffer input voltage
Vbo buffer output voltage
Vss supply voltage
Rin circuit input resistors
R integrator input resistor
IR current in resistor R
Rz zener diode ‘pull-up’ resistor
i current in feedback capacitor
Vo output voltage
V- inverting input voltage, operational amplifier A
V+ non-inverting input voltage, operational amplifier A
Figure Q4
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5) For the purpose of considering noise coupling, figure Q5 represents the equivalent of an
aircraft undercarriage retractor mechanism, which is controlled using a position sensory
system. The undercarriage position sensor system signal leads and undercarriage motor
drive leads run parallel in a single loom along much of the length of the aircraft cable
trunking system.
The current in the undercarriage motor drive leads cause magnetic coupling, by means of
mutual inductance M1 and M2 as indicated in figure Q5, within the wiring loom and
subsequent noise into the input of the undercarriage position sensor control circutry.
The undercarriage motor drive lead inductance L2 and L3 is measured to be 0.05 H.
The voltage drop across the motor drive lead is measured to be 100 mV maximum. This
voltage is coupled into the undercarriage position sensor lead through the mutual M1 and
M2. The position sensor control circuit is known to be immune to noise voltage levels of
up to 60 mV.
a) What is the minimum rate of change of current I2, measured in milliamps per
nanosecond in the undercarriage motor drive leads that will cause 100 mV of noise in
the lead it self?
(4)
b) The coupling coefficient between L1 and L2 is 0.1. The position sensor control
leads are designed to be lightweight and consequently are very thin, having an
inductance L1 that is nine hundred times larger than the undercarriage motor drive
lead inductance L2 and L3. What is the noise voltage introduced solely by the mutual
inductance M1 into the position sensor control lead?
QUESTION 5 CONTINUES ON THE NEXT PAGE
(7)
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c) The mutual inductance M2 has the effect of coupling a noise voltage into the
undercarriage position sensor lead, which has an opposing effect to that of M1. The
noise cancellation caused by the mutual inductance M2 is determined by the
coupling coefficient between L1 and L3. What must the coupling coefficient between
L1 and L3 be kept too, if the noise induced into the undercarriage position sensor
circuitry is to be kept down to half of the known noise voltage immune level, of the
position sensor control circuit?
(10)
d) Suggest, ways in which the noise coupling caused through mutual magnetic
inductance in the system above, may be overcome.
motor
drive
circuit
L2
(4)
I2
M1
position
sensor
L1
motor
I1
M2
position
sensor
control
circuit
L3
I3
Aircraft frame potential
Figure Q5