Sample Question Paper for 9210-112 Graduate Diploma in Engineering Circuits and waves 'XUDWLRQWKUHHKRXUV

Sample Question Paper for 9210-112 Graduate Diploma in Engineering Circuits and waves 'XUDWLRQWKUHHKRXUV

Sample Question Paper for 9210-112
Graduate Diploma in Engineering
Circuits and waves
'XUDWLRQWKUHHKRXUV
You should have the
following for this examination
• one answer book
• non-programmable calculator
• pen, pencil, drawing
instruments
General instructions
• This paper consists of ten questions over two sections A and B.
• Answer five questions, at least two from each section.
© The City and Guilds of London Institute
Section A
1
a
Differentiate the circumstances which need nodal analysis versus those
that need mesh analysis.
b
A circuit with a voltage source and a current source is shown in Figure
Q1b.
(2 marks)
6k
6k
6k
6 V +-
I0
2k
5 mA
Figure Q1b
Find the current I0 using
i
ii
iii
2
a
superposition theorem
nodal analysis
mesh analysis.
The voltage across a 200 mH inductor is given by the expression,
v(t )
b
(6 marks)
(6 marks)
(6 marks)
­(1 3t )e 3t mV, t t 0
®
0,
t0
¯
Derive,
i
the current waveform,
ii
the power waveform.
(4 marks)
(4 marks)
An impedance function is given as,
(6 marks)
Z (s)
s 4 4s 2 3
s 3 2s
Develop the first Cauer form of the network.
c
Consider the circuit in Figure Q2c.
1H
1:
+
1:
vi(t) +
-
8F
v0(t)
-
Figure Q2c
i
ii
Derive its transfer function.
Sketch the pole-zero plot.
(4 marks)
(2 marks)
2
3
a
Consider the two-port network shown in Figure Q3a.
+
Port 1 V1
-
I1
I2
I1
I2
+
V2 Port 2
-
Figure Q3a
i
ii
b
Write down expressions for V1 and V2 using Z parameters.
How can each of the Z parameters be measured?
Y parameters are defined by,
(2 marks)
(8 marks)
(10 marks)
I1
Y11V1 Y12V2
I2
Y21V1 Y22V2
Use the Y parameters to compare the two circuits shown in Figures Q3b1
and Q3b2.
Note that the first circuit has dependent voltage sources and the second
has dependent current sources.
I1
+
2:
5:
v1 (t ) 2I2 +
-
+ I1
-
I2
+
v2 (t )
-
Figure Q3b1
+
I1
V1 6:
-
I2
+
2.4: V2
1
V1
12
1
V2
6
-
Figure Q3b2
3
See next page
4
Consider the circuit shown in Figure Q4.
L
R
+
vi(t) +
-
vo(t)
C
Figure Q4
a
Obtain an expression for the voltage gain transfer function in the Laplace
domain.
(6 marks)
b
i
(4 marks)
Show that the undamped natural frequency is
1
.
LC
Zo
ii
Show that the damping ratio is
]
c
(4 marks)
R C
.
2 L
Assuming that the undamped natural frequency is 2000 rad/s, L=10 mH
and C=25 ȝF , characterise the response of the circuit when R is,
i
ii
(3 marks)
(3 marks)
40 :
10 :
4
5
a
Sketch the ideal transmission characteristics of the following filter types,
i
ii
b
Low-pass
Band-pass
(2 marks)
(2 marks)
A realisation of a second order filter function is shown in Figure Q5b.
L
+
vi
+
-
R
C
vo
-
Figure Q5b
i
ii
c
Derive the transfer function.
Show that this is a low pass filter.
(4 marks)
(4 marks)
The magnitude function for an Nth-order Butterworth filter with a
passband edge Z p is given by,
T ( jZ )
(8 marks)
1
§Z ·
¸
1 H ¨
¨Z ¸
p
¹
©
2N
2
where H determines the maximum variation in the passband transmission,
Amax where Amax
20 log 1 H 2 . Find the Butterworth transfer
function that meets the following low-pass filter specifications:
f p 10 kHz , Amax 1 dB , f s 15 kHz , Amin 25 dB , dc gain = 1.
5
See next page
Section B
6
a
Express Gauss’s Law in integral form.
(4 marks)
b
A coaxial line of infinite length is shown in Figure Q6b. In regular notation,
show that the capacitance per unit length of the coaxial line is,
(6 marks)
C
2SH
§b·
ln¨ ¸
©a¹
Figure Q6b
c
A cross-section of a coaxial transmission line is shown in Figure Q6c. Vo is
the potential of the centre conductor, and the outer shield is grounded.
There are two dielectrics between them, of relative permittivity Hr1 and Hr2
as shown in Figure Q6c.
Figure Q6c
i
Show that the capacitance per unit length of this transmission line
iis,
C
ii
2SH1H 2
§r ·
§r ·
H 2 ln¨¨ 2 ¸¸ H1 ln¨¨ 3 ¸¸
© r2 ¹
© r1 ¹
Determine the maximum electric intensity in each dielectric, if
V0 1.2 kV , H r1 4.5 , H r 2 3 , r1 10 mm , r2 20 mm , and
r3
(5 marks)
40 mm .
6
(5 marks)
7
a
Express Ampere’s Circuital law in integral form.
b
A coil of N turns carrying a current I is wound in a symmetrical manner all
around the toroid as shown in Figure Q7b.
(3 marks)
Figure Q7b
c
i
Obtain an expression for the magnetic flux density along the dashed
circular line of radius r.
(3 marks)
ii
What is the flux through the core?
(2 marks)
A magnetic device is shown in Figure Q7c. The data for the device are
given below:
(12 marks)
Number of turns of coil = 500;
length of air-gap = 5 mm;
area of cross-section of core = 20 mm x 20 mm.
Assuming that there is no fringing, estimate the current I needed to
establish a flux density of 0.25 T in the air-gap on the right arm of the core,
if the relative permeability of the core is to be taken as 6000.
Figure Q7c
7
See next page
8
a
b
i
Write down Maxwell’s equations in differential form for time varying
fields.
(2 marks)
ii
Obtain the free-space wave equation for a time-harmonic field.
(2 marks)
iii
Write down the expression for the propagation constant.
(2 marks)
iv
Consider a uniform plane wave travelling in free space, whose rms
electric field strength is 1 V/m. Compute the average power density.
(2 marks)
Assuming that the propagation constant for a lossy medium is given by
J
(6 marks)
jZPV Z 2 PH ,
obtain an expression for the attenuation constant.
c
Wet, marshy soil is characterised by V = 10-2 S/m, Hr = 15 and Pr = 1.
Determine whether the soil may be considered as a conductor, or a
dielectric at
i
ii
50 Hz
10 GHz
(3 marks)
(3 marks)
8
9
a
Mention two special properties of metal waveguides compared to coaxial
lines used in RF and microwave systems.
b
The field components inside a rectangular waveguide of internal
dimensions ‘a’ and ‘b’ as in Figure Q9b, for the TE10 mode are,
i
Ex
0
Hx
§S x ·
Eo
¸
sin¨¨
ZTE © a ¸¹
Ey
§S x ·
¸¸
Eo sin¨¨
© a ¹
Hy
0
Ez
0
Hz
§S x ·
¸¸
Eo sin ¨¨
© a ¹
Sketch the electric and magnetic field lines within the guide in the
x-y, x-z and y-z planes shown in Figure Q9b.
(4 marks)
(6 marks)
y
z
b
a
x
Figure Q9b
ii
Show that the power delivered by the waveguide using the TE10
mode, to a load is,
PT
iii
(5 marks)
E 2a b
4 ZTE
If the maximum value of the electric field inside the guide is 1 kV/m,
determine the power delivered to a matched load if the waveguide
is air-filled and has dimensions of a = 2.09 cm and b = 1.02 cm. You
may assume that ZTE for the TE10 mode is 520 Ÿ.
(5 marks)
9
See next page
10
a
i
Draw the current distribution along a centre-fed half wave (HW)
dipole.
(1 mark)
ii
The far field electric field due to a HW dipole, as shown in Figure
Q10a, is given by,
(2 marks)
Er
0,
ET
ªS
º
cos « cos(T )»
¬2
¼,
E0
sin(T )
EM
0.
P (r, T, I)
Vertical dipole T
r
I
Figure Q10a
Sketch the radiation patterns in the vertical and horizontal planes of
the HW dipole, when the dipole is vertical.
b
c
iii
What are the beam-widths of the vertical HW dipole, in the vertical
and horizontal planes?
(2 marks)
iv
Obtain an approximate value for the gain of the HW dipole in dBi.
(2 marks)
v
What is the polarisation of the radiation of the dipole in the direction
of maximum radiation?
(2 marks)
i
Draw the horizontal plane radiation pattern of a linear array of 4
identical vertical HW dipoles spaced O/2 apart, if they are fed by
currents of equal magnitude and phase.
(5 marks)
ii
What is the beam-width of the above linear dipole array?
(2 marks)
Mention with reasons, one advantage and one disadvantage of using
antenna arrays in point to point microwave links.
(4 marks)
10