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DUBLIN INSTITUTE OF TECHNOLOGY
KEVIN STREET, DUBLIN 8
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Diploma in Applied Electronics
YEAR II
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SUMMER EXAMINATIONS 1999
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ELECTRIC CIRCUITS
MR. P. Tobin
MR. C. Bruce
DATE
Attempt FIVE questions with a maximum of three questions selected from
Section A or Section B
Laplace/Z Transform Tables
2
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SECTION A
1. (a) Draw the circuit diagram, and derive the transfer function, for a simple first
order low-pass RC filter. Sketch the asymptotic amplitude response. Explain
the terms: cut-off frequency and roll-off rate.
[12 marks]
(b) Show how this circuit can be modified to ensure a constant attenuation at
high frequencies. Determine the component values for this modified circuit
if the two cut-off frequencies are 10 kHz and 100 kHz using a 10 nF
capacitor.
[8 marks]
2. (a) Develop an appropriate Thévenin equivalent circuit for the circuit shown in
Figure1. Calculate a value for the load ZL connected across AB for the
condition of maximum power transfer.
[12 marks]
(b) Use the Thévenin equivalent circuit to obtain a Norton equivalent circuit.
R1 = 5 Ω, R2 = 3 Ω, XL1 = j4 Ω, XL2 = j5 Ω, V1 = 10 V RMS.
[8 marks]
Figure 1
3. (a) Apply mesh analysis to the circuit shown in Figure 2 and write the resultant
equations in matrix form. Hence solve for the current in R2 using determinant
algebra.
[14 marks]
(b) Write a set of equations for the node voltages v1, v2, and v3 expressing the
equations in matrix form (Do not solve for any node voltages).
R1 = 1 Ω, R2 = 2 Ω, Xc1 = -j1 Ω, Xc2 = -j0.25 Ω, Xc3 = -j0.25 Ω, XL1 = j4 Ω,
V1 = 5∠60 V.
[6 marks]
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Figure 2
4. A single-tuned RF amplifier stage, using a self-biased common source JFET, is
required to operate at a centre frequency of 1 MHz and with a bandwidth of 50
kHz. Sketch the circuit diagram and briefly explain the circuit operation.
[7 marks]
For this amplifier, calculate
i) The loaded Q-factor of the circuit
ii) The source bias resistance value,
iii) The inductance value for resonance,
iv) The ac resistance of the coil, and
v) The maximum voltage gain.
The transconductance of the transistor is gm = 2 mS. It may be assumed that the
total tuning capacitance is 100 pF and the unloaded Q-factor of the coil is 50.
The quiescent drain-source current I dsq is 2 mA with Vgsq = 2 V. Justify any
assumptions made in the analysis.
[13 marks]
SECTION B
5. The output signal from digital filters can be characterised according to the
equation:
m
L
k =0
k =1
y ( n) = ∑ a ( k ) x ( n − k ) − ∑ b ( k ) y ( n − k )
Use this definition to classify FIR and IIR type filters. Give a simple block
diagram using a first-order representation for each filter.
[8 marks]
Obtain the system function H(Z) for the DSP system represented in block
diagram form as shown in Figure 3. Plot the pole-zero map and state with
justification, whether the system is BIBO stable.
a = -0.5, b =- 0.75
[12 marks]
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Figure 3
6. (a) Obtain the Z - transform for the step function f(n) = u(n) if the unilateral Z
transform is defined as:
∞
f ( z ) = ∑ f (n).Z − n
n =0
[6 marks]
(b) A difference function for a system is given as:
y (n) = x(n) + 0.5 x(n − 1) + 0.25 y (n − 1) + 0.75 y (n − 2)
Draw a block diagram representation and derive the system function H(Z).
[8 marks]
(c) Outline a graphical technique for obtaining the frequency response of a system
using the pole-zero map.
[6 marks]
7. (a) Explain the importance of digital convolution.
[4 marks]
(b) Discrete convolution of an input signals x(n) and the impulse response of a
system h(n) is related by the equation:
m
y ( n) = ∑ x ( k ) h( n − k )
k =0
Using the convolution sum, obtain the output response y(n) for a system if a
input signal x(n) shown in Figure 4 is applied. The impulse response h(n) is
identical to x(n).
[10 marks]
(c) Verify that the output Y(Z) is the product of the individual Z- transforms of
x(n)and h(n).
[6 marks]
Figure 4
5
8.
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(a) The circuit shown in Figure 5 has a 1V step applied at time t=0 seconds.
Redraw the circuit in the s-domain and show how initial conditions are
represented.
[6 marks]
(b) Obtain an expression for the current I(t) in the circuit before the switch is
closed.
[6 marks]
(c) Obtain a value for the current at t = 0.2 seconds if the switch is closed at
time t = 0.1 seconds. The initial conditions at t = 0 seconds are zero.
R1 = R2 = 5 Ω, L = 2 H, V1 = 1 V.
[8 marks]
Figure 5