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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering- Stage 2
(NFQ Level 8)
Summer 2007
Linear Systems and Electrodynamics
(Time 3 hours)
Answer any five questions Examiners: Prof. G. Hurley Dr. S. Foley Mr. M. Hill Dr. J. Connell Q1. (a) Signals can be either discrete or continuous. Illustrate the difference between continuous and discrete signals with examples of both. Describe how the audio signals from a tape recording and an MP3 music file can be classified as continuous or discrete signals. [4 marks] (b) Given the signal f(t), shown in Figure 1(b), express the signal f(t) as the sum of unit step and ramp functions and illustrate your answer. If the response of a linear RL circuit to a unit step input u(t) is given by (2(1-e-t^ )), write an expression for the output in response to input f(t) and sketch the output waveform. [8 marks]
(c) Decompose the voltage signal shown in Figure 1(c) below into its Odd and Even components. Illustrate the method used. [8 marks]
0
1
2
3
4
-3 -2 -1 0 1 2 3 4 5 6 time t[s]
f(t)
Figure 1(b)
0
1
2
3
4
-3 -2 -1 0 1 2 3 4 5 6 time t[s]
f(t)
Figure 1(c)
Q2. (a) Determine the poles and zeros of the following function. Plot the pole-zero diagram and describe and sketch the corresponding time response. [6 marks]
s s s
I s
(b) Describe and illustrate the unit impulse function. Describe how a signal is approximated as a series of impulses and how this can be used to derive the convolution integral. [6 marks] (c) Using the convolution integral, calculate the output voltage of the RC network of Figure. 2(c), whose impulse response is given below, to a step input voltage of amplitude 20V.
vo ( t )= 10 [ e −^20 t ]
Figure 2(c) [8 marks]
25kVA three-phase induction motor load at a power factor of 0.75 lagging, the other is a star-connected set of impedances, each having a resistance of 12Ω and an inductive reactance of 16Ω. Calculate the power factor of the overall system. [15 marks]
Q6. (a) Distinguish between iron losses and copper losses in a transformer. Describe with diagrams how the iron losses in a transformer might be measured. (b) In a 100kVA transformer, the iron loss is 800W and the full-load copper loss is 1.5kW. Calculate the efficiency at half-load and at full-load for unity power factor. [4 marks] (c) What is the maximum efficiency of the transformer in (b)? [6 marks]
Q7. (a) What is the purpose of slip-rings in an AC generator? [4 marks]
(b) What is “commutation” in a DC generator? [4 marks] (c) A three-phase induction motor is wound for 4 poles and is supplied from a 50Hz system. The rotor impedance per phase at standstill is 0. 2 + j 1. 2. Calculate: (i). The synchronous speed [1 mark] (ii). The slip when the speed of the rotor when is 800rpm [1 mark] (iii). The rotor frequency when the speed of the rotor is 800rpm [2 marks] (iv). The impedance and power factor per phase of the rotor at 800rpm
[4 marks]
