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Cork Institute of Technology
Bachelor of Engineering (Honours) in Electronic Engineering – Stage 3
(Bachelor of Engineering in Electronic Engineering – Stage 3)
(NFQ – Level 8)
April 2005
Electromagnetic Propagation
(Time: 3 Hours)
Answer six questions including two from Section A and four from Section B. Use separate answer books for each Section Smith Charts are available
Values for constants; εo = 8.854 x 10 -9^ Fm- μo = 4π x 10 -7^ Hm- Speed of light in a vacuum = 3 x 10 8 m s -
Examiners: Mr. J. Ryan Prof. C. Burkley Dr. R. A.Guinee Dr. O. Gough
Section A
Q1. (a) Determine the poles of an n th^ order low pass Butterworth filter whose magnitude function has the form H j 1 2 n ( )^1 Ω
Draw a sketch illustrating the pole location in the S -plane. (4.66 marks) (b) Design a Butterworth low pass passive filter with a cut off frequency of 10 6 rad/sec, 600 Ω load termination impedance and whose pole location are shown in Fig. Q1.
Σ
j Ω -0.5+0.866j
-0.5-0.866j
-
Fig. Q
(7 marks) (c) Using the maximally flat response in (b) design a high pass filter with a cut off frequency of 10 4 rad/sec feeding into a 1kΩ load termination. (5 marks) [Total Q1: 16.67 marks]
Q2. (a) Briefly compare the low pass Chebyshev filter approximation with that of the
Butterworth type in (i) the passband and (ii) the stopband using magnitude plots. (3.66marks) (b) The voltage transfer function vvo^ i ( s )of the VCVS network shown in Fig. Q2, with gain
a
b
R
K = 1 + R
is (^0) Y 5 ( Y 1 Y 2 Y 3 Y 4 ) 1 Y 44 [ Y 1 Y 2 ( 1 K ) Y 3 ]
KYY
v
v
i + + + + + − +
= (^).
Using this VCVS topology draw a high pass filter structure and derive its voltage transfer function vvo^ i ( s ). Determine the filter parameters (i) dc gain H 0 , (ii) pole frequency ωP and (iii) pole Q-factor QP in terms of the network RC components. (6 marks)
Y 2 Y 4 Y 5
K vi (^) Y 3 Vo
Y 1
Fig. Q
(c) From your high pass filter structure from (b) above determine the sensitivity of the network parameter 1/ Q (^) P with respects to the capacitor components. Using minimum 1/ QP sensitivity design a second order Chebyshev low pass filter with a passband loss of 0.5dB and edge frequency ωp of 20× 103 rads/sec given that the normalised Chebyshev transfer is
14256 15162
14314 2
2
..
S S
H S S.
Choose capacitors with values of 0.01μF as the starting point in the filter synthesis. (7 marks) [Total Q2: 16.67 marks]
Section B
Q4 (a) State Maxwell’s Equations in differential form and explain your understanding of them, giving the units for each term. (10 marks) (b) Show how the Helmholtz Wave Equation can be derived. (Useful relation: F F F
ρ ρ 2 ρ ∇ ×( ∇× )=∇(∇⋅ )−∇ for any vector field F ) (6.67 marks) [Total Q4: 16.67 marks]
Q5 (a) A dielectric window tilted at the Brewster angle to incident radiation will partially polarize the transmitted wave. Explain briefly how this occurs (4.67 marks) (b) A plane wave of wavelength 30 cm in free space is incident on a dielectric medium. The reflections produce a standing wave ratio of 5 with a minimum at the interface. Compute the thickness and dielectric constant of a dielectric layer to be applied to the face of the first dielectric that will eliminate the reflections. (12 marks) [Total Q5: 16.67 marks]
Q6 (a) Starting with the solutions for the transmission line equations V x ( ) = Ae −^ γ x^ + Be +γ x^ and
I x ( ) = (^) ZA e −^ x^ − ZB e + x 0 0
γ γ (^) , show that the input impedance of a transmission line of length l
terminated in Z (^) L ≠ Z 0 , is given by (^)
cosh( ) sinh( )
cosh( ) sinh( ) 0
0 0 Z l Z l
Z Z Z l Z l L
in L
γ γ. (8.67 marks)
(b) A transmission line is 12 km in length and has the following primary constants per loop km. R = 25 Ohm, L = 0.6 mH, C = 0.04 uF, G = 0. Calculate the characteristic impedance of the line and the total loss over the length of the line in dB at a frequency of 10kHz. (Hint: Don’t assume low frequency approximation is valid) (2 x 4 marks) [Total Q6: 16.67 marks]
Q7 (a) At high frequencies it is important to operate at minimum VSWR. Several methods are available to match a load to a line or to match cascaded lines with different characteristic impedances. Discuss this statement. (7.67 marks) (b) A 50 Ohm high frequency, lossless transmission line is used at a frequency of 600 MHz and v =c. It is terminated with a load of (160 + j 80) Ohms. Use the Smith chart to determine: (i) The VSWR (3 marks) (ii) If an 11 nH inductor is placed across the line 10 cm from the load determine the new VSWR. (6 marks) [Total Q7: 16.67 marks]
Q8 (a) Explain with the aid of a diagram how intermodal dispersion can occur in a step index fiber-optic cable. How could intermodal dispersion be reduced or eliminated? Derive an expression for the degree of pulse spreading in multimode step index fiber in terms of the core and cladding refractive indices and the length of the fibre. (8.67 marks)
(b) A repeater system has the following components: Transmitter: Optical Launch power +6 dBm, rise/fall time = 1ns Receiver: Min. receive power –50 dBm, dynamic range 30 dB, rise/fall time 2 ns. Fibre: Graded Index fibre, Attenuation 0.4 dB/km in 500m spools, dispersion 0.4 ns/km Splice Loss: 0.2 dB +/-0.1 dB Include a safety margin of 3 dB Determine i) the maximum and ii) the minimum repeater spacing for this system and the maximum operating bit rates for both conditions (2 x 4 marks) [Total Q8: 16.67 marks]
