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Summer Examinations 2011
Exam Code(s) 4BN1, 4BP Exam(s) Final Year Electronic Engineering Final Year Electronic & Computer Engineering
Module Code(s) EE328.II Module(s) Engineering Electromagnetics
Paper No. Repeat Paper
External Examiner(s) Professor G.W. Irwin Internal Examiner(s) Prof. G. Ó Laighin Dr. P. Corcoran
Instructions:
Answer any three of four questions (20 marks each)
Duration: 2 hrs
No. of Pages Department(s) Electrical & Electronic Engineering Course Co-ordinator(s)
Requirements : MCQ Handout Yes (appended) Statistical Tables Graph Paper Log Graph Paper Other Material
Attempt 3 questions only – 20 marks per question. (NB: where applicable you must include rough-work calculations to obtain full marks for these questions.)
Question 1(a) Given a 2.0cm length of AWG20, radius 406 × 10 −^6 m copper wire calculate, (i)
R DC , (ii) R AC , at 800 MHz, and (iii) estimate the inductance, L.
[4 marks] (b) Starting with a 1.0 mm diameter solid copper wire you are to design a 75 ohm coaxial T-Line using mica as the dielectric. Determine (i) the inner diameter of the outer copper conductor; (ii) the propagation velocity of the line; and (iii) the approximate attenuation in dB/m at a frequency of 1 MHz. [6 marks] (c) The impedance and propagation constants at 100 MHz for a transmission line are measured as
Z 0 = 18. 6 − j0. 253 and γ= 0. 0638+j4. 68 per metre. Calculate the distributed
parameters of this T-line. [5 marks]
(d) A 2.4 GHz signal is launched on a 1.5 m length of T-Line terminated in a matched load. If it takes 6.25 ns to reach the load and suffers 1.2 dB of loss find the propagation constant..
[5 marks]
Question 2 (a) Derive the differential phasor form of (i) Gauss's Law, and (ii) Ampere's Circuit Law. [4 marks]
(b) Given a UPW incident from medium (^1) σ= 0,^ μr =^1 .0,^ εr =^25 , to medium 2 σ=^0.^ 0080,^ μr =^1 .0,^ εr =^81 calculate the reflection and transmission coefficients and the standing wave ration (SWR) at 1 kHz, 1 MHz and 1 GHz. [6 marks]
(c) A 100 MHz TE polarized wave with amplitude 1.0 V/m is obliquely incident from air (z < 0)
onto a slab of lossless, non-magnetic material with εr =^25 (z > 0). The angle of incidence is
40 °. Calculate (i) the angle of transmission; (ii) the reflection and transmission coefficients, and (iii) the incident, reflected and transmitted fields. [10 marks]
Some Useful Constants & Relationships (EM Waves)
ε 0 = 8. 854 × 10 −^12 F / m = 10 −^9 / 36 πF / m η 0 = 120^ π^
μ 0 = 4 π × 10 −^7 H / m c = 2. 998 × 108 m / s
∇ ×∇ × A= ∇. A −∇ 2 A
Pavg =
ηH so^2 a n =
E^2 so^ a n
Some Useful Constants & Relationships (T-Line)
Z 0 =
R'+jωL'
G'+jωC' Z^ L^ =Z^0
V^ 0 +V 0 -
V^ 0 − V 0 -
γ= (^) ^ R'+jωL' × G'+jωC' ^ VSWR=^1 ∣ Γ ∣
Lossless Line
Z in =Z 0
Z L +jZ 0 tan βl
Z 0 +jZL tan βl
Distributed Parameters at High Frequencies
Coaxial Cable Twin-Lead Cable
R’ (/m) (^1 1 ) (^2) c
f a b
c
f a
L’ (H/m) ln 2
b a
cosh 1 2
d a
^
G’ (S/m)
ln
d b a
cosh 1 2
d d a
C’ (F/m)
ln b a
cosh 1 ^ d^ 2 a
Material Properties
Electrical Conductivity Relative Permittivity
Relative Permeability
Copper 5. 8 × 107 Siemens/m 1 1
Nickle 1. 5 × 107 Siemens/m 1 ~ 600
Sea Water (^) 4.8 Siemens/m ~ 72 1
Deionized Water 0.08^ Siemens/m^
Mica 1. 1 × 10 −^15 Siemens/m 5.4 1
