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jan syiYkdäl? STÄMTTIN 4
ELT-47426 Transmission lines and waveguides

Small Exam I, January 27th 2014. Answer to all guestions.
Jari Kangas

1. Consider following description in wikipedia under title Transmission line: ae Ca
Valforni ari I K =
ALS In communications and electronic engineering, a transmission line is a specialized cable or
Ea 5 other structure designed to carry alternating current of radio freguency, that is,
; currents with a freguency high enough that their wave nature must be taken into account.”
[n foinrr eleer Vengs |

Do you consider that this is an accurate definition? If not, highlight points to be clarified. Give
also precise and concise reasoning on how you would correct them. (3 p.)

2. You find in the opposite side of the paper field plots of a simulation case on a transmission
line (coaxial cable with non-circular inner conductor). The case has been further analyzed and
data given in the table below is gathered. On the white board additional information about the
curves and domains is provided.

Your task is to use the given data to analyze the case, to derive relevant guantities and parameters
in terms of transmission line analysis (the more, the better). Pay attention to details and support
your analysis with reasoning (again, try to give precise and concise answers). (4.5 p.)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Domain Function | Expression | Value Unit
Curve 1,2,3,4 Integral | n-D 81869209 | O/m |/ hu.
Curve 1,2,3,4 Integral | u;-Js -1.58429 A Loran
Curve 5 Integral | Ez 59.90137 Vv Vol hae
Domain D1, D2, D3, D4 | Integral TE -:D 2.4536e-07 | J/m 5.
Domain D1, D2, D3, D4 | Integral | /H-B 24536007 | J/m | tmmy
Curve 5 Integral | By 3.09543e-7 | Wb/m negatre (ly
Curve 1,2,3,4 Integral |t-H -1.58429 A Cvulrvr"
Curve 6 Integral | Bz -3.09543e-7 | Wb/m | Myacre Ply
3. (a) Let us consider the transmission line below that consists of three conductors and dielectric in
o, between (lets assume ideal dielectric with relative permittivity €, and relative permeability
s 1,0 ; Hr). What could you say about possible TEM-wave solutions to the problem, how could
A you characterize them? (2.5 p.) =
Eo. 150
Ko 1 ot -

tv v a |) n 7
| hv en z Chi hes

Candven”

(b) A phone line has R = 309/Km, L = 0.1H/km, G = 0 and C = 204F/km. Assume that
f = 1kHz, find
i. The line characteristic impedance.
ii. The propagation constant.

 

30 N

iii. The phase velocity. 405 0/9
iv. The attenuation in dB after 2 km. — 3-4 44

(In total 2 p.)

 
 

Effective mode Index=1.549193

i
O

Figure 1: Plot of E-field

 

Effective mode index=1.549193

  

Figure 2: Plot of H-field

 

E I | i
Constants in free space and some formulas: | Do JA ] Er 55100 | Valve | Un:'r +
e dielectric constant €, = 8.854 « 10 2F/m SA o sn | x |
|
€ permeability jo = 4r « 107H/m |

speed of light c = 2.997925 x 108m/s

3 intrinsic impedance 79 = 4 ja = 1207 9

e" =1+=xif|x| small

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