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COMM.RF.430 Transmission lines and waveguides

Small Exam I, January 31st 2023. Answer to all questions.
Jari Kangas

1. Consider a segment of a lossless parallel plate transmission line. Figs. 1-2 give “side-view”, the
plates are on top and bottom, the TL is fed from its left end and connected to a (matched) load at
its right end. The Figs. show how fields vary along the z ~axis on the line, the Figs. are of the same
case.

In the Figs. the positive y ~axis points upwards and the positive 2 —axis points away from you.

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(a) Find the relative permittivity of the insulator, assume py = 1.
(b) Sketch the surface charge density (in reasonable manner). Explain also briefly how it is detex-
mined.

 

(c) Derive expression for the H-field.
(d) How would the picture 1 change if ey and py are doubled.
Power fed to the TL and other settings stay the same.

In total 4 p.

2. (a) Use the given data sheet to estimate vp, C, L, and Zp in lossless case.

(b) Explain what is y = a+ jf and the terms included. Use the data sheet to find a and results of
the (a)-item to find y (at 400 MHZ).
In total 4 p.

3. Let us consider the transmission line below that consists of two conductors and dielectric in be-
tween (lets assume ideal conductors and ideal dielectric with relative permittivity ¢, and relative
permeability py).

Explain options and the related expressions to find L from appropriate field quantities, use of suitable
drawings is suggested. You may assume that the field quantities are solved via numerical simulation
(e.g. in Comsol). (2 p.)

 

 

Constants in free space and some formulas:

e dielectric constant €q % 8.854 * 1071? F/m
© permeability pio © 4 * 107? H/m

e speed of light ¢ = 2.997925 * 108 m/s

© intrinsic impedance 7 = va 12070 Q
© e* 2 1+2 if |e| small

0 y= WRF jwl)(GF jaO) = a+ §8
el(z)= Reet (2)

° w x B= 2B