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ELT-47426 Transmission lines and waveguides

Exam, April 28th 2014. Answer to all guestions.
No material. Own calculators (not programmable) allowed.
Jari Kangas

1. Through a non-magnetic material (/4r = 1) is traveling a wave. Its electric field is given as
E(z,t) = 4sin(2r « 107t — 0.86x)u; — [V/m]

(a) Could this expression hold for a plane wave?
(b) Find the phase velocity, relative permittivity, and wave impedance of the material.

(c) Find the accompanying magnetic field intensity H(z,?).
In total 4.5 p.
2. Define in an appropiate way

(a) Transmission line eguations.

(b) Inductance per unit length in transmission lines.
(c) Telegrapher's eguation.

(d) Hybrid mode.

In total 6 p.

3. (a) Explain briefly key properties of dielectric waveguides.
(b) In the last page are two plots that are obtained after simulation of a rectangular waveguide.
The plots are taken in the zy-plane. Based on them, explain which mode is propagating
(with proper reasoning).
(c) State how to form so called leap frog algorithm to simulate EM waves in ideal transmission
lines.

In total 7.5 p.

4. In the course, we considered first ideal transmission lines and assumed such structure to have as
materials either ideal dielectric or perfect electric conductor (PEC). Let us consider a structure
that has as materials either ideal dielectric or perfect magnetic conductor. Could the latter
structure support TEM waves? If, so what kind of properties would EM fields need to fullfil?
Support your answer with proper reasoning. (HINT: try to find logical steps that allow your
reasoning. You will need the Maxwell laws, but try not to get too much into their details.)

(7.5 p.)
5. (a) Define briefly guality factor of a cavity resonator. Which factors affect on its value (when
considering cavities in practice)?
(b) Consider a rectangular cavity resonator whose dimensions are a x b x c=5x4x3cm3

i. What is the lowest resonance mode and resonance freguency of such a cavity when it
is filled with air?

ii. It is known that the lowest resonance freguency of such a cavity is 3437MHz when it
is filled with snow. Determine the relative permittivity of (this kind of) snow.

In total (4.5 p.)

TURN OVER
Miscellaneous information about rectangular waveguides etc.

e The propagation constant can be expressed as

090

where jo = 4r x 10" 7H/m and eo = 8.854 x 10 ?F/m.

 

e For good conductors skin depth is
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o Conductivities:

Silver 6.17 « 107 [S/m]
Copper 5.80 « 107 9 4 +/2 + 107 [S/m]
Brass 1.57 x 107 [5/m]
Iron 107 [5/m]

e speed of light in vacuum c = 2.99792458 x 108m/s % 3 x 108m/s
e intrinsic impedance 719 = 4 [= = 120m O

o e =1+oif|x| small
 

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