ECE 485/585 - Microwave Design Techniques
Spring Term 2020

Take-home Midterm

The exam is posted on Wednesday, May 13 at noon and is due on Thursday, May
14 at noon. By submitting this take-home exam, you certify that you have not used
or consulted any resources other than the class notes, class homework
assignments, class lab notes, information posted on the Canvas class space, and
the textbook while working on the following problems. Total number of points: 40
pts.

1. (10 pts.) A waveguide load with an impedance of 377W for the dominant mode
is to be matched to an air-filled rectangular waveguide at 10 GHz using a
quarter-wave matching transformer. All waveguide sections have the same
cross-sectional dimensions (WR-90). The quarter-wave section is realized by
filling the space inside the waveguide section with a dielectric material.
Determine the required dielectric constant of the dielectric material and the
physical length of the quarter-wave section. Discuss limitations of this matching
technique.

For ECE585 students only: What is the return loss of the quarter-wave
matching transformer at = 11 GHz?

2. (a) (4 pts.) An air-filled rectangular waveguide contains a solid rectangular
conductor of width w and thickness t placed in parallel to the waveguide axis,
as shown in the cross-sectional view below. Determine the cutoff frequency
and phase velocity of the fundamental (dominant) propagation mode of this
structure. (Assume all conductors to be perfect.)

(b) (2 pts.) Consider two microstrip lines A and B with identical dimensions
(strip width and ground plane spacing) but on different substrates of relative
permittivities %,' and %,( where %,' < %,( (% = 1 for both dielectrics). If both
microstrips are fabricated to have length 8⁄ at the operating frequency, which
line is physically longer? Explain.
metallic
waveguide
conductor
a
b t
w x y
3. (14 pts.) Without using tables, derive the impedance, ABCD, and scattering
parameters for the two-port network shown below. Determine the insertion loss
and return loss of the network. The port impedances are: /0 = ; /3 = 2,
where is purely resistive.

4. (10 pts.) A four-port network has the scattering parameters shown below (all
four port impedances are equal to 5). Now, ports 3 and 4 are connected with
a lossless transmission line having characteristic impedance 5 and electrical
length . For the resulting two-port network, determine the insertion loss and
phase delay between ports 1 and 2 in terms of , , , and . Give numerical
values for
= 0.3 exp(−30°) ; = 0.8; = 0.7 exp(−30°) = 0.7 exp(−45°)
and = 60°.

() = K 0 0 0 00 0 00 L

For ECE585 students only: Also determine the return loss at port 1.

Port 1 Port 2
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