# − = 001 00 1 1 00 100 2 1 j j j j S

```EE172
Fall 09
Sample Final
Microwave Engineering
Dr. Ray Kwok
1) An air-filled cavity has dimensions 5 x 8 x 10 cm. Find the lowest resonant frequency.
2) Two networks [A] and [B] are connected in parallel as shown. Both networks are well defined. I.e., all [S],
[Z], [Y] and [ABCD] matrices are available. What’s the easiest way to calculate the combined [S] matrix for
this network? [Note: You don’t need to write out everything explicitly. But the procedure and the matrix
elements should be clearly defined.]
A
B
3) Write down the general Z-matrix, Y-matrix, ABCD-matrix and the S-matrix for the following circuit without
using the conversion table.
C
L
4) An attenuator can be made using a section of waveguide operating below cutoff. If WR75 rectangular
waveguide is used and the operating frequency is 10 GHz, determine the required length of the below cutoff
section (width = a/2) of a waveguide to achieve an attenuation of 100 dB between the input and output
guides. Ignore the effect of reflection at the step discontinuities.
5) A four-port network has the scattering matrix shown below. If ports 2 and 3 are connected with a lossless
o
matched transmission line with an electrical length of 90 , find the resulting insertion loss and phase delay
between ports 1 and 4.
0 0 1 j


−1  0 0 j 1 
S=
2  1 j 0 0 
 j 1 0 0


6) A lossless 50 ohms air line has Vmax=2.5 V and Vmin=1 V when terminated with an unknown load. The
distance between the successive voltage minima is 5 cm and the first voltage minimum from the load end is
1.25 cm.
a) Use a Smith Chart to locate this load impedance.
b) Design a matching network using a lumped element and a quarter-wave transformer.
c) Design a matching network using 2 open stubs only.
d) Design a double-stub matching network using a 100 Ω open series stub (load side) and a 100 Ω shorted
shunt stub (input side) separated by a 50 Ω transmission line of 0.1 λ.
```