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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.