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 Z 3∙Z
