IOWA STATE UNIVERSITY College of Engineering OF SCIENCE AND TECHNOLOGY and Computer Engineering Problem Set No. 5 Spring Term 1998 Department of Electrical EE 313 Issued: 980217T Due: 980224T Reading Assignments: Sadiku, 12.1; and your lecture notes. Problem 1 Calculate the cutoff frequencies for the lowest 5 modes guided in a parallel-plate waveguide for which the upper and lower plates are separated by 5 cm, and the permittivity of the medium between the two plates is ² = 2 ²o . Problem 2 Consider a parallel-plate waveguide filled with a dielectric material for z > 0 , as shown. The dielectric material has permittivity ²1 . The operating frequency is 30/(2π) GHz. √ (a) Let d = 2 3π cm and consider the empty waveguide case when ²1 = ²o (in the absence of the dielectric). Which TEm and TMm modes can propagate in this waveguide? (b) Find expressions for the E and H fields for the TM2 mode. √ (c) Let ²1 = 3 ²o and d = 2 3π cm. For waves propagating in the +z -direction, for which values of m will the TMm modes be totally reflected at the dielectric boundary? Why? x d µo , ² 1 µo , ² o z z=0 Problem 3 An air-filled parallel-plate waveguide has a plate separation of 1 cm. At what frequencies can the modes TE1 , TE2 , TM0 , TM1 , and TM2 propagate? What are the phase velocities for the TE1 mode at 20 GHz? Near 15 GHz?