(1) A rectangular waveguide with dimensions a = 2.5 cm, b = 1 cm is to operate below 15.1 GHz. How many TE and TM modes can the waveguide transmit if the guide is filled with a medium characterized by s = 0, e = 4e0, µr = 1? Calculate the cutoff frequencies of the modes.
Calculate the phase constant, phase velocity, and wave impedance for TE10 and TM11 modes at the operating frequency of 15 GHz.
(2) A brass waveguide (s = 1.1 ´ 107 mhos/m) of dimensions a = 4.2 cm, b = 1.5 cm is filled with Teflon (er = 2.6, s = 10-15 mhos/m). The operating frequency is 9 GHz. For the TE10 mode:
(a) Calculate ad and ac.
(b) What is the loss in decibels in the guide if it is 40 cm long?
(3) A microwave transmitter is connected to a rectangular waveguide filled with polyethylene (e = 2.25 e0) to an antenna and operates at 24 GHz. If the cutoff frequency of a certain TE mode is 16 GHz, find the group velocity and intrinsic impedance of the mode.
(4) If the walls of a 4 cm square waveguide are made of brass (s = 1.5 ´ 107 S/m) and is excited with the TM21, find the attenuation ac if the waveguide operates at 10% above the cut-off frequency and the distance over which the wave is attenuated by 30%.