ELEC 306 HOMEWORK #2       Spring 2001

 

 

(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%.