Fundamentals of Electromagnetic Fields

Chapter 9: The Wave Guides

In order to transmit an electromagnetic wave along a certain path, it has to be configured in the vicinities of the boundaries, where it propagates by successive reflection. A hollow conducting metallic tube of uniform cross-section for transmitting an electromagnetic wave by successive reflection from the inner wall of the tube is called a wave guide.

The propagation in the wave guide can be considered as a phenomenon in which waves are reflected from wall to wall and hence pass down the wave guide in zig-zag fashion. The resultant wave travels longitudinally down along the wave guide and has no component of either electric or magnetic fields in the direction of propagation. A large number of distinct field configurations or modes are theoretically possible in the wave guide, which can be determined from the solution of Maxwell s equations and which satisfy the boundary condition.

An essential feature of the waveguide is that it exhibits a frequency characteristic similar to that of the high-pass filter, in that there is a lower limiting frequency below which there is no transmission. At frequencies below the cutoff value, the wave is simply reflected backward and makes no forward progression.

9.1 ANALYSIS OF AN ELECTROMAGNETIC WAVE IN RECTANGULAR GUIDES

While studying the electromagnetic field configuration in a wave guide, we fix upon the following few constraints to make our discussion meaningful and compact.

  • Assume that walls of the rectangular wave guides are perfect conductors.

  • This gives boundary conditions on E

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