helix Antenna Theory Regular
Joined: 29 Jan 2015 Posts: 64
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Posted: Tue Sep 08, 2015 4:41 am Post subject: |
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Check W.C. Chu's book, one of the early chapters describes it mathematically.
http://www.amazon.com/Waves-Fields-Inhomogenous-Media-Weng/dp/0780347498/
Basically, if i recall correctly, the non-transverse (to the direction of wave propagation -- assume it's the z-direction) component of one field defines the transverse components of the other field via each of Maxwell's curl equations.
That is, for TM, the Ez field is non-transverse, and that defines the two transverse components of H. For TE, the Hz field is non-transverse, and that defines the two transverse components of E. Now if you count up what I just said, you have two non-transverse components, and four transverse components derived from those... That's all there is: 3 components of E and 3 of H. So the two non-transverse components are all you need to know to completely define the fields. Furthermore, the relationship between the two non-transverse field components Ez and Hz can often be determined via boundary conditions of the problem at hand. Thus, all the fields are defined within a scalar constant, and the field distribution of the entire problem is thus considered solved. |
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