EAN: 9783031005695

SYNTHESIS LECTURES ON COMPUTATIONAL ELECTROMAGN...

This book introduces the Mellin-transform method for the exact calculation of one-dimensional
definite integrals  and illustrates the application if this method to electromagnetics
problems. Once the basics have been mastered  one quickly realizes that the method is extremely
powerful  often yielding closed-form expressions very difficult to come up with other methods
or to deduce from the usual tables of integrals. Yet  as opposed to other methods  the present
method is very straightforward to apply  it usually requires laborious calculations  but little
ingenuity. Two functions  the generalized hypergeometric function and the Meijer G-function 
are very much related to the Mellin-transform method and arise frequently when the method is
applied. Because these functions can be automatically handled by modern numerical routines 
they are now much more useful than they were in the past. The Mellin-transform method and the
two aforementioned functions are discussed first. Then the method is applied in three examples
to obtain results  which  at least in the antenna electromagnetics literature  are believed to
be new. In the first example  a closed-form expression  as a generalized hypergeometric
function  is obtained for the power radiated by a constant-current circular-loop antenna. The
second example concerns the admittance of a 2-D slot antenna. In both these examples  the exact
closed-form expressions are applied to improve upon existing formulas in standard antenna
textbooks. In the third example  a very simple expression for an integral arising in recent 
unpublished studies of unbounded  biaxially anisotropic media is derived. Additional examples
are also briefly discussed.

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