# Computational Modelling Techniques for Slot Antennas

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## Abstract

Given the computational power, and the sophisticated software, which modern design engineers and scientists can readily access, it is perhaps not too surprising to learn that the vast majority of the novel antenna developments of today, rely heavily on electromagnetic modelling packages, which embed within them all of the macroscopic level physics governing linear antenna operations. These simulation tools, which can readily be used in the design of compact antenna arrays described later in this book, rely firstly on modelling of the EM boundary value problem represented by a radiating aperture and secondly by accurate representation of the EM interactions when the radiating elements are embedded in an array (Chap. 5). In fact it is probably true to say that, for engineers today, rather than applying mathematical skills and theoretical diligence to construct EM solutions in their analytically simplest form in order to ease the computational burden—this was the customary route before massive computer power became readily available—it is more sensible now to employ methods which represent these linear antenna problems in their originally unreduced formats (i.e. as coupled bounded regions with all of the relevant physics specified), and rely on the computer modelled mathematics to do the rest. This chapter addresses the issue of formulating a generally applicable mathematical procedure capable of accurately and efficiently modelling elemental radiators, which is important if the elements are to be embedded in an array simulation with many repetitive calculations. It is shown that the origin of such a model relies on Chap. 3 where succinct integral relationships are established between radiation field quantities **A** and **A**_{m} and source terms, which are usually represented by current density vectors **J** and **J**_{m}. These integral equations while succinct are comprehensive, and are shown to belong to a class of mathematical formulation, which can be converted to ‘computer friendly’ matrix form. In antenna problems this is commonly achieved by employing techniques which are generally referred to as moment methods. The evolution of the moment method as a mathematical tool for securing fast and versatile computational models of radiation from slot configurations is explored in this chapter.

## Keywords

Antenna Problems Moment Method Compact Antenna Arrays Friendly Computer Order Inhomogeneous Differential Equation## References

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