Abstract
The determination of directivity values for circular microstrip patches on thin substrates involves the use numerical integration procedures, which have to be repeated every time there is a change in patch-substrate permittivity, By a judicious use of certain approximations, it is shown here that it is possible to secure surprisingly accurate alternative descriptions of the patch directivity behavior (as a function of permittivity), in terms of either known tabulated functions, or functions that can be easily accommodated using a hand-held calculator.
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