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A comment on the radiation resistance

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A comment on the radiation resistance - Antennas and Propagation Magazine, IEEE A Comment on the Radiation Resistance Sava V. Savov Department of Electrical Engineering, Eindhoven University of Technology 5600 MB Eindhoven, The Netherlands E-mail: [email protected] Keywords: Analytical methods; antenna theory; power radiation integrals; directivity; radiation resistance: clrcular loop antenna; circular microstrip antenna; loop antennas; cylindrical antennas; microstrip antennas; Bessel functions irst, I would like to thank Dr. John D. Mahony for his valuable Equation (1) in my paper [l]. I also would like to thank him for the observed misprints in the paper: a multiplier (1/2) was missing in Equations (7) and (E), and a superscript must be changed from (1) to(-l)inthelasttermofEquation(13). F’ comments regarding Q-integrals representation, introduced by Second, by using the following simple recurrence for the Bessel functions, one can obtain an altemative expression for the auxiliary function T ( 5 ) involved in Equation (16) for the radiation resistance, RF1 (4) , in the case of a sinusoidal excitation of the circular-loop antenna: instead of Equation(15). This expression has the advantage of being in terms of only three QLk) (5) functions (with m = n ) , For the particular case of n = 1, an explicit expression in terms of Bessel functions was given by Equation (8) in the paper (for the case of a constant excitation). In the very recent paper of Mahony in the same column [Z], he offered a generalization of this repre- sentation for the case of an arbitrary n in his Equation (4): which transforms the equation given above for the T ( 5 ) function into the following final equation: I have performed calculations using both expressions: the old one, Equation(15), and the new one, Equation(15a). They gave very similar results in the interval (0 < 5 < 15), with a relative differ- ence less than 0.2%, so theoretically they are both equivale

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