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Methods, formulas, and tables for the calculation of antenna capacity

1926; The National Institute of Standards and Technology; Volume: 22; Linguagem: Inglês

10.6028/nbsscipaper.222

0096-6231

F. W. Grover,

Antenna Design and Analysis

To calculate the capacity of an antenna a certain charge is assumed upon the antenna and the resulting potential is calculated.In carrying out this method the difficulty is met that, in general, the law of distribution of the charge is not known.Howe made the assumption that sufficient accuracy is attained if first a uniform distribution of charge is supposed to exist and the potential calculated at various points of the antenna, the average of these potentials being taken as the final equilibrium potential.Howe called attention to discrepancies between the values obtained by his method and published values for the same antennas by the inductance method.The present paper shows that the two methods agree if appropriate inductance formulas are employed.The Howe method is more general, and it is believed to give suffi- cient accuracy for engineering requirements.Formulas are given for the common types of single and multiple wire antennas in a form convenient for numerical computation, together with tables of constants which will be found useful in such calculations.In addition, tables of the capacities of both horizontal and vertical single-wire antennas and horizontal two-wire antennas have been included, which should render all calculation unnecessary in many inportant practical cases.CONTENTS I. Introduction 570 II.General method used for calculating the capacity 572 III.Single horizontal wire 573 IV.Howe's approximation 575 V. Method of successive numerical approximations 576 VI.Treatment of combinations of wires 579 VII.Derivation of working formulas for the capacity 584 VIII.Working formulas for calculating capacity of various practical forms of antennas 585 1. Single horizontal wire 586 2. Single vertical wire 586 3. Single-wire inverted L antenna 587 4. Single-wire T antenna 588 5. Parallel horizontal wires in the same horizontal plane 588 6. Antenna of parallel wires equally spaced in a vertical plane 59 1 7. Parallel wire inverted L antenna 591 8. Parallel wire T antenna 592 9. Horizontal "cage" antenna 593 10.Vertical "cage" antenna 594 11.Single V antenna 595 569 570 Scientific Papers of the Bureau of Standards i voi.gg VIII.Working formulas for calculating capacity of various practical forms of antennas-Continued.Page 12. Two horizontal wires inclined to one another13. Single-wire inclined to the earth 's surface 14.Parallel wire V antenna 15.Antenna of parallel wires in a plane inclined to ground 16.Conical antenna 17.Umbrella antenna 18. Fan or harp antenna IX.Use of tables for three common forms of antennas X. Calculation of capacity of lead-in wires XI.Tables for antenna capacity calculation ' Elec.World, Oct. 27, 1910.Qrover]Capacity of Antenna Systems 571The formulas for wires of infinite length suffice for calculations with transmission lines, but in the very important case of an antenna, the wires of which it is composed are seldom of such a length that their distances from one another and from the earth, can be neglected in comparison with their lengths.A correction for the lack of uniformity of distribution of the charge along the wires has to be taken into account.The capacity of a single wire has sometimes been calculated from the formula for a very long thin ellipsoid, isolated in space, but only in recent years have formulas for the more common forms of antenna been derived.Of these, especial mention may be made of the work of Cohen,ŵ ho derived formulas for the capacity of an antenna consisting of a number of wires, arranged parallel to one another and to the surface of the earth (flat-top antenna) by assuming the reciprocal of the capacity per unit length to be equal to the inductance per unit length of the system of wires, assumed to be joined in parallel with the earth as return.This reciprocal relation holds exactly only when the wires are of infinite length.The most extensive contribution is, however, furnished by the papers of Howe,* who has obtained formulas for a number of common forms of antenna from electrostatic considerations.The distin- guishing feature of his treatment is the method used to take into account the lack of uniformity of distribution of the charge along the wires.Howe called attention to the considerable difference in the value of the capacity calculated by Cohen for a certain flat-top antenna and the value obtained by his own formula for the same case, but gave no explanation of the discrepancy.