Calculations of electromagnetic fields of radiating conductors

Two methods are available for the calculation of the electromagnetic field in the neighbourhood of a radiating conductor, that employing the so-called vector and scalar potentials and that based on Hertz's solution for the field of a small dipole. The first is well-suited for calculating the field surrounding a linear radiator a half-wave or a number of half-waves in length, the current in the radiator being assumed to be in the form of a standing wave. It is shown that this method applies only to systems which are complete in themselves and no current must enter or leave the radiating conductor, a condition which renders the method useless for calculations concerning the terminated aerials which are now universally employed. The second method consists of breaking up the radiating conductor into an infinite number of small dipoles, the field due to each dipole is known from Hertz's work, and the total field can be obtained by integration. The second method is described in detail and the application to both terminated and unterminated aerial systems is shown, and, in some cases, the results are compared with those obtainable by the vector method. A method of calculating the radiation resistance is included, together with examples of the application of the theoretical work to the calculation of the field due to wires of any length and terminated by any impedance. Phase-delay devices placed at the centre of a wire terminated by its surge impedance are also studied.