The problem of radiation and reception of electromagnetic waves associated with a spherically capped biconical antenna having unequal cone angles 1 and 2 is investigated. Both cones that comprise a bicone are excited symmetrically at the apices by a voltage source so that the only higher order modes are TM. A variational expression for the terminal admittance is derived. Under the wide-angle approximation, expressions for the radiated field, the effective height, and the terminal admittance are obtained. In addition, limiting values of these quantities are derived for electrically small and electrically large wideangle bicones. The results for arbitrary cone angles are new and subsume results that appear in the existing literature as special cases such as where 1 = 2 or 2 = =2. Moreover, the approximations of this paper are more accurate than many in the literature. It is argued that the radiation pattern of an electrically small cone is proportional to sin , which is similar to that of a short dipole; whereas the pattern behaves like 1= sin for electrically large cones. The parameter is the angle from the bicone's axis of symmetry to the observation direction. Consequently, the direction of maximum radiation changes with exciting frequency for a bicone of fixed length. Although most of the analyses are presented in the frequency-domain, time-domain responses of bicones are discussed for some special cases that are similar to situations considered by Harrison and Williams. In particular, the time-domain radiated field and the received voltage are shown to depend on the input's passband and on the match between the source and the bicone.
The essential portion of a received Loran‐C signal of 100 kHz consists of groundwave only. The phase velocity of the groundwave which is related to TOA (time of arrival) and TD (time difference) values depends on various parameters, such as ground conductivity (or surface impedance), terrain variation, and the refractive index profile of the atmosphere. In order to calculate exactly the phase velocity, signal strength, etc., it is necessary to solve the electromagnetic wave equation, rigorously incorporating all of the above mentioned parameters. Since this is an impossible mathematical task, several approximate methods with various degrees of complexities had been sought by various authors in the past. Among these approximate methods or propagation models, the following are notable: (1) homogeneous flat earth model of Sommerfeld and Norton, (2) homogeneous spherical earth model of Watson, Van der Pol and Bremmer (the last two authors included also the effect of inhomogeneous atmosphere), (3) Millington's empirical model for an earth with mixed surface conductivities for computing signal strength, (4) Pressey and his associates' empirical model for earth with mixed surface conductivities for computing phase, (5) Wait's multisection spherical earth model, (6) Hufford's integral equation approach to the propagation over an irregular surface, and (7) Jollier's integral equation approach which is a generalization of Hufford's method with the aid of a computer. This paper presents a general overview of these methods and their limitations with a special emphasis directed towards Loran‐C.
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