Abstract :
The paper is concerned with the behaviour of earthed openaerial receiving systems. The analysis of such systems is based on the classical transmission-line equations, as modified by Moullin to apply to distributed excitation. Part 1 gives the theoretical formulae so obtained for the case of a plain aerial with uniformly distributed constants, and the detail of the variation with frequency of the resistance and reactance components of the effective impedance of such an aerial. It is shown that successive resonances (i.e. conditions of zero reactance) are given by an equation of the form ?=(4h/n)(I+Ah2) where n is any integer and A is a small factor depending on n and on the attenuation constant of the aerial considered as a transmission line. The corresponding values of the resistance are shown to be Rh/2 (approximately) when n is odd, and a very high value when n is even, R being the total effective resistance per unit length of the aerial. The actual variation of the impedance of a plain uniform aerial as a function of frequency was determined experimentally, and a detailed analysis of the results in relation to the theory is given. The observed variations of resistance and reactance are shown to be in substantial agreement with those deduced from the analysis, but it appears that the actual length of the aerial (h) must be replaced by an effective length h + ?, ? being about 5 per cent of h. This is in agreement with a more rigid analysis by Abraham, and with experimental results obtained by Wilmotte. The observed aerial resistance was found to be mainly due to parasitic eddy-current and dielectric losses. It was reduced to less than one-third of its value by using a single-wire ?earth screen.? The validity of the fundamental assumptions, to a useful degree of approximation, having been established by measurement, Part 2 of the paper is devoted to obtaining additional information by purely analytical methods. The analysis is mainly based on the case of a plain aer- ial divided into three parts in each of which a uniformly distributed e.m.f. is assumed to be induced, the intensities being different in the three parts. By an analytical manipulation of this three-part case a line integral formula is found for the effective e.m.f. induced in a uniform aerial by a non-uniform field (Section 7). The variation of the effective e.m.f. induced by a uniform field is considered as a function of frequency and. aerial height, and it is shown that no advantage is gained by making h > ?/4 unless certain parts of the aerial are compressed (Section 8). The relative effectiveness of different parts of a receiving aerial is considered in Section (9), and it is found that in an L aerial short compared with the wavelength the addition of a down-lead from the open end nearly to the ground may actually increase the total effective e.m.f. in spite of the reversed e.m.f. induced in the added length. An earthed aerial of this shape with the vertical members of length ?/4 and the horizontal member of length ?/2 is shown to have a figure-of-eight polar diagram with a law of. the form cos (1/2? cos ?) (Section 10). The effective e.m.f. formulae of the three-element case are applied to the Franklin suppressed half-wave construction and afford means of allowing for the effect of aerial resistance in this system (Section 11). In Section (12) the effective e.m.f. of the present formulation is related to the original conception of ?effective height.? It is suggested that the idea of ?effective height? is one which has to a great extent outlived its usefulness. The analysis of a receiving aerial considered as a collector of energy from the incident wave is given in Section (13). The figure of merit from this point of view is |e6|2/R6, which is determined as a function of h and ?. It reaches a maximum when h is very approximately ?/4, and thereafter oscillates with rapidly diminishing amplitude. Considered as a collector of energy the suppressed half-wave
