G28 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1957 



arbitrary aspect.* The number and size of the reflecting layers, as well 

 as the magnitude of the discontinuities in the gradient of dielectric con- 

 stant which form them, influence the received power. 



The reflecting properties of the layers are discussed first. Next, an ex- 

 pression for the received power is obtained by summing the contributions 

 of many layers in the volume common to the ideaUzed patterns chosen 

 to represent the transmitting and receiving antenna beams. f This ex- 

 pression is then used to calculate the effect on received power of changes 

 in such parameters as the orientation of the antennas, wavelength, dis- 

 tance, and antenna size. 



The MKS system of units is used throughout. 



REFLECTING 

 ' SURFACE 



Fig. 1 — Reflection bj' a layer. 



EFFECT OF LAYER SIZE 



Propagation from a transmitting antenna of effective area At to a 

 recei\-ing antenna of effective area Ar by means of a reflecting layer is 

 illustrated in Fig. 1. The ray from transmitter to receiver grazes the 

 layer at angle A. The reflection from the layer depends on the ampli- 

 tude reflection coefficient, q, which is a function of the grazing angle, and 

 on the dimensions of the layer relative to the dimension of a Fresnel 

 zone. I Three cases, depending on the layer dimensions, will be considered. 



* After this paper was submitted for publication, a report was received giving 

 some measurements of sharp variations in dielectric constant gradient and esti- 

 mates of the horizontal dimensions of layers in the troposphere. J. R. Bauer, 

 The Suggested Role of Stratified Elevated Layers in Transhorizon Short -Wave 

 Radio Propagation, Technical Report No. 124, Lincoln Laboratory, ^LI.T., Sept., 

 1956. 



t Under some conditions, layers outside the volume common to the antenna 

 beams maj' contribute appreciablj^ to the received power. Phenomena such as 

 multiple reflections and trapping mechanisms are not considered in this study. 



J The power received bj- reflection from the layer in Fig. 1 can be calculated 

 approximateh" bj- assuming it to be the same as the power that would be received 

 by diffraction through an aperture in an absorbing screen, the dimensions of the 

 aperture being the same as the dimensions of the layer projected normally to the 

 directions of propagation. The field at the receiver is calculated from the distri- 

 bution of Huj'gens sources in the aperture. The received power, e.xpressed in 



