( Chapter 5 

 STANDARD PROPAGATION 



51 INTRODUCTION 



By standard propagation is meant radio wave 

 propagation through an atmosphere free from 

 irregular stratifications, particularly of vertical dis- 

 tributions of water vapor and temperature. With 

 irregular stratification the propagation is said to be 

 nonstandard and will be treated extensively in the 

 later chapters. 



In this chapter the fundamental general relations 

 between transmitted and received power is first re- 

 viewed ; then the main factors influencing the trans- 

 mission of electromagnetic waves such as refraction, 

 diffraction, and dielectric properties of the ground 

 are surveyed; and finally the computation of the 

 field at the receiver for various heights of transmitter 

 and receiver above a homogeneous smooth earth of 

 given electromagnetic properties is very briefly dis- 

 cussed. The last subject divides naturally into the 

 determination of the field above the line of sight and 

 the determination of the field below the line of sight 

 in the earth's shadow. - 



The text of the present chapter largely follows the 

 book, issued by the Columbia University Wave 

 Propagation Group [CUDWR WPG] under the title 

 Propagation of Radio Waves through the Standard 

 Atmosphere which is Volume 3 of the Summary 

 Technical Report of the Committee on Propagation. 



5.2 



POWER TRANSMISSION 



Certain relations occur so frequently in wave 

 propagation problems that it is convenient to 

 summarize them here before entering into a descrip- 

 tion of the characteristic features of short wave 

 propagation. Some of these are mere definitions; 

 some are consequences of electromagnetic theory. 



It is convenient to use, as a standard antenna, one 

 which has a length which is small compared to the 

 wavelength, designated as "doublet." Such doublets 

 may be used for both the transmitting and receiving 

 antennas. In the latter case it is assumed that the 

 load resistance is matched to the output resistance 

 of the antenna. In free space, optimum transmission 

 is achieved when the two doublets are parallel to 



each other and perpendicular to the line connecting 

 their centers. If their distance apart, d, is large com- 

 pared to the wavelength, the ratio of power trans- 

 mitted to maximum useful power received is found 

 from electromagnetic theory to be 



Pi \8ttcIJ 



(1) 



where X and d are measured in the same units. Here 

 P 2 is the power delivered to a matched load at the 

 output terminal of the receiver and P x the power fed 

 to the transmitting antenna. 



The gain G of any directive antenna is the ratio of 

 the power transmitted by a doublet to the power 

 transmitted by the antenna in question, to produce 

 the same response in a distant receiver, when both 

 transmitting antennas are adjusted for maximum 

 transfer of power. The gain of a receiving antenna is 

 similarly the ratio of the power delivered to the 

 transmitting antenna when a doublet receiving an- 

 tenna is used to the power delivered to the transmit- 

 ting antenna to produce the same response when the 

 antenna in question is used at the receiver. 



Two methods of expressing antenna gain are in 

 common use: the one just indicated where the gain 

 is measured as the ratio of the power in the optimum 

 direction relative to that of a doublet, and the other 

 where the gain is that relative to a hypothetical iso- 

 tropic radiator which is one assumed to radiate the 

 same power density in all directions. Simple geomet- 

 rical considerations show that the gain of a doublet 

 over that of an isotropic radiator is 3/2 so that the 

 gains expressed in the former system are converted 

 into the latter system by multiplying them by 3/2. 

 In the equations below, the gain is expressed relative 

 to the doublet. 



If transmission takes place, not in free space, but 

 over a conducting ground, in a refracting atmosphere, 

 etc., the power ratio will be expressed as 



Pi 



= G\Gi 



(— V 



\8ird) 



(2) 



where G1G2 are the antenna gains of the transmitting 

 and receiving systems, respectively, and A v is the 



31 



