Chapter 5 

 CALCULATION OF RADIO GAIN 



5.1 



5.1.1 



INTRODUCTION 



Objectives 



THIS CHAPTER is devoted to the definition and 

 calculation of the various factors -whicli enter 

 into a computation of the field strength of radio 

 waves propagated in the standard atmosphere above 

 the earth. 



In Chapter 2, particularly in Sections 2.1 and 2.2, 

 are given the basic definitions of path-gain factor 

 and radio gain for transmission between doublets 

 and other antenna types in free space. The present 

 chapter shows how these quantities must be modified 

 to account for the influences introduced by the 

 curvature and electrical properties of the earth. 



The methods of computation are presented in 

 considerable detail to enable the interested reader to 

 apply them to his particular problem, and sample 

 calculations are given which should assist in reducing 

 to a minimum the time required for obtaining the 

 answers in a given case. 



^•'•^ Definitions Relative to Radio Gain 



The radio gain is defined as the ratio of received 

 power Pi, delivered to a load matched to the receiver 

 antenna, to transmitted power Pi, with both an- 

 tennas adjusted for maximum po\\er transfer. For 

 doublet antennas in free space this ratio is given by 

 (3X/87rrf)- and is denoted by Ao', that is, 



P-2 



P, 



^ = Ao 



iTTdJ 



and the free-space gain factor is given b> 



3X 



Ao = 



87rd 



(1) 



(2) 



reflection and difi'raction effects of the ground are 

 taken into account, the expression for the radio gain 

 becomes a very complicated affair. 



For the general case of one-way transmission, the 

 radio gain is given by 



in which d denotes the distance from the transmitter 

 to the receiver measured in the same units as the 

 wavelength X. 



When the radiation is emitted and received by 

 directive antennas and the propagation takes place 

 through a refracting and absorbing atmosphere, and 



Pi 



= GiG^A^ 



(3) 



where (7i and G^ are the gains of the transmitting and 

 receiving antennas, respectively, and A, the gain 

 factor, is equal to 



A- 



AgAj, 



(4) 



with Ap equal to the path-gain factor. [See equation 

 (27) in Chapter 2.] 



For radar or two-way transmission, the radar gain 

 is decreased because the energy traverses the path 

 both ways and is influenced by the radiating proper- 

 ties of the target as given by the radar cross section a. 

 Combining equations (46) in Chapter 2 and (2) in 

 this chapter, the radar gain equals 



P 

 Pi 



' = ^'^'^C-S?) [-'"^^^^^ = ^-^^^Cd?)-'' ^'^ 



Comparing equations (3) and (5), it is seen that the 

 gain factor A may be used also for two-way trans- 

 mission, provided the additional term IGwa/QX- is 

 included in the formula. 



Later on it will be shown how to split up A and Ap 

 into a product of various factors, represented by 

 graphs which make it possible to carry out computa- 

 tions in specific cases. 



The gain factor A may also be expressed in terms 

 of the field strength E and free-space field strength of 

 a doublet transmitter Eo. From equation (28) in 

 Chapter 2, 



E = Eo^GiAp. 



Combining this equation with equation (4) 

 A _E 1 



(6) 



(7) 



where PoVf/i is the free-space field of the trans- 

 mitting antenna with gain Gi. 



60 



