DIELECTRIC PROPERTIES OF WATER AND ATMOSPHERE 



181 



the teiuperatuve dependence of its dielectric properties 

 at 1.25 and 1.58 cm. 



11 the pwwer transmitted through two tliicknesses 

 di and d.2 of tiie material in question are 



Pi = Foe-"-*., 



tlicji tlic absorption coefficient a is given by 



2.3 



Pi 



d2 — di Pi 



(77) 



where P^ is the incident power. 



Tlie absorption index k in the complex refractive 

 index 



A' = n - jk (78) 



is related to the absorption coefficient by 



47r/c 



a = 



X 



and hence 



(79) 



, 2.3X A 



iwd Pi 



(80) 



where d stands for (t/, — (^i). Also 



iV2= (^n-jky=er-jei, 



= fr- jQOaX. (81) 



Er is the real part of the dielectric constant, c; its 

 imaginary part; o- is the conductivity of the sub- 

 stance is mhos per meter; and X the wavelength in 

 meters. Ojie obtains readily from equation (81) 



n^ — fc^ = Cr 



2nk = ti = GOcrX. 



(82) 



The absoi-ption index k is measured directly by two 

 galvanometer readings proportional to P^ and P^. 

 The refractive index n is derived from the reflection 

 coefficient B^ for almost perpendicular incidence, 



2 ?i' + fc' + 1 - 2n 



(S3) 



n^ + fc' + 1 + 2n 



Then ■« and Z; determine e,- and cr. Saxton claims that 

 in this method at least one quantity, the absorption 

 index, is measured directly while the other, the re- 

 fractive index, is derived from the measurement of 

 the reflection coefficient. 



In the other methods, giveir later, neither of these 

 quantities is measured directly. 



Standing Wave Eatio Method 



By limiting the electromagnetic field to the en- 

 closure of a hollow pipe or coaxial line, the energy 

 is completely confined, stray effects are eliminated, 

 and small amounts of any dielectric can be inves- 

 tigated accurately.^""*- The following gives the the- 

 oretical foundation of this "standing wave ratio" 

 method for measuring complex dielectric constants. 



1. A transmitter radiates waves of a given fre- 

 quency into one end of a closed wave guide. These 

 are reflected by the metallic boundary at the other 

 end. Standing waves are set up in the guide, and 

 they can be measured by a probe detector traveling 

 along a slot in the pipe parallel to its axis. The dielec- 

 tric is inserted at the closed end of the pipe, opposite 

 the transmitter, and fills the pipe up to a height d. 

 Above it the standing wave pattern is measured in air. 

 The real and imaginary parts e,- and ii of the dielec- 

 tric constant are calculated from the ratio of the field 

 strengths in node and antinode Emny/Enuxx, fuel the 

 distance .i\^ of the first node from the surface of the 

 dielectric. 



The modulus and the argument of the reflection 

 coefficient are obtained from 



R = pe-J* = 



{ZiO)/Zoi) 



1 



(84) 



(Z(0)/Zoi) + 1' 

 where Z(0) is the characteristic impedance of the pipe 

 section filled with the dielectric understudy, Z^ is 

 the intrinsic impedance of the air-filled portion of 

 the pijje. By denoting 



Z(0) 



= tanh 5 = tanh (5r + j5,) , 



(85) 



where 8,- and 8; are, respectively, the real and im- 

 aginary part of 8, the reflection coefficient R can be 

 written as 



R= |fl|e-'*, 



= pe-'* , 

 with 



(86) 



p= \R\ =e-"^';argR= -7r-25. = -$. (87) 



From the expression of the reflected field strengths 

 one finds that the distance .!■„ of the first node from 

 the surface is given by 



Xo 



- 5,Xi 

 2ir 



(88) 



where Si is connected directly to the phase shift $ at 

 reflection through equation (87), and Ai is the wave- 



