COAXIAL IMPEDANCE STANDARDS 691 



It is the open (Zop) and short circuit (Zah) input impedances which are of 

 utiHty for bridge calibration work, however, and except for lines much less 

 than quarter wave in length, Zop and Zsh must be computed from the dis- 

 tributed constants using the transmission line equations. 



The propagation constant and characteristic impedance may be computed 

 from the distributed constants by means of the equations: 



7 = V(R + joiLYJG + >C), and (1) 



= 4/^44^, (2) 



G +joiC' 



where the numerical values of the distributed constants are, of course, de- 

 pendent on the appropriate quantities as in Table I and the length of the 

 Hne. Further, for any coaxial line terminated in an open circuit or a short 

 circuit, respectively: 



J_=G'+icoC' = ^, and (3) 



Z,h = R' + J03L' = Zo tanh 7 (4) 



Equations (3) and (4) rigorously relate the input impedances for open 

 and short circuited far-end conditions to 7 and Zo in (1) and (2), and 

 thus back to the physically measurable quantities of the coaxial structure. 

 Precise values of the apparent distributed primary constants R', L', G' and 

 C are the final objective, as these quantities comprise the standards. As 

 is shown, they are computed from basic data on the dielectric of the co- 

 axials and on a single metal comprising the conductors of the coaxials. 



It is of interest to note that, because of the mutual effects of the dis- 

 tributed constants on each other, the conductance component of the input 

 admittance of a coaxial line becomes increasingly a function of the dimen- 

 sions and resistance of the conductors of the line, as frequency is increased. 

 Thus calculable standards of conductance are obtained which are essentially 

 independent of losses in the insulating material used to support the center 

 conductor. 



Coaxial Standards for Laboratory Use 



General Description 



Although short-length coaxials have been used by the Laboratories for 

 some years as impedance standards for cable measurements, refinements in 

 measurement techniques have made it desirable to construct a new set of 

 standards with very uniform components and improved structural qualities. 



