704 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



of 50 kc to 20 mc using equations (3) and (4). From an error standpoint 

 it is not piacticable to use lengths much longer than 7 ft. as standards at 

 20 mc. However, shorter lengths of which there are twelve may be used to 

 provide standards at higher frequencies. There are six longer lengths, and 

 the entire group of eighteen may be used to provide eighteen numerical 

 values of each ''prime" in the frequency range of 50 kc to 10 mc. There is 

 the restriction, from the standpoint of application, that the impedance com- 

 ponents are available only in ''pairs"; each R' has a definite L' associated 

 with it, or each G' has a value of C in association. 



Error Considerations 



Examination of Figs. 7-10 shows that the "primes" as computed from 

 (3) and (4) exceed the distributed constants by a gradually increasing 



Table IV 

 Estimated Errors in Computed Input Impedance Components of 7.0 ft. Length 



Coaxial Standard 



* Assumes possible error of ± 25% in knowledge of power factor of the dielectric 

 material. 



amount as frequency is increased. Except for G' the excess is largely pro- 

 portional to the product oj^LC ^, where t is the length of the line, and L 

 and C are in terms of unit length. The total error in a "prime" at a given 

 frequency is then approximately the error in the distributed value com- 

 bined with the proportioned error in co^LC ^. Table IV shows the computed 

 errors for the 7.0 ft. standard at 1 mc where the contribution of co^LC /^ is 

 small and at 20 mc where it is relatively large. The errors quoted were com- 

 puted from estimated errors involved in determination of the various physi- 

 cal quantities associated with the constants of Tables II and HI.® 



G' was mentioned above as an exception. This results from the fact that G' 

 is largely proportional to co^C^R^ above 1 mc. That is, the excess of G' 

 over G rapidly increases with frequency so that the value of G may be 

 neglected above 1 mc. The precision of G' is that of the determination of 

 w^C^R^, a quantity which can be determined with very good precision as 



• "Electrical Measurements, and the Calculation of the Errors Involved," D. Raro, 

 Macdonald & Co., Ix)ndon. 



