422 BELL SYSTEM TECHNICAL JOURNAL 



known, the magnitudes of the capacitances can be determined from 

 the knowledge of one only of the resistances, e.g., that in the series arm. 

 Since the ratio of any two capacitances may be obtained with a high 

 degree of precision by supplementary measurements, it therefore be- 

 comes possible to use the bridge just described without a knowledge of 

 the parallel resistance, the measurement of which presents certain 

 practical difficulties. 



Although the Wien circuit is fundamentally simple, it is subject to 

 many severe requirements when used to make an accurate determina- 

 tion of capacitance in terms of resistance and frequency, and must 

 embody in its construction the refinements necessary for work of such 

 high precision. In the Bell Telephone Laboratories there is available a 

 capacitance bridge ^ of high precision, which is ordinarily used for the 

 direct comparison of capacitances, and which, with slight modifications, 

 is readily adapted to this purpose. 



Theory of the Circuit 



If in Fig. 1 the ratio arms are equal in resistance and phase angle, 

 the equation of balance may be written 



and separating reals from imaginaries 



Ci R 



^=^-i (1) 



and 



^^' - i? • (2) 



From these two equations it is obvious that, if the values of r, R and 

 w, are known, the true values of C and Ci can be determined. 



However, the method of calibrating the capacitance bridge, which 



is described below and which is carried out irrespective of this determ- 



C . . 



ination gives the value of ^r , precisely, and this allows the reduction of 



the quantities to be determined to two, co and R or w and r. 



Let C and Ci now be taken as the values of the two condensers as 



C 

 measured on the capacitance bridge to determine their ratios jr . 



^ G. A. Campbell, Elect. World and Engineer, April 2, 1904; Bell System Teclmical 

 Journal, July 1922; W. J. Shackelton and J. G. Ferguson, Bell System Technical 

 Journal, Jan. 1928. 



