156 BELL SYSTEM TECHNICAL JOURNAL 



For a given capacitance unbalance of the ratio arms, it is seen 

 that the error in inductance is inversely proportional to the time 

 constant LjR of the impedance arm and is independent of the fre- 

 quency, while the error in resistance is proportional to the frequency 

 and to the ratio of reactance to resistance, that is, to the tangent of 

 the phase angle. The inductance error is, therefore, maximum for the 

 minimum time constant apparatus to be tested. Within the range 

 previously mentioned this occurs when an impedance having the 

 minimum reactance to resistance ratio of 10 is being measured at the 

 minimum frequency of 500 cycles. Under this condition RjL has a 

 value of (27r X 500)/10 or approximately 300. The corresponding 

 percentage error in inductance per micro-microfarad of capacitance 

 unbalance is then 300 X 1000 X lO-io = 3 X 10"^ or 0.00003 per cent. 

 Evidently a very considerable unbalance can be tolerated. In the 

 case of the resistance component, the error is maximum when an 

 unknown impedance having the maximum reactance to resistance 

 ratio is being tested at the maximum frequency. A reactance to 

 resistance ratio of 300 is very rarely exceeded. For this value, the 

 error per micro-microfarad unbalance at a frequency of 50,000 cycles 

 amounts to about 9.5 per cent. Hence, to limit the error from this 

 source to the order of 1 per cent requires a balance of about 0.1 

 micro-microfarad. It will be appreciated that this is an extremely 

 close balance, the maintenance of which, under the different conditions 

 of temperature and humidity to which the bridge may be subjected, 

 requires careful consideration of the effects of these factors. 



The effective phase-angle balance, though discussed above in terms 

 of capacitance only, is, of course, the resultant of the inherent residual 

 inductances and capacitances of the coil windings plus the additional 

 capacitance effects due to the coil shields. The component due to 

 residual magnetic induction is not appreciably affected by tempera- 

 ture or frequency changes. The capacitance component of the wind- 

 ing, however, tends to vary with temperature in accordance with the 

 temperature coefficient of capacitance of the dielectric used for insulat- 

 ing the wire and with frequency to the extent that the capacitance is 

 affected by absorption. 



It is common practise to employ silk-insulated wire treated with 

 varnish or wax for purposes of protection against moisture in such 

 coils. In order to obtain data covering the temperature and absorp- 

 tion effects and also the phase-angle characteristics of silk insulation, 

 both untreated and when treated with a number of the more common 

 materials, various samples were constructed and tested as indicated 

 in Table I. 



