BRIDGE METHODS OF MEASURING IMPEDANCES 463 



sidered. It may be well to point out that the performance of the 

 bridge is determined very much by the degree to which the phase 

 angle requirements are met. If there is appreciable error here, the 

 two balances will not be entirely independent and necessary corrections 

 will be complicated and difficult to make. Consequently, the first 

 essential for a satisfactory bridge is that its fixed arms meet their 

 phase angle requirements. For a general purpose bridge these require- 

 ments must hold independent of frequency at least over an appreciable 

 frequency range. 



The forms given in Fig. 2 meet their phase angle requirements at 

 all frequencies provided the arms are actually pure resistances or 

 reactances. If they have residuals associated with them, it is still 

 possible to meet the phase angle requirements in most cases, at least 

 over a reasonable frequency range, as discussed below. 



Resistances can be made to have practically zero phase angle, and 

 condensers, particularly air condensers, may be made to have phase 

 angles of practically 90°. In the case of condensers having dielectric 

 loss, this loss may be kept quite small. However, it takes such a 

 form that the phase difference of the condenser is approximately 

 independent of frequency. For this reason, it can not be represented 

 accurately either as a fixed resistance in series with the condenser or 

 as a fixed conductance in shunt, when considered over a frequency 

 range. Due to the small amount of this loss, it is usually satisfactory 

 to represent it in either one form or the other, whichever is the more 

 convenient. 



In the case of inductance, there is always a quite appreciable series 

 resistance which, for the usual size of coil, can not be neglected and 

 must accordingly be corrected for. 



With the above considerations in mind, the forms of Fig. 2 may 

 now be reconsidered from the practical standpoint. It is readily 

 seen that the requirements of the real ratio type bridge can be met 

 using resistances, capacitances, or inductances. In the case of the 

 imaginary ratio type, the requirements can be met, at least very 

 approximately, in the case of Figs. 2d and 2e. However, in the case 

 of Figs. 2/ and 2g, any resistance in series with the inductance must 

 be corrected by a capacitance in series with the resistance, if the 

 correction is to be independent of frequency. Since the value of this 

 series capacitance will, in general, be large, this form of correction is 

 unsatisfactory. For instance, for a bridge in which the value of R is 

 1000 ohms and the inductance has a high time constant, the series 

 capacitance required is in the order of 3 ^f- By using a standard of 

 inductance having larger series resistance, we may reduce this 



