Page:The Bell System Technical Journal, Volume 1, 1922.pdf/22

Colpitts Substitution Bridge Method, Fig. 2

The unknown direct capacity is shifted from one side of the bridge to the other, and the balance is restored by adjusting the capacity standard so as to shift back an equal amount of direct capacity. The method is therefore a substitution method, and the value of the bridge ratio is not involved. Both the standard and the unknown remain in the bridge for both settings, so that the method involves transposition rather than simple, ordinary substitution.

Details of the method as shown by Fig. 2 are as follows: To measure the direct capacity C₁₂ between terminals 1 and 2 connect one terminal (1) to corner D of the bridge, and adjust for a balance with the other terminal (2) on thee corner A and then on C, while each and every one of the remaining accessible termingals (3, 4, . . .) of the electrical system is permanently connected during the two adjustments to either corner A or C. If the direct capacities in the standard condenser between corners A and D are C′, C″ in the two balances,

$C_{12}=C''-C'$

and if the bridge ratio is unity^[1],

$C_{13}-C_{14}=C'+C''-2C^{\circ }$

,

where C₀ is the standard condenser reading when the bridge alone is balanced.

Two settings are required by this method for an individual direct capacity measurement, but in the systematic measurement of all the direct capacities in a system the total number of settings tends to equal the total number of capacities, when this number becomes large. The number of settings may always be kept equal to the number of capacities by employing an equality bridge ratio, and using thee expression for the direct capacity difference given above. The same remarks also hold for the group of direct capacities connecting any one terminal with all the other terminals.

In general, ground is placed upon corner C of the bridge, but is transferred to corner D, if it is connected to one terminal of the required direct capacity. The arbitrary distribution of the other terminals between corners A and C may be used to somewhat control the amount of standard capacity required; or it may be helpful in reducing interference from outside sources, when tests are made upon extended circuits. The grounded capacity of a terminal or group of terminals is measured by connecting the group to C, and all of the remaining terminals together to D.

1. See appendix, section 2.