Comparison Bridge:

There are two types of Comparison Bridge, Namely

1. Capacitance Comparison Bridge
2. Inductance Comparison Bridge

1. Capacitance Comparison Bridge:

Figure 11.18 shows the circuit of a capacitance comparison bridge. The ratio arms R₁, R₂ are resistive. The known standard capacitor C₃ is in series with R₃. R₃ may also include an added variable resistance needed to balance the bridge. C_x is the unknown capacitor and R_x is the small leakage resistance of the capacitor. In this case an unknown capacitor is compared with a standard capacitor and the value of the former, along with its leakage resistance, is obtained. Hence.

The condition for balance of the bridge is

i.e.

Two complex quantities are equal when both their real and their imaginary terms are equal. Therefore,

i.e.

and

Since R₃ does not appear in the expression for C_x, as a variable element it is an obvious choice to eliminate any interaction between the two balance controls.

2. Inductance Comparison Bridge:

Figure 11.20 gives a schematic diagram of an inductance comparison bridges. In this, values of the unknown inductance L_x and its internal resistance R_x are obtained by comparison with the standard inductor and resistance, i.e. L₃ and R₃.

The equation for balance condition is

The inductive balance equation yields

and resistive balance equations yields

In this bridge R₂ is chosen as the inductive balance control and R₃ as the resistance balance control. (It is advisable to use a fixed resistance ratio and variable standards). Balance is obtained by alternately varying L₃ or R₃. If the Q of the unknown reactance is greater than the standard Q, it is necessary to place a variable resistance in series with the unknown reactance to obtain balance.

If the unknown inductance has a high Q, it is permissible to vary the resistance ratio when a variable standard inductor is not available.