Practical Bridge Circuits for LCR Measurement

The dial of potentiometer R8 need be calibrated on only one range (say, the X lK range) by successively connecting a number of accurately known resistors in that range to unknown terminals X-X and successively balancing the bridge. However, the dial should be graduated from 0.1 ohm to 10 ohms - the basic range. If all of the standard resistors are accurate (1% or better), each range will track with the dial calibration.

Because of stray capacitances in the circuit, Cx values lower than 100 pf cannot be measured accurately.

Unless the potentiometer has a special taper, such as logarithmic, the graduations will crowd at the ends of the dial, seriously impairing accuracy, and for that reason the capacitance range with any one standard capacitor C3 should not exceed 0.1 to 10 times Cs, even though the potentiometer can afford a wider range.

A complete null occurs only if losses in the unknown capacitor equal those in the standard capacitor. 

The degrading effect of stray capacitances in the useful ranges of the bridge may be reduced somewhat by keeping the potentiometer resistance, R2, reasonably low—say, 5000 ohms. Also, the wasted ends of the potentiometer in the simple circuit may be resolved by means of extension arms (R1 and R3) which allow the useful 100:1 capacitance range to be spread over the entire resistance range of the potentiometer.

It is convenient to express the relationship between losses (resisttive component) and inductance (reactive component) as the figure of merit or Q of the inductor. 

Numerically, Q = XL/R — tangent of the phase angle of the equivalent LR network. 

A low-loss inductor has a high Q. 

A complete null is obtained only when the Q of the unknown inductor equals that of the standard inductor. When the Q’s are unequal, as they almost always are in practice, enough resistance must be added in series (sometimes in parallel) with the lower-loss inductor to reduce its Q to that of the higher-loss inductor. Addition of resistance to one or the other of the inductors will complete the balance of the bridge.

Generators and Detectors