Noise Considerations in Resistance Bridges

A signal-to-noise analysis is made of the Wheatstone bridge, where the unknown and standard resistors may be at different temperatures, a situation which occurs in resistance thermometry. The limiting condition is assumed to be dissipation in the unknown resistor. It is shown that the ratio arms should be low in resistance compared with the unknown resistor, while the standard resistor should be high. This is true to an extreme degree when the unknown resistor is at liquid helium temperatures, and the standard resistor at room temperature. This factor is much less important in high temperature thermometry, where the noise in the unknown resistor will predominate strongly. An impedance step-up device (transformer or tuned circuit) is valuable in raising the bridge signal and noise level above the noise of the first amplifier tube. However, as the step-up ratio is increased, two counterfactors appear, namely, noise in the loss resistance of the step-up device, and grid current noise. There is therefore an optimum step-up ratio, which has been found. The step-up device is permitted to have a different temperature from the unknown and standard resistors, to evaluate the advantage of cooling it. With certain assumptions about the noise and grid current of the first tube it is found that the equivalent temperature of a unity ratio (Mueller) bridge used for liquid helium measurements may be 400°K.