Null detector

A null detector indicates whether a residual signal has been brought sufficiently close to zero in a null measurement method. A galvanometer between the middle junctions of a Wheatstone bridge is a concrete example: equal junction potentials give zero detector current.^[ref] Its useful property is the ability to distinguish small residuals and their sign near balance.

For an original electronic model, let the detector output bewhere $ϵ$ is the residual electric potential difference, $G$ is gain, $z$ an output zero offset and $n$ an output noise term. With known zero offset and negligible noise, an output threshold $|d|\le 1\mathrm{mV}$ at $G=1000$ corresponds to $|ϵ|\le 1\mu \mathrm{V}$. It is a resolution criterion for this model, not a total measurement uncertainty.

A false zero exposes another limit. If $z=2\mathrm{mV}$, a displayed $d=0$ can occur at $ϵ=-2\mu \mathrm{V}$ for the same gain. Increasing gain improves the output response to a given residual, but measurement calibration must still address offset and noise. Polarity reversal measurement can help separate signal from an unchanged internal offset: ifthen $ϵ=(d_{+}-d_{-})/(2G)$ and $z=(d_{+}+d_{-})/2$. The separation assumes reversal changes the signal sign while leaving the offset unchanged.

Detector loading also matters away from null. For a residual source with series electrical resistance $R_s$ connected to detector input resistance $R_d$, the detector receives $ϵR_d/(R_s+R_d)$. The ideal zero stays at $ϵ=0$, but a low input resistance reduces the response to a small departure from it. Verify the response with known small positive and negative signals, allow settling, and investigate persistent offsets. A quiet zero may otherwise reflect a broken connection or insufficient sensitivity rather than actual balance. Check the working range when approaching null because detector saturation invalidates the assumed linear response.