Polarity reversal measurement

Polarity reversal measurement separates a signal that changes sign on reversal from an additive contribution that does not. If readings in two polarities obeythen the half-difference estimates the signal, $\hat{s}=(y_{+}-y_{-})/2$, while the half-sum estimates the unchanged offset, $\hat{b}=(y_{+}+y_{-})/2$. The procedure depends on reversing the intended signal while preserving the relevant offset.

A primary electrical application is cancellation of thermoelectric offset in low-level measurements. The Keithley handbook describes reversing sources when comparing small electric potential differences, and reversing test current for low-electrical resistance measurements. A thermal offset can arise at dissimilar-metal junctions and remain approximately unchanged during a sufficiently short cycle.^[ref]

For an original resistance example, a bipolar current source applies $+I$ and $-I$ to a resistor while a voltmeter measuresLet $I=10\mathrm{mA}$ and readings be $103$ and $-97\mu \mathrm{V}$. Their half-difference is $100\mu \mathrm{V}$, giving $R=10\mathrm{m\Omega }$; their half-sum reveals a $3\mu \mathrm{V}$ offset. Using only the positive reading would instead give $10.3\mathrm{m\Omega }$.

An offset changing from $b_{+}$ to $b_{-}$ leaves resistance error $(b_{+}-b_{-})/(2I)$. A $2\mu \mathrm{V}$ change in this example therefore leaves $0.1\mathrm{m\Omega }$ error. Allow electrical settling after reversal while keeping the cycle short relative to material temperature changes. The handbook explicitly notes this time-scale requirement.^[ref] Reversal does not automatically remove lead resistance, current-magnitude errors, self-heating or every offset in the circuit. Record the actual reversal operation and timing with the measurement procedure.