= Polarity reversal measurement
\b[Polarity reversal measurement] separates a signal that changes sign on reversal from an additive contribution that does not. If readings in two polarities obey
$$
y_+=s+b,\qquad y_-=-s+b,
$$
then the half-difference estimates the signal, $\widehat s=(y_+-y_-)/2$, while the half-sum estimates the unchanged offset, $\widehat b=(y_++y_-)/2$. 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.<Low Level Measurements Handbook, Seventh Edition by Keithley Instruments>[§3.2.2, Figure3-4, reversing sources; §3.3.2, Figure3-18, current-reversal method]{ref}
For an original resistance example, a bipolar <current source> applies $+I$ and $-I$ to a resistor while a <voltmeter> measures
$$
V_+=IR+b,\qquad V_-=-IR+b,\qquad
\widehat R=\frac{V_+-V_-}{2I}.
$$
Let $I=10\,\mathrm{mA}$ and readings be $103$ and $-97\,\mathrm{\mu V}$. Their half-difference is $100\,\mathrm{\mu V}$, giving $R=10\,\mathrm{m\Omega}$; their half-sum reveals a $3\,\mathrm{\mu V}$ 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 $2\,\mathrm{\mu V}$ 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.<Low Level Measurements Handbook, Seventh Edition by Keithley Instruments>[§3.3.2, current-reversal method, thermal-time-constant limitation]{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>.
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