 Reference resistor

A reference resistor is a resistor whose assigned electrical resistance supplies the comparison value in a resistance-measurement circuit. Its value may come from measurement calibration rather than its nominal marking. The useful reference is its value under the stated temperature, loading and connection conditions, together with the associated measurement uncertainty.

In a shared-excitation resistance ratio measurement, the sensor and reference resistor carry the same electric current. Measuring their electric potential differences gives $r=V_T/V_{\mathrm{ref}}=R_T/R_{\mathrm{ref}}$, so $R_T=r{R}_{\mathrm{ref}}$. A reference value error therefore sets a scale error even when excitation cancels perfectly. Reference-resistor error in ratiometric resistance measurement derives the exact relation and distinguishes a correction from its remaining measurement uncertainty.^[ref]

The connections define which resistance is compared. In four-terminal sensing, two leads carry the electric current while a separate high-impedance pair senses the electric potential difference at the reference terminals. This avoids including the current-lead drops in the assigned reference value, within the sensing instrument's limitations.

For an original ideal example, a $100\Omega$ reference resistor carries $1\mathrm{mA}$ through two current leads, each of electrical resistance $0.20\Omega$. The reference element has a potential difference of $0.1000\mathrm{V}$, while a reading outside both leads is $0.1004\mathrm{V}$. If this latter reading is used as the denominator while the calculation assumes $100\Omega$, a true $50\Omega$ sensor is inferred asSensing directly at the reference terminals removes this idealized lead contribution. It does not correct a wrong reference value. The circuit guide explicitly shows a Kelvin connection at the reference terminals for this purpose.^[ref]

A small temperature change shifts the value approximately by $\Delta R_{\mathrm{ref}}/R_{\mathrm{ref}}\simeq {\alpha }_R\Delta T$, with temperature coefficient of resistance ${\alpha }_R$. Excitation also dissipates electric power $I^2{R}_{\mathrm{ref}}$; a reference with a different temperature or load from its measurement calibration may require a correction or additional measurement uncertainty. A proposed check compares the reference before and after the measurement sequence under the same connection and loading conditions. Repeating the comparison at a lower electric current tests for a heating contribution. Stability of the observed ratio alone cannot certify the reference's assigned value.