= Shared-excitation resistance ratio measurement
A <shared-excitation resistance ratio measurement> compares two <electrical resistances> by passing the same <electric current> through them and comparing their <electric potential differences>. It is the circuit realization of a <ratiometric measurement>: the unknown excitation becomes a common multiplicative input.
For a sensor $R_T$ in series with a <reference resistor> $R_{\rm ref}$, ideal high-input-impedance sensing gives
$$
V_T=IR_T,\qquad V_{\rm ref}=IR_{\rm ref},\qquad
r=\frac{V_T}{V_{\rm ref}}=\frac{R_T}{R_{\rm ref}}.
$$
The <electric current> must be nonzero and shared at the time relevant to each sample. One implementation feeds $V_T$ to an <analog-to-digital converter> input and $V_{\rm ref}$ to its external reference pins; the conversion is then scaled by their <ratio>. The primary circuit guide shows this wiring and includes the programmed gain when translating a digital code to resistance.<A Basic Guide to RTD Measurements by Joseph Wu>[§§2.1.1 and 2.1.4, printed pp. 10–11, Figure 2-1 and equations (17)–(18)]{ref}
For an original check, choose $R_T=180\,\Omega$ and $R_{\rm ref}=1200\,\Omega$. Excitation at $0.4\,\mathrm{mA}$ gives $0.072\,\mathrm V$ and $0.480\,\mathrm V$; excitation at $1.2\,\mathrm{mA}$ gives $0.216\,\mathrm V$ and $1.440\,\mathrm V$. Both give $r=0.15$ and recover $180\,\Omega$. This calculation assumes unchanged resistances; the larger excitation dissipates nine times the sensor <electric power>, making <sensor self-heating in a ratiometric resistance measurement> an independent test.
A common supply is insufficient if different branch currents pass through the two resistances. With currents $I_T,I_{\rm ref}$,
$$
r=\frac{I_T}{I_{\rm ref}}\frac{R_T}{R_{\rm ref}}.
$$
This is <branch-current mismatch in a resistance ratio measurement>. Sequential sampling of a changing excitation has the same problem unless the two paths retain the same effective excitation history. <Ratiometric cancellation with matched signal and reference filters> specifies the dynamic condition.
Wiring matters even with an ideal shared <current source>. A two-wire sensor reading includes lead <electrical resistance>; <four-terminal sensing> separates the current leads from high-impedance potential-sensing leads. The reference itself needs the same care if lead drops would otherwise enter its measured denominator.<A Basic Guide to RTD Measurements by Joseph Wu>[§2.1.3, printed p. 11, Kelvin reference connection and two-wire lead error]{ref}
A bench check can replace the sensor with a stable known <resistor>, sweep excitation, and compare each measured potential with their <ratio>. A constant <ratio> accompanied by changing individual potentials tests shared excitation. It does not establish reference accuracy, eliminate sensor heating, or prove operation outside the converter's input and reference ranges.
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