A wide variety of sensors and transducers of physical phenomena work via the mechanism of variable resistance. These devices sense temperature, light, pressure, humidity, conductivity, and force, for example. Such sensors measure the physical parameter of interest by reading out the inherent parameter-sensitive resistance or conductance. All resistive sensors share the need for interface circuitry that provides a suitable source of excitation current and appropriate gain and offset of the resulting parameter-dependent voltage. The circuit in Figure 1 and the design equations provide a universal solution for an application-specific, optimum-resolution, ratiometric interface of almost any resistive sensor. The technique works with any unipolar ADC with an externally accessible full-scale reference. When you configure it properly, the interface circuit selectively maps the range of interest of sensor output resistance (R_MIN to R_MAX) onto the full-scale span of the ADC. The circuit thus optimally uses available resolution that might otherwise be wasted on sensor resistances that lie outside the range of a given application.

The circuit works as follows: R₁ sources the sensor excitation/bias current, I_B. The op amp boosts and offsets the resulting sensor voltage, I_BR_T, as a function of the R₁-R₂-R₃ network. When R_T=R_MIN, V_OUT=0V, and, when R_T=R_MAX, V_OUT=V_REF. Thus, R_T=(V_OUT/V_REF)(R_MAX–R_MIN)+R_MIN. Positive feedback via R₄ cancels the effect of voltage variation across R₁ and thus maintains constant-current excitation of the sensor throughout the R_MIN to R_MAX range. You select R₁ through R₄ as follows: First, select a value for I_B. Sometimes, sensor limitations determine an appropriate value for I_B. Self-heating errors, for example, may limit the maximum excitation current you can apply to temperature sensors such as thermistors and RTDs. But if the given sensor is indifferent to the magnitude of I_B, then you'll obtain optimum tolerance of op-amp offset and gain errors with I_B=V_REF/(R_MAX+R_MIN). With I_B known, you can compute the required gain: G=V_REF/(R_MAX–R_MIN). Then,

R₁=(Z–R_MAX)(1+1/G).

R₂=Z–R₁.

R₃=(G–1)(R₁R₂/Z).

R₄=GR₁, where Z=V_REF/I_B. For a practical example of how this circuit can be handy in a real application, consider a system in which you use a 100Ω platinum RTD to sense temperatures in the range of 25 to 50°C with 0.1° resolution. The corresponding resistance range is 109.73 to 119.4Ω. The 0.39Ω/°C temperature coefficient would require at least 12 bits of conversion resolution without scale expansion. But you can make an 8-bit ADC suffice using the circuit in Figure 1 with the values shown. The calculations are as follows: I_B=1 mA limits self-heating power to an acceptable 120 µW. Assuming V_REF=2.5V, Z=2.5V/1 mA=2500Ω. G=2.5/9.67/1 mA=258.5. It therefore follows that

R₁=(2500–119.4)(1+1/258.5)=2390Ω.

R₂=2500–2390=110Ω.

R₃=(257.5)(2390×110/2500)=27,100Ω.

R₄=258.5×2390=618,000Ω.

R_T=9.67(V_OUT/V_REF)+109.73.

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