Optimize linear-sensor resolution

Figure 1 This circuit allows you to optimize resolution for sensors using resistive elements.

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 (RMIN to RMAX) 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, IB. The op amp boosts and offsets the resulting sensor voltage, IBRT, as a function of the R1-R2-R3 network. When RT = RMIN, VOUT = 0V, and, when RT = RMAX, VOUT = VREF. Thus, RT = (VOUT/VREF)(RMAX – RMIN) + RMIN. Positive feedback via R4 cancels the effect of voltage variation across R1 and thus maintains constant-current excitation of the sensor throughout the RMIN to RMAX range. You select R1 through R4 as follows: First, select a value for IB. Sometimes, sensor limitations determine an appropriate value for IB. 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 IB, then you’ll obtain optimum tolerance of op-amp offset and gain errors with IB = VREF/(RMAX + RMIN). With IB known, you can compute the required gain: G = VREF/(RMAX – RMIN). Then,

R1 = (Z – RMAX)(1 + 1/G).

R2 = Z–R1.

R3 = (G – 1)(R1R2/Z).

R4 = GR1, where Z = VREF/IB.

For a practical example of how this circuit can be handy in a real application, consider a system in which you use a 100W 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 119.4W. The 0.39W/° 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: IB=1 mA limits self-heating power to an acceptable 120 µW. Assuming VREF = 2.5V, Z = 2.5V/1 mA = 2500W. G = 2.5/9.67/1 mA = 258.5. It therefore follows that

R1 = (2500 – 119.4)(1 + 1/258.5) = 2390W.

R2 = 25002 - 2390 = 110W.

R3 = (257.5)(2390 × 110/2500) = 27,100W.

R4 = 258.5 × 2390 = 618,000W.

RT = 9.67(VOUT/VREF) + 109.73.