英文原文：
Design an RTD interface with a spreadsheet
Using a spreadsheet and some simple math, you can design a linearizing interface to a non-linear RTD.
Robert S Villanucci, Wentworth Institute of Technology, Boston; Edited by Charles H Small and Fran Granville -- EDN, 2/7/2008
RTDs (resistance-temperature detectors) are the preferred sensor choices for designs requiring precision. Although RTDs are approximately linear over the limited temperature range of 0 to 100°C, these sensors exhibit a slight but progressively more nonlinear temperature-versus-resistance characteristic as the measurement range widens. Consequently, over an extended span, curve fitting is necessary if the system is to achieve a high level of precision. One way to obviate the nonlinear characteristic of an RTD sensor is to design analog hardware to perform the curve-fitting mathematics before any additional signal processing occurs. This approach is especially attractive if you can keep both cost and component count low and if a microprocessor-driven design is not feasible. With low component count comes the added benefit of a small PCB (printed-circuit-board) footprint.
The most popular RTDs are made from platinum with a resistance value of 100Ω at 0°C and a metal purity that allows them to follow a standard European curve with a positive-temperature coefficient, α, equal to 0.00385Ω/Ω/°C. Less popular but still common are RTDs with a slightly higher metal purity. These RTDs have α of 0.00392Ω/Ω/°C and follow the US curve. The circuit in Figure 1 uses a standard RTD to measure temperature over the extended range of 0 to 350°C, an output voltage of 0 to 3.5V, and overall system accuracy greater than 0.5°C. The following linear equation expresses this sensor system:
IC1 is pin-configured to drive a constant current of 400 µA through the grounded sensor, T1. Driving T1 with this level of current—“zero-power” operation—keeps the worst-case power that the circuit dissipates in the sensor to less than 40 µW and reduces the self-heating errors to a second-order effect (Reference 1). Also, driving the RTD with a current source preserves its intrinsic nonlinearity and allows you to express the sensor’s output voltage, VS, as: 400 µA×RS, where RS is the resistance of the sensor.
IC2 initially signal-conditions the sensor’s output by first scaling the output voltage and then offsetting the result so that VT is slightly larger than the 3.5V output at 350°C and that VT equals 0V at 0°C. Adding gain and offset before linearization places less of a burden on the curve-fitting circuitry and helps to meet the system’s precision specification. The combination
of C1 and R5 implements a lowpass filter with a pole at approximately 10 Hz to remove power-supply noise. The following term describes the performance of IC2 and its accompanying circuitry: VT="75VS"–3V.
Next, an Excel spreadsheet creates the nonlinear-mathematical relationship between the voltage, VT, and the system output, VO (Table 1). The spreadsheet features 17 temperature entries—starting at 0°C, increasing in increments of 25°C, and ending at 400°C—for the measured temperature. Using a data set that extends beyond the intended measurement range of 350°C can reduce end errors in nonlinear systems. Values for RS—which you derive from a standard RTD-resistance-versus-temperature table—and the equations allow you to compute VS and VT. The VT and VO columns are the input and output signals, respectively, for the linearization circuitry; you chart them using Excel’s XY-scatter feature. You can use Excel’s Trendline feature to create the following equation, the mathematical representation of the curve-fitting circuitry you need to linearize the sensor’s output: VO="0".0005V+0.8597VT+0.0123VT 2. IC3 and four 1%-tolerant resistors or, optionally, five resistors implement a second-order polynomial: VO="a"+bVT+cVT 2, where a is the offset term, b is the linear coefficient, and c is the square-term coefficient.