Making Accurate Ratiometric Measurements of Resistance Temperature Detectors (RTDs)

Accurately measuring temperature with Resistance Temperature Detectors (RTDs) requires more than just a high-resolution ADC. The measurement architecture—specifically whether the system is ratiometric or non-ratiometric—has a first-order impact on accuracy, drift, and long-term stability.

In this tutorial we cover: what RTDs are and how they are measured, why ratiometric measurements fundamentally outperform non-ratiometric ones, the math that explains where error terms cancel (and where they do not), and practical RTD measurement circuit concepts. 

Quick Overview of Resistance Temperature Detector (RTD) Sensors

RTD probes or sensors typically have a name that starts with a couple of letters and then a number, such as PT1000. The letters in the sensor name tell you the metal that the RTD sensor is made from: Platinum --> PT, Nickel --> Ni, and Copper --> Cu. The number in the RTD sensor name corresponds to its resistance at 0 °C in Ohms, common RTD resistance values are: 100, 200, 500, 1000, 2000. By far platinum or PT RTD sensors are the most common, specifically PT100 and PT1000 RTD sensors are the most widely used. 

RTD sensors come in 2-wire, 3-wire, and 4-wire configurations. 3 and 4 wire configurations allow you to compensate for wire or lead resistance in the sensor. Wiring resistance directly contributes to RTD temperature measurement error. This means 2-wire RTD sensor measurements are less accurate then 3 and 4-wire. But 3-wire and 4-wire sensors are more expensive and a bit more tedious to setup and configure. 

The Three Main Factors Affecting RTD Measurement Accuracy

Accuracy of RTD temperature measurements depends on three factors: the RTD sensor's accuracy, the accuracy of the measurement hardware, and the accuracy of the calculation method that converts a measured resistance value into a temperature value. RTD sensor or probe accuracy is defined by the probes accuracy class rating. Accuracy classes for RTD probes are defined at 0 °C and are as follows in °C (+/-) : AA – 0.1, A – 0.15, B – 0.3, C – 0.6.

The accuracy of the RTD measurement hardware is the focus of this tutorial and will be covered in more detail in the following sections. We will see that combining a ratio metric measurement approach with a high resolution ADC can really reduce the error contribution from the measurement hardware. The third factor of an RTD temperature measurement's accuracy is the method used to convert the measured RTD resistance to temperature. Although RTD sensors can behave linearly at temperatures close to 0 °C, as you move farther from 0 °C the curve is no longer linear and complex math is needed to properly follow the RTD's temperature curve. The most accurate RTD temperature calculation algorithm is defined by the IEC-60751 standard approach. See the Gitub link at the end of this tutorial to access example code that implements the IEC-60751 standard for RTD temperature calculations.

The Ratiometric RTD Measurement Concept

Figure 1 below shows a circuit design approach for measuring RTDs that uses a current source, differential ADC, and a reference resistor for making RTD measurements. In this ratiometric RTD measurement circuit, the same excitation current (Iexc) flows through both the RTD and a precision reference resistor (Rref). The ADC input measures the voltage across the RTD, and the ADC's voltage reference for making measurements is set by the voltage across Rref. Because the same current excites both resistors, current source-related errors cancel mathematically as we will see next. 

Figure 1. RTD ratiometric measurement circuit using a current source

Image from TI’s “A Basic Guide to RTD Measurements”

Ratiometric Measurement Math (Why It Works)

Let's look at that math that makes this approach ratiometric and highly accurate for measuring temperature. We can define the RTD voltage and the reference voltage as follows using Ohm's Law:

RTD voltage: Vrtd = Iexc × Rrtd

Reference voltage: Vref = Iexc × Rref 

Next let's use these terms in the transfer function for our ADC in figure 1.

 Digital code that the ADC returns: Code = (Vrtd / Vref) × MaxCode

Where "MaxCode" is the maximum code value the ADC can return based on 2 to the power of it's resolution in bits. Substituting in the RTD and reference voltage expressions gives the following:

Code = (Iexc × Rrtd) / (Iexc × Rref) × MaxCode

Since the excitation current is both in the numerator and denominator, algebraically it cancels. We can then rearrange it to give us the RTD resistance:

Code = (Rrtd / Rref) × MaxCode

Rrtd = Rref × (Code / MaxCode)

Key point: Since calculating the resistance value of the RTD sensor does not include the current source value, any error in the current source does not affect the accuracy of the measurement. The same is true for the ADC's voltage reference, any error in the reference has no effect on the measurement. This is because the values cancel and therefore the error from the same current source cancels. This is the definition of a ratiometric measurement. If we look at the equation the only sources of error left are the reference resistor and ADC errors not related to the voltage reference, such as input offset voltage error, gain error, and random noise. We can control the accuracy of the reference resistor by choosing its accuracy (better accuracy = higher price) or by measuring its "real" value with a precision multimeter and compensating in software. We can also compensate for offset and gain error in the ADC by using the two point calibration approach which Anabit covers in another tutorial which we provide a link for at the end of this tutorial. 

Ratiometric Measurement Circuit for 4-Wire and 3-Wire RTDs

The RTD sensor shown in figure 1 is only 2-wire so even though the measurement circuit is setup for very low error, the resistance in the RTD wiring can add significant error to the measurement. Figure 2 features a circuit configuration with a 4-wire RTD sensor that allows you to cancel out error due to wiring resistance. In the 4-wire setup current flows through wires or leads 1 and 4. But the measurement is made through leads 2 and 3. Leads 2 and 3 are connected to a high impedance input, such as a op amp or ADC. This means that very little current flows through wire lead 2 and 3 so little we can assume zero. Therefore the ADC is only measuring the voltage drop caused by the resistance of the RTD sensor and not the RTD wiring. 

Figure 2. 4-wire RTD ratiometric measurement circuit

Image from TI’s “A Basic Guide to RTD Measurements”

The figure 2 circuit also has a programmable gain amplifier or what could be a instrumentation amplifier. This would be optional and depends on the current source value and the resolution of the ADC. The RTD resistance in the 4-wire circuit is calculated the same as in the previous circuit but this time we can add a "gain" variable in the case an amplifier is used in the setup:

Code = (Rrtd / Rref) x MaxCode x Gain 

Rrtd = (Rref x (Code / Max Code)) / Gain

Figure 3 shows the measurement circuit for a 3-wire RTD circuit. 3-wire RTD sensors also give the user the ability to compensate or cancel out RTD wire or lead resistance. But with a 3-wire RTD sensor to cancel out wire resistance requires two ADC measurements. With a 3-wire RTD sensor it is assumed that:

Wiring resistance is the same for each wire or lead: Rlead1 = Rlead2 = Rlead3

To cancel out the lead resistance a resistance measurement is made across Lead 1 and Lead 2. A second resistance measurement is made from Lead 2 to Lead 3. For each of the two measurements we can assume no current flows through Lead 2 because it is connected to a high impedance measurement input:

Resistance in the first measurement: Rrtd + Rlead1

Resistance in the second measurement: Rlead3

Since we are assuming that Rlead1 = Rlead3, if we subtract the first measurement by the second we are left with just the RTD resistance (Rrtd) and the resistance of the wiring has been canceled out.

Figure 3. 3-wire RTD ratiometric measurement circuit

Image from TI’s “A Basic Guide to RTD Measurements”

One key downside to this approach is two measurements are needed to accurately calculate the RTD temperature. This means your circuit design requires either two ADCs or a multiplexer switch setup to route the ADC to the two measurement points. This adds more complexity and measurement time to the circuit with the tradeoff that 3-wire RTD sensors are lower cost compared to 4-wire RTD sensors. To perform a ratio metric resistance measurement of a 3-wire RTD sensor with only a single measurement you could use a Wheatstone Bridge circuit. Click here to access Anabit's tutorial on Wheatstone Bridge circuits.

Example Error From Non-Ratiometric RTD Measurement Approach

To demonstrate the accuracy benefits of a ratiometric approach, let's look at an example measurement that uses a non-ratiometric approach. Let's assume we are measuring a 4-wire PT1000 RTD sensor using the setup in Figure 2, but with one key difference. Instead of using the reference resistor to generate the ADC's voltage reference from the current source. We will use a dedicated voltage reference that has no correlation to the current source. For this simple example we will assume the voltage reference and other ADC factors in this setup are ideal but the current source has 0.8% error. Here is our example setup and resulting temperature measurement error due to error in our current source:

• Measuring a 4-wire PT1000 RTD sensor, its current value is 2000 Ω which corresponds to a temperature of about 267 °C
• Current source used in this setup is: 0.25 mA but with 0.8% error its actual value is 0.252 mA.
• Ideally the ADC would measure a 500 mV drop across the RTD sensor which has a value of 2000 Ω, but because of the non-ideal current source it measures 504 mV.
• At 504 mV we calculate the RTD resistance to be 2016 Ω
• At 2016 Ω our software calculates the temperature to be 271 °C, when it is actually 267 °C. 

In this simple example only 0.8% of error in the current source and an ideal voltage reference led to 4 degrees of error in the RTD temperature measurement. With the ratio metric approach the current source's error would have cancelled out. 

Final Takeaway

Ratiometric RTD measurements are powerful because they remove entire error terms at the circuit level. If you are designing precision temperature measurement systems, industrial/scientific instrumentation, or long-term stable sensing hardware, a ratiometric  RTD measurement architecture should be your default starting point. For more detailed information on the ratiometric measurement approach covered in this tutorial check out Texas Instrument's Application Note "A Basic Guide to RTD Measurements" using the link below. If you are looking for an open source reference design to get started making ratiometric RTD measurements check out Anabit's Precision Logger which features a differential 32 bit ADC, 2x built-in current sources, a programmable gain amplifier, and multiple measurement channels. Any questions of comments from this tutorial go to Anabit's ADC forum by clicking here.

TI's Application Note "A Basic Guide to RTD Measurements" by Joseph Wu: https://www.ti.com/lit/an/sbaa275a/sbaa275a.pdf?ts=1766916366350

Anabit's Precision Logger Reference Design: https://anabit.co/products/precision-logger

Example C code on Github that implements the IEC-60751 standard approach for calculating RTD temperature: https://github.com/anabit-LLC/PrecLoggerPT100RTD4Wire

Anabit's tutorial on increasing ADC accuracy using the two point calibration method: https://anabit.co/blogs/data_converter_u/increasing-the-accuracy-of-adc-measurements-using-the-two-point-calibration-approach