RTD Sensor Measurement Techniques

RTD Sensor Measurement Techniques

RTDs can deliver excellent accuracy and long-term stability, but only if the measurement system accounts for wiring resistance, self-heating, reference and gain errors, and the installation environment. It is common to see multi-degree error when lead resistance, grounding, or excitation choices dominate the error budget.

Thermocouples generate voltage from the Seebeck effect; RTDs change resistance. The resistance change is more predictable, which makes RTDs better for precision work. The most common RTD configurations are PT100 and PT1000 sensors, where "PT" indicates platinum as the sensing element and the number represents the nominal resistance at 0°C. Platinum is preferred because it's linear, stable, and well-characterized.

RTD Resistance-Temperature Relationship

The resistance of a platinum RTD follows the Callendar-Van Dusen equation, valid from -200°C to +850°C. For temperatures above 0°C, the relationship simplifies to $R(T) = R_0(1 + AT + BT^2)$, where $R_0$ is the resistance at 0°C (100Ω for PT100, 1000Ω for PT1000), $A = 3.9083 \times 10^{-3}$ °C⁻¹, and $B = -5.775 \times 10^{-7}$ °C⁻². Below 0°C the full equation adds a third term $C(T-100)T^3$ with $C = -4.183 \times 10^{-12}$ °C⁻⁴. The temperature coefficient of resistance (TCR) for platinum RTDs is approximately 0.385% per °C, meaning a PT100 sensor increases by approximately 0.385Ω per degree Celsius. Getting this accuracy in practice is the hard part.

2-Wire RTD Configuration

Two-wire is the simplest topology: excitation current flows through the same wires used to measure voltage. The problem: $R_{measured} = R_{RTD} + 2R_{lead}$. Lead resistance adds directly to your reading.

A 2-meter round-trip of 24AWG wire adds about 0.17Ω, which is 0.44°C error on a PT100. A 10-meter round-trip: 2.2°C error. And lead resistance changes with ambient temperature, adding drift you can't easily compensate. Only use 2-wire for short runs where sub-degree accuracy is acceptable.

3-Wire RTD Configuration

The 3-wire configuration adds a third wire to enable lead resistance compensation. This is the most common industrial configuration, good enough for most applications without the wiring cost of 4-wire. In a 3-wire measurement, current is sourced through two wires connected to each end of the RTD, while voltage is measured across the RTD using the third wire. By measuring both the voltage across the RTD and the voltage across one lead wire, the lead resistance can be subtracted. The measurement follows $V_{RTD} = V_{measured} - V_{lead}$, allowing calculation of the true RTD resistance as $R_{RTD} = V_{RTD}/I_{excitation}$.

The 3-wire configuration assumes both lead resistances are matched. Under this assumption, it can cancel lead resistance errors to first order. However, several factors limit accuracy in practice. Lead resistance mismatch is typically 2-5% due to manufacturing tolerances and variations in wire length. Temperature gradients along the cable length create resistance variations that cannot be compensated. The residual error is typically 5-10% of single lead resistance. For a 5-meter cable run with 0.26Ω per lead, a 3% mismatch introduces approximately 0.008Ω error (0.02°C), which is acceptable for many industrial applications but insufficient for laboratory-grade measurements.

4-Wire RTD Configuration

4-wire is the precision approach, largely eliminating lead resistance error through a Kelvin (4-wire) connection. In this configuration, excitation current is sourced through one pair of wires while voltage is measured through a separate pair. Since modern ADCs and instrumentation amplifiers have very high input impedance, the sense current is tiny, so the resistance of the sense leads contributes negligible error in practice. The measurement simplifies to $V_{sense} = I_{excitation} \times R_{RTD}$, allowing direct calculation of the RTD resistance without the lead resistance term dominating your error budget.

4-wire is often essential for laboratory-grade measurement, calibration standards, long cable runs, and traceable workflows. It requires additional wiring and connector pins, but removing lead resistance from the measurement to first order is often the difference between meeting a tight spec and chasing ghosts in production.

Precision ADCs for RTD Measurement

The Texas Instruments ADS1220 is a 24-bit delta-sigma ADC designed for precision sensor measurement, including RTDs. It integrates several features that simplify RTD interface design. Two matched programmable current sources (IDACs) can eliminate the need for an external precision current source. A programmable gain amplifier optimizes dynamic range for the small voltage signals produced by RTDs. The built-in reference and flexible input multiplexer support common 2-wire, 3-wire, and 4-wire measurement approaches. Noise and resolution depend heavily on data rate, PGA setting, layout, and filtering. Sub-0.01°C resolution can be achievable in well-designed systems, but always verify against the datasheet and your real noise environment.

The excitation current must be carefully chosen to balance measurement resolution against self-heating effects. Self-heating occurs when the excitation current causes power dissipation in the RTD element according to $P_{dissipation} = I_{excitation}^2 \times R_{RTD}$. This power dissipation causes temperature rise in the RTD element given by $\Delta T_{self-heating} = P_{dissipation} \times \theta$, where $\theta$ is the sensor’s self-heating coefficient (strongly dependent on probe construction and mounting, and often on the order of ~0.1 to 1°C/mW). As an example, for a PT100 around 100Ω with $\theta \approx 0.5$ °C/mW, limiting self-heating to 0.1°C implies $P \le 0.2$ mW and $I \lesssim 1.4$ mA. In practice, excitation currents of 500µA to 1mA are common starting points, but you should use the actual coefficient for your sensor and installation.

Noise Sources and Mitigation

The RTD itself generates thermal noise due to random electron motion, quantified by the Johnson noise equation $V_{n,RTD} = \sqrt{4k_BTR_{RTD}\Delta f}$, where $k_B = 1.38 \times 10^{-23}$ J/K is the Boltzmann constant, $T$ is absolute temperature, $R_{RTD}$ is the RTD resistance, and $\Delta f$ is the measurement bandwidth. For a PT100 at room temperature (300K) with 10Hz bandwidth, the thermal noise is 4.07nV_RMS. This sets the fundamental noise floor for RTD measurement. PT1000 sensors have 10× higher resistance and therefore 3.16× higher thermal noise, but this is generally negligible compared to other noise sources in the measurement chain.

Power line interference is a dominant noise source in many RTD measurement systems. Mains frequency noise couples into the measurement through capacitive coupling from nearby AC wiring, magnetic coupling through ground loops, and common-mode voltage on the sensor ground. Effective mitigation strategies include configuring the ADC data rate and digital filter for strong 50/60Hz rejection (check the filter response curves for your specific settings), using differential ADC inputs to reject common-mode interference, and using shielded twisted pair cabling with the shield grounded at one end to avoid ground loops while providing electrostatic shielding.

Radio frequency interference from wireless transmitters, switching power supplies, and digital circuits can rectify in the ADC input stage, causing DC measurement errors. Mitigation techniques include placing RC filters at ADC inputs (100Ω + 100nF creates a 16kHz lowpass filter), using ferrite beads on long cable runs (impedance exceeding 100Ω at 100MHz), implementing proper PCB layout with ground planes and guard rings around sensitive traces, and keeping digital circuitry separated from analog measurement paths. Low-frequency 1/f noise from ADC input stages and amplifiers increases at frequencies below 1Hz. Chopper-stabilized amplifiers in modern ADCs like the ADS1220 largely suppress this flicker noise.

Common Errors and Pitfalls

When using multiplexed measurements or intermittent excitation to reduce power consumption, insufficient settling time after enabling the excitation current leads to measurement errors. The settling time constant is $\tau = (R_{RTD} + R_{lead}) \times C_{cable}$. For a 10-meter cable with 100pF/m capacitance and 100Ω RTD, the time constant is approximately 103ns. Allowing 5τ settling time (approximately 500ns minimum) ensures the voltage has settled to within 1% of its final value before initiating ADC conversion. In practice, 1µs is a safe minimum settling time for most configurations, and longer delays may be necessary for high-capacitance cables or high-impedance configurations.

ADC input bias currents flow through source impedance, creating offset voltage errors. The ADS1220 datasheet specifies this through typical-characteristics curves rather than a single number; expect input currents on the order of a few nanoamps at room temperature, rising substantially at high temperature. A few nA through a 100Ω source impedance produces sub-microvolt offsets, which is negligible. Through a 100kΩ source impedance the same current produces hundreds of microvolts, which is not. The solution is to use low excitation current source impedance and avoid high-value series resistors in the signal path.

The ADC reference voltage drift directly affects measurement accuracy. If using the internal reference, apply temperature coefficient correction according to $V_{ref}(T) = V_{ref,nom}(1 + TC_{ref} \times \Delta T)$. The ADS1220 internal reference has a typical temperature coefficient of 5ppm/°C. Over a 50°C ambient range, this introduces 250ppm (0.025%) error. For 0.1°C accuracy in temperature measurement, this is often acceptable, but precision applications should use an external low-drift reference like the REF5025 with 3ppm/°C temperature coefficient.

Junctions between dissimilar metals in the signal path generate thermoelectric voltages of 1-50µV/°C through the Seebeck effect. For example, junctions between copper PCB traces and tin-plated connector pins can generate several microvolts per degree of temperature difference. These errors can dominate precision measurements. Mitigation strategies include maintaining thermal symmetry by keeping all junctions at the same temperature, using isothermal terminal blocks at the sensor connection point, and employing DC-canceling techniques by alternating excitation current polarity and averaging measurements. This last technique effectively cancels any DC offset voltage including thermoelectric EMF.

When the RTD sensor and measurement system have separate ground connections, ground potential differences create common-mode voltage that can exceed either the ADC's input common-mode range or its CMRR limits. Ground loops can introduce hundreds of millivolts of error, completely overwhelming the RTD signal which is typically only a few hundred millivolts. Use differential measurement with good common-mode rejection and consider isolation for sensors on grounded equipment. Optical or transformer isolation can break ground loops while still allowing signal transmission.

The excitation current accuracy directly affects resistance measurement accuracy. The ADS1220 IDAC has typical accuracy of ±1% and temperature coefficient of 50ppm/°C. Over a 50°C ambient temperature range, drift is 0.25%, which on a PT100 amounts to 0.25Ω, or roughly 0.65°C. In a ratiometric configuration most of this cancels because the reference voltage is derived from the same current, but it is worth knowing the raw number. For ultra-precision applications, characterize the IDAC by measuring a known precision resistor and apply a calibration factor to compensate for the systematic error.

Calibration and Linearization

RTD resistance-to-temperature conversion requires either polynomial evaluation of the Callendar-Van Dusen equation or lookup tables with interpolation. Solving the Callendar-Van Dusen equation for temperature requires root-finding algorithms such as Newton-Raphson or pre-computed polynomial approximations. For industrial applications, piecewise linear approximation provides a good balance of accuracy and computational simplicity. The approximate relationship $T \approx (R_{measured} - R_0)/(R_0 \times \alpha)$, where $\alpha = 0.00385$ °C⁻¹ for standard PT100/PT1000 sensors, stays within about 0.5°C from roughly -25°C to +125°C. Push it to the full -50°C to +150°C span and the error grows to a bit over 1°C at the extremes, since α is the mean slope over 0 to 100°C and the real curve bends away from it.

System-level calibration compensates for ADC gain and offset errors, IDAC inaccuracies, and PCB parasitic resistances. The two-point calibration process involves measuring at known temperature T₁ (such as an ice bath at 0°C) to record resistance R₁, then measuring at known temperature T₂ (such as boiling water at 100°C) to record resistance R₂. The calibration coefficients are calculated as $\alpha_{calibrated} = (T_2 - T_1)/(R_2 - R_1)$ and $T_{offset} = T_1 - \alpha_{calibrated} \times R_1$. Subsequently, temperature is calculated from measured resistance as $T = \alpha_{calibrated} \times R_{measured} + T_{offset}$. Two-point calibration typically achieves ±0.1°C accuracy across the calibrated range, which is sufficient for most industrial applications.

I offer precision measurement system design services including RTD interface design, ADC selection and configuration, noise analysis and mitigation, calibration procedures, and full system integration. Whether you need help troubleshooting accuracy issues in an existing design or developing a custom RTD measurement solution for demanding applications requiring sub-0.1°C accuracy, I can help you achieve your performance targets. Get in touch to discuss your temperature measurement challenges.

Precision analog front-end design, including RTD measurement circuits, is part of my precision analog design services for instrumentation and industrial applications.