Chris Collins

Tools · sensors

RTDs, thermocouples and load cells

Signal conditioning for the three classic analog sensors — RTDs (Callendar–Van Dusen both ways, tolerance classes, 2/3/4-wire lead error, self-heating, a front-end designer and the MAX31865 registers), thermocouples (the NIST ITS-90 functions for eight types, cold-junction compensation step by step, Seebeck plot, colour codes, amplifier gain, wiring faults, MAX31855/MAX6675/MAX31856 decoding) and strain gauges and load cells (bridge output, cantilever strain, HX711 calibration, noise and filtering, drift and creep).

Added

Works with

How to use it

The three sensors that turn temperature or force into a small resistance change or a few microvolts, and everything between them and a number: the standard equations both ways, the errors you will meet (leads, self-heating, cold junctions, wrong extension wire, bridge nonlinearity, drift and creep), how to size the front end, and how to read the converter chips makers actually use. The thermistor tool covers NTCs; this one goes deeper on RTDs and adds thermocouples and strain.

How to use it

  1. RTD R ↔ T: pick PT100, PT500, PT1000, Ni120 or Cu10 and convert either way; the steps show the Callendar–Van Dusen terms (and Newton’s method below 0 °C), the sensitivity, and the IEC 60751 class AA/A/B/C tolerance at that temperature with a plot of all four.

  2. RTD wiring & self-heating: enter the lead gauge and length (or resistance) and compare the error of 2-, 3- and 4-wire connections; enter the excitation current and the medium to see the self-heating.

  3. RTD front end: choose a ratiometric reference resistor, a current source, a divider or a bridge, the ADC bits and PGA gain, and read the code, °C per LSB, nonlinearity and whether it fits the ADC across your range. The examples load a MAX31865, an ADS1220, an MCU divider and a bridge.

  4. MAX31865: build the configuration byte and the fault thresholds as SPI writes, decode the RTD register bytes (and the fault status) to resistance and temperature, or simulate a temperature.

  5. Thermocouple & CJC: pick a type and convert temperature ↔ EMF; enter the terminal voltage and the cold-junction temperature to watch compensation done properly, beside the constant-Seebeck shortcut and its error. The table lists alloys, ranges and ANSI and IEC colour codes.

  6. Seebeck plot: the sensitivity (or EMF) of all eight types against temperature.

  7. TC amplifier & errors: the gain and offset to fit a temperature range into an ADC, °C per LSB, a wiring-fault calculator (copper, reversed or wrong-type extension wire across a temperature gradient) and how far an AD8495’s 5 mV/°C output strays from the NIST curve.

  8. MAX31855/6675/31856: paste a 32-bit MAX31855 frame, a MAX6675 word or MAX31856 registers; the bits are split into fields and faults, and MAX31855 readings are corrected for its linear approximation.

  9. Strain & bridges: a cantilever (material, load, distance, width, thickness) gives the surface strain, then the bridge output for quarter, half and full bridges, exactly and to first order.

  10. Load cell & HX711: from the cell’s capacity and mV/V, the HX711 counts per gram, the noise and noise-free resolution; a two-point calibration (tare and a known mass) gives the scale factor and the library calls; decode raw DOUT bytes; compare moving-average, exponential and median filters.

  11. ADS1232/1220, drift: the alternatives to the HX711, and zero, span and creep errors of a load cell.

  12. Which sensor?: enter a temperature range and accuracy and see which of thermistor, RTD, thermocouple, DS18B20, TMP117 and SHT45 fit.

Method and sources

  • Platinum RTDs follow IEC 60751:2022: R(t) = R0(1 + At + Bt² + C(t − 100)t³), A = 3.9083×10⁻³, B = −5.775×10⁻⁷, C = −4.183×10⁻¹² below 0 °C (zero above). Above 0 °C the quadratic inverts in closed form; below, Newton’s method on the quartic. PT100 gives 100 Ω, 138.506 Ω and 60.256 Ω at 0, 100 and −100 °C. Tolerances are ±(0.1 + 0.0017|t|) for class AA, ±(0.15 + 0.002|t|) A, ±(0.3 + 0.005|t|) B and ±(0.6 + 0.01|t|) C, each over a range that is narrower for film elements.

  • Ni120 and Cu10 have no international equation; the tool interpolates Minco’s published tables (NA, TCR 0.00672, and CA, 9.035 Ω at 0 °C, TCR 0.00427) every 10 °C with a monotone cubic.

  • Lead error: 2-wire adds both leads; 3-wire cancels one lead against the other and leaves only their mismatch; 4-wire senses with no current in the sense leads. Copper wire is ρ = 1.724×10⁻⁸ Ω·m. Self-heating is ΔT = I²R/δ with δ the dissipation constant.

  • Thermocouples use the NIST ITS-90 reference functions and approximate inverse polynomials of NIST Monograph 175 (Burns et al., 1993), from the NIST ITS-90 Thermocouple Database (SRD 60), including type K’s exponential term. The tests check every type against the NIST tables (K at 100 °C = 4.096 mV). The exact inverse is Newton’s method on the reference function; the NIST inverse polynomial and its stated error are shown beside it. Type B’s EMF has a minimum near 21 °C, so it cannot be inverted below about 42 °C. Tolerances are the ANSI MC96.1 standard and special limits; colours ANSI MC96.1 and IEC 60584-3.

  • Cold-junction compensation adds E(Tcj) to the measured voltage and inverts the sum; the wiring fault model integrates each wire’s EMF across its own temperature span (the law of intermediate temperatures).

  • MAX31855 frame: D31–D18 thermocouple (14-bit, 0.25 °C), D16 fault, D15–D4 cold junction (12-bit, 0.0625 °C), D2–D0 SCV/SCG/OC. The chip assumes a constant Seebeck coefficient (41.276 µV/°C for K), so the correction recovers V = S·(Treported − Tcj), adds E(Tcj) and inverts with NIST. MAX6675: D14–D3 at 0.25 °C, D2 open input. MAX31856: 19-bit linearised result at 2⁻⁷ °C, 14-bit cold junction at 2⁻⁶ °C, the CR0/CR1 fields and the fault status bits (Maxim/Analog Devices datasheets). The AD8495 model is Vout = 122.4·(E(T) − E(Tamb)) + 5 mV/°C·Tamb (AN-1087).

  • Bridges are solved exactly — Vout/Vexc = R3/(R3 + R4) − R2/(R1 + R2) with each arm R(1 + GF·ε·k) — so the quarter- and Poisson-bridge nonlinearity falls out; the formulas match the usual tables (e.g. NI’s strain gauge measurement guide). A rectangular cantilever has surface stress σ = 6Fx/(bh²).

  • HX711: full scale ±0.5·AVDD/gain, 24-bit two’s complement, 25/26/27 clock pulses for A×128, B×32 and A×64, 10 or 80 SPS, and input noise 50 nV rms (10 SPS) or 90 nV rms (80 SPS) at gain 128 from the datasheet. With the bridge excited from AVDD the reading is ratiometric, so counts per gram depend only on mV/V, capacity and gain. Noise-free resolution is 6.6 σ peak-to-peak. Datasheet noise figures for the alternatives are typical values; check the current datasheet.

Sharing

Share link copies a URL that opens this tool with your current settings — every value it remembers between visits, packed into ?s=. Opening a link replaces your saved settings for this tool.

Runs entirely in your browser; nothing you type leaves this page.