Signal conditioning and sensors
A Pt100 connected with two wires and 10 m of thin cable reads 4.5 °C too high. The sensor is accurate; the cables introduce the error.
01From the phenomenon to the number
To measure a temperature, a force or a pressure, a sensor converts the quantity into an electrical signal: a resistance that changes, a voltage of microvolts, a current. That signal can almost never be connected directly to the converter. Signal conditioning is everything between the two: exciting the sensor, amplifying, filtering, isolating, compensating and linearizing. The errors of that chain are usually larger than those of the sensor itself. Sensors and actuators are presented in the technician program, in sensors and actuators.
02Temperature sensors
| Sensor | Principle | Typical range and accuracy | Conditioning |
|---|---|---|---|
| Pt100 (RTD) | Platinum resistance, 100 Ω at 0 °C, rises 0.385 Ω/°C | −200 to 600 °C, ±0.3 °C (class B at 0 °C) | Excitation current, three or four wires |
| Thermocouple | Seebeck voltage between two metals: about 41 µV/°C for type K | −200 to 1250 °C (K), ±2 °C | Cold-junction compensation and high amplification |
| NTC thermistor | Resistance that falls sharply with temperature | −40 to 150 °C, very sensitive | Divider and Steinhart-Hart linearization |
| Integrated (LM35 and similar) | Junction voltage of transistors, already calibrated | −55 to 150 °C, ±0.5 °C | Almost none: 10 mV/°C |
The resistance of a Pt100 follows the Callendar-Van Dusen equation, which for positive temperatures is:
03Strain gauges and bridges
A strain gauge is a resistor that stretches with the part it is bonded to. Its relative change is proportional to the strain \( \varepsilon \), with a gauge factor close to 2. Strains are in thousandths, so the change in resistance is tiny, and it is measured in a bridge:
Load cells and piezoresistive pressure sensors are full bridges specified in millivolts per volt of excitation: a 2 mV/V cell excited with 10 V gives 20 mV at full load. That is why they are measured ratiometrically: the converter uses the same excitation voltage as its reference, and its variations cancel.
04The instrumentation amplifier
The output of a bridge is a difference of millivolts sitting on a common voltage of several volts. An ordinary operational amplifier would also amplify that common voltage and the errors of its resistors. The three-op-amp instrumentation amplifier has a high-impedance differential input, a gain set with a single resistor and a common-mode rejection of 100 dB or more:
Before the converter goes an anti-aliasing low-pass filter, and in industrial environments, an isolator that breaks the ground connection between the sensor and the system.
05Excitation, cables and self-heating
A two-wire Pt100 adds the resistance of the cables to that of the sensor: 10 m of thin cable has almost 1 Ω per conductor, and 1.7 Ω is equivalent to 4.5 °C of error. The three-wire connection compensates the cables in a bridge, assuming they are equal; the four-wire one carries the current through two and measures the voltage through the other two, with no current, and eliminates the error completely.
The excitation current heats the sensor, which then measures a little more than the ambient. With a self-heating coefficient of 0.4 °C/mW, 1 mA in a Pt100 produces 0.06 °C of error; 5 mA, 1.4 °C. More current gives more signal, but not a better measurement.
A Pt100 10 m from the equipment, with cable of 0.84 Ω per conductor, excited with a constant current. An instrumentation amplifier takes the 0 to 300 °C range to the 4.096 V of a 12-bit ADC. The graph shows the error of each source over the whole range; the dot, the chosen temperature.
06Other non-electrical parameters
| Quantity | Usual sensor | Output |
|---|---|---|
| Force and weight | Load cell with strain gauges | Bridge of 1 to 3 mV/V |
| Pressure | Piezoresistive diaphragm | Bridge, or 4 to 20 mA already conditioned |
| Position | Potentiometer, LVDT, optical encoder | Voltage, modulated AC or pulses |
| Illumination | Photodiode | Current, with a transimpedance amplifier |
| Humidity | Capacitive | Capacitance, or digital over I²C |
In industry, many transmitters deliver a current of 4 to 20 mA: the current is not lost in long cables, and the zero at 4 mA makes it possible to detect a cut cable, which would give 0 mA.
07In the laboratory
Measure a Pt100 in ice water and in boiling water with the three connections, through 10 m of cable. Calculate the error of each.
Condition a load cell with an instrumentation amplifier and a 24-bit ADC, calibrate with two known weights and measure the repeatability.
Measure with a type K thermocouple and an amplifier without compensation, and then with a cold-junction compensation IC. Compare with a reference thermometer.
08Common mistakes
- Measuring a two-wire Pt100 with long cables. Each ohm of cable is 2.6 °C.
- Raising the excitation to get more signal. Self-heating grows.
- Forgetting the cold junction of a thermocouple. The reading is shifted by the temperature of the terminals.
- Amplifying a bridge with a simple op amp. The common-mode voltage and the mismatched resistors add errors larger than the signal.
09Self-assessment
What resistance does a Pt100 have at 50 °C?
\( 100\,(1 + 0.195 - 0.00144) \approx 119.40\ \Omega \).
What output does a quarter bridge give with a gauge factor of 2, at 500 µε and 10 V of excitation?
\( 10 \cdot 2 \cdot 500 \cdot 10^{-6} / 4 = 2.5 \) mV.
What gain resistor gives G = 101 with the formula 1 + 50 kΩ / RG?
500 Ω.
Why do industrial transmitters use 4 to 20 mA and not 0 to 20 mA?
To distinguish the minimum of the scale from a cut cable, and so that the transmitter can be powered from the 4 mA of the loop.
10Further reading
- Ramón Pallás Areny. Sensores y acondicionadores de señal (in Spanish). 4th ed., Marcombo, 2003. The reference in Spanish: each type of sensor with its conditioning circuit.
- Jacob Fraden. Handbook of Modern Sensors. 5th ed., Springer, 2016. The physics of all sensors and their interfaces.
- Walt Kester (ed.). Sensor Signal Conditioning. Analog Devices, 1999. Bridges, instrumentation amplifiers and temperature conditioning with real circuits.