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June 2013

Simple Circuit Resolves Very Small Temperature Differences
By Chau Tran, Analog Devices

In many applications, measuring the temperature difference between two points in a system is more important than measuring the absolute temperature at either of them. For example, the temperature difference between the entry and exit pipes is used to calculate the efficiency of a heating system that circulates hot steam through radiators in an apartment, so knowing the absolute temperature is irrelevant.

One way to determine the temperature difference is to measure the voltage difference between two resistance-temperature detectors (RTDs), one at the entrance of the heating system and one at the exit. Unfortunately, RTDs are expensive, have low sensitivity, and must be excited by a stable current source.

Figure 1: Simple circuit measures differential temperature

Figure 1 shows a simple circuit that measures differential temperature. Used for heat balancing, it could improve production efficiency and provide significant savings. The AD590 temperature transducers generate output currents that are proportional to absolute temperature (PTAT). These currents flow though resistors R1 and R2. The voltage difference between them represents the differential temperature between the two sensors. This voltage drop is amplified to produce a high-level ground-referenced output voltage that can be measured with an ADC. Calibration and error correction can be performed by software to achieve a precise measurement.

The temperature transducers produce output currents proportional to absolute temperature, with a typical value of 1 µA/K, or 298.2 µA at room temperature (25°C). The sensor, connected with a shielded, ungrounded, twisted-pair cable, can be located up to 1000 feet from the circuit. The temperature measurement is differential, so self-heating effects will cancel out, and a precise linearization circuit is not required.

The output current of the AD590 flows through a 10 kΩ resistor, developing a 10 mV/K voltage. The AD8220 JFET-input instrumentation amplifier, configured for a gain of 10, delivers a 100 mV/°C output voltage. Thus, the output range achievable on a 5-V power supply corresponds to a ±25°C differential temperature range within a –55°C to +150°C range. The AD8220 specifies 10 pA max input bias currents, so bias current induced errors are negligible.

VDIFF , the voltage difference between the two inputs of the instrumentation amplifier, is

Therefore, the transfer function of the circuit is

Where G is the gain of the in-amp, which can be calculated as follows:

Where RG is the external resistor across the RG pins.

Small temperature differences can be detected by increasing R1 and R2 or the system gain, with measurement range traded for accuracy. For example, if the resistance is lowered to 2 kΩ, the sensitivity decreases to 20 mV/°C but the measurement range increases to ± 125°C. Using this circuit, the temperature difference between two points within the temperature range can be recorded at any given time.

Table 1 shows the temperature range and the sensitivity of the circuit based on the value of resistors R1 and R2, and gain G. It can resolve a temperature differential with an error of 0.05°C.

Table 1

The tolerance of the two resistors can introduce a gain error. One percent (1%) resistors could produce a gain error of up to 2%, resulting in an output error of 0.5°C. The offset and gain errors can be measured and eliminated through software calibration, however. R1 and R2 should be a matched pair or low temperature coefficient devices (<10 ppm/°C).

The voltage at the REF pin is set to mid-supply (2.5 V). For convenience, use a resistor divider from the supply followed by a buffer to the REF pin to ensure low impedance.

The topology of this design is not limited by the –55°C to +150°C range of the AD590. For a larger range, the AD590s can be replaced with RTDs to measure differential temperatures over a –250°C to 850°C (–418°F and 1562°F) range. With RTDs, the voltage drops in the wires will contribute to the total error, so Kelvin sensing must be used.

Analog Devices
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