This article presents methods for ambient temperature estimation for wearable device applications by measuring the temperature gradient from a skin-side temperature sensor to an ambient-side temperature sensor, as well as considerations for the placement of these sensors.

Introduction

Medical-grade thermometers are generally required to be accurate within +/-0.1°C in a normal human body temperature range of 37 to 39°C. While integrated circuit solutions are available to meet this accuracy, it is also possible to calibrate the final thermometer in a limited temperature range in a precision bath.

While it is tempting to assume that the problem is as simple as choosing the right temperature sensor or doing an accurate calibration, in many applications, such as wearable electronics, there are other factors to consider. These include how well the temperature sensor is connected to the skin and how the skin temperature reflects core temperature.

Skin Temperature Measurement

It is desirable to place the skin-side temperature sensor in good contact with the skin and in a location where the correction for core temperature is not large. The thermal impedance for skin contact is about 1°C/W-cm2, which is very low compared to convection away from a PCB of about 1000°C/W-cm2. Therefore, it is generally not difficult to sense skin temperature quickly and accurately.

Core Body Temperature Estimation

Core body temperature is most accurately measured by using traditional thermometers. At other places on the body, the skin temperature range will fall between the core temperature and the ambient temperature.

To project core temperature from skin temperature, the location of the temperature measurement device must be considered. A nominal ambient temperature (23°C) can be used as a simple approximation, and the actual ambient temperature, if known, can be factored in.

Another option is to use a temperature sensor well coupled to the skin and a second temperature sensor to measure ambient temperature. The core temperature can then be estimated from the skin temperature and the gradient from skin temperature to ambient temperature. Here is the new equation:

Tcore = Tskin + α × (Tskin − Tambient)

Where:

Location	ɑ
Rectal	0.0699
Head	0.3094
Torso	0.5067
Hand	0.7665
Foot	2.1807

 

Estimation of Ambient Temperature

In a wearable device, accurate projection of “Tambient” is very difficult unless it is possible to access data from a remote sensor. If the skin sensor is placed in such a way that the ambient correction is small, then this issue is not critical. PCB material has fairly low thermal conductance (0.1 Watt/cm-°C), and the thermal impedance from PCB to air by convection is quite large (1000°C/W-cm2) for the surface area. It is therefore important that the ambient-side sensor is insulated from the skin-side sensor by more than just PCB material. Even the use of cotton or fiberglass insulation is difficult in these applications.

Consider the following model. The thermal conductivity of cotton or fiberglass is in the range of 0.003 to 0.005 Watt/cm-°C. This means that for a 1 cm-thick insulating layer, the thermal impedance from the skin-side PCB to the ambient-side PCB is 200 to 300 °C/W per cm2 of area, while convective thermal impedance from the ambient-side PCB to the ambient is about 1000°C/W per cm2 of area. The ambient-side PCB is not sufficiently well insulated from the skin-side PCB.

It is impractical to further increase the insulation for this kind of arrangement. A better solution is to sense the ambient temperature with a leaded thermistor. The concept is to embed the ambient sensing thermistor in an aluminum bezel to minimize thermal contact to the skin-side PCB material and maximize thermal contact to the ambient conditions.

The sensors will probably not sense skin temperature and ambient temperature precisely, and typical use cases might be different than the above model (i.e., wearing clothes, exercise, placement of sensor on the body, circulation, etc.). However, with all these variations, the form of the following equation will still be correct, and parameter ɑ must be empirically deduced.

Tcore = Tskin + α × (Tskin − Tambient)

If the sensor can be worn in a way that enables it to sense core temperature fairly well (for example, on the forehead or under the arm), then the parameter alpha will be small and can be estimated by testing a number of subjects and averaging.

For an ambient temperature sensor that is well coupled to the ambient temperature, the ambient-side sensor will react more quickly to the ambient conditions than the skin, and there may be some “overshoot” of the projected core temperature. In general, this effect will not be significant enough to make temperature compensation a worthwhile effort, especially if the skin-side senor is placed in close proximity to the core temperature.

Conclusion

In wearables that measure skin temperature, it is often necessary to know how well the area where the device is placed will reflect the core temperature, as well as how skin temperature can vary with ambient temperature. The approach requires either knowledge of the ambient temperature or estimating and correcting for ambient temperature.