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handbook of modern sensors

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488 16 Temperature Sensors<br />

flat junctions may provide intimate thermal coupling with the measured surface. Foil<br />

thermocouples are very fast (a typical thermal time constant is 10 ms) and can be used<br />

with any standard interface electronic apparatuses. While measuring temperature with<br />

<strong>sensors</strong> having small mass, thermal conduction through the connecting wires always<br />

must be taken into account. Because <strong>of</strong> a very large length-to-thickness ratio <strong>of</strong> the film<br />

thermocouples (on the order <strong>of</strong> 1000), heat loss via wires is usually negligibly small.<br />

To attach a film thermocouple to an object, several methods are generally used.<br />

Among them are various cements and flame or plasma-sprayed ceramic coatings. For<br />

ease <strong>of</strong> handling, the <strong>sensors</strong> <strong>of</strong>ten are supplied on a temporary carrier <strong>of</strong> polyimide<br />

film which is tough, flexible, and dimensionally stable. It is exceptionally heat resistant<br />

and inert. During the installation, the carrier can be easily peeled <strong>of</strong>f or released by<br />

application <strong>of</strong> heat. The free foil <strong>sensors</strong> can be easily brushed into a thin layer, to<br />

produce an ungrounded junction. While selecting cements, care must be taken to<br />

avoid corrosive compounds. For instance, cements containing phosphoric acid are<br />

not recommended for use with thermocouples having copper in one arm.<br />

16.3 Semiconductor P-N Junction Sensors<br />

A semiconductor p-n junction in a diode and a bipolar transistor exhibits quite a<br />

strong thermal dependence [11]. If the forward-biased junction is connected to a<br />

constant-current generator (Fig. 16.19A) (Section 5.3.1 <strong>of</strong> Chapter 5), the resulting<br />

voltage becomes a measure <strong>of</strong> the junction temperature (Fig. 16.20). A very attractive<br />

feature <strong>of</strong> such a sensor is its high degree <strong>of</strong> linearity. This allows a simple method<br />

<strong>of</strong> calibration using just two points to define a slope (sensitivity) and an intercept.<br />

The current-to-voltage equation <strong>of</strong> a p-n junction diode can be expressed as<br />

I = I 0 exp<br />

( qV<br />

2kT<br />

)<br />

, (16.45)<br />

where I 0 is the saturation current, which is a strong function <strong>of</strong> temperature. It can be<br />

shown that the temperature-dependent voltage across the junction can be expressed as<br />

V = E g<br />

q − 2kT (ln K − ln I), (16.46)<br />

q<br />

(A)<br />

(B)<br />

Fig. 16.19. Voltage-to-temperature dependence<br />

<strong>of</strong> a forward-biased semiconductor<br />

junction under constant-current conditions.

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