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handbook of modern sensors

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13.4 Thermal Conductivity Sensor 401<br />

Figure 13.7B shows an electrical equivalent circuit <strong>of</strong> the sensor [13]. The values<br />

<strong>of</strong> R 1 and C 1 depend on the Al 2 0 3 average pore sizes and density. These components<br />

<strong>of</strong> resistance and capacitance vary with the number <strong>of</strong> water molecules that penetrate<br />

the pores and adhere to the surface. R 2 and C 2 represent the resistance and capacitance<br />

components <strong>of</strong> the bulk oxide material between the pores and are therefore<br />

unaffected by moisture. C 3 is an equivalent series capacitance term as determined by<br />

the measurement <strong>of</strong> the total resistance components in a dry atmosphere at very low<br />

frequencies. The sensor’s resistance becomes very large (> 10 8 ) as the frequency<br />

approaches dc. Thus, the measurement <strong>of</strong> humidity involves the measurement <strong>of</strong> the<br />

sensor’s impedance. The residual <strong>of</strong> nonhumidity-dependent resistance and capacitance<br />

terms that exist in a typical sensor shunt the humidity-dependent variables,<br />

thus causing the continuous reduction in slope (sensitivity) as the humidity is lowered,<br />

which, in turn, reduces the accuracy at lower humidities. Because temperature<br />

is a factor in humidity measurement, the sensor usually combines a humidity sensor,<br />

a thermistor, and a reference capacitance in the same package, which is protected<br />

against humidity influence and has a low-temperature coefficient.<br />

13.4 Thermal Conductivity Sensor<br />

Using the thermal conductivity <strong>of</strong> gas to measure humidity can be accomplished<br />

by a thermistor-based sensor (Fig. 13.8A) [14]. Two tiny thermistors (R t1 and R t2 )<br />

are supported by thin wires to minimize thermal conductivity loss to the housing.<br />

The left thermistor is exposed to the outside gas through small venting holes, and<br />

the right thermistor is hermetically sealed in dry air. Both thermistors are connected<br />

into a bridge circuit (R 1 and R 2 ), which is powered by voltage +E. The thermistors<br />

develop self-heating due to the passage <strong>of</strong> electric current. Their temperatures rise<br />

up to 170 ◦ C over the ambient temperature. Initially, the bridge is balanced in dry air<br />

to establish a zero reference point. The output <strong>of</strong> this sensor gradually increases as<br />

(A)<br />

(B)<br />

Fig. 13.8. Absolute humidity sensor with self-heating thermistors: (A) design and electrical<br />

connection; (B) output voltage.

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