handbook of modern sensors

3.5 Resistance 63
resistor) and the so-called resistive temperature detector (RTD). 5 The most popular
RTD is a platinum (Pt) sensor which operates over a broad temperature range from
about −200 ◦ C to over 600 ◦ C. The resistance of a Pt RTD is shown in Fig. 3.18. For
a calibrating resistance R 0 at 0 ◦ C, the best-fit straight line is given by
R = R 0 (1.00 + 36.79 × 10 −4 t), (3.57)
where t is the temperature in ◦ C and R is in . The multiple at temperature (T ) is the
sensor’s sensitivity (a slope), which may be expressed as +0.3679%/ ◦ C.
There is a slight nonlinearity of the resistance curve which, if not corrected, may
lead to an appreciable error. A better approximation of Pt resistance is a second-order
polynomial which gives an accuracy better than 0.01 ◦ C:
R = R 0 (1 + 39.08 × 10 −4 t − 5.8 × 10 −7 t 2 ). (3.58)
It should be noted, however, that the coefficients in Eqs. (3.57) and (3.58) somewhat
depend on the material purity and manufacturing technologies. To compare accuracies
of the linear and the second-order models of the platinum thermometer, consider the
following example. If a Pt RTD sensor at 0 ◦ C has resistivity R 0 = 100,at+150 ◦ C,
the linear approximation gives
R = 100[1.0036 + 36.79 × 10 −4 (150)]=155.55,
whereas for the second-order approximation (Eq. 3.58)
R = 100[1 + 39.08 × 10 −4 150 − 5.8 × 10 −7 (150) 2 ]=157.32.
The difference between the two is 1.76 . This is equivalent to an error of −4.8 ◦ Cat
+150 ◦ C.
Thermistors are resistors with large either negative (NTC) or positive (PTC) temperature
coefficients. The thermistors are ceramic semiconductors commonly made
of oxides of one or more of the following metals: nickel, manganese, cobalt, titanium,
iron. Oxides of other metals are occasionally used. Resistances vary from a fraction
of an ohm to many megohms. Thermistors can be produced in the form of disks,
droplets, tubes, flakes, or thin films deposited on ceramic substrates. Recent progress
in thick-film technology allows us to print the thermistor on ceramic substrates.
The NTC thermistors often are fabricated in the form of beads. Usually, bead
thermistors have platinum alloy lead wires which are sintered into the ceramic body.
Platinum is a convenient choice for the thermistor wires because it combines a relatively
low electrical resistance with a relatively high thermal resistance. During the
fabrication process, a small portion of mixed metal oxides is placed with a suitable
binder onto a pair of platinum alloy wires, which are under slight tension. After the
mixture has been allowed to set, the beads are sintered in a tubular furnace. The metal
oxides shrink around the platinum lead wires and form intimate electrical bonds. The
beads may be left bare or they may be given organic or glass coatings.
5 See Section 16.1 of Chapter 16