Page 167 - Mechanical Engineers' Handbook (Volume 2)

156 Temperature and Flow Transducers

In the following paragraphs, these six circuits used for reading the resistance of the
thermometer will be briefly discussed. The determination of probe temperature from probe
resistance is discussed in a future section.
The two-wire, constant-current method is the simplest way to use a resistance thermom-
eter. One simply provides it with a known current and measures the voltage drop across the
probe and its lead wire (Fig. 18a). The resistance of the circuit is determined from Ohm’s
law in the cold and the hot condition, and the temperature is determined from the resistance
ratio.
In this approach, the lead-wire resistance is ignored, which leads to underestimating the
temperature change by approximately the ratio of the lead-wire resistance to the total circuit
resistance:
R TOT,H 1 R P (6)
R TOT,C R P,C R L
Errors can be avoided by properly accounting for the lead-wire resistance, either by
measuring it using a shorting plug to replace the probe or by calculating it from standard
tabular data on wire resistance.
The two-wire bridge circuit (Fig. 18b) suffers from the same lead-wire error as the two-
wire direct method but has one advantage: It can be used with an unstable power supply.
The probe resistance can be measured in terms of the calibrated reference resistor, indepen-
dent of the bridge voltage value.
The three-wire bridge circuit (Fig. 18c) compensates, to a considerable extent, for the
effect of lead-wire resistance. The circuit uses a matched pair of lead wires to connect the
bridge to the probe. One member of the pair is inserted into each of the two arms of the
bridge, so changes in the lead-wire resistance affect both arms. For a bridge with equal
resistances in both arms, this provides an approximate compensation for lead-wire resistance.
Many commercial probes are supplied with three-wire lead connection.
The most accurate technique for measuring the probe resistance is the four-wire direct
method (Fig. 18d). Lewis describes the advantages of the four-wire direct system in process
36
industry measurements and points out that significant advantages in accuracy can be achieved
at relatively low cost.
The probe is driven from a known source of constant current through one pair of leads,
while the voltage drop across the sensing resistor is measured using the other pair. Since
there is no current flow in the voltage-sensing leads, there is no error introduced by the lead-
wire resistance. With current and voltage drop known, the resistance can be calculated di-
rectly using Ohm’s law. Modern, regulated power supplies and high-impedance voltmeters
make this an increasingly attractive option.
Two four-wire bridges are shown: the four-wire Callendar bridge and the reversing
bridge. The Callendar bridge inserts equal lengths of lead wire in each of the two arms of
the bridge, which provides good compensation for the effect of lead-wire resistance. The
reversing bridge allows the operator to exchange lead wires, thus measuring the resistance
in each arm with two different pairs of leads. The average of the two values is usually used
as the best estimate, since the two measurements are equally believable.
Several manufacturers offer linearizing amplifiers as accessories for resistance thermom-
eters. These devices produce signals that are linearly proportional to sensor temperature by
correcting its nonlinear response.
The increasing use of computers in data interpretation has reduced the need for line-
arizing circuitry in laboratory and research work, but the commercial market still prefers
linear systems for control and monitoring.