### Resistance temperature detectors : Basics

_{ϑ}and R

_{0}- are the values of electrical resistance of a metal conductor at temperatures ϑ and 0,̊C, respectively, Ohm;

**α**- thermal coefficient of electrical resistance, 1/̊C .

**Fig.1**shows relationship between resistance of platinum and copper RTD and temperature.

^{o}C (they are used as reference RTDs, as well), copper RTD - from -50 to 150

^{o}C, and Nickel RTD - from -215 to 320

^{o}C.

**Figure 1:**Resistance vs temperature for platinum and copper RTD.

**Fig. 2**shows the assembly of RTDs. Sensitive elements of RTDs are made of a thin wire

**with outside diameter equal to 0.025 mm (platinum RTD) and 0.1 mm (copper RTD) double wounded (non-inductive) on a micaceous or porcelain stem**

*1***. For mechanical strength the sensitive element is placed in the ceramic insulator tube**

*2***filled by extremely fine granular powder; extension wires are placed in the ceramic insulator**

*3***, and entire assembly is covered by a protective sheath of stainless steel**

*4***. The space between the sheath and ceramic insulator is filled by ceramic packing powder**

*5***. To avoid contact of sensitive element with environment, sensitive assembly is protected by high-temperature hermetic seal**

*6***. The contact between the wire of the sensitive element and the ceramic encapsulation permits a rapid speed of response.**

*7*

**Figure 2:**RTD assembly.

*Wheatstone bridge*(

**Figure**

**3**). In this case RTD is connected to the bridge by two connecting cables (conductors). The bridge is powered by direct current power supply in the points "a" and "b". RTD is immersed in the media, which temperature to be measured. When this bridge is in balance, then there is no voltage between points "c" and "d", and zero-indicator (ZI) shows no current. For this condition we can write the following equation:

_{1}and R

_{2}- electrical resistance of two invariable resistors, usually, R

_{1}=R

_{2}, Ohm;

_{ϑ}

**- electrical resistance of RTD, Ohm;**

**R**- electrical resistance of a connecting cable, Ohm;

_{c}_{sr}

**- electrical resistance of a slide (variable) resistor, Ohm.**

**Figure 3.:**Two-conductor connecting.

**Figure 4:**Three-conductor connecting.

_{sr}) corresponds to each value of a measuring temperature (ie, for each value of R

_{ϑ}) at any balance condition of the bridge. Therefore, the scale of the bridge may be calibrated in degrees Celsius.

*a two-conductor connecting scheme*(see

**Fig.3**), variation of an ambient temperature will effect values of an electrical resistance of connecting cables R

_{c}and, therefore, the results of measurements will be erroneous.

*a three-conductor connection scheme*is recommended (see

**Fig. 4**). One conductor is common to both sides of the bridge, while other two connect the RTD to each side of the bridge. Any change in the cable temperature (as the result of variations in ambient temperature) will be cancelled because the resistance of both sides of the bridge change by the same value (providing three connecting cables are at the same temperature).

*four-conductor connection scheme*is used when very accurate measurements of temperature are required, up to ±0.01 °C of accuracy.

**Derivation of a balanced condition for a Wheatstone Bridge**

**Figure 4a.:**Wheatstone bridge.

*the total current flowing into any junction is equal to the total current flowing out of this junction*. The second Kirchoff’s law states:

*the total change in potential around any closed circuit loop is equal to zero.*

**a. First method**

*dc*voltage, and U≠ 0.

_{1}; I

_{3}and I

_{5}.

_{1}; I

_{3}and I

_{5}.

_{5}is substituted by an ampmeter. Ampmeters have a negligibly small resistance, so we can write that R

_{5 }= 0. With this condition we can re-write (13) as follows:

_{i}> 0 we have that ∆ > 0 and ∆ ≠ 0.

_{5}we have:

_{5}= 0, and because ∆ > 0, and ∆ ≠ 0 and U ≠ 0, we can give an expression for the balanced condition for the Wheatstone bridge as follows:

**b. Second method**

_{5}= 0, and current

*f*is at earth potential, then potential at point

*e*is equal to U

_{a}= U. Potential at point

*b*is equal to

*d*is equal to

*b*and

*d*is equal to

**(26)**

_{3}≠ 0 and R

_{1}≠ 0, then

_{5}= 0, then voltage U

_{bd }= 0. Because U ≠ 0, then