## Thermistor linearization using two resistors. Two parameters of the equivalent resistance can be chosen.

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To obtain this expression, we did not use any mathematical model for *RT. *Thus this method can also be applied to PTC thermistors and other nonlinear resistive sensors.

Another analytical method consists of forcing the resistance-temperature curve to have an inflection point just in the center of the measurement range *(Ta). *To obtain the necessary value for *R, *we must take the derivative of (2.33) again with respect to the temperature and equate the result to zero.

This gives for *R *a value of

— * B—2T R *— RT + (2.38)

The preferred method depends on the application. Equation (2.38) gives a better linearity in the central zone of the measurement range and a worse linearity at the ends. Equation (2.37) gives its best linearity at the zones near each one of the adjusting points. Subsection 3.2.2 will describe an additional method based on the documentation provided by some manufacturers.

**Example: **The circuit in Figure E2. I archieves the linearization of an NTC thermistor over a limited measurement range. Calculate the value for *R1 *and *R2 *so that at the temperature T0 the equivalent resistance shows an inflection point and has a slope *in. *Model for the thermistor is

To determine the inflection point we must set the second derivative of *R *with respect to *T *to zero

Some “linear” NTC units are available that include one or more resistors in series and parallel combination with one or more thermistors following the preceding criteria. Obviously their “linearity” is limited to the meagurement range specified by the manufacturer. The network in

Figure 2.20 is an example of such a unit. If digital computer time is available for linearization, then an algorithm such as that in [4] permits us to linearize the thermistor by software rather than by adding a resistor.

**Permanent Magnet DC Motor Equivalent Circuit Diagram**

A permanent magnet DC (PMDC) motor consists of a permanent magnet stator and armature windings in the rotor. The armature winding is supplied with a DC voltage that causes a DC current to flow in the windings. Interaction between the magnetic field produced by the armature current and that of the permanent magnet stator causes the rotor to rotate. The following schematic shows a Permanent Magnet DC Motor Equivalent Circuit Diagram.

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