The value of each resistor varies with temperature as a logarithmic function. Hence, if two conductors are separated by an NTC material the resistance between the two conductors can be calculated using the equation:
where a and b are constants and depend upon the volume of NTC material, surface area contact between the conductors, NTC material and unit length, and T is the temperature of the NTC material. The overall NTC resistance is the reciprocal of the sum of all unit lengths.
When resistors are connected parallel, if a resistor has a much lower resistance than other resistors the overall resistance can be approximated to the lowest resistance.
It can be seen, therefore, that if a portion of NTC material significantly increases in temperature the overall resistance between the two conductors is approximately equal to the resistance of the hottest part of the NTC material. For short lengths of NTC material (i.e. less than 20m) an increase of 30C in a small amount of element wire (say, less than 0.5m) has a pronounced effect on the overall resistance of the NTC material. Therefore, by monitoring the resistance of NTC separation layer the controller may determine a localized area of over-heating is arising if a dramatic decrease in resistance is seen.
Measuring the NTC resistance
Several methods of measuring the NTC resistance are possible and have different benefits and considerations which need to be taken into account when designing such circuits. Primarily, it should be noted that inherently the resistance of NTC material is very high at low temperatures, in the order of tens of Mohms. Accordingly to Ohm's law at low voltages (such as 12V for automotive applications) this equates to very low current through the separation layer. For example, if the resistance of the NTC separation layer was say 30 Mohms at 20C, at 12V the current through the layer is 0.4 microA. One method of measuring the NTC resistance may be achieved using a differential amplifier and a small value resistor in series with the NTC layer (see below).
A further method for measuring the resistance of the NTC layer is to create an RC filter where a fixed capacitor is placed in series with the NTC resistance. As the resistance of the NTC layer changes the transfer function of the filter will change accordingly.
Therefore for an AC signal of the appropriate frequency (i.e. close to the cut-off frequency of the filter when the NTC material is at 20C), as the temperature of the NTC material increases, the cut-off frequency will either become lower or higher depending upon the configuration of the filter. The AC signal will also be subject to a phase shift, again dependant on temperature. This introduces two possible ways of measuring the NTC resistance.
Measuring the PTC resistance
PTC technology uses the known temperature coefficient of resistance of specific metals to allow the average element temperature to be calculated. As the temperature of such a metal increases the resistance increases also in a linear fashion. Conversely to an NTC separation layer, a PTC wire may be modeled as many resistors in series. This has the effect that any localized area of over-heating will have a negligible impact on the overall measured PTC resistance.
The simplest method of measuring the PTC resistance is to apply a constant current through PTC wire. As the temperature of the wire increases and hence the resistance increases, the voltage across the PTC wire will decreases according to Ohm's law. The voltage across the PTC wire may be monitored by an analogue-to-digital converter on a micro-processor which can then calculate the element temperature.
Economics
The total technology of thermistor conductor and control module described above is economically competitive against existing seat heating technology while providing robust and safe use.
Mike Daniels is development director and Tom Robst is an electronic design engineer at Thermocable UK. They can be reached at: [email protected] and [email protected].
