Resistance Calibration and Monitoring of Thermal Systems

Abstract

A method for calibrating the temperature of a resistive element having a Curie temperature material includes generating a standard resistance-temperature (RT) curve for the resistive element at isothermal conditions to identify the value of the RT curve and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over an operating period; comparing the standard RT curve to the operating RT curve; and adjusting the operating curve to the standard RT curve at the Curie temperature to calibrate the temperature of the resistive element.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of U.S. Provisional Application No. 63 / 007,272, filed April 8, 2020, the disclosure of which is incorporated herein by reference. [Technical Field]

[0002] FIELD OF THE DISCLOSURE This disclosure relates to temperature measurements, and more particularly to calibrating the temperature of a resistive heater based on resistance measurements. [Background technology]

[0003] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0004] Instead of or in addition to using a separate temperature sensor, it is known in the art to calculate the temperature using resistance measurements of a resistive heater, however, the resistance of the heating element in the resistive heater often shifts over time or during manufacturing, causing an error in the calculated temperature relative to the actual temperature.

[0005] To compensate for these resistance changes and provide a more accurate temperature correction, various calibration techniques can be employed, including using multiple thermocouples to compare the calculated temperature with the measured temperature and apply the appropriate correction to the resistance calculation. While these calibration techniques are somewhat effective, they suffer from drawbacks in terms of complexity and accuracy.

[0006] Among other issues related to the control of heating / resistance elements, those issues related to calibrating the resistance of heating / resistance elements over time are addressed by the present disclosure. Summary of the Invention

[0007] This section provides a general overview of the disclosure and is not an exhaustive disclosure of its full scope or all of its functionality.

[0008] Generally, in this disclosure, the inflection point / area on the resistance-temperature (RT) curve at the Curie temperature when a resistive heater (or sensor, or other resistive element) is used is used to provide a known temperature signal used for calibration. As described in more detail below, this inflection point or calibrated RT curve can be used for a variety of purposes, including, but not limited to, predicting the remaining life of the heater, measuring the temperature profile along the length of the heater (or sensor, or other resistive element), identifying heat loss from the heating system for improved system modeling and control, improving identification of the thermal path between the heating element and the process for improved system modeling and control, reducing the cost of calibrating a thermal system, self-calibrating the heating system, improving the level of accuracy in combined two-wire resistor and thermocouple power pin (TCPP) thermal systems, two-wire thermocouple junction systems (including other thermal systems with temperature-sensing resistors / lead wires), and field recalibration in sensing systems that change over time. Therefore, the term "power lead" should be interpreted to mean a power pin, lead wire, or other conductive element operably connected to a resistive element to provide power to the resistive element.

[0009] It should also be understood that while remaining within the scope of this disclosure, the teachings herein may be applied alone or in combination with other calibration techniques, whether part of the inventive subject matter herein or known.

[0010] In one aspect, a method is provided for calibrating the temperature of a resistive element having a Curie temperature material by generating a standard resistance-temperature (RT) curve for the resistive element at isothermal conditions, generating an operating RT curve for the resistive element over an operating period, comparing the standard RT curve to the operating RT curve, and adjusting (by both offset and gain) the operating curve to the standard RT curve at the Curie temperature to identify the RT curve value and an inflection point at the Curie temperature.

[0011] In one embodiment, the resistive element is within the heater, but the resistive element may be a sensor, such as a thermocouple, among other resistive elements. In another embodiment, the resistive element is coupled at a junction to a power supply lead, and the power supply lead is of a different material than the resistive element, such that a second calibration temperature is determined at the junction.

[0012] In another form, multi-point calibration is achieved when a resistive element is electrically coupled to power leads and thermocouple junctions having different materials, and at least one power lead is connected to the resistive element. The method includes generating a standard resistance-temperature (RT) curve for the resistive element under isothermal conditions to identify a value of the RT curve and an inflection point at the Curie temperature, generating an operating RT curve for the resistive element over an operating period, comparing the standard RT curve to the operating RT curve, adjusting the operating curve to the standard RT curve at the Curie temperature, calculating a temperature of the junction, and calculating a corrected temperature of the resistive element based on the adjustment step and the temperature of the junction.

[0013] Further areas of applicability will become apparent from the description provided herein. It should be understood that the description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. [Brief explanation of the drawings]

[0014] In order that the present disclosure may be more fully understood, various forms thereof will now be described, by way of example, with reference to the accompanying drawings, in which:

[0015] [Figure 1] FIG. 1 is a graph showing the inflection point at the Curie temperature of a resistive material on a resistance versus temperature (RT) curve.

[0016] [Figure 2] FIG. 2 is a graph showing the inflection point at the Curie temperature of a resistive material in a change in resistance (dR / dT) versus temperature curve.

[0017] [Figure 3] FIG. 3 is a graph illustrating a shifted RT curve for calibrating the resistance of a resistive element in accordance with the teachings of the present disclosure.

[0018] [Figure 4] FIG. 4 is a graph showing the error before and after calibration shown in FIG.

[0019] [Figure 5] FIG. 5 is a schematic side view of a resistive heater with multiple thermocouples used in testing in accordance with the teachings of the present disclosure.

[0020] [Figure 6] FIG. 6 is a graph of simulated temperature distribution along the length of the resistive heater of FIG. 5 at different power levels.

[0021] [Figure 7] FIG. 7 is a graph of an operational RT curve calibrated using both slope and offset compared to a standard RT curve according to testing of the present disclosure.

[0022] [Figure 8A] FIG. 8A is a graph of simulated temperature distribution along the length of the resistive heater of FIG. 5 at different power levels and with different temperature end conditions. [Figure 8B]FIG. 8B is a graph of simulated temperature distribution along the length of the resistive heater of FIG. 5 at different power levels and with different temperature end conditions. [Figure 8C] FIG. 8C is a graph of simulated temperature distribution along the length of the resistive heater of FIG. 5 at different power levels and with different temperature end conditions.

[0023] [Figure 9] FIG. 9 is a graph of the calculated RT curves for the different temperature end conditions of FIGS. 8A-8C.

[0024] [Figure 10] FIG. 10 is a graph of the calculated dR / dT curves for the different temperature end conditions of FIGS. 8A-8C.

[0025] [Figure 11A] FIG. 11A is a graph of resistance over time of a resistive element in an isothermal salt bath for both partial and full immersion according to testing of the present disclosure. [Figure 11B] FIG. 11B is a graph of the change in resistance over time of a resistive element in an isothermal salt bath for both partial and full immersion according to testing of the present disclosure.

[0026] [Figure 12A] FIG. 12A is a graph showing the change in resistance over time of a partial immersion salt bath throughout a heating cycle, according to testing of the present disclosure. [Figure 12B] FIG. 12B is a graph showing the change in resistance over time of a partial immersion salt bath across a heat lamp, according to testing of the present disclosure. [Figure 12C] FIG. 12C is a graph showing the change in resistance over time of a partial immersion salt bath over a cooling ramp, according to testing of the present disclosure.

[0027] [Figure 13A]FIG. 13A is a graph showing the change in resistance over time of an entire immersion salt bath throughout a heating cycle according to tests of the present disclosure. [Figure 13B] FIG. 13B is a graph showing the change in resistance over time of an entire immersion salt bath across a heat lamp according to testing of the present disclosure. [Figure 13C] FIG. 13C is a graph showing the change in resistance over time of an entire immersion salt bath over a cooling ramp according to tests of the present disclosure.

[0028] [Figure 14A] FIG. 14A is a graph showing the change in resistance over time for both partial and full immersion salt baths over an accumulation period according to testing of the present disclosure. [Figure 14B] FIG. 14B is a graph showing the change in resistance over time for both partial and full immersion salt baths over a cumulative period after removal from the salt bath, according to testing of the present disclosure.

[0029] [Figure 15A] FIG. 15A is a schematic diagram of another form of resistive element having a thermocouple power pin configuration and using multi-point calibration in accordance with the teachings of the present disclosure. [Figure 15B] FIG. 15B is a schematic diagram of another form of resistive element having a thermocouple power pin configuration and using multi-point calibration in accordance with the teachings of the present disclosure.

[0030] [Figure 16A] FIG. 16A is a graph showing simulated temperature distributions along a hypothetical heater having multiple coils with an isothermal temperature distribution and different power levels in accordance with the teachings of the present disclosure. [Figure 16B] FIG. 16B is a graph showing simulated temperature distribution along a virtual heater with multiple coils at different power levels with high end losses, i.e., lower temperatures at both ends, in accordance with the teachings of the present disclosure.

[0031] [Figure 17]FIG. 17 is a graph of the dR / dT curves for a virtual heater corresponding to FIGS. 16A and 16B in accordance with the teachings of the present disclosure.

[0032] [Figure 18] FIG. 18 is a graph of dR / dT versus maximum wire temperature corresponding to FIGS. 16A and 16B in accordance with the teachings of the present disclosure.

[0033] [Figure 19] FIG. 19 is a graph of the second derivative d2R / dT2 corresponding to FIGS. 16A and 16B in accordance with the teachings of the present disclosure.

[0034] [Figure 20A] FIG. 20A is a graph showing simulated temperature distribution along a heater with thermocouples in two different locations in accordance with the teachings of the present disclosure.

[0035] [Figure 20B] FIG. 20B is a graph of dR / dT versus wire temperature for two different thermocouple locations along the length of the hypothetical heater of FIGS. 16A and 16B in accordance with the teachings of the present disclosure.

[0036] [Figure 21] FIG. 21 is a schematic diagram of a heater having multiple different materials for the resistive element and multiple power lead sensors constructed in accordance with the teachings of the present disclosure.

[0037] [Figure 22] FIG. 22 is a schematic diagram of a self-calibrating thermocouple constructed in accordance with the teachings of the present disclosure.

[0038] The drawings described herein are for illustrative purposes only and are not intended to limit the scope of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0039] The following description is merely exemplary in nature and is in no way intended to limit the disclosure, application, or uses. It should be understood that throughout the drawings, corresponding reference numerals indicate like or corresponding parts and features.

[0040] The Curie temperature, or Curie point, is known in physics and materials science as the temperature at which a particular material loses its permanent magnetic properties. As shown in Figure 1, the Curie temperature has been shown to create an inflection point in the resistance-temperature (RT) characteristics of some materials, including, as examples, nickel, iron, cobalt, and some of their alloys.

[0041] Referring to FIG. 2 , the inflection point can be more clearly identified by measuring the rate of change of resistance with temperature (or the rate of change with time as it passes through the inflection point), or dR / dT. The inventors discovered that the inflection point remains largely unaffected by shifts in resistance due to manufacturing processes and use over time. In other words, the inflection point generally remains the same temperature regardless of the operating environment / constraints and the physical structure of the heater / thermal system. Therefore, when a resistive heater (or sensor, or other resistive element) is in use, identifying the inflection point provides a known temperature signal that can be used for calibration. As described herein, the inventors' discovery of this principle can be applied in a variety of cases to more easily and accurately determine the temperature at and along a resistive element, calibrate thermal models, self-calibrate resistive elements, predict resistive element lifetime, and control power to thermal systems, among other applications.

[0042] Referring now to Figure 3, an example of using the Curie temperature to calibrate RT, a standard RT curve, or a curve generated under isothermal conditions, is shown along with an actual measured or errored operational RT curve for a resistive element. Because the inflection point at the Curie temperature does not change, the operational RT curve can be offset or shifted up as shown in the standard RT curve at the Curie temperature to calibrate the RT curve for the resistive element.

[0043] As shown in FIG. 4, this shift in the RT curve reduces errors in resistance measurements, and the resistance of a resistive element over a temperature range can be easily and accurately calibrated according to the principles of the present disclosure.

[0044] Returning to FIG. 3, the operational RT curve is generally "flatter" than the standard RT curve. This occurs because the ends of the resistive element are at a lower temperature than the center of the resistive element; due to this temperature difference, the flatter curve indicates the average temperature across the resistive element. Due to the shift in the RT curve with its inflection point, the teachings of this disclosure can be applied to determining the temperature profile along the length of the resistive element. Note that in one example, the calibrated RT curve will actually have a lower resistance at lower temperatures than the calculated resistance, while the calibrated resistance at higher temperatures will generally track the standard RT curve, but be slightly higher. More specific examples and tests are described in detail below.

[0045] Test / Calculation.

[0046] 5 and 6, tests were conducted on a tubular heater 20 having 71 coils of resistance wire, an internal thermocouple located in the center of the heater 20, and four additional thermocouples, labeled TC1 through TC4, attached to the sheath 22 of the heater 20 as shown. The temperature profile along the length of the heater 20, over a temperature range of 0 to 600°C, is shown in FIG. 6, and it can be observed that heat loss occurs at the ends of the heater 20 as the temperature increases.

[0047] Referring now to Figure 7, two resistive elements were tested, one in an isothermal condition, as indicated by the upper dashed curve, and one in ambient air, as indicated by the lower dashed curve. The ambient air curve was adjusted for offset and gain so that the curves could be compared. Finally, the lower solid curve applied the isothermal resistivity data to the measured temperature profile. The resulting similarity in curvature between the lower dashed curve and the solid curve indicates the effectiveness of the calibration technique, reducing errors caused by the "flatness" of the curves, as shown below.

[0048] In general, the "flatness" of a measured RT curve compared to an isothermal RT curve can provide calibration information about the temperature profile along the length of the resistive element. As used herein, the term "flatter" is interpreted to mean having no distinctive inflection points or area, or that the curve has a relatively consistent slope. The term "flatter" should not be interpreted to mean being more horizontal on a Cartesian plane. For example, the flatter the curve, the greater the heat losses likely to occur across the resistive element. Offsetting the isothermal RT curve at the Curie temperature can compensate for these losses, similar to losses due to manufacturing variations and changes in the resistance of the resistive element over time.

[0049] 8A-8C and 9, the principle of calibrating the temperature profile along the length of a resistive element using simulated data is illustrated in more detail. FIGS. 8A-8C show several temperature measurements using the individual thermocouples described above for resistive elements with air loss at both ends (FIG. 8A), air loss at one end (FIG. 8B), and an isothermal temperature profile (FIG. 8C). The corresponding RT curves are shown in FIG. 9, where curve A represents air loss at both ends, curve B represents air loss at one end, and curve C represents the isothermal case. As shown, in the isothermal case of curve C, when more resistive elements reach temperature simultaneously, the resistance becomes higher and the inflection point becomes more pronounced. The greater the heat loss at the ends of this example, the less pronounced the inflection point becomes ("flatter").

[0050] Referring now to Figure 10, the first derivative of resistance over temperature, or the change in resistance over temperature (dR / dT), highlights these differences with and without thermal end losses. As shown by curve C, the maximum dR / dT point is higher when more resistive elements reach the inflection temperature simultaneously, and decreases very rapidly at higher temperatures. As shown by curves B and C, the maximum dR / dT point is lower when fewer resistive elements reach the inflection temperature simultaneously, and decreases more slowly at higher temperatures (because other portions of the material are still near the inflection point). Notably, despite these differences, the inflection point (or Curie temperature) remains the same for all three conditions, providing a constant for calibrating the resistance of resistive elements in various thermal environments.

[0051] Salt bath test.

[0052] To further demonstrate the use of Curie temperature for resistor calibration, a series of tests were conducted with resistor elements immersed in a molten salt bath at 420°C (to simulate isothermal conditions). Data was collected with resistor elements both partially immersed in the salt bath and fully immersed in the salt bath under these two test conditions.

[0053] As shown in Figures 11A and 11B, the resistive element was partially immersed in a salt bath, removed from the bath, cooled at room temperature, and then fully immersed in the salt bath and cooled at room temperature.

[0054] Additionally, several observations were made, shown for partial immersion in Figures 12A-12C and for full immersion in Figures 13A-13C. First, the magnitude of dR / dt (change in resistance with respect to time, time = "t") was higher for the full immersion test condition. Also, the magnitude of dR / dt was higher for the full immersion test condition during both the heat ramp / period and the cool ramp / period. This difference in the magnitude of dR / dt during the heat ramp / period and the cool ramp / period is also shown in Figures 14A and 14B.

[0055] Self-calibration.

[0056] Yet another application of the teachings of the present disclosure is the use of different materials for power pins that provide resistive elements. The use of different materials for power pins to form temperature sensing or "thermocouple" power pins is described in U.S. Patent No. 10,728,956, entitled "RESISTIVE HEATER WITH TEMPERATURE SENSING POWER PINS," which is commonly owned with this application and its contents and is incorporated herein by reference in its entirety.

[0057] 15A and 15B, two exemplary configurations of a resistive element having at least one power lead made of different materials are shown. The resistive element 30 (in this case, the heater resistive wire) is made of a resistive material with a measurable inflection point at its Curie temperature, such as, for example, nickel 201 (UNS N02201) with a 99% Ni content. The power lead 40 is of a different material, but different from the material of the resistive element 30, which may be, for example, a NiCr alloy. A multi-point calibration can be provided by measuring the temperature at the junction 50 along with the inflection point at the Curie temperature of nickel 201. One calibration point is from the Curie temperature inflection point, and the other calibration point is from the thermocouple power lead junction 50.

[0058] Advantageously, the teachings of the present disclosure may be used for a variety of purposes, including, but not limited to, calibration of the resistance of resistive elements, compensation for heat losses along a heating system, calibration of thermal models, multi-point calibration, lifetime prediction of resistive elements, and power control, among others.

[0059] In another aspect of the present disclosure, the partial gain correction of the operating RT curve is The RT curve The second derivative of, or d 2 R / dT 2 , and other forms of standard deviation or other mathematical expressions of the shape of dR / dT. Generally, as described in more detail below, the shape of the operating RT curve leading to and leaving the Curie inflection point provides information for gain adjustment. Also, while gain adjustment using second derivatives is shown and described below, second derivatives, along with other mathematical expressions of the shape of dR / dT, can be used for either or both offset and gain and are within the scope of this disclosure.

[0060] 16A and 16B, simulated temperature distributions for a heater with multiple coils (70 coils total in this example) at different power levels are shown, with an isothermal temperature distribution shown in FIG. 16A and one with high end losses shown in FIG. 16B. Both the isothermal and high end loss conditions are further analyzed using various mathematical expressions for the shape of dR / dT, as shown below.

[0061] First, the resistance at the isothermal condition is higher and more pronounced at the inflection point, as shown in Figure 17. Furthermore, the area under the RT curve at the isothermal condition is larger than at the high end loss condition.

[0062] Referring now to FIG. 18, the isothermal condition has a higher maximum dR / dT and a higher standard deviation. The mean and standard deviation of the dR / dT values ​​for each curve were calculated, and based on these calculations, the standard deviation of dR / dT for the isothermal condition is 0.0048, while the standard deviation of dR / dT for the high end loss condition is 0.0021. As further shown, the slope of the dR / dT curve for the isothermal condition is greater moving away from the inflection point (toward higher temperatures) than toward the inflection point, while the slope of the dR / dT curve for the high end loss condition is similar. Therefore, this difference indicates that a positive gain adjustment should be performed for the high end loss condition to calibrate the heater to the isothermal condition. In other words, this information confirms that the average temperature of the heater with high end loss is lower.

[0063] Next, in Figure 19, the second derivative, or d 2 R / dT 2 is taken for both isothermal and high end loss conditions, increasing the Curie inflection point. d 2 R / dT 2 The maximum and minimum values ​​of d show that the isothermal condition requires significantly higher and lower gain adjustments than the high end loss condition. Also, similar to the dR / dT case shown and described above, the d 2 R / dT 2 The slope of the curve can be used to adjust the gain.

[0064] Referring to Figures 20A and 20B, using thermocouples in addition to adjusting the operating RT curve based on the Curie inflection point described above can provide additional calibration information. For example, a first thermocouple, TC1, is placed near the hottest part of a resistive heating element, and a second thermocouple, TC2, is placed near the coldest part of the resistive heating element. While the resistance signals from both thermocouples are the same, the second thermocouple, TC2, is at a lower temperature, resulting in a smaller dT value and a larger dR / dT, which is shifted relative to the first thermocouple, TC1. The second thermocouple, TC2, has an inflection point below the Curie temperature, indicating that it is in a lower temperature region. This inflection point can be used to calibrate the second thermocouple, TC2.

[0065] Another variation of the present disclosure is shown in FIG. 21 , which includes a multi-coil (or multi-segment, although the resistive element need not be coil-shaped as shown) heater 50, in which each coil 52, 54, and 56 is made from a different material having a different Curie temperature to provide temperature calibration in accordance with the teachings herein. Additionally, each coil 52 / 54 / 56 can be connected to a power supply having power leads 62, 64, 66 made from a different material than each coil 52 / 54 / 56, thus providing temperature at each junction A / B / C for additional calibration purposes. Any number of coils, power leads, and materials can be used and combined in accordance with the principles of the present disclosure; therefore, the illustrations herein are merely illustrative and should not be construed as limiting the scope of the present disclosure.

[0066] Yet another variation of the present disclosure is shown in FIG. 22 , which is a self-calibrating thermocouple 100. The self-calibrating thermoelectric element 100 includes a first thermoelectric element 102 in the form of a coil for increased resistance and a second thermoelectric element 104 made from a different material than the first thermoelectric element 102. An inorganic insulating material 106 surrounds the thermoelectric elements 102 / 104, and a sheath 108 surrounds the inorganic insulating material 106, as is typical of many thermocouple structures. The first thermoelectric element 102 is made of a material with a Curie temperature that exceeds the operating temperature range of the self-calibrating thermocouple 100. This Curie temperature can then be used to calibrate the self-calibrating thermocouple 100 according to the teachings herein. It should also be understood that the specific thermocouple structures shown and described are merely exemplary, and that other structures are considered within the scope of the present disclosure. For example, polymeric insulation could be used in place of inorganic insulation 106, or the thermocouple junction could be exposed rather than located within sheath 108. These and other configurations should be construed as being within the scope of the present disclosure.

[0067] As mentioned above, the teachings of the present disclosure and the use of the Curie inflection point can be used for many purposes. One such purpose is the measurement / calculation of the temperature profile along the length of a heater (or sensor, or other resistive element), as shown in Figures 23A-23F. In this example, the "first case" is a condition of high end loss, and the second case is an isothermal temperature distribution.

[0068] As described in more detail below, this inflection point or calibrated RT curve may be used for a variety of purposes, including, but not limited to, predicting the remaining life of a heater, measuring the temperature profile along the length of a heater (or sensor, or other resistive element), identifying heat loss from a heating system for improved system modeling and control, improving identification of the thermal path between the heating element and the process for improved system modeling and control, reducing the cost of calibrating a thermal system, self-calibrating a heating system, improving the accuracy level of coupled two-wire resistor and thermocouple power pin (TCPP) thermal systems, two-wire thermocouple junction systems (including other thermal systems with temperature sensing resistors / lead wires), and field re-calibrating sensing systems that change over time.

[0069] As used herein, the term "resistive element" should be taken to mean, for example, a resistive element used in a heater, a resistive wire used in a thermocouple, or other resistive element whose resistance changes over time to which the teachings of the present disclosure may be applied. Furthermore, heaters may take any number of forms, including cartridge heaters, cable heaters, layered heaters, and flexible heaters, as well as tubular heater structures as shown herein, among others.

[0070] Unless otherwise expressly indicated herein, all numerical values ​​expressing mechanical / thermal properties, composition percentages, dimensions and / or tolerances, or other characteristics should be understood as being modified by the word "about" or "approximately" when describing the scope of this disclosure. This modification is desirable for various reasons, including industry practices, materials, manufacturing, assembly tolerances, and testing capabilities.

[0071] As used herein, the phrase at least one of A, B, and C should be interpreted to mean the logical (A OR B OR C), using a non-exclusive logical OR, and not to mean "at least one A, at least one B, and at least one C."

[0072] The description of the present disclosure is merely exemplary in nature and, thus, variations that do not depart from the content of the disclosure are intended to be within the scope of the disclosure. Such variations should not be considered a departure from the spirit and scope of the disclosure. The inventions described in the original claims of this application are set forth below. [1] 1. A method of calibrating the temperature of a resistive element including a Curie temperature material, comprising: generating a standard resistance-temperature (RT) curve of the resistor element under isothermal conditions to identify the RT curve value and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over an operating period; comparing the standard RT curve to the operating RT curve; and adjusting the operating RT curve to the standard curve at the Curie temperature. [2] The method of [1], wherein the resistive element is within a heater. [3] 10. The method of claim 1, wherein the resistive element is coupled to a power supply lead at a junction, the power supply lead being of a material different from the material of the resistive element such that at least one additional calibration temperature is determined at the junction. [4] The method of [3], wherein the power lead is made of a NiCr material and the resistive element is made of a Ni material having a Ni content of at least 99%. [5] The method of [1], further comprising applying an adjustment if the slope of the operating RT curve is shallower than the slope of the standard RT curve. [6] A thermocouple, a first thermoelectric element made from a resistive material having a Curie temperature; a second thermoelectric element made from a different material than the first thermoelectric element; The Curie temperature of the first thermoelectric element is used to calibrate the thermocouple according to the method of [1]. [7] 1. A method for calibrating the temperature of a resistive element made of a Curie temperature material, comprising: the resistive element is electrically coupled to power leads having different materials and to a thermocouple junction, at least one of the power leads being connected to the resistive element; generating a standard resistance-temperature (RT) curve of the resistor element under isothermal conditions to identify the RT curve value and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over an operating period; comparing the standard RT curve to the operating RT curve; adjusting the operating curve to the standard RT curve at the Curie temperature; calculating the temperature at the junction; calculating a corrected temperature of the resistive element based on the adjusting and the temperature at the junction. [8] The method of [7], wherein the power lead is made of a NiCr material and the resistive element is made of a Ni material having a Ni content of at least 99%. [9] A resistive heater, a plurality of segments, each segment defining a different material than adjacent segments, each segment being made from a resistive material having a Curie temperature; a plurality of power leads extending from a power source, each power lead connected to a segment, each power lead defining a material different from the material of the segment to which the power lead is connected; The Curie temperatures of the segments and the different materials of the power leads are used to calibrate the resistive heater according to the method of [7].

[10] 1. A method of calibrating the temperature of a resistive element including a Curie temperature material, comprising: generating a standard resistance-temperature (RT) curve of the resistor element under isothermal conditions to identify the RT curve value and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over an operating period; developing a mathematical representation of the shape of the RT curve; and adjusting the operating RT curve to the standard curve at the Curie temperature based on the mathematical expression.

[11] The method of

[10] , wherein the mathematical expression is the second derivative of dR / dT of the RT curve.

[12] The second derivative is used for gain adjustment, the method of

[11] .

[13] The method of

[10] , wherein the mathematical expression is the standard deviation between the operating RT curve and the standard RT curve.

[14] A thermocouple, a first thermoelectric element made from a resistive material having a Curie temperature; a second thermoelectric element made from a different material than the first thermoelectric element; The Curie temperature of the first thermoelectric element is used to calibrate the thermocouple according to the method of

[10] .

Claims

1. 1. A method of calibrating the temperature of a resistive element including a Curie temperature material, comprising: generating a standard resistance-temperature (RT) curve for the resistive element under isothermal conditions to identify the value of the RT curve and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over a period of operation; comparing the standard RT curve to the operating RT curve; adjusting the operational RT curve to the standard RT curve at the Curie temperature; calculating a temperature of the resistive element; calculating a corrected temperature of the resistive element based on the adjusting and the temperature of the resistive element.

2. The method of claim 1 , wherein the resistive element is within a heater.

3. 2. The method of claim 1, wherein the resistive element is coupled at a junction to a power lead, the power lead being of a material different from the material of the resistive element such that at least one additional calibration temperature is determined at the junction.

4. 4. The method of claim 3, wherein said power leads are made of NiCr material and said resistive element is made of Ni material having a Ni content of at least 99%.

5. 10. The method of claim 1, further comprising applying an adjustment if the slope of the operating RT curve is flatter than the slope of the standard RT curve.

6. The method of claim 1, wherein the resistive element includes a thermocouple.

7. 1. A method for calibrating the temperature of a resistive element made of a Curie temperature material, comprising: the resistive element is electrically coupled to power leads having different materials and to a thermocouple junction, at least one of the power leads being connected to the resistive element; generating a standard resistance-temperature (RT) curve for the resistive element under isothermal conditions to identify the value of the RT curve and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over a period of operation; comparing the standard RT curve to the operating RT curve; adjusting the operating curve to the standard RT curve at the Curie temperature; calculating the temperature at the junction; calculating a corrected temperature of the resistive element based on the adjusting and the temperature at the junction.

8. 8. The method of claim 7, wherein said power leads are made of NiCr material and said resistive element is made of Ni material having a Ni content of at least 99%.

9. The method of claim 7, wherein the resistive element includes a resistive heater.

10. 1. A method of calibrating the temperature of a resistive element including a Curie temperature material, comprising: generating a standard resistance-temperature (RT) curve for the resistive element under isothermal conditions to identify the value of the RT curve and an inflection point at the Curie temperature; generating an operating RT curve for the resistive element over a period of operation; generating a mathematical representation of the shape of the operational RT curve; adjusting the operational RT curve to the standard RT curve at the Curie temperature based on the mathematical expression.

11. The method of claim 10, wherein the mathematical expression is the second derivative of the operating RT curve.

12. The method of claim 11 , wherein the second derivative is used in the adjustment.

13. The method of claim 10, wherein the mathematical expression is the deviation between the operating RT curve and the standard RT curve.

14. The method of claim 10, wherein the resistive element comprises a thermocouple.

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