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AGUILLON

Operation and Characterization of NTC Thermistors

Summary For almost all process in industry and applications for home appliances, temperature is the variable most frequently measured. The three most common types of contact electronic temperature sensors in use today are the thermocouples, Resistance Temperature Detectors (RTD), and thermistors. Thermistors are divided in positive and negative temperature coefficient thermistors (PTC and NTC), according to their resistive behave against temperature. This application note will examine the Negative Temperature Coefficient Thermal Resistors and its applications in order to sense the temperature inside the Mod..

The main disadvantage is that the relationship between resistance and temperature is nonlinear. However, the resistance-temperature curve is monotonic and can be very accurately described with a 3rd. order polynomial. The operating temperature is limited to 60°C ~ 300°C, which is smaller than that of metal RTD’s.

Thermistor Types and Fabrication Thermistors are available in many configurations including beads, disks, wafers, SMTs, flakes rods, tape and washers. Non-bead thermistors are also known as surface electrode thermistors and their manufacturing process has many similarities to the construction of ceramic capacitors.

After a theoretical background on NTC’s, some linearizing networks, circuit setups and experimental results will be exposed for temperature acquisition at the HPM elements. It is important to remark that, the term NTC thermistor, NTC or just thermistor can be interchangeable along the manuscript.

The NTC Thermistor Introduction The term thermistor is an abbreviation of Thermal Resistors, these elements are made from different kinds of metal oxides. Common metals are magnesium, cobalt, nickel, copper, and iron. The oxides are semiconductors with resistivity that decreases with temperature, hence the name. The temperature dependence of resistance is enormous when compared to other materials. For example, an NTC thermistor’s resistance at 100°C may be as little as 5.10% of the thermistor’s resistance at 25°C, while the resistance of a platinum RTD may double over the same range. Roughly speaking, NTC thermistors are an order of magnitude more sensitive than other temperature sensors. This high temperature sensitivity is one of the main advantages of NTC thermistors. Also, high resistance values are available, which makes lead resistance negligible in many instances. Thus, there is no need for 4-terminal measurement arrangements. Another advantage is that fabrication technology is mature and thermistors are inexpensive, stable, and available in many physical configurations, and with a wide range of electrical specifications.

Figure 1. Thermistor types, from left to right: Screw-type, washer-type, rod-type (3), disk-type, bead-type (4), tapetype, axial-type and SMD [1].

In fact, a disk NTC thermistor may easily be mistaken for a disk ceramic capacitor. First, powdered metal oxides are combined with a plastic binder and additives that enhance stability. The mixture is then formed into sheets that are cut to component size or formed into pellets and pressed into disks. The bodies are then sintered at temperatures in excess of 1,000°C that forms the final polycrystalline NTC thermistor body. The sides are then silvered, leads are attached, and the thermistors are sealed, varnished, and labeled. Bead thermistors often resemble small tantalum electrolytic capacitors. Manufacturing starts with platinum or copper alloy wires and slurry of the metal oxide and suitable binder. Drops of the slurry are dabbed onto the wires. The surface tension pulls the drops into small elliptical beads. The string of beads is then allowed to dry and then sintered at high temperature. During sintering, the beads shrink and form an excellent electrical connection with the wires. Next, the wires are cut to form the individual thermistors. The next

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figure shows several possible cutting options. Finally, the thermistors are coated and most often hermetically sealed with glass.

to understand the datasheets and what all those numbers mean.

Glass bead are small and range from 0.25 ~ 1.5 mm in diameter. The small size means fast thermal response (low dissipation constant) and bead thermistors have high stability, but they are more costly to manufacture than surface electrode thermistors.

Uses of Thermistors NTC thermistors have two broad areas of applications: The first is where the thermistors are used to sense temperature in appliances such as coffee makers, refrigerators and freezers, dehumidifiers, room air conditioners, meteorological instrumentation, deep ocean temperature probes, dialysis equipment, neonatal warmers, battery charger temperature monitoring, intravenous catheters, control of liquid crystal displays (LCD’s are temperature sensitive and the brightness/contrast depends on the ambient temperature; a feedback loop to sense the ambient temperature and adjust the LCD brightness/contrast appropriately). A sub-classification is temperature compensation of electronic components (e. g. fan speed control). Normally, cooling fans in electronic equipment and switch mode power supplies (SMPS) are powered by brushless DC motors that run at constant speed. Inrush current limiting is the second application area. Unless appropriate precautions are taken, then many electronic circuits are prone to high inrush currents. An example is that of a power supply where the smoothing capacitors are initially discharged. When power is turned on, the capacitors present very low impedance, and the initial current is limited by the capacitor’s stray resistance, and large currents can flow, possibly damaging the diodes. Once powered, the currents are within the design specifications. One solution is to specify components that can handle the peak inrush currents, but this is costly and often impractical. NTC thermistors often provide a simple and effective solution. An NTC thermistor is placed in series with a main current path of the electronic device that needs protection. Initially, the NTC thermistor has a high resistance and limits the current that can flow. However, the dissipated power (I2RTHERM, where I is the current through the NTC and RTHERM is the rated NTC’s resistance) heats the thermistor and lowers its resistance. This decreases its resistance and increases the current, which increases the dissipated power, which leads to more heating, and so on [1]. Eventually the NTC reaches a thermal equilibrium where an increase in temperature does not lead to a significant decrease in resistance. The final resistance is a fraction of the initial resistance and is small from the circuit’s point of view. NTC thermistors are very useful components and not really too hard to work with. The main challenge is probably

Figure 2. Thermistor Resistance-Temperature characteristic.

NTC Thermistor Physical Features Electrical Characteristics The voltage-current characteristic of an NTC thermistor (rated for 10kΩ@25°C), is shown in figure 3, and its behave is typical of mostly a wide variety of thermistors. It is possible to observe that at a very small current the I2RTHERM losses in the thermistor are very small and the thermistor is essentially linear. At higher currents I2RTHERM losses cause self-heating and this reduces the resistance, but the thermistor still has a positive resistance (increase in I results in an increase in V). As the current increases, the self-heating causes the resistance to decrease even more. Eventually, a point is reached when an increase in current (and dissipated power) heats the thermistor so much that the resulting decrease in resistance causes the voltage across the thermistor to drop. This is the part of the slope where the graph has a negative slope, and is the negative resistance region of the thermistor.

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Figure 4. Resistance-Temperature tolerance. Figure 3. Voltage vs. Current of a thermistor.

Commonly the four constants that determine the thermistor characteristics are [1]:

Material Constant β (or Sensitivity Index or B): This constant expresses a change rate in resistance between two temperatures, which is derived from the equation:

Rated Resistance/Rated Temperature (or Tolerance): There are two dominant factors that that determine the resistance tolerance. The first is the manufacturing tolerance (TF) in the NTC’s nominal resistance. The second factor is the tolerance in the Material Constant β. Tolerance is normally referred to the nominal resistance (RNOM, R25 or R0) at the specification temperature (TNOM or T0), typically at 25ºC. The approximate relationship between resistance and temperature is given as follows:

R1  R2e

1 1     T1 T2 

where, R1: Resistance (Ω) at absolute temperature T1 (°K). R2: Resistance (Ω) at absolute temperature T2 (°K). β: Material Constant (°K).

NTC thermistor resistance R at any Temperature T is determined from previous equation, observe figure 2 and figure 4.



R  ln R1  ln R2 TT  1 2 ln  2  1 1 T1  T2  R1   T1 T2

   log R  log R  1 2   2.3026  1 1      T1 T2   where, R1: Resistance (Ω) at absolute temperature T1 (°K). R2: Resistance (Ω) at absolute temperature T2 (°K). β: Material Constant (°K). The term “constant” is misleading since β is a function of temperature. Alternatively, different (T1, R1) pairs in the equation above give different values for β. Some manufactures provide a table of β as a function of temperature, while others may provide it at two points in the rated operating range. In general, the material constant value ranges are β25°C~85°C = 2,000°K ~ 6,000°K. The higher the β value, the higher the change rate in resistance per 1°C. Thermal Dissipation Constant δ: Is the expression of a degree of radiation from surface and lead wires of a thermistor element when an electric current is applied to heat it up. It can be determined by the following equation as the ratio between power consumption applied to a thermistor and a degree of temperature increased by the power:

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

P I 2R  T  TA T  TA

Temperature Coefficient: The relative change in resistance R1T1 at a temperature T1 is as:



where, δ: Thermal dissipation constant (mW/°C). P: Power consumption in the thermistor (mW). T: Temperature of heat equilibrium after rising (°C). TA: Ambient temperature (°C). I: Current flowing in the thermistor at temperature T(mA). R: Resistance of a thermistor at temperature T(kΩ).

In order to measure the temperature accurately and to control precisely, it is important to look closely at the value of δ and minimize the electric current so that the measurement error caused by self-heating is eliminated. Generally the thermal dissipation constant shows a value when a discrete element is placed in still air. That value may change for an assembled thermal sensor. Thermal Time Constant τ: This constant indicates how fast the resistance value of a thermistor follows the change of the surrounding temperature or electric current injected. This constant is expressed by the time to reach the 63.21% (or 1-1/e), of a difference between initial and final achieving temperatures of a thermistor element. An example of the thermal time constant is shown in figure 5.

1 dR1   2 R1 dT1 T1

where, R1: Resistance (Ω) at absolute temperature T1 (°K).

This coefficient is measured in percent per °C or percent per °K and is valid only over small temperature ranges. Interchangeability/Curve Matching: This is expressed as a temperature tolerance over a temperature range. However, it is possible to manufacture NTC thermistors with temperature tolerances as small as ±0.005°C over a 0.100°C range. Interchangeability gauges how close the resistancetemperature curves of two thermistors match. High interchangeability helps keep costs down since equipment does not need to be calibrated or adjusted for individual thermistors. Interchangeability is also a major advantage where NTC thermistors are used as cheap, disposable temperature probes (e. g. medical applications).

Resistance-Temperature Operation There are three basic electrical configurations that account for virtually all the applications in which NTC thermistors may be used: 1.

Current-Time characteristics.

2.

Voltage-Current characteristics.

3.

Resistance-Temperature characteristics.

This application note will be focused on the third point which is more relevant in the temperature sensing at the HPM power modules. For most applications based on R-T characteristic, the selfheating effect is undesirable and it is necessary to work as close to zero-power as possible. Zero-power is a term that is often encountered in NTC thermistor literature. When current flows through the NTC thermistor it heats itself, which changes the resistance. When this is small enough to neglect it is called the zeropower condition. By definition in MIL-PRF-23648, the power is considered negligible when any further decrease in power will result in no more than 0.1% of change in resistance (i. e. 1/10 of the specified measurement tolerance) [2].

Figure 5. Thermal Time Constant on a thermistor.

Other constant that can be found in vendor’s datasheets and could be useful for certain designs are as follows:

Graphically this is the region of the current-voltage graph where that has a constant positive slope. Mathematically the concept of zero-power or no-self-heating implementation will be defined in the following section.

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Heat Transfer Characteristics When a thermistor is connected in an electrical circuit, power is dissipated as heat and the body temperature of the thermistor will rise above the ambient temperature of its environment. The rate at which energy is supplied must be equal the rate at which energy is lost or dissipated plus the rate at which energy is absorbed (the energy storage capacity of the device), and is as:

dEsup dt



dEloss dEabsorved  dt dt

Then, the thermal energy that is supplied to the thermistor in an electrical circuit is equal to the power dissipated in the thermistor:

dEsup dt

 P  I 2R

Hence, thermal energy lost from the thermistor to its surroundings and which is proportional to the temperature rise of the thermistor is:

dEloss  T   T  TA  dt And finally, the thermal energy absorbed by the thermistor to produce specific amount of rise in temperature is expressed as follows:

dEabsorved dT dT  sm  Cth dt dt dt where, s: Specific heat (J/grs°K). m: Thermistor’s mass (grs.). Cth: Heat Capacity (J/°K). It is important to realize that while the heat capacity Cth of a thermistor is a property of the thermistor material, the dissipation factor is not constant. For, example it depend on the environment the thermistor is. In water a thermistor has higher dissipation factor than the thermistor in still air, since the water conducts heat better. Since the thermal time constant depends on the dissipation factor, is follow that it too is not a true constant, but depends on the environment the thermistor is placed in. Thus, manufacturers normally give the dissipation factor in both air and water. Therefore, in function of the thermistor electrical behave at any instant in time after power has been applied to the circuit; it is possible to write the thermistor heat transfer equation as:

P  Cth

dT   T  TA  dt

Utilizing previous definitions and equations, it is possible now to define mathematically the concept of zero-power measurement. If the power at the general thermal transfer equation is set as P≈0, then the following equitation is obtained:

dT   T  TA  dt dT  T  TA    dt Cth 0  Cth

The ratio Cth/δth is equivalent to the thermal time constant of the thermistor τ. For example, consider a thermistor operated in the zero-power (no self-heating) condition at an initial temperature T0. Now if the thermistor is placed in an environment with ambient temperature TA. Then it is possible to solve the zero-power equation above for the thermistor body temperature as a function of time:

T  TA  T0  TA  e

   t   C   th   th  

 TA  T0  TA  e

 t    

The larger τ, the longer it takes for the thermistor to reach thermal equilibrium when it is subjected to a sudden change in temperature, and the longer it takes for the accompanying resistance change to reach its final value (i. e. 63.21% of its final value). Thus far, the thermal properties of the NTC have been based upon a simple device structure with a single time constant. When any thermistor device is encapsulated into sensor housing, the simple exponential response functions no longer exist. The mass of the housing and the thermal conductivity of the material used in the sensor will normally increase the dissipation constant of the thermistor and will invariably increase the thermal response time. The thermal properties are somewhat difficult to predict by mathematical modeling and manufacturing variances will introduce enough uncertainty so the testing of the finished sensor is usually required to obtain data on the response time τ and dissipation constant δ.

Resistance-Temperature Linearization The Hart-Steinhart Thermistor Equation There are two models presently to explain the electrical mechanism for the NTC thermistors. One explanation involves the so called “hopping” model and the other explanation is based upon the “energy band” model. Both conduction models have difficulty when it comes to a complete explanation of the R-T characteristics of metaloxide thermistors [3]. Fortunately, there are a number of equations that can be used to define the resistance-

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temperature of the devices. The more recent literature on thermistors account for the non-linearity of R-T characteristics by using the standard curve fitting technique. The most known technique is the Hart-Steinhart curve fitting equation [4]. The Hart-Steinhart equation is named after two oceanographers during their investigation on deep sea [5]. The equation was published in 1968 and is derived from the mathematical curve-fitting techniques and examination of resistance versus temperature characteristics of thermistor devices. In particular, using the plot of the natural logarithm of the resistance value versus the inverse of temperature for a thermistor component, an equation of the following form is developed:

1 2  A0  A1  ln R   A2  ln R   T

An  ln R 

n

where, T: Temperature (°K). R: Resistance (Ω). A0...An: Polynomial coefficients.

The order of the polynomial to be used to model the relationship between R-T depends on the accuracy of the model that is required and on the non-linearity of the relationship for a particular thermistor. It is generally accepted that the use of a third order polynomial gives a very good correlation with measure data, and that the squared term is not significant. The equation then is reduced to a simpler form, and is given as:

1 3  A  B  ln R   C  ln R  T where, T: Temperature (°K). R: Resistance (Ω). A, B, C: Constant factors for the thermistor that is being modeled.

Although characteristic curves are useful for deriving interpolation equations, it is more common for manufacturers to provide nominal thermistor resistance values at a standard reference temperature (usually specified as 25°C), as well as resistance-ratio versus temperature characteristics.

Thermistor Calibration and Testing Some applications have accuracy requirements which are tighter than the conventional limits on interchangeable devices. For these applications the thermistors must be

calibrated. To use one of the interpolation equations over a specified range, the thermistor must be calibrated at two or more temperatures. The accuracy of the calculated R-T characteristic over the temperature range depends upon the proper selection of equation and reference temperatures as well as upon the calibration uncertainties. Obviously, not all thermistors or assemblies can be calibrated at all temperatures over the range. There will be limitations which are imposed by the type of thermistor and its nominal resistance as well as by the materials used in the construction of the assembly. When a current source and digital voltmeter are used for calibration, suitable averaging and integration techniques are used to eliminate noise spikes. Thermal electromotive forces are eliminated by either subtracting the zero current readings or averaging forward and reverse polarity readings. There are several calibration plans and the types of thermistor to which they apply. As an informative remark the plan utilized for glass enclosed beads, currently used inside the HPM’s, is disclosure; the application of this procedure is beyond the focus of this application note. The method for all glass enclosed beads and probes as well as epoxy encapsulated discs or chips and sensor assemblies’ using these devices is as follows: A precision constant temperature bath is set using two or more thermistor temperature standards [6], [7]. Resistance measurements are performed using a precision Wheatstone bridge or a stable precision current source and digital voltmeter in conjunction with a data acquisition system verified against standard resistors and an ohmic standard precision resistance decade.

Testing Equipment Uncertainty The first step in setting up a thermistor test system is to determine the level of uncertainty allowable for the application. Determining the level of uncertainty is an important part of the process used for setting up a thermistor testing system. The National Institute of Standards and Technology (NIST) [8], and the International Organization for Standardization [9] have formed an international consensus to adopt the guidelines recommended by the International Committee for Weights and Measures (CIPM) to provide a uniform approach to expressing uncertainty in measurement. In these guidelines, terms such as accuracy, repeatability, and reproducibility have definitions that may differ from those used by some equipment manufacturers. For example, at the NIST guidelines, accuracy is defined as a qualitative concept and should not be used quantitatively. The current approach is to report a measurement result accompanied by a quantitative statement of its uncertainty [8]. Because the cost of equipment increases as the level of uncertainty decreases, it is important not to over specify the equipment. Generally speaking, test system uncertainty should be 4 to 10 times better than that of the device to be

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tested. A 4:1 ratio is adequate for most applications; for more stringent requirements, a 10:1 ratio may be necessary and will probably result in a more costly system [10], [11] (e. g. using the 4:1 ratio, a thermistor with a tolerance of ±0.2°C should be tested on a system with an overall uncertainty of (±0.2°C)/4 or ±0.05°C; if a 10:1 ratio were required, the overall system uncertainty would need to be ±0.02°C). To calculate the uncertainty of the overall test system, the uncertainties of the individual components are combined using a statistical approach [8]-[11]. Each component is represented as an estimated standard deviation, or the standard uncertainty. The two statistical methods most commonly used by NIST are the combined standard uncertainty and the expanded uncertainty [8]. The combined standard uncertainty uC is obtained by combining the individual standard uncertainties using the usual method for combining standard deviations. This method is called the law of propagation of uncertainty (i. e. RMS). The expanded uncertainty U is obtained by multiplying the combined standard uncertainty by a coverage factor k, which typically has a value between 2 and 3 (i.e., U = kuC). For a normal distribution and k = 2 or 3, the expanded uncertainty defines an interval having a level of confidence of 95.45% or 99.73%, respectively. The NIST policy is to use the expanded uncertainty method with the coverage factor k = 2 for all measurements other than those to which the combined uncertainty method traditionally has been applied. The expanded uncertainty of a system thus can be determined once the uncertainties of the bath, the temperature standard, and the resistance measuring instrument are known.

Module NTC Thermistor A Word on Mod.’s Thermal Characteristics In power electronics, semiconductor devices are operated as switches, taking on various static and dynamic states in cycles. In any of these states, one power dissipation or energy dissipation component is generated, heating the semiconductor, and adding to the to the total power losses of the switch. At the Mod., the commutation components are enclosed on a single unit in order to, between another reasons, minimize stray elements which contribute to electric loss. However, the proximity of these switching elements has the potential of increase the thermal dissipation on the overall module’s real-state. Therefore, suitable power semiconductor rating and above all, cooling measures must be taken to ensure that the maximum junction temperature specified by the manufacturer is complied with at any standard moment of converter operation. To facilitate the tight temperature monitoring during Mod.’s electrical operation, a NTC thermistor is incorporated to the module system, figure 6.

Figure 6. Inner Mod. real-state architecture, the NTC thermistor is located in the upper-left corner.

As can be observed, the NTC thermistor is located on the DCB (Direct Copper Bonding), which afterwards will be potted with silicone gel in order to enhance electrical isolation of the components during normal operation, to protect the electronic components from mechanical stresses and pollutants from the environment [12]. It is important to remark that silicone gel will help to avoid, in certain amount, convection and radiative thermal exchange towards the NTC thermistor. Hence, it is fair to assume that the NTC thermistor will acquire the temperature through conduction effect from the DBC where the power components will displace the thermal components during their operation. Thermal analysis of Mod.’s is beyond the scope of this Article, for more information about thermal properties on power modules, consult the references

Resistance-Temperature Implementation Circuits Applications that are based upon the R-T characteristics include temperature measurement, control, and compensation. Also included are those applications for which the temperature of the thermistor is related to some other physical phenomena. Unlike the application based upon the current-time or voltage-current characteristics, these applications require that the thermistor be operated in zero-power condition. In the previous treatment of the R-T characteristic, data was presented on the derivation of interpolation equations that can be used for NTC thermistors. The various equations discussed, when used under the proper set of conditions, can

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adequately and accurately define the zero-power R-T characteristic of the NTC thermistors.

The output voltage as a function of temperature can be expressed as follows:

There are a variety of instrumentation/telemetry circuits in which a thermistor may be used for temperature measurements. In most cases, a major criterion is that the circuit provides an output that is linear with temperature.

  Rset VO T   Vin    Rset  Rtherm 

When the use of a constant-current source is desired, the circuit used should be a two-terminal network that exhibits a linear resistance-temperature characteristic. The output of this network is a linear voltage-temperature function. Under these conditions, a digital voltmeter connected across the network can display temperature directly when the proper combination of current and resistance level are selected. If the use of a constant voltage source is more desirable, the circuit used should be a two-terminal network that exhibits a linear conductance-temperature characteristic. Conversely, the output of this network is a linear current-temperature function. Consequently, the design of thermistor networks for most instrumentation/telemetry applications is focused on creating linear R-T or linear conductance-temperature circuits.

Rtherm

-t°

where, Vin: Circuit polarization (V). Rtherm: NTC zero-power resistance at temperature T (Ω). Rset: Voltage divider/linearizing resistance (Ω). VO(T): Resultant output voltage (V).

From the plot of the output voltage, we can observe that a range of temperatures exists where the circuit is reasonably linear with good sensitivity at certain range. Therefore, the objective will be to solve for a fixed resistor value Rset that provides optimum linearity for a given resistancetemperature characteristic and a given temperature range. A very useful approach to the solution of a linear voltage divider circuit is to normalize the output voltage with respect to the input voltage. The result will be a standard output function (per unit volt) that can be used in many design problems. In this case, the normalization is obtained utilizing previous equation; the normalized output is as follows:

VO T  1  1 Vin  Rtherm     Rset 

Vin Rset

VO(T)

VO(T) Vin

In most thermistor literature, the thermistor reference temperature T0 is 25°C (298.15°K) and the thermistors are cataloged by their nominal resistance value at 25°C (defined as Rtherm0, the zero-power resistance at a standard reference temperature). Thus, the thermistor resistance is normalized with respect to its resistance at the specified temperature as:

0

rtherm  Linear Approximation

T

Figure 7. Voltage divider configuration.

Voltage Divider: The simplest thermistor network used in many applications is the voltage divider circuit shown in figure 7. In this circuit, the output voltage is taken across the fixed resistor. This has the advantages of providing an increasing output voltage for increasing temperatures and allows the loading effect of any external measurement circuitry to be included into the computations for the resistor R and thus the loading will not affect the output voltage as temperature varies.

Rtherm  rtherm Rtherm0  Rtherm Rtherm0

In the actual solution of many applications problems, it is desirable for T0 and Rtherm0 to be specified at the midpoint of the intended operating temperature range. The ratio S of the zero-power resistance of the thermistor at the desired reference temperature to the fixed value resistor in the voltage divider circuit is as:

S

Rtherm0 Rset

From where the transfer function is derived as follows:

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G (T ) 

VO T  1   Vin 1  Srtherm

1 R  1   therm   Rset 

The transfer function G(T) is dependent upon the circuit constant S and the resistance-ratio versus temperature characteristic rtherm. If we allow the circuit constant to assume a series of constant values and solve for the transfer function, we shall generate a family of S curves. Figure 8 illustrates a family of such curves. These curves were generated using the resistance-ratio temperature characteristic given for the NTC Thermistor.

the standard curve (first derivative with respect to temperature) is at a maximum and the curvature (second derivative with respect to temperature) is zero. The reference temperature will be selected as the midpoint temperature of the desired operating range. At the equal slope method it is desired to set the slopes of the standard function equal to each other at the endpoints of the temperature range (Tmin and Tmax). This method can provide good linearity over wider temperature ranges. When using this method for solution, the polynomial equations for the R-T characteristic are used. Both discussed above have been based on a single thermistor voltage divider. When the thermistor is connected to more complex circuits which contain only resistances and voltage sources, the problem can be reduced back to the simple voltage divider by considering the Thevenin equivalent circuit as seen at the thermistor terminals. Voltage Divider Variants: Figure 9 shows two simple modifications to the basic voltage divider which can be converted to/from a Thevenin equivalent circuit as required for any given application. The voltage divider of figure 9a is used where it is desired to reduce the output signal while figure 9b is used where it is desired to reduce the source voltage and translate the output signal by adding a bias voltage. Of the two circuits, figure 9b is commonly used, especially in bridge circuits. It permits the use of conventional source voltages and reduces the voltage placed across the thermistor to an acceptable level of self-heating. The bias voltage can be compensated in the bridge design.

Figure 8. Transfer function G(T) curves for a NTC thermistor.

It is obvious from the design curves that a value for the circuit constant S exists such that optimum linearity can be achieved for the divider network over a specified temperature range. The design curves can be used to provide a graphical solution or a first approximation for many applications. For the best solution to a design problem an analytical approach is required. There are two analytical methods employed to solve for the optimum linearity conditions of the divider network: the Inflection Point Method and the Equal Slope Method. In the inflection point method, the “inflection point” is the position where the slope of the curve is a maximum; therefore, it is desired to have the change point of the standard function occur at the midpoint of the operating temperature range. The sensitivity of the divider network would therefore be at a maximum at this point. This method is recommended for the solution of temperature control applications. However, does not provide good linearity over wide temperature ranges. Its use should be restricted to temperature spans that are narrow enough for β to be considered constant and thus the intrinsic equations can be used. At the inflection point, the slope of

Bridge Architectures: Bridge circuits are actually two voltage divider circuits. In most applications, the bridge consists of a linear thermistor voltage divider and a fixed resistor voltage divider. For differential temperature applications, the bridge consists of matching thermistor linear voltage dividers. Figure 10a illustrates a basic Wheatstone bridge circuit with one linearized thermistor voltage divider and Figure 10b illustrates the Wheatstone bridge circuit used for differential temperature applications. Both of the circuits in figure 10 represent cases where the load resistance is infinite and thus does not affect the output voltage of the voltage divider or dividers.

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bridge circuit for a finite load resistance, while figure 11b shows the Thevenin equivalent circuit.

a) R1

Rtherm

-t°

Vin Rset

R2

VO(T)

Ohmmeter Circuit: Another circuit which is commonly employed in temperature measurement applications is the basic ohmmeter circuit which is shown in figure 12. This circuit is also a basic voltage divider of sorts. It is generally used for low cost temperature measurement applications; thus, the trimming potentiometer may not always be in the circuit. In this architecture the objective is to produce a linear current. This current can be expressed as a constant times the standards function G(T). The value of the constant is the source voltage divided by the circuit resistance as seen by the thermistor.

b) R1

Rtherm

-t° a)

Vin Rset

VO(T)

R1

Rtherm

-t°

RL

Figure 9. Different Voltage divider configurations.

Vin R2

iL

Rset

a)

R1

Rtherm

-t°

b)

UB

Vin R2

VO(T)

vB

Rtherm

Rset

-t°

VTHEV RTHEV

b)

Figure 11. Wheatstone bridge configuration (finite load). Rtherm2

Rtherm1

-t°

-t°

UB

Vin Rset2

VO2(T)

VO1(T)

Rset1

Figure 10. Wheatstone bridge configurations (infinite load).

When the Wheatstone bridge circuit is more complex and the load resistance cannot be considered infinite, the Thevenin theorem is used to reduce the circuit to its equivalent form. Figure 11a shows the basic Wheatstone

Note that the circuit consisting of a thermistor in series with a fixed resistance is a linear conductance versus temperature network. The voltage divider circuits, the Wheatstone bridge circuits and the Ohmmeter circuit discussed so far have all been examples of linear conductance versus temperature networks. They may all be solved by the use of the standard function S curves, the inflection point method or the equal slope method as preferred. Linear Resistance Networks: Many applications based upon the R-T characteristic require the use of a linearized resistance network. The linear conductance-temperature networks are driven by a constant voltage source, whereas, the linear R-T networks will be driven by a constant current source. Note that one is the dual of the other.

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RM

Rtherm

-t°

VTHEV Rset Rp

Figure 12. Ohmmeter configuration circuit.

RP a)

network resistance with respect to the shunt resistor, we observe that the standard function G(T) can be used for the design of linear resistance networks. In order to increase the overall network resistance to a higher value, a series resistor can be inserted as illustrated by figure 13b. This can also be done to increase the voltage drop across the network when a constant current is applied to the terminals (as will be mentioned afterwards). Obviously, the linear R-T characteristic is translated by the series resistor and the slope remains unchanged. Figure 13c shows the circuit of figure 13b with the addition of a resistor in series with the thermistor. This circuit is used to permit the use of a standard value for the thermistor. The standard value thermistor must be slightly lower than the desired value for optimum linearity and both thermistors must have the same resistance ratio-temperature characteristic. Figure 30d shows the basic circuit of figure 13a with the addition of a resistor in series with the thermistor, for the purpose of utilizing a standard value of thermistor. Going back to the network on figure 13a, it is possible to obtain a better linearization when the fixed resistor and the nominal temperature value of the NTC thermistor are related by the following formula:

-t°

  T  RP  Rtherm0      2T 

Rtherm RP b)

where,

RS

Rthermo0: NTC nominal resistance value at 25°C (Ω). β: Material Constant (°K).

-t°

T: Centered temperature 298.15°K (25°C). Rtherm RP c) RS R1

-t°

Rtherm RP d)

-t°

R1

Rtherm

Figure 13. Linearization networks.

Figure 13 illustrates the basic linear R-T networks used in most compensation applications. The simplest network is obviously that shown in figure 13a. If we normalize the

Figure 14. Linearization curves for NTC thermistor.

The best linearization is obtained by laying the turning point in the middle of the operating temperature range. Figure 14 shows the curve for a NTC thermistor with Rthermo0 = 10kΩ (@ 25°C) and a material constant β(25°C~50°C) = 3450°K; hence, the calculated normalizing parallel resistor is equal to

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RP = 7.79kΩ (i. e. 7.7kΩ). This value gives a good linear span for a range between 0°C ~ 65°C (other values can be traced for different span needs). The rate of rise of the linearized characteristic is given by:

Rtherm0 dR    2 2 dT  Rtherm0  T 1   RP   It is important to remark that the sensitivity of the measured temperature decreases with linearization. In the case where the curve is necessary to be shifted for higher impedance value (with same linear slope), then it is necessary to adopt the normalizing circuit of figure 13b. The resultant family of curves for previous given values are shown in figure 15. Figure 16. Signal voltage and power dissipation curves of the linearized NTC thermistor. a)

R1

Rtherm

-t°

DZ

Vin

VO(T)

+

R2

Rset Rfeed

b)

R2

Figure 15. Impedance of normalized curves shifted due to series resistance.

It is obvious that the values selected should be a trade-off in order to have all the measurements at zero-power mode. Then, if the circuit is biased in the previous example with Vin = 1V, the voltage measured at the normalized network VNTC, and the power displaced on it will be as plotted in figure 16. It is possible to observe that at the peak of the power curve (i. e. Pdiss ≈ 0.25mW) and knowing that the dissipation constant δ for this element is equal to 1.4mW/°C, then the self-heating will be accounted as 0.178°C which in that point (around 92°C) correspond to a temperature error of approximately 0.2%, enough accurate for any kind of applications.

Rset VO(T)

Vin

+ R1

Rtherm

-t° Rfeed

VO(T) c)

0

T

Figure 17. Op-Amp application with NTC thermistor.

Operational Amplifier Circuits: As observed in previous section, generally to obtain a smooth measurement from a thermistor it is necessary to utilize some sort of linearizing

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aid network; however, the necessity of measurement at zeropower resistance on those architectures make the whole setup susceptible of noises due to the small scale of voltage/current utilized. One solution is employ high performance precision instrumentation amplifiers with rail-to-rail I/O. Which have the advantage of very low DC errors, long-term stability and very low 1/f noise. Two examples of a Wheatstone bridge with an Op-Amp are shown in figure 17. Figure 17a shows a temperature Wheatstone bridge with an Op-Amp acting as differential amplifier, this kind of circuitry can have very high sensitivity (zener diode can be omitted if bias voltage is set for zero-power resistance). By the other hand, on figure 17b, the Op-Amp acts as a Schmitt-trigger which generates the transfer characteristic given in figure 17c. Another variant from figure 17a can be seen in figure 18. This circuit is a temperature dependent reference voltage that can be implemented using thermistor/resistive parallel combination illustrated in figure 13a as feedback element in an operational amplifier circuit.

output of the amplifier. This could be use in a logic circuitry utilizing any 12-bit DAC. Another Op-Amp based topology is shown in figure 19a; due to RP and Rset the voltage at point U varies linearly with the NTC thermistor temperature. The voltage at point V is equal to that of point U when the NTC thermistor is 0°C. Both voltages are fed to the comparator circuitry and sampled according to the clock pulses figure 19b. The output pulse train can be utilized in any digital circuit.

a)

RP

R1

Rtherm

-t° VO2(T)

V Vpulse(T)

Rset

Vin

Clock Gen.

VO1(T)

U R2

R3 Sawtooth Gen.

b)

R1 Vin

RP

Rtherm

0°C Ref.

-t°

DZ VX R2

+

VO(T)

VO1(T)

Rset VO2(T)

Figure 18. Amplifier gain changed by NTC thermistor.

Vpulse(T)

0

t

In this circuit, a zener diode reference is used to drive the inverting input of an Op-Amp. The gain of the amplifier portion of the circuit is:

Figure 19. Bridge sensing with 0°C offset.

  Rtherm RP   V0 T   VX 1   Rset  

It is obvious that for certain applications, the part-count is not desirable; therefore, exist other solutions that have a high component integration allowing a very good temperature monitor precision at relative low cost.

If R1 = 8.06kΩ, R2 = 1kΩ, Rset = 549Ω and RP = 10kΩ with a zener voltage of 2.5V are used (for a NTC thermistor of 10kΩ@25°C), it will generate the 0.276V at the input to the operational amplifier VX.

One of those solutions is an integrated circuit optimized for use in 10kΩ NTC thermistor. This IC provides the necessary NTC thermistor excitation and generates an output voltage proportional to the difference in resistances applied to the inputs. It uses only one precision resistor plus the NTC thermistor reducing the part-count issue. It maintain excellent accuracy for temperature control applications, figure 20. Several other topologies based on precision instrumentation amplifiers with rail-to-rail I/O [17] can be observed in Appendix A. In more advance architectures towards digital acquisition of temperature there is one topology that can be extended to any kind of logical control, figure 21.

When the temperature of the NTC thermistor is equal to 0°C Rtherm is approximately 32,650.8Ω. The value of the parallel combination of this resistor and RP is equal to 7655.38Ω. This gives a operational amplifier gain of 14.94 V/V or an output voltage V0(T) of 4.093V. When the temperature of the NTC thermistor is 50°C, the resistance of the thermistor is approximately 3601Ω. Following the same calculations above, the operational amplifier gain becomes 5.8226V/V, giving a 1.595V at the

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TM in figure 21b. At this point, GP1 and GP2 are again set as inputs and GP0 as an output low. Once the integrating capacitor C, has time to discharge, GP2 is set to a high output and GP0 as an input. A timer counts the amount of time before GP0 changes to 1, giving the time TC. The difference on timing between TM and TC will determine the actual resistance (and temperature), in the thermistor and after consulting a look-up table stored at the controller. The values of RREF and C are calculated according to the number of bits of resolution required. RREF should be approximately one half the highest resistance value to be measured, hence:

C Figure 20. NTC thermistor signal amplifier.

tres

R

therm

 V  10k    ln 1  bias   V  ref  

where, a)

Rtherm: NTC nominal resistance value 25°C (Ω).

RREF

GP1

tres: Time to acquire the required resolution bits (sec). Vbias: Threshold voltage of controller being used (V). CONTROLLER

10kΩ

GP2 -t°

Vref: reference voltage (V).

Resistance-Temperature Experiments General Information on Mounting Requirements: The mounting instructions outlined below are taken from several Application Notes [13]-[16]. These recommendations are based on the knowledge acquired during laboratory and field examinations.

Rtherm

100Ω

GP3 C

b)

TM

The power modules are intended to be mounted on a PCB circuit board from the pin side and to a heatsink from the backside. The contact area of the module and heatsink must be free of any particles or damages.

TC

VC

Before the module is installed onto the heatsink, it is necessary to apply a thin film of thermal compound of approximately 100 ~ 200μm. As a ruler of thumb, a small rim of thermal compound around the edge of the module should be visible after the module is attached. 0

Rtherm 10k  

TM RREF TC

t

Figure 21. NTC thermistor Calibrator/Sensor.

In this topology, on the first step the sensing circuit is implemented by setting GP1 and GP2 of the controller as inputs. Additionally, GP0 is set low to discharge the capacitor, C. Once C is discharged, the configuration of GP0 is changed to an input and GP1 is set to a high output. A timer counts the amount of time before GP0 changes to 1, giving the time

To fasten the module to the heatsink in a simple and reliable way, the power module has a pair of screw flanges, figure 22; which should be bolted with M4 type screws. One screw should be slotted in a flange but not tightened until the opposite screw is in its place. After both crews are inserted, then the screws are tightened one after the other with a recommended mounting torque of 2.0 ~ 2.3Nm.

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The measurements will be carried utilizing the Agilent 34411A DMM, with 4-wire Kelvin terminals at 90min warm-up and integration of 100PLC (Power-Line Cycles), accuracy specification error equal to 0.06°C at TCAL ±5°C and 0.003°C at TCAL +10°C [18], which fits by far the 4:1 and even the 10:1 uncertainty level ratio (i. e. NTC tolerance at 25°C = ±1.25°C, uncertainty level 10:1 = 0.125°C). The modules are similar as figure 22, and will be divided in two categories, Sample A: complete standard module (power components and NTC immersed in silicone gel), Sample B: same as Sample A but without silicone gel. Samples will be subjected to temperature range from -30°C to 150°C; what is more, in Sample A the measure of the lag on the thermal constant τ caused by the silicone gel will be obtained. The measurements will be taken at 10°C at 10min intervals in a thermal isolated enclosure to suppress micro thermal currents and other stray effects; also, in order to achieve zero-power measurements the NTC will be polarized at the measurement instant (i.e. 1V@100μA). Figure 23 shows the experimental and the manufacturer’s values of both samples without any normalizing network. Observe the variation found against the original data. This variation goes in hand with the already mentioned thermal dissipation constant δ alteration in the Heat Transfer Characteristics section. Figure 22. Mod.and mounting draft.

If the power module is correctly installed onto the heatsink, then an optimal thermal resistance between module and heatsink is ensured. For more detailed information on mounting configurations, package characteristics and power modules requirements, please visit the knowledge base web page at:

It is important to keep in mind this alteration during temperature measurements because the value tolerance given by the manufacturer’s data is shifted; for example, a variation of ±5% will occur between 0°C and 100°C and not at 3% for 0°C as specified on the datasheet.

Materials and Methods: The circuits to be tested are the most significant in the industry environment: the Voltage Divider configuration (figure 7), the Wheatstone Bridge (figure 10) and the Linearization Network (figure 13b). All these topologies will utilize the NTC Thermistor which its R-T values can be observed in Appendix B and the physical characteristics are as follows: 

Operating Temperature Range: -50°C ~ +200°C.



Thermal Dissipation Constant δ: ~ 1.4mW/°C



Thermal Time Constant τ: ~ 10sec.



Material Constant β: 3450°K ±2% (25°C ~ 50°C).

Figure 23. Experimental resistive values and temperature variations on the addition of silicone gel.

Now, for the Voltage Divider network, note that RSET is not subjected to the temperature variation due to it is considered that this element is elsewhere in the PCB circuit.

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The value of polarization voltage is set as Vin = 1V. After several testing iterations the best linear fitting gives RSET as 3.6kΩ. Hence, the graphic of the experimental output voltages VO(T) for the standard commercial sample (Sample A) is shown at figure 24. Utilizing the same RSET and bias voltage values obtained in previous network analysis and for 0°C, 25°C, 80°C and 100°C setting points; the curves obtained at the Wheatstone Bridge (figure 10a), in function of the voltage divider are as:

vB  Vin

any set point in the cooling system (observe the curves crossing UB at the required temperature settings). Finally, in the Linearization Network (figure 13b), maintaining the value of RS as 3.6kΩ and varying the RP value, the family of curves obtained is shown in figure 26. As can be seen, the value of RP = 5.1kΩ is the values which approaches to a more linear response from all those family curves.

R2 R1  R2

V0 T   Vin

Rset Rtherm  Rset

U B  vB  V0 T 

Figure 26. Linearization Network tuning to obtain the best linear fitting.

Figure 24. Voltage Divider network response.

Figure 25. Wheatstone bridge setting points at several temperatures.

The results are shown in figure 25 in function of UB and adjusted R1 and R2 in a manner to obtain the indicated vB values. These curves are useful as guideline for triggering

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Appendix A

Figure A4. Low-side current Shunt mode.

Figure A1. Bridge to Digital Controller.

Figure A5. Low-side -V current Shunt mode. Figure A2. Generating Output Offset Voltage.

Figure A3. High-side current Shunt mode.

Figure A6. High-side current Shunt mode.

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Appendix B Temp (°C)

RNTC (kΩ)

Temp (°C)

RNTC (kΩ)

-30 -20 -10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

121.9 72.37 44.41 28.08 26.86 25.7 24.6 23.55 22.56 21.61 20.7 19.84 19.02 18.24 17.49 16.78 16.11 15.46 14.84 14.25 13.69 13.15 12.64 12.15 11.68 11.23 10.8 10.39 10 9.625 9.266 8.922 8.592 8.277 7.975 7.685 7.408 7.142 6.887 6.642

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76

6.408 6.182 5.966 5.759 5.56 5.369 5.185 5.009 4.839 4.676 4.52 4.369 4.224 4.085 3.951 3.822 3.698 3.579 3.464 3.354 3.247 3.144 3.045 2.95 2.858 2.77 2.685 2.602 2.523 2.446 2.372 2.301 2.232 2.166 2.102 2.04 1.98 1.923 1.867 1.813

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Temp (°C)

RNTC (kΩ)

Temp (°C)

RNTC (kΩ)

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

1.761 1.711 1.662 1.615 1.57 1.526 1.483 1.442 1.402 1.364 1.326 1.29 1.255 1.221 1.189 1.157 1.126 1.096 1.068 1.04 1.013 0.9863 0.9609 0.9362 0.9123 0.8891 0.8665 0.8447 0.8235 0.8029 0.783 0.7636 0.7448 0.7266 0.7088 0.6916 0.6749 0.6587 0.6429 0.6276

117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150

0.6127 0.5982 0.5841 0.5705 0.5572 0.5443 0.5317 0.5195 0.5076 0.496 0.4848 0.4738 0.4632 0.4528 0.4428 0.4329 0.4234 0.4141 0.405 0.3962 0.3876 0.3792 0.3711 0.3632 0.3554 0.3479 0.3405 0.3334 0.3264 0.3196 0.313 0.3065 0.3002 0.2941

Fitting equation :

T    T       Rtherm  2 7566.263e 35.036    13303.198e 16.21   46.733  

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References [1] [2] [3] [4]

[5] [6] [7] [8] [9] [10] [11] [12]

D. Hill and H. Tuller, “Ceramic Sensors: Theory and Practice,” Ceramic Materials for Electronics, R. Buchanan, ed., Marcel Dekker, Inc., New York, 1991. MIL-PRF-23648F, Performance Specification: Resistors, Thermal (Thermistor) Insulated, General Specification For; Jan. 2009. P. V. E. McClintock et. al., “Matter at Low Temperatures,” Blackie, ISBN 0-216-91594-5, 1984. M. Sapoff et al. “The Exactness of Fit of Resistance-Temperature Data of Thermistors with Third-Degree Polynomials,” Temperature, Its Measurement and Control in Science and Industry, Vol. 5, James F. Schooley, ed., American Institute of Physics, New York, NY, p. 875, 1982. J.S. Steinhart and S.R. Hart, “Calibration Curves for Thermistors,” Deep Sea Research, 15(497), 1968. IPTS-68, Bureau International des Poids et Mesures, 1968. ITS-90, Bureau International des Poids et Mesures, ISBN 92-822-2108-3, Dec. 1990. B.N. Taylor and C. E. Kuyatt. Sept. 1994. "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results," NIST Technical Note 1297, U.S. Government Printing Office, Washington, DC. "ISO, Guide to the expression of Uncertainty in Measurement," ISO Technical Advisory Group 4 (TAG 4), Working Group 3(WG 3), Oct. 1993. G.N. Gray and H.C. Chandon. 1972. "Development of a Comparison Temperature Calibration Capability," Temperature, Its Measurement and Control in Science and Industry, Vol 4, Instrument Society of America:1369. B. Pitcock. 1995. "Elements of a Standards Lab That Supports a Manufacturing Facility," Bench Briefs, Pub. No. 5964-6003E, 2nd/3rd/4th Quarters, Hewlett-Packard Co., Mountain View, CA. W. W. Sheng and R. P. Colino, “Power Electronic Modules: Design and Manufacture,” ed., CRC Press, Boca Raton Florida, 2005.