ntc thermistors in power components

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  • 7/28/2019 NTC Thermistors in Power Components



    Operation and Characterization of NTC Thermistors


    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 orderto sense the temperature inside the Mod..

    After a theoretical background on NTCs, 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


    The NTC Thermistor


    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

    thermistors resistance at 100C may be as little as 5.10% of

    the thermistors resistance at 25C, 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 mainadvantages 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


    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 3 rd. order polynomial. The

    operating temperature is limited to 60C ~ 300C, which is

    smaller than that of metal RTDs.

    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.

    Figure 1. Thermistor types, from left to right: Screw-type,washer-type, rod-type (3), disk-type, bead-type (4), tape-

    type, 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


    The bodies are then sintered at temperatures in excess of

    1,000C 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.

    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 (LCDs 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


    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 capacitors stray resistance, andlarge 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


    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 NTCs resistance) heats the thermistor

    and lowers its resistance. This decreases its resistance andincreases 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 ofview. NTC thermistors are very useful components and not

    really too hard to work with. The main challenge is probably

    to understand the datasheets and what all those numbers


    Figure 2. Thermistor Resistance-Temperaturecharacteristic.

    NTC Thermistor Physical Features

    Electrical Characteristics

    The voltage-current characteristic of an NTC thermistor(rated for [email protected]), 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 3. Voltage vs. Current of a thermistor.

    Commonly the four constants that determine the thermistor

    characteristics are [1]:

    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 NTCs

    nominal resistance. The second factor is the tolerance in the

    Material Constant . Tolerance is normally referred to the

    nominal resistance (RNOM, R25 orR0) at the specification

    temperature (TNOM or T0), typically at 25C. The

    approximate relationship between resistance and

    temperature is given as follows:

    1 2

    1 1

    1 2

    T T

    R R e


    R1: Resistance () at absolute temperature T1 (K).

    R2: Resistance () at absolute temperature T2 (K).

    : Material Constant (K).

    NTC thermistor resistance R at any Temperature T is

    determined from previous equation, observe figure 2 and

    figure 4.

    Figure 4. Resistance-Temperature tolerance.

    Material Constant (or Sensitivity Index or B): This

    constant expresses a change rate in resistance between two

    temperatures, which is derived from the equation:

    1 2 1 2 2

    1 2 1

    1 2

    1 2

    1 2

    ln lnln

    1 1

    log log2.3026

    1 1

    R R TT R

    T T R

    T T

    R R

    T T


    R1: Resistance () at absolute temperature T


    R2: Resistance () at absolute temperature T2 (K).

    : Material Constant (K).

    The term constant is misleading since is a function of

    temperature. Alternatively, different (T1, R1) pairs in the

    equation above give different values for . Some

    manufactures provide a table of 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 are25C~85C=

    2,000K ~ 6,000K. The higher the value, the higher thechange rate in resistance per 1C.

    Thermal Dissipation Constant : 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


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    A A

    P I R

    T T T T


    : 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(k).

    In order to measure the temperature accurately and to

    control precisely, it is important to look closely at the value

    of 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 : 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.

    Figure 5. Thermal Time Constant on a thermistor.

    Other constant that can be found in vendors datasheets and

    could be useful for certain designs are as follows:

    Temperature Coefficient: The relative change in resistance

    R1T1 at a temperature T1 is as:



    1 1 1

    1 dR

    R dT T


    R1: Resistance () 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 0.005C over a 0.100C

    range. Interchangeability gauges how close the resistance-

    temperature 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 advantagewhere 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-Tcharacteristic, the self-

    heating 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 zero-

    power condition.

    By definition in MIL-PRF-23648, the power is considered

    negligible when any further decrease in power will result inno more than 0.1% of change in resistance (i. e. 1/10 of the

    specified measurement tolerance) [2].

    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:

    sup loss absorved dE dE dE

    dt dt dt

    Then, the thermal energy that is supplied to the thermistor in

    an electrical circuit is equal to the power dissipated in the


    sup 2dE

    P I Rdt

    Hence, thermal energy lost from the thermistor to its

    surroundings and which is proportional to the temperature

    rise of the thermistor is:

    loss AdE

    T T Tdt

    And finally, the thermal energy absorbed by the thermistor

    to produce specific amount of rise in temperature is

    expressed as follows:


    dE dT dT sm C

    dt dt dt


    s: Specific heat (J/grsK).

    m: Thermistors 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 bothair 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:

    th AdT

    P C T Tdt

    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 P0, then the following equitation is


    0 th A



    dTC T T


    T TdT

    dt C

    The ratio Cth/th is equivalent to the thermal time constant of

    the thermistor . 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:







    A A


    A A

    T T T T e

    T T T e

    The larger , 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 nolonger 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 and dissipation constant .


    LinearizationThe 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 metal-

    oxide 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


    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



    0 1 2

    1ln ln ln


    nA A R A R A R



    T: Temperature (K).

    R: Resistance ().

    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:


    ln lnA B R C RT


    T: Temperature (K).

    R: Resistance ().

    A, B, C: Constant factors for the thermistor that is being


    Although characteristic curves are useful for derivinginterpolation equations, it is more common for

    manufacturers to provide nominal thermistor resistance

    values at a standard reference temperature (usually specified

    as 25C), as well as resistance-ratio versus temperature


    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 becalibrated 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 usedinside the HPMs, 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 UncertaintyThe 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

    0.2C should be tested on a system with an overall

    uncertainty of (0.2C)/4 or 0.05C; if a 10:1 ratio were

    required, the overall system uncertainty would need to be


    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.


    The expanded uncertainty Uis obtained by multiplying thecombined 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

    factork= 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 potentialof increase the thermal dissipation on the overall modules


    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 powercomponents 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 ImplementationCircuits

    Applications that are based upon the R-T characteristics

    include temperature measurement, control, and

    compensation. Also included are those applications forwhich 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 theR-Tcharacteristic, 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.

    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.

    When the use of a constant-current source is desired, the

    circuit used should be a two-terminal network that exhibits alinear 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 linearR-T or linear conductance-temperature











    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.

    The output voltage as a function of temperature can be

    expressed as follows:

    setO inset therm

    RV T V

    R R


    Vin: Circuit polarization (V).Rtherm: NTC zero-power resistance at temperature T().

    Rset: Voltage divider/linearizing resistance ().

    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 resistance-

    temperature 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




    in therm


    V T

    V R


    In most thermistor literature, the thermistor referencetemperature T0 is 25C (298.15K) and the thermistors are

    cataloged by their nominal resistance value at 25C (defined

    as Rtherm0, the zero-power resistance at a standard reference


    Thus, the thermistor resistance is normalized with respect to

    its resistance at the specified temperature as:



    thermtherm therm therm therm


    Rr r R R


    In the actual solution of many applications problems, it is

    desirable forT0 andRtherm0 to be specified at the midpoint of

    the intended operating temperature range.

    The ratio Sof the zero-power resistance of the thermistor at

    the desired reference temperature to the fixed value resistor

    in the voltage divider circuit is as:





    From where the transfer function is derived as follows:

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    1 1( )



    in therm therm


    V TG T

    V Sr R


    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 transferfunction, we shall generate a family ofScurves.

    Figure 8 illustrates a family of such curves. These curves

    were generated using the resistance-ratio temperature

    characteristic given for the NTC Thermistor.

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

    It is obvious from the design curves that a value for the

    circuit constant Sexists 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 to be considered constant and thus the intrinsic

    equations can be used. At the inflection point, the slope of

    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

    theR-Tcharacteristic 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


    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 requiredfor 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.

    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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    b )

    Figure 9. Different Voltage divider configurations.







    R2vB VO(T)










    Figure 10. Wheatstone bridgeconfigurations (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

    bridge circuit for a finite load resistance, while figure 11b

    shows the Thevenin equivalent circuit.

    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 )

    Figure 11. Wheatstone bridge configuration (finite load).

    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 Scurves, 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 linearR-Tnetworks will be driven by a constant current

    source. Note that one is the dual of the other.

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    Figure 12. Ohmmeter configuration circuit.


















    b )

    c )

    d )

    Figure 13. Linearization networks.

    Figure 13 illustrates the basic linearR-T networks used in

    most compensation applications. The simplest network is

    obviously that shown in figure 13a. If we normalize the

    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 linearR-Tcharacteristic 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 thenominal temperature value of the NTC thermistor are

    related by the following formula:

    0 2P therm

    TR R



    Rthermo0: NTC nominal resistance value at 25C ().

    : Material Constant (K).

    T: Centered temperature 298.15K (25C).

    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= 10k

    (@ 25C) and a material constant (25C~50C) = 3450K;

    hence, the calculated normalizing parallel resistor is equal to

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    RP = 7.79k (i. e. 7.7k). This value gives a good linear

    span for a range between 0C ~ 65C (other values can be

    traced for different span needs). The rate of rise of the

    linearized characteristic is given by:



    2 2






    dT TR


    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 15. Impedance of normalized curvesshifted 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 dissipationconstant for this element is equal to 1.4mW/C, then the

    self-heating will be accounted as 0.178C which in that

    point (around 92C) correspond to a temperature error of

    approximately 0.2%, enough accurate for any kind of


    Figure 16. Signal voltage and power dissipationcurves of the linearized NTC thermistor.







    + VO(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 zero-

    power 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.





    + VO(T)




    Figure 18. Amplifier gain changed by NTC thermistor.

    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:

    0 1therm P



    R RV T V


    IfR1= 8.06k,R2= 1k,Rset= 549 andRP= 10k with a

    zener voltage of 2.5V are used (for a NTC thermistor of

    [email protected]), it will generate the 0.276V at the input to the

    operational amplifierVX.When the temperature of the NTC thermistor is equal to 0C

    Rtherm is approximately 32,650.8. The value of the parallel

    combination of this resistor and RP is equal to 7655.38.

    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 50C, the

    resistance of the thermistor is approximately 3601.

    Following the same calculations above, the operational

    amplifier gain becomes 5.8226V/V, giving a 1.595V at the

    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 toRP andRset the voltage at point Uvaries linearly with

    the NTC thermistor temperature. The voltage at point V is

    equal to that of point U when the NTC thermistor is 0C.

    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.












    Sawtooth Gen.

    Clock Gen.








    0C Ref.

    Figure 19. Bridge sensing with 0C offset.

    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.

    One of those solutions is an integrated circuit optimized for

    use in 10k NTC thermistor. This IC provides the necessary

    NTC thermistor excitation and generates an output voltage

    proportional to the difference in resistances applied to theinputs. 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.

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    Figure 20. NTC thermistor signal amplifier.













    10 Mtherm REF C

    TR k R




    TM TC

    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

    TM in figure 21b. At this point, GP1 and GP2 are again set

    as inputs and GP0 as an output low.

    Once the integrating capacitorC, 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


    The values ofRREFand 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:

    10 ln 1





    VR k



    Rtherm: NTC nominal resistance value 25C ().

    tres: Time to acquire the required resolution bits (sec).

    Vbias: Threshold voltage of controller being used (V).

    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.

    The power modules are intended to be mounted on a PCBcircuit 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.

    Before the module is installed onto the heatsink, it is

    necessary to apply a thin film of thermal compound of

    approximately 100 ~ 200m. 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.

    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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    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:

    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-Tvalues can be observed in Appendix B and the physical

    characteristics are as follows:

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

    Thermal Dissipation Constant : ~ 1.4mW/C

    Thermal Time Constant : ~ 10sec.

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

    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 0.06C at TCAL 5C

    and 0.003C at TCAL +10C [18], which fits by far the 4:1

    and even the 10:1 uncertainty level ratio (i. e. NTC

    tolerance at 25C = 1.25C, uncertainty level 10:1 =


    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.

    Sampleswill be subjected to temperature range from -30C

    to 150C; what is more, in Sample A the measure of the lag

    on the thermal constant caused by the silicone gel will be


    The measurements will be taken at 10C 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. [email protected]).

    Figure 23 shows the experimental and the manufacturers

    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 alteration in the Heat Transfer

    Characteristics section.

    It is important to keep in mind this alteration during

    temperature measurements because the value tolerance

    given by the manufacturers data is shifted; for example, a

    variation of 5% will occur between 0C and 100C and not

    at 3% for 0C as specified on the datasheet.

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

    Now, for the Voltage Divider network, note thatRSET 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

    3.6k. 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 0C, 25C, 80C and

    100C setting points; the curves obtained at the Wheatstone

    Bridge (figure 10a), in function of the voltage divider are



    1 2



    B in


    therm set

    B B

    Rv V

    R R

    RV T V

    R R

    U v V T

    Figure 24. Voltage Divider network response.

    Figure 25. Wheatstone bridge setting pointsat 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

    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 ofRS as 3.6k and varying the RP

    value, the family of curves obtained is shown in figure 26.

    As can be seen, the value ofRP = 5.1k is the values which

    approaches to a more linear response from all those family


    Figure 26. Linearization Network tuning toobtain the best linear fitting.

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    Appendix A

    Figure A1. Bridge to Digital Controller.

    Figure A2. Generating Output Offset Voltage.

    Figure A3. High-side current Shunt mode.

    Figure A4. Low-side current Shunt mode.

    Figure A5. Low-side -V current Shunt mode.

    Figure A6. High-side current Shunt mode.

  • 7/28/2019 NTC Thermistors in Power Components



    Appendix B

    Temp (C) RNTC(k) Temp (C) RNTC(k)

    -30 121.9 37 6.408

    -20 72.37 38 6.182

    -10 44.41 39 5.966

    0 28.08 40 5.7591 26.86 41 5.56

    2 25.7 42 5.369

    3 24.6 43 5.185

    4 23.55 44 5.009

    5 22.56 45 4.839

    6 21.61 46 4.676

    7 20.7 47 4.52

    8 19.84 48 4.369

    9 19.02 49 4.224

    10 18.24 50 4.085

    11 17.49 51 3.951

    12 16.78 52 3.822

    13 16.11 53 3.698

    14 15.46 54 3.579

    15 14.84 55 3.464

    16 14.25 56 3.354

    17 13.69 57 3.247

    18 13.15 58 3.144

    19 12.64 59 3.04520 12.15 60 2.95

    21 11.68 61 2.858

    22 11.23 62 2.77

    23 10.8 63 2.685

    24 10.39 64 2.602

    25 10 65 2.523

    26 9.625 66 2.446

    27 9.266 67 2.372

    28 8.922 68 2.301

    29 8.592 69 2.232

    30 8.277 70 2.166

    31 7.975 71 2.102

    32 7.685 72 2.04

    33 7.408 73 1.98

    34 7.142 74 1.923

    35 6.887 75 1.867

    36 6.642 76 1.813

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    Temp (C) RNTC(k) Temp (C) RNTC(k)

    77 1.761 117 0.6127

    78 1.711 118 0.5982

    79 1.662 119 0.5841

    80 1.615 120 0.5705

    81 1.57 121 0.557282 1.526 122 0.5443

    83 1.483 123 0.5317

    84 1.442 124 0.5195

    85 1.402 125 0.5076

    86 1.364 126 0.496

    87 1.326 127 0.4848

    88 1.29 128 0.4738

    89 1.255 129 0.4632

    90 1.221 130 0.4528

    91 1.189 131 0.4428

    92 1.157 132 0.4329

    93 1.126 133 0.4234

    94 1.096 134 0.4141

    95 1.068 135 0.405

    96 1.04 136 0.3962

    97 1.013 137 0.3876

    98 0.9863 138 0.3792

    99 0.9609 139 0.3711

    100 0.9362 140 0.3632101 0.9123 141 0.3554

    102 0.8891 142 0.3479

    103 0.8665 143 0.3405

    104 0.8447 144 0.3334

    105 0.8235 145 0.3264

    106 0.8029 146 0.3196

    107 0.783 147 0.313

    108 0.7636 148 0.3065

    109 0.7448 149 0.3002

    110 0.7266 150 0.2941111 0.7088

    112 0.6916

    113 0.6749

    114 0.6587Fitting equation : 35.036 16.212 7566.263 13303.198 46.733

    T T

    thermR e e

    115 0.6429

    116 0.6276

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    [2] MIL-PRF-23648F, Performance Specification: Resistors, Thermal (Thermistor) Insulated, General Specification For; Jan. 2009.[3] P. V. E. McClintock et. al.,Matter at Low Temperatures,Blackie, ISBN 0-216-91594-5, 1984.[4] M. Sapoff et al. The Exactness of Fit of Resistance-Temperature Data of Thermistors with Third-Degree Polynomials,

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    [10] G.N. Gray and H.C. Chandon. 1972. "Development of a Comparison Temperature Calibration Capability," Temperature, ItsMeasurement and Control in Science and Industry, Vol 4, Instrument Society of America:1369.

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    [12] W. W. Sheng and R. P. Colino, Power Electronic Modules: Design and Manufacture, ed., CRC Press, Boca Raton Florida, 2005.