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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 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

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

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

specifications.

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

disks.

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

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 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

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 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

mean.

Figure 2. Thermistor Resistance-Temperaturecharacteristic.

NTC Thermistor Physical Features

Electrical Characteristics

The voltage-current characteristic of an NTC thermistor(rated for 10k@25C), 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

where,

R1: Resistance () at absolute temperature T1 (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

where,

R1: Resistance () at absolute temperature T

1(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

power:


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2

A A

P I R

T T T T

where,

: 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

2

1 1 1

1 dR

R dT T

where,


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

thermistor:

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:

absorvedth

dE dT dT sm C

dt dt dt

where,

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

obtained:

0 th A

A

th

dTC T T

dt

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:

0

0

th

th

t

C

A A

t

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 .

Resistance-Temperature

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

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:

2

0 1 2

1ln ln ln

n

nA A R A R A R

T

where,

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:

31

ln lnA B R C RT

where,

T: Temperature (K).

R: Resistance ().

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

modeled.

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

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 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

0.02C).

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 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

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 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

circuits.

Vin

-t

RsetVO(T)

T0

VO(T)

Vin

Rtherm

Linear

Approximation

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

where,

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

follows:

11

O

in therm

set

V T

V R

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

temperature).

Thus, the thermistor resistance is normalized with respect to

its resistance at the specified temperature as:

0

0

thermtherm therm therm therm

therm

Rr r 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:

0therm

set

RS

R

From where the transfer function is derived as follows:


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1 1( )

11

O

in therm therm

set

V TG T

V Sr R

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

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 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.


10/20

AGUILLON

Vin

-t

RsetVO(T)

RthermR1

R2

Vin

-t

RsetVO(T)

RthermR1

a)

b )

Figure 9. Different Voltage divider configurations.

VO1(T)

Vin

-t

Rset

UB

RthermR1

R2vB VO(T)

Vin

-t

Rset1

UB

Rtherm1-t

VO2(T)Rset2

Rtherm2

a)

b)

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.

Vin

-t

Rset

RthermR1

R2

VTHEV

-t

RTHEV

Rtherm

RL

iL

a)

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.


11/20

AGUILLON

VTHEV

-t

Rset

Rtherm

RM

Rp

Figure 12. Ohmmeter configuration circuit.

RP

Rtherm

-t

Rtherm

-t

RP

RS

Rtherm

-t

RP

RS

R1

RP

R1

Rtherm

-t

a)

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

T

where,

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


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


12/20

AGUILLON

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:

0

0

2 2

1

therm

therm

P

RdR

dT TR

R

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

applications.

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

Vin

-t

Rset

RthermR1

R2

a)

+ VO(T)

Rfeed

Vin

R2

R1

b)

+

VO(T)

Rfeed

Rset

-tRtherm

DZ

T0

VO(T)

c)

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


13/20

AGUILLON

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.

Vin

Rset

R1

R2

+ VO(T)

DZ

-tRthermRP

VX

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

X

set

R RV T V

R

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

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

10k@25C), 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.

Vin

-t

Rset

RthermR1

R2

a)

VO2(T)

t0

b)

R3

RP

Sawtooth Gen.

Clock Gen.

VO1(T)

Vpulse(T)

U

V

VO2(T)

VO1(T)

Vpulse(T)

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.


14/20

AGUILLON

Figure 20. NTC thermistor signal amplifier.

10k

Rtherm

-t

a)

RREF

100

CONTROLLER

C

GP1

GP2

GP3

b)

10 Mtherm REF C

TR k R

T

t0

VC

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

controller.

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

res

biastherm

ref

tC

VR k

V

where,

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.


15/20

AGUILLON

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 =

0.125C).

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

obtained.

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. 1V@100A).

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.


16/20

AGUILLON

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

as:

2

1 2

0

0

B in

setin

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

curves.

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


17/20

AGUILLON

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.


18/20

AGUILLON

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


19/20

AGUILLON

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


20/20

AGUILLON

References

[1] D. Hill and H. Tuller, Ceramic Sensors: Theory and Practice, Ceramic Materials for Electronics, R. Buchanan, ed., MarcelDekker, Inc., New York, 1991.

[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,

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.

[5] J.S. Steinhart and S.R. Hart, Calibration Curves for Thermistors, Deep Sea Research, 15(497), 1968.[6] IPTS-68,Bureau International des Poids et Mesures, 1968.[7] ITS-90,Bureau International des Poids et Mesures, ISBN 92-822-2108-3, Dec. 1990.[8] 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.[9] "ISO, Guide to the expression of Uncertainty in Measurement," ISO Technical Advisory Group 4 (TAG 4), Working Group 3(WG 3),

Oct. 1993.

[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.

[11] 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.

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

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