## Calibration theory

Calibration can be translated to comparison. Swedish Standard SS020106 defines calibration as follows in brief version:

"Calibration is an action in order to settle the connection between the displayed value of a measurement system and the corresponding values realized by using standards."

It is like when you call the speaking clock service to find that your watch leads 1 minute. To adjust the watch 1 minute backwards is no calibration, possibly an adjustment which could be motivated by a previous calibration. Neither calibration nor adjustment are exact actions. There are many factors of uncertainty involved, not the least your own handling.

Temperature scale

Temperature is defined according to the laws of thermo dynamics and is made real by the aid of a gas thermometer. The thermo dynamic scale is expressed in Kelvins, K.

One Kelvin (1 K) is defined as 1/273.15 of the temperature at the triple point of water. By definition the temperature of the triple point of water equals 273.16 K alternatively 0.01 ºC. The numbers are chosen in order to make the step 1 ºC correspond to 1 K. The absolute zero point of temperature thus will be 0 K or -273.15 ºC.

The gas thermometer consists of a complicated set of laboratory equipment which is used to carry out the thermo dynamic scale. Stable phase transitions are compared to the thermo dynamic scale and today ITS-90, the International Temperature Scale 1990, is the practical temperature scale.

Improved technology and increased knowledge make the deviations from the thermodynamic scale compared to the practical one becoming less by time. Up to now the fixed temperature values of the practical scale has resulted in a rewised scale approximately every 20th year.

All contact thermometer constructions are based on measuring temperature indirectly, e g via resistance or voltage, and after that conversion to temperature.

Fixed points

The conversion is made by using a number of "fixed points", stable phase shifts for some selected chemical elements. The triple point of water is the most important fixed point as it is also used in the original thermodynamic scale.

Other examples are melting and freezing points for different metals. The table below shows fixed points that are used to calibrate thermocouples and Pt100/RTDs. For higher temperatures other methods have to be used.

 No T (ºC) T (K) Element Phase shift 16 1064.18 1337,33 Gold Freezing point 15 961.78 1234.93 Silver Freezing point 14 660.323 933.473 Aluminium Freezing point 13 419.527 692.677 Zink Freezing point 12 231.928 505.078 Tin Freezing point 11 156.5985 429.7485 Indium Freezing point 10 29.7646 302.9146 Gallium Melting point 9 0.01 273.16 Water Triple point 8 -38.8344 234.3156 Mercury Triple point 7 -189.3442 83.8058 Argon Triple point 6 -218.7916 54.3584 Oxygen Triple point 5 -248.5939 24.5561 Neon Triple point 4 ≈-252.85 ≈20.3 e-H2/He Boiling point 3 ≈-256.15 ≈17.0 e-H2 Boiling point 2 -259.3467 13.8033 e-H2 Triple point 1 -270.15/-268.15 3...5 Helium Boiling point

The green rows of the table show the fixed points used by Pentronic's accredited laboratory, Swedac's registration number 0076. For limits of uncertaity see Calibration.

Interpolation

The gaps between the fixed points temperatures are filled out by the use of an interpolation thermometer. This thermometer is in normal temperature ranges of the type SPRT, Standard Platinum Resistance Thermometer. Platinum is an electrically very stable element in these ranges. The SPRT changes its resistance very predictably with temperature and a good resistance bridge is used to present the measuring result.

Practically the SPRT will be fixed-point calibrated within 14 K - 962 ºC and then it will be used as reference at temperatures between the fixed points. At calibration reference and object are held at the same temperature in different types of baths and furnaces. This is what we call comparison calibration.

The reference sensor's reading at the calibration temperature is not identical to the true value and this applies to the object as well. Always there is an uncertainty about the measured temperatures depending on fluctating errors that you can not measure. This is what we call measurement uncertainty and it can be calculated.

As an example Pentronic's laboratory measures fixed points with a measurement uncertainty down to ±0.0016 ºC at the triple point of water. At comparison calibration the best uncertainty Pentronic can perform is ±0.015 °C.

Traceability

Traceability is a key word in calibration. Traceability is required to make sure that the measured temperature with its calculated measurement uncertainty agrees with the ITS-90.

Traceability is a very important demand in quality assurance management systems such as ISO 9000. Calibration with no traceability is no calibration at all. Traceability always starts with internationally set definitions. See below.

Accreditation

The international bureau of measures and weight, the BIPM, in Paris is the authority for all quantities of the world. BIPM is probably most welknown for keeping the kilogramme prototype, the last "visible" standard. At European level the EA, European co-operation for Accreditation runs the co-operation among the laboratories.

The member countries have committed themselves to accept calibrations performed by other nations' labs. Practically this means that a calibration made by Pentronic is adequate in the other member nations. Each country has a delegate in the EA.  Swedac is the representative body of Sweden, DKD in Germany etcetera. The task of the national bodies is to accredit - approve - and currently supervise the national laboratory and other accredited labs.

Pentronic's laboratory is accredited for temperature calibration since 1988 and is able to realize the most used range of the temperature scale by using its own fixed points. See table above. Pentronic was among the first manufactures of temperature sensors in Europe with an in-house accredited calibration laboratory.

On probation

The accreditation is quality assured by the ISO/IEC 17025 standard. This standard requires much more from the lab than other general quality assurance standars do:

• Scrutinized and approved premises. Temperature calibration requires constant room temperature (23 ºC), among other things.

• All crusial equipment have to be checked at regular intervals.

• Operation procedures and competence of the technicians have to fulfil high requirements. If a key person leaves his emplyment the accreditation can be subject to review.

• Audit calibrations for comparison to other accredited labs. If your measurement uncertainty is too small compared to your deviation from the set "true" value of the audit object you will loose the accreditation for that method until the problem is solved.

• Swedac and their counterparts in other member countries regularly visit their accredited labs in order to check that all operations are performed according to the rules of the standard ISO/IEC 17025. If not in order, corrections are a must not to loose the accreditation status.

Calibration of industrial temperature sensors can, depending on accuracy requirements (measurement uncertainty), take place in an accredited laboratory or in your own industrial lab with traceability to an accredited laboratory and thus to the ITS-90 scale.

The fastest, simplest and most economic way to calibrate a temperature sensor is to compare it a sensor which is traceably calibrated. This comparison can also be performed "in the field", i e on site or in an industrial lab. For this purpose there are a variety of calibration equipment in the market: Baths, furnaces, dry-block portabel furnaces and even portable fixed point cells as well as indispensable instrumentation.

 Portable dry-block furnaces A dry-block furnace can be the most practical solution in order to calibrate not too large a number of sensors at a time, and with moderate accuracy requirements. A modern dry-block furnace is compactly built and can easily be brought for on-site missions. There are many designs available and the one by first sight most easily operated furnace is provided with built-in reference sensor measuring the temperature of the bottom of the hole for the sensor to be calibrated. This design is not very accurate as heat transfer and unwanted temperature differences in the block affect both temperature readings: The best design is the classic one, one hole for the reference sensor and one or more holes for the sensor to be calibrated. Besides all these sensors should be in equal distance from the heat windings, normally in the same radius from the center of a cylindrical block. See pictures. Dry-block furnaces are available for temperatures ranging from -25 °C to 1200 °C. Axial error contribution depends on different stem losses due to varying probe thickness or due to different probe lengths. ΔTp indicates pressure depen-dent temperature drop in case of replaceable inserts being used. Normally the gradient ΔTis the radial error contribution used in uncertainty calculation.

Liquid baths

Liquid baths give you the best accuracy at comparison calibration. They are available in different sizes and the largest ones can also be used for mass calibration.

A high quality liquid bath is much better than a dry-block furnace with air gaps between sensors and temperature block. Liquid flows about the sensor probes which improves heat transfer considerably.

The most advanced calibration baths that Pentronic can offer are used by national labs worldwide. At comparison calibrations the baths' contribution to measurement uncertainty can be reduced to parts of milliKelvins. The liquid in the bath is chosen to suite the temperature range of the calibration:

• From -80 °C to room temperature alcohol is used.
• Water is a very good medium up to +95 °C.
• Different oils are used up to about 300 °C.
• From 200 °C up to 550-600 °C salt baths can be used.

Fluidized baths

For temperatures above 100 ºC closed fluidized baths are available. Working ranges span from +50 to +700 °C. Here aluminum powder is used as heat transfer medium. The powder is stirred by the aid of flowing air.

Old types of fluidized baths are noisy and have a tendency to scatter aluminum powder dust. Isotech's design, the Ayres' bath, is completely closed and free from this disadvantage.

Furnaces

For temperatures above 500 °C tubular and spherical furnaces are being used.  Their working principle is not far from that of a dry-block calibrator. Due to the high temperature radiation and convection in air dominate the  transfer of heat. These furnaces are mostly intended for laboratory use. Normally the upper temperature limit is about 1300 °C.

Instrumentation

Calibration requires accurate and stable instrumentation. Normally two indicators are used, the one connected to the reference sensor and the other one connected to the senser to be calibrated. Also there are combined indicators with two input channels A and B which also can show the difference between the sensors' temperatures, A-B. Even indicators with combined inputs for Pt100(RTD) and thermocouples are available as well as multi channel indicators for simultaneous calibration of several sensors.

Accurate resistance thermometers like working standards need so called resistance bridges to be accurately calibrated. There are three types of such bridges:

• DC bridges. Primarily for simple calibration though there are advanced high accuracy constructions available.

• AC bridges. These will balance off measurements errors depending on inevitable thermo voltages from the sensor circuit. The technique yields very good long time stability.

• Polarity-reversal DC bridges. This technique unites the advantages of the bridges above without bringing their disadvantages, and is used by national labs worldwide.

Four-wire connection is an absolute requirement for high-accuracy calibration regardless of the measurement technique being used.

Reference temperature sensors

By comparison calibration the test sensor is compared to a reference sensor - a temperature sensor with known properties mapped at an accredited calibration laboratory.

The ultimate reference temperature sensor, the SPRT, is constructed solely for careful use in the lab. Its construction is fragile as the high purity platinum wire coil has to be freely suspended in a quartz tube. The SPRT sensor is most accurate but not for use in the field.

For industrial calibration a "working standard" is used which is an improved version of an industrial Pt100 sensor (IPRT) or a traceably calibrated sensor of the same type as the sensor which is to be calibrated.

Pentronic delivers all types. A way increasingly appreciated by Pentronic's customers is that a sensor from the manufactured batch is traceably calibrated at Pentronic's accredited laboratory. This temperature sensor will be kept at the customer's lab and to  be used as reference sensor to maintain the requirements for traceability according to the ISO 9000 standard.

 Interval of calibration Permissable time interval between calibrations depends on the actual use of the sensor. A usual thumb rule says once a year but special circumstances can cause need for either shorter intervals or longer ones. High accuracy requirements and harsh environment call for short intervalls while longer intervals can be allowed when accuracy is not too big a demand and when the measuring environment is not influencing the sensor. Recurrent calibration map the measurement equipment over time. It is usual to start with dense calibration intervals and when the long time drift is observed the interval could be extended if relevant. Always there is the risk for unexpected incidents like anybody drops the sensor on the floor. This motivates the introduction of regular functional checks to the reference equipment several times between the regular calibrations. For platinum sensors, e g Pt100s, 0 ºC ice water baths are suitable. Also the very-simple-to-use fixed point of gallium at 29 ºC is very suitable but more expensive than the ice bath. The dots between the yearly calibrations are check ups madeby the user which gives a hint of the drift by time.