Wednesday, April 27, 2016

Measuring Thermistors in a Half-Bridge


Publish Date: Feb 23, 2011 | 6 Ratings | 3.17 out of 5 |  PDF | Submit your review

Overview

A thermistor is a type of resistor whose resistance varies significantly with temperature. Thermistors are typically desirable for applications that require a very accurate temperature measurement over a relative narrow temperature range. Thermistors are available for temperatures between -50°C to 100 °C. Many thermistors have a sensitivity of 3-6%/°C which means that they may vary in resistance by more than +/- 500% of their nominal value over their full measurement range. This wide range presents a measurement challenge that can be addressed by making a half bridge measurement with a correctly chosen reference resistor.

Table of Contents

  1. The Measurement Circuit (Half-Bridge)
  2. Choosing a Reference Resistor
  3. Scaling the Data to Resistance and Temperature
  4. Example Temperature Measurement Accuracy Calculation

1. The Measurement Circuit (Half-Bridge)

From page 19 of the NI 9219 Operating Instructions and Specifications we can see the input circuitry for full and half bridge configurations.  With slight modifications to this image, here is the circuit used to measure thermistors:
Figure 1:  Dotted lines indicate circuitry connected inside the NI 9219 module.  Only the Thermistor, Rtherm, reference resistor, Rref, the two wires connecting to EX+ and EX-, and the wire connected to HI are external.

2. Choosing a Reference Resistor

In order to maximize the accuracy of your measurement, the reference resistor should be chosen such that the min and max resistances are centered around the NI 9219’s input range.  That is, when your thermistor and reference resistor are placed in a voltage divider, you should choose the reference resistor so that the min and maximum thermistor values will create equal, but opposite imbalances from a nominally balanced voltage divider.  This will keep the measurement error to a minimum because the resistance measurement error becomes larger as Vout approaches ground or Vex.  Here’s an example to make things more clear:
Figure 2:  Circuit diagram used for the derivation of the optimal reference resistor value.
Let’s say that we have chosen the PR103J2 thermistor from US Sensor and we are interested in measuring -8 C to 65C.  Using this sensors data sheet, we can see that -8 C corresponds to a thermistor resistance of ~50 kΩ and 65 °C corresponds to thermistor resistance of ~2 kΩ.    This means that we want to optimize Rref to allow Rtherm to vary between 2 and 50 kΩ.  In order to do this, we can solve a system of voltage divider equations with the assumption that we want the min and max Rtherm values to provide equal but opposite imbalances from a balanced bridge (balanced bridge condition is equivalent to Vout = ½ Vex which is equivalent to Rtherm = Rref) in our voltage divider.
Eq. 1:      
Eq. 2:     
We can set Eq. 1 equal to (-1) * Eq. 2 to solve the system of equations for Rref.
Eq. 3:     
Since Vex cancels out, we can solve the following quadratic equation for Rreference,
Eq. 4:     
Taking the positive value, we find that Rref should be 10000 Ω.
Eq. 5:     
Given the above thermistor resistance measurement range and target reference resistor value, the next step is to choose a reference resistor.  In order to maintain excellent accuracy, a high accuracy resistor with a very low temperature coefficient of drift should be used.  One example of such a resistor is the Vishay, Z201T 10K000 B, A, or Q for 0.1%/0.05%/0.02% resistor with 0.6 ppm/C drift. 

3. Scaling the Data to Resistance and Temperature

Since the NI 9219 half bridge mode can only return data in units of mV/V we must scale the data to resistance and then temperature.  The scaling from mV/V to Ω can be derived from the voltage divider equation with the knowledge that the reading returned by the NI 9219 in half bridge mode when wired as shown in Figure 1 is equal to Vout/Vex – 0.5 V/V. 
Eq. 6:    
Then, solving Eq. 6 for Rtherm we can get the following scaling equation for Rtherm in terms of the NI9219 Reading and Rref.
Eq. 7:  
You can use Eq. 7 to scale the NI9219 Reading from mV/V to Ω.  From this point you can use the scaling equation provided by your thermistor manufacturer to scale the data from Ohms to temperature.

4. Example Temperature Measurement Accuracy Calculation

First of all, we’ll calculate our measurement range in the units that the 9219 measures which are mV/V.  We can do this by plugging Rref = 10000 Ω into equations 1 and 2 and solving for Vout/Vex.
For Eq. 1 & 2 with Rref = 10000 Ω:
                                        
This corresponds to a maximum reading of ± 333 mV/V for the NI 9219, and we can use this to calculate the measurement accuracy using the formula:
Eq. 8:     
Using Eq. 8, we can compute the max error in high resolution mode at the desired full scale ( ±333.33 mV/V) over the full operating temperature range -40°C to 70 °C in units of mV/V,

Eq. 9:  
Now that we know the mV/V measurement error as well as the reference resistor tolerance, we can compute the Max % Error in Resistance using the scaling equation (Eq. 7).  In order to determine the maximum error you must check the effect of ±Measurement Error and ±Reference Resistor Error.  In the circuit configuration shown, with the reference resistor as the lower leg of the bridge and a reference resistor that has been chosen to be in the middle of the range, the max error case is for opposite signs (i.e. +0.68 mV/C measurement error and -0.1% resistor tolerance).
Eq. 10:  
Solving Eq. 10 for a 333.33 mV/V reading and a ±0.1% reference resistor we can determine that the maximum error is 13.7 Ω, or ±0.68% at Rtherm = 2000 Ω.  Since most thermistors have sensitivities in the range of 3%/°C to 6%/°C, 0.68% error in resistance corresponds to 0.11°C to 0.23°C error.  In this case, the thermistor referenced above has a sensitivity of 3.46%/°C at Rtherm = 2000Ω so the total error is ±0.20°C.

Memilih sensor suhu untuk peralatan BMKG

Improving the accuracy of temperature measurements

The article first appeared in Sensor Review, The international journal of sensing for industry. This article is also available in German (published in Elektronic Journal) andNorwegian (published in Elektronic Norden Magazine).

Abstract

Technology advances in the field of temperature measurement have led to a huge variety of sensors and measuring instruments now being available for making accurate measurements at relatively low costs.
This article takes a ‘back to basics’ look at three of the most popular temperature sensor technologies and offers advice on how to avoid the many pitfalls and traps that often destroy the accuracy of a temperature measuring system.

Introduction

Highly accurate temperature measuring equipment is now widely available at very reasonable costs but, whilst this should be making the task of making temperature measurement easy, many users make simple mistakes that negate the benefits of using high specification sensors and measuring equipment.
When most people have a requirement to measure a temperature, their first reaction is to purchase the highest specification, most expensive sensor and measuring instrument they can afford. Speaking as a manufacturer, this is a reaction we applaud as it sells a lot of equipment. It is however the wrong way to set about making accurate measurements.

Making the right measurement

Temperature Gradients
Figure 1
Consider what you are trying to measure the temperature of. An example that seems simple at first is measuring room temperature to 1°C accuracy. The problem here is that room temperature is not one temperature but many.
Figure 1 shows sensors at three different heights record the temperatures in one of Pico Technology's storerooms. The sensor readings differ by at least 1°C so clearly, no matter how accurate the individual sensors, we will never be able to measure room temperature to 1°C accuracy.
Another seemingly obvious but frequently overlooked point is that you are only ever recording the temperature of the sensor. Any difference between the temperature of the sensor and the temperature you are trying to measure will be a direct error. For example, if you clamp a temperature sensor around a pipe (figure 2) it would be wrong to assume you are measuring the temperature of what is flowing in the pipe.
Pipe Temperature
Figure 2
In Figure 2 a temperature difference exists between inner and outer surfaces of the pipe, and ambient air temperature and airflow around the sensor will cause additional errors. However, for practical and/or safety reasons, you may have no choice but to make your measurement in this way — in which case errors can be reduced by thermally lagging both the sensor and the section of pipe to which the sensor is attached.
In addition, give thought to how the presence of your sensor may actually affect the measurement. Figure 3 demonstrates this point.
Different sensors measuring water being heated
Figure 3
Figure 3: In this experiment, high and low accuracy sensor and instrument pairs were used to observe the rising temperatures of equal volumes of water being heated. A large, expensive and accurate Pt100 sensor was connected to a PT-104 (both with 0.01 °C accuracy) and partially immersed in one beaker, whilst a low–cost thermocouple, connected to a TC-08 (0.5 °C accuracy), was immersed in the second beaker. Using the Pt100 sensor in this manner invalidated the accuracy of both the sensor and the instrument because of ‘thermal shunting’. The dissipation of heat from the larger, partially immersed probe into the atmosphere reduced the rate at which the water could be heated. Furthermore, in this experiment, the temperature of the PT100 never reached 100 °C even though the water did boil. The low–cost, lower accuracy solution afforded the more accurate and representative measurement.
Having considered what you are going to measure, the next step is to decide which type of sensor to use. The three sensors most commonly used in research and industry are: the thermocouple; the resistance temperature detector (RTD or ‘resistance thermometer’); and the thermistor. Table 1 compares and contrasts the three.

Table 1 — the most commonly used temperature sensors and their properties

 ThermocoupleRTD
(Pt100)
Thermistor
Operating Range-200 °C to 2000 °C-250 to 850 °C-100 to 300 °C
AccuracyLow
1 °C common
Very High
0.03 °C common
High
0.1°C common
Linearity*MediumHighLow
Thermal Response**FastSlowMedium
CostLowHighLow to moderate
Noise ProblemsHighMediumLow
Long term stabilityLowHighMedium
Cost of measuring instrumentMediumHighLow
* Linearity is not an issue if using modern digital measuring instruments, as look–up tables stored in memory provide compensation.
** Thermal response is considered for the measuring element only, not its enclosure.

Thermocouples

In 1822, an Estonian physician named Thomas Seebeck discovered (accidentally) that the junction between two metals generates a voltage that is a function of temperature, and all thermocouples rely on the so-called ‘Seebeck effect’. Thermocouples are not, however, precision sensors: errors of 2 °C are typical. However, thermocouples have a wide temperature range (-200 to 2000 °C) and are often needed simply because alternative devices do not operate at the desired temperature. In addition, they are relatively low-cost and versatile.
Although almost any two types of metal can be used to make a thermocouple, a number of standard types are used (see table 2) because they possess predictable output voltages and large temperature gradients.
Standard tables show the voltage produced by thermocouples at any given temperature. For example, a K type thermocouple (the most popular) at 300 °C will produce 12.2 mV. This generation of a voltage, albeit small, does mean thermocouples (unlike RTDs and thermistors) are self-powered and require no excitation current. Unfortunately it is not possible to simply connect a voltmeter to the thermocouple to measure this voltage as doing so creates a second, undesired thermocouple junction. To make accurate measurements a technique known as cold junction compensation (CJC) is employed. All standard thermocouple tables allow for this second thermocouple junction by assuming that it is kept at exactly 0 °C. Traditionally, this was done with a carefully constructed ice bath. Maintaining an ice bath however is not practical for most applications; instead the actual temperature at the point of connection of the thermocouple wires to the measuring instrument is recorded and compensated for. Typically, cold junction temperature is sensed by a precision thermistor in good thermal contact with the input connectors of the measuring instrument. This second temperature reading, along with the reading from the thermocouple itself, is used by the measuring instrument to calculate the true temperature at the thermocouple tip. Understanding of CJC is important, as any error in the measurement of the cold junction temperature will lead to the same error in the measured temperature from the thermocouple tip.
On a general note, avoid subjecting the thermocouple connections — and indeed the measurement instrument — to sudden changes in temperature, such as those produced by drafts, as this will lead to errors.
As mentioned, different choices of metals for the thermocouple's two conductors produce sensors with different characteristics. Table 2 summarises the most popular types.

Table 2 — Popular thermocouple types

Thermocouple typeOverall rangeTypical accuracy*Comments
Type B
(Platinum / Rhodium)
100 to 18005 °C (at 1000°C)Suited for high temperature measurements. Unusually, type B thermocouples give the same output at 0 °C and 42 °C. This makes them useless below 50 °C.
Type E
(Chromel / Constantan)
-200 to 9001.7 °CType E has a high output (68 µV/°C) which makes it well suited to low temperature (cryogenic) use. Another property is that it is non-magnetic.
Type J
(Iron / Constantan)
-40 to 7602.2 °CLimited range makes type J less popular than type K. J types should not be used above 760°C as an abrupt magnetic transformation will cause permanent decalibration.
Type K
(Chromel / Alumel)
-200 to 13002.2 °CType K is the ‘general purpose’ thermocouple. It is low cost and popular. Sensitivity is approx 41 µV/°C. Use type K unless you have a good reason not to.
Type N
(Nicrosil / Nisil)
-200 to 13002.2 °CHigh stability and resistance to high temperature oxidation makes type N suitable for high temperature measurements without the cost of platinum (B,R,S) types. Designed to be an 'improved' type K, it is becoming increasingly popular.
Type R
(Platinum / Rhodium)
-50 to 17601.5 °CSuited for high temperature measurements up to 1600 °C. Low sensitivity (10 µV/°C) and high cost makes them unsuitable for general purpose use.
Type S
(Platinum / Rhodium)
-50 to 17601.5 °CSuited for high temperature measurements up to 1600 °C. Low sensitivity (10 µV/°C) and high cost makes them unsuitable for general purpose use. Due to its high stability type S is used as the standard of calibration for the melting point of gold (1064.43 °C).
Type T
(Copper / Constantan)
-200 to 4001 °CBest accuracy of common thermocouples, often used for food monitoring and environmental applications.
* At 0 °C unless indicated. Many manufacturers offer ‘special’ thermocouples with improved accuracy down to 0.5 °C
Thermocouples are made of thin wire to minimise thermal shunting and increase response times. This thin wire causes the thermocouple to have a high resistance that can cause errors due to the input impedance of the measuring instrument. A typical exposed junction thermocouple with 32 AWG wire (0.25 mm diameter) will have a resistance of about 15 Ω/m. If thermocouples with thin leads or long cables are needed, it is worth keeping the thermocouple leads short and then using thermocouple extension wire (which is much thicker and has a lower resistance) to run between the thermocouple and measuring instrument. It is always good practice, before you make precision measurements using thermocouples, to check the input impedance of the measuring instrument and also the resistance of each thermocouple.
If you need to increase the length of the leads from a thermocouple, use only the correct type of thermocouple extension wire. Using any other type of wire will introduce an undesirable thermocouple junction. Ensure any plugs, sockets or terminal blocks used to connect the extension wire are made from the same metals as the thermocouples and correct polarity must be observed at all times.
With signal levels from thermocouples measuring only microvolts, noise pickup can be a problem. Noise from stray electrical and magnetic fields is typically orders of magnitude higher than the signal level. Most measuring instruments reject any common mode noise (signals which are the same on both wires) — but this rejection is not perfect, so it makes sense to minimise the noise where possible. This can be done by routing wires away from noisy areas and twisting the two (insulated) leads of the thermocouple cable together to help ensure both wires pick up the same noise. If operating in an extremely noisy environment (such as near a large motor) it is worth considering using a screened extension cable.
A final note on thermocouples: decalibration. This is the process of unintentionally altering the makeup of the thermocouple. The usual cause is the diffusion of atmospheric particles into the metal at the extremes of the operating temperature range. Another cause is impurities and chemicals from the insulation diffusing into the thermocouple wire. If operating at high temperatures, check the specifications of the probe insulation. In addition, it is always good practice to use thermocouples with insulated junctions as this helps protect against oxidation and contamination.

RTDs

Another common type of temperature measuring device is the resistance temperature detector — the most stable and accurate (although expensive and fragile) of the three sensor types discussed in this article. The electrical resistance of any metal varies according to its temperature — in most cases resistance increases with temperature and is said to have a positive temperature coefficient (PTC).
Perhaps the most common type of RTD is the platinum resistance thermometer (PRT), the practical operating range of which is -250 to 850 °C. Depending on type, RTDs have an accuracy of between 0.03 and 0.3 °C. The most frequently used PRT is the Pt100 — so called because it has a resistance of 100 Ω at 0 °C.
PRTs are either wire–wound or metal film resistors. Of these, the latter exhibits the faster response time. As a Pt100 sensor is basically a resistor, its value can be measured with an Ohmmeter as per figure 4. However, the low resistance of the sensor and its low sensitivity (0.385 Ω/°C) make accurate measurements difficult due to lead resistance. A 1 Ω resistance in each lead connecting the Pt100 to the meter will cause an error of more than 5 °C.
To avoid the problem of lead resistance errors, most Pt100 measurements are made using a 4-wire configuration (figure 4). Here, two of the wires are used to provide an excitation current and the other two connect a voltmeter over the PRT. Provided the impedance of the voltmeter is high then a few Ohms of resistance in the cables will not cause an error.
A compromise between the 2 and 4-wire configurations shown is the so-called 3-wire measurement. Discount this for high accuracy measurements as it assumes, often falsely, that all three wires have the same resistance. In practice, accurate measurement requires the 4-wire configuration. Furthermore, a thermistor will often give a better accuracy than a 3 or 4-wire Pt100 measurement.
RTD
Figure 4
Figure 4: The 4-wire configuration (right) affords the best accuracy, but beware: low resistance and low sensitivity of the RTD place considerable demands on the measuring instrument and a compromise has to be made between excitation current, noise and resolution.
Excitation current should be as low as possible (< 1 mA) in order to minimise self–heating of the sensor. This reduces the sensor’s output voltage, the signal to noise ratio (through increased noise pickup) and resolution of the instrument. Fortunately advanced instruments are to hand. The new PT-104 from Pico Technology, for example, uses a drive current of only 0.25 mA yet — thanks to a novel design and use of a 24 bit analog to digital converter — still provides 0.001 °C resolution.
For high accuracy measurement, self-heating errors should always be taken into account — and values for drive current and self–heating for a given sensor should be available from the manufacturer. Physically small sensors have self-heating errors as high as 1 °C/mW in free air. A 1 mA drive current into 100 Ω dissipates 0.1 mW, so causes a 0.1 °C error. Using a physically large sensor will minimise self–heating errors, but can lead to thermal shunting errors (as demonstrated in the experiment in figure 2).
The small signals from a Pt100 sensor lead to noise pickup problems similar to those encountered for thermocouples and the same precautions against pickup should be used.
One final trap that often catches the unwary is the existence of two different compensation curves. The DIN 43760 standard, also called the ‘European Curve’, is 0.385 Ω/°C for a Pt100 sensor. However, there is also an ‘American Curve’ based on platinum wire of a higher purity (often used for reference standards), and this defines the temperature co–efficient as 0.392 Ω/°C. Of the two, the European curve is the more dominant (even in America) and most measurement instruments compensate for it. If however, the PRT has an American curve and the instrument is compensating for a European sensor, then a small error will result.

Thermistors

Many people unfairly regard thermistors as inaccurate sensors. This may have been true in the past, when thermistors had 5% tolerances at best. For extreme accuracy the RTD is still the best choice, but modern thermistors are not far behind. Thermistors with 0.1 °C accuracy are now widely available and at very reasonable costs. They have a fast response time and a greater output per °C than RTDs.
As with RTDs, thermistors also exploit the fact that a material’s resistance changes with temperature. However, the majority of thermistors employ a metallic oxide and have a negative temperature coefficient (NTC). Thermistors provide relatively high accuracy (0.1 to 1.5 °C) but only operate over a limited temperature range: –100 to +300 °C. Furthermore, no single thermistor will cover this range and a lack of standards means it is often necessary to buy the sensor and measuring equipment together. The thermistor’s response is non-linear and, as with RTDs, we must avoid providing too large an excitation current through the thermistor because of self-heating.
Connection to instruments is a simple 2-wire configuration, as — unlike RTDs — we do not need to compensate for lead resistances: this is small compared to the thermistor’s resistance (typically between 1 and 100 kΩ).
Thermistors, because of their high sensitivity, are ideal for detecting small changes in temperature — especially when it is the change and not the absolute value that is important.

Measuring equipment and calibration

Having chosen our temperature sensor, and ensured we are using it in such a way so as to reap all of its benefits, all that remains is to get the most from our measurement equipment. Here, check the accuracy specifications of the instruments as these vary widely between types of instrument and manufacturers. In some cases, when using RTDs for example, the majority of system error may come from the instrument. When using thermocouples however, the measurement instrument usually has a small error when compared to the sensor. With thermistors, because they have look-up curves particular to the device, it is usual to purchase matched sensors and instruments together from the same manufacturer.
For accurate measurements, calibration is a must and where possible instrument and sensor(s) should be calibrated together as a system.

Conclusion

High precision temperature measurement is possible through the use of well-specified and suitably calibrated sensors and instrumentation. However, the accuracy of these measurements will be meaningless unless the equipment and sensors are used correctly.