Temperature sensor error

This error is not indicated in the sensor data sheet, since the sensor itself does not have it. It can be eliminated by changing the sensor switching circuit (by replacing the voltage stabilizer supplying the sensor with a current stabilizer and switching from a three-wire line to a four-wire line). But if this is not done, then the resulting error, at least approximately, should be taken into account when calculating the resulting channel error.

Changes in readings due to deviation of operating conditions from normal, i.e. additional errors are normalized by indicating the coefficients of influence of changes in individual influencing quantities on changes in readings in the form. Although in fact these functions of the influence of influencing factors are, as a rule, nonlinear, for ease of calculation they are approximately considered linear and the resulting additional errors are determined as

where is the deviation from normal conditions.

Maximum temperature error value at = 3K:

To move from the calculated maximum value of this error, which occurs when maximum deviations temperatures up to 5 or 35 °C, to standard deviation it is necessary to know the law of temperature distribution in the workshop. We do not have any data about this. Let us accept a completely heuristic assumption that the temperature is distributed normally and 8 days a year reaches critical values, and the remaining 365 - 8 = 357 days, i.e. 357/365 = 0.98 cases, not out of bounds. According to the normal distribution table, we find that the probability P = 0.98 corresponds to a limit of ± 2.3y. From here:

Normal distribution parameters k = 2.066, h = 0.577, e = 3

The temperature error is multiplicative, i.e. obtained by multiplication (sensitivity error). The width of the error band increases in proportion to the increase in the input value x, and at x=0 it is also equal to 0.

Sensor error due to supply voltage fluctuations

This error is purely multiplicative and is distributed according to the same law as the deviation of the network voltage from its nominal value of 220V. The network voltage distribution is close to triangular with the limits accepted above ± 15%. The stabilizer removes the swing of voltage fluctuations by K=25 times, i.e. at the output of the stabilizer, the distribution is also triangular, but with a swing of 15%/25=0.6%. The maximum value of this error: gUD = 15%. Standard deviation for a triangular distribution.

Mechanical and electrical temperature sensors in contact with the medium whose temperature is being measured (this does not include radiation pyrometers) are subject to the following methodological errors.

1. Error due to losses from thermal radiation and thermal conductivity. This error is due to the fact that the temperature of the pipeline walls differs from the measured temperature of the gas or liquid flowing through this pipeline. As a result, along with beneficial heat exchange between the medium and the sensor, harmful heat exchange occurs between the sensor and the walls of the pipeline due to radiation and thermal conductivity (due to the outflow of heat to the location where the sensor is attached). This leads to the fact that the temperature of the sensor differs from the temperature of the medium and a methodological error occurs. To reduce this error, it is necessary to increase the length of the immersed part and the perimeter of the sensor, reduce the wall thickness, and thermally insulate inner surface pipeline, the non-immersed part of the sensor and its mounting location.

2. Error due to incomplete braking of the gas flow. In thermometers designed to measure true temperature T counter flow of air, an error occurs, the cause of which is an increase in the temperature of the sensor due to the transition to heat kinetic energy air flow when it is braked by the sensor.

Full braking temperature

Due to incomplete flow deceleration, the sensor temperature does not reach the temperature T P, it is determined by the formula

,

Where r – braking coefficient depending on the shape of the sensor.

For some sensor forms the coefficient r has the following meanings:

for a cylinder located transverse to the flow, r = 0,65;

for a cylinder located along the flow, r=0,87;

for sphere r = 0,75.

Relative error of true temperature measurement

.

This error can be taken into account by introducing a correction; in navigation computing devices, this correction is introduced automatically.

In thermometers designed to measure temperature T P inhibited gases, the error arises due to incomplete inhibition of the flow by the sensor.

Relative error of braking temperature measurement

.

This error can also be taken into account by introducing a correction.

3. Dynamic error. This error is due to the fact that heat is transferred from the medium to the sensing element with some delay due to the finite rate of heat transfer, which depends on the material of the mass and the surface of the thermal cartridge.

The thermal inertia of a thermometer in a linear approximation is characterized by its transfer function (3.3):

,

Where S T – sensitivity

T 1 – time constant()

It is clear that after 4 years the question is no longer relevant, but as I understand it, at +23C an error was obtained (25.04/25-1)*100%= +0.16% (in% of URL, which is 25MPa), at +55C it was The resulting error is (24.97/25-1)*100% = -0.12%.

And the sensor error at +23C is normalized as 0.2% of URL, and at +55C it should be 0.2%+0.08%*(55C-23C)/10C = 0.456% of URL.

that is, there cannot be any problems with verification (at +23C we have +0.16% with a tolerance of +/-0.2%, at +55C we have -0.12% with a tolerance of +/-0.456%). At +55C the device even turned out to be more accurate than at normal (+23C) temperature.

That is, there can be no problems with verification (at +23C we have +0.16% with a tolerance of +/-0.2%...

Everything seems to be readings taken fit within the basic error , equal in this case to 0.05MPa....

Arose next question: at the pressure sensor, which is preparing for type testing on the measuring instrument...

During these tests, the correctness and validity of the MX... proposed by the developer of this sensor must be established, in this case additional sensor error due to temperature changes environment...

The measured values ​​showed that the main error of the tested sensor did not exceed the value of the limits of permissible error proposed by the developer for it - ±0.2% or in absolute values ​​±0.05 MPa, but

the obtained value of the additional error from the temperature change for this sensor exceeded The developer's proposed value for the limits of permissible additional error:

According to the method for calculating the additional temperature error, we obtain:

(24.97-25.04)/(25*0.1*(55-23)) * 100 = -0.0875%, i.e. The sensor does not fit into the additional temperature error!!!

Those. the developer assumed that this type of sensor has additional error from a change in temperature of ±0.08% of URL for every 10°C, and when checking this value on the first sensor it came across, it turned out to be -0.0875%....

Here the question immediately arises as to whether the developer has set the value correctly additional error from a temperature change equal to ±0.08% of URL for every 10°C..., because it is necessary to check not the total error of the sensor at a temperature of +55°C, as you do (imagine what would happen if the obtained value of the main error was at the permissible limit for this sensor...), namely, the parameter which is normalized..., i.e. size changes errors from the corresponding changes temperatures....

Moreover, the measured values ​​make it possible to estimate the additional error from temperature changes only up from the temperature taken as normal +23°C.

It is also necessary to estimate the additional error from temperature changes down from the temperature taken as normal +23°C, i.e. at -40°C, and this change is not 32°C, as up to a temperature of +55°C, but 63°C...., i.e., most likely, the value of the additional error from the temperature change down the result will be even greater than the value obtained for this sensor up (-0.0875%)....

As a rule, the additional error from temperature changes for SI is set to the maximum of the additional errors up And down...., or, in rare cases, two - different...

Therefore, in this case, it is necessary to carry out a series of additional tests on a representative sample of the sensors under consideration in order to establish an adequate additional error for them (for this type of sensor) from temperature changes...

When choosing pressure sensors, any consumer sets the goal of measuring pressure with the accuracy stated in the technical documentation. This is one of the sensor selection criteria. In the passport for the sensor, GOST standards require that acceptable values ​​be indicated basic error measurements (+ - from true pressure). These values ​​according to GOST 22520 are selected from the range 0.075; 0.1; 0.15; 0.2; 0.25; 0.4; 0.5%; etc. depending on the technical capabilities products. The main error indicator is normalized for normal (i.e. ideal) conditions measurements. Normal conditions are determined according to GOST 12997. These conditions are also specified in the measuring instrument verification procedure. For example, according to MI1997, to determine the main error you need to set following conditions env. Wednesday:
- temperature 23+-2оС,
- humidity from 30 to 80%,
- atm. pressure 84-106.7 kPa,
- power supply 36+-0.72V,
- absence of external magnetic fields, etc.
As you can see, the operating conditions for the sensor when determining the main error are almost ideal. Therefore, each calibration laboratory must have the ability to regulate them. For example, to regulate the temperature in a room, microclimate devices (heater, air conditioner, etc.) are used. But what readings from the sensor we will get in real operating conditions at the facility, for example at +80°C or -30°C, is a question. The answer to this question is given by the indicator additional error, which is also standardized in TU and GOST.
Additional error- Deviation of the conversion function caused by one influencing quantity (temperature, pressure, vibration, radio interference, supply voltage, etc.). Calculated as difference(ignoring the sign) between the error value in workers(actual) measurement conditions, and the error value under normal conditions.
Of course, all operating conditions factors influence the output signal. But for pressure sensors (transmitters) the most significant effect is the deviation of the ambient air temperature. In GOST 22520, the additional error is normalized for every 10°C deviation from normal conditions (i.e. from 23°C). Tolerances according to GOST look like this:

If the sensor meets these tolerances during temperature testing, then it “complies with GOST 22520,” which in most cases is written in the documentation for the sensor.
Let's analyze the accuracy of the sensor, which complies with GOST 22520, when exposed to temperature. For example, a sensor with a basic error of 0.5% and an operating temperature range of -30..+80°C at 30°C can err by 0.5+0.45=0.95%, at 40°C (deviation of 2 deci.°C) 1.4% accordingly, and finally at 80°C we get an accuracy of 3.2% - this is the sum of the main and additional errors. Let me remind you that we are dealing with a 0.5% sensor, and when operating at 80°C we get an accuracy of 3.2% (approx. 6 times worse), and such a sensor meets the requirements of GOST 22520.
The results do not look very nice and will certainly not please the buyer of a sensor with a stated accuracy of 0.5%. Therefore, most manufacturers do thermal compensation of the output signal and the requirements for additional sensors are tightened in the specifications for a specific sensor. errors due to temperature. For example, for SENSOR-M sensors, in the technical specifications we set a requirement of less than 0.1% per 10°C.
Purpose of temperature compensation– reduce additional error from temperature to zero. Nature additional We will consider temperature errors and methods of temperature compensation of sensors in detail in the next article. In this article I would like to summarize.
Need to take into account main error and additional depending on the required measurement accuracy within operating temperatures sensor Additional error each sensor can be found in the passport, operating manual or technical specifications for the product. If the indicator is additional errors are not specified in those. Documentation for the sensor, then it simply meets the GOST requirements that we analyzed above.
One should also distinguish temperature compensation range And Operating temperature range. In the temperature compensation range additional. the error is minimal; when you go beyond the temperature compensation range, the requirements apply again

Design and production of sensors, devices and systems

UDC 681.586"326:621.3.088.228

ON NORMALIZING THE TEMPERATURE ERROR OF STRAIN GAUGE SEMICONDUCTOR SENSORS

V. M. Stuchebnikov

For strain gauge sensors of mechanical quantities operating in a wide temperature range, normalizing the additional temperature error using a linear temperature coefficient leads to a significant distortion of the measurement results. The article shows that it is more correct to normalize the temperature error zone in the temperature range in which the sensors are thermally compensated. This is especially important for semiconductor strain gauge sensors with nonlinear temperature dependence of the output signal.

Additional temperature error is important characteristic sensors of mechanical quantities, which determines the error of their measurement. Therefore, it is always indicated among the main parameters of these sensors. Most manufacturers normalize the additional temperature error using a linear temperature coefficient, that is, as a percentage of the sensor output range of one or ten degrees Celsius (or Fahrenheit in English-speaking countries). In this case, as a rule, it is assumed that the sign of the temperature error can be of any kind, so it is usually indicated as ±y %/°C (or ±y %/10 °C). So it is recommended to normalize the temperature error and regulations IEC (for example,), and after them Russian standards (for example,).

This article discusses the disadvantages of this method of normalizing the additional temperature error of sensors of mechanical quantities, which are especially evident in strain gauge sensors. semiconductor sensors, which today constitute the majority of sensors used for pressure, force, motion parameters, etc. IN specific examples strain-resistive pressure sensors based on heteroepitaxial “silicon on sapphire” (SOS) structures, widely used in Russia, are used.

It is quite obvious, firstly, that the specified rationing makes sense only when linear dependence sensor output signal from temperature. However, a linear approximation of the temperature dependence of the output signal of a strain gauge sensor with an acceptable degree of accuracy can only be used for sensors with metal strain gauge resistors and/or in a relatively small temperature range. Since semiconductors are characterized by a strong and nonlinear dependence of parameters on temperature, the output signal of semiconductor strain gauge sensors, as a rule, is significant.

strongly nonlinearly depends on temperature, which is especially noticeable when operating in a wide temperature range.

Secondly, this rationing actually disorients the consumer, forcing him to double the real measurement error. The fact is that for specific sensors with a linear temperature dependence of the output signal, the slope of this dependence has a very definite sign, so the signal can only either decrease or increase with temperature. By expressing the normalization of the temperature error in %/°C indicating a certain value and sign, the consumer can actually evaluate and take into account the measurement error, for example, pressure, at certain temperature; however, if the sign is not determined, then the measurement uncertainty increases greatly.

This is illustrated in Fig. 1. In Fig. 1a shows the case when the measured pressure (proportional to the sensor output signal) decreases linearly with increasing temperature. In this case, at a known temperature "meas", the consumer can take into account the temperature error and bring the pressure measured by the sensor rms to the actual pressure rn, which is normalized at the "normal" temperature "n:

Рн = Rizm - U ("izm - "nX (1)

where y is the slope of the dependence p (") (y< 0). Конечно, при этом, как минимум, сохраняется неопределенность фактического давления, определяемая основной погрешностью датчика (полоса, ограниченная штриховыми прямыми на рис. 1, а).

The situation is completely different when the sign of the temperature error is not determined (see Fig. 1, b). In this case, even at a known measurement temperature, the uncertainty of the measured pressure is Dr = (рн1 - рн2) even without taking into account the main error of the sensor.

Of course, if the measurement temperature is unknown even approximately, and all that is known about it is that it

Rice. 1. Temperature error of pressure measurement with a linear dependence of the sensor output signal on temperature in the case of a negative (a) and uncertain (b) sign of the linear temperature coefficient y

lies within the (max - min) operating temperature range, the resulting pressure measurement uncertainty is

"Рм = (Р2 - Р1) = IУI ("max - "min) (2)

regardless of whether the sign of the slope coefficient of the straight line p(") is known or not.

Let us consider the case of nonlinear temperature dependence of the output signal of a strain gauge transducer (TC). For example, for pressure transformers based on SOS structures, the temperature drift of which is compensated by a circuit with thermally independent resistors, the dependence of the output signal on temperature is close to parabolic. Silicon TCs with diffusion or implanted strain gauges have a similar dependence. Accordingly, the pressure measured by a sensor with such a TP (proportional to the output signal of the sensor) is also not

linearly depends on temperature (Fig. 2), unless special measures are taken to further correct it in electronic circuit, for example, using a microprocessor. In this case, in accordance with the letter of the regulatory documents, if we normalize the temperature error linear coefficient, then it is necessary to indicate the maximum (in absolute value) value of the slope + umax of the tangent to the parabola (thin straight lines in Fig. 2). As a result, the standard total temperature error in the operating temperature range "max..." min should be determined by expression (2):

"Рн = (Р2 - Р1) = 1 Umax _ ("max - "min") (3)

Obviously, this value far exceeds the actual total temperature error (see Fig. 2)

"Rf = (Rn - Rmin). (4)

It follows that with a nonlinear temperature dependence of the sensor output signal, it is meaningless to use the linear temperature coefficient y to normalize the additional temperature measurement error, since within the operating temperature range it changes in magnitude and sign (including passing through zero), and existing rules in the operating manual it is necessary to indicate the maximum (in absolute value) value of Y.

It is for this reason that in MIDA-13P pressure sensors, as a measure of additional temperature error, the temperature error zone is normalized in the operating temperature range "Rf", which is indicated in the sensor passport. Statistical data on the size of the temperature error zone of MIDA-13P sensors are given in the article. It is necessary to say that Gosstandart fully agrees with this approach and all regulatory documents of MIDA sensors are recognized by the State Register of the Russian Federation.

Rice. 2. Determination of the zone of temperature error in pressure measurement for a sensor with a nonlinear temperature dependence of the output signal:

"Рф - actual zone of temperature error; "Рн - standard zone of temperature error when normalizing the temperature error by a linear coefficient of temperature dependence

ZepBOGB & Sysfems No. 9.2004

Rice. 3. Typical temperature dependence of the additional temperature error in pressure measurement with a MIDA-13P sensor, temperature compensated in a 120-degree temperature range (-40...+80 °C)

"Normal" temperature "n = (20 ± 5) °C. With thermal compensation in another temperature range of the same width (for example, 200...320 °C), the temperature dependence of the error has a similar form (but in this case for the given example “normal” temperature should be Tn = (260 ± 5) °C)

Measurement errors in the temperature error zone (along with the linear temperature coefficient) are also allowed by some foreign standards.

A few more points need to be made. Firstly, in sensors with a temperature dependence of the output signal close to parabolic (namely, this is what it is in MIDA pressure sensors), the temperature error zone is minimal when the “normal” temperature “n”, at which the sensor is calibrated and its main error is determined, is in the middle of the operating temperature range (in which temperature compensation of the output signal is carried out).In MIDA-13P sensors this is performed automatically (operating temperature range from -40 to +80 °C, normalization at 20 + 5 °C - see Fig. 3 In high-temperature MIDA-12P sensors, in which the temperature of the measured medium can reach 350 °C, the situation is somewhat more complicated and will be discussed in more detail below.

Secondly, if in the case of a linear temperature dependence, when the operating temperature range is reduced, the total temperature error decreases linearly, then with a parabolic dependence this decrease is quadratic - for example, with a symmetrical reduction in the operating temperature range by half (for example, from -40...+80 ° From to -10...+50 °C) the temperature error zone is reduced by four. This makes it possible to create high-precision pressure sensors operating in a limited temperature range without the use of complex electronics. Thus, in the range of 0...40 °C, the typical temperature error zone of MIDA-13P pressure sensors with a resistive temperature compensation circuit does not exceed 0.2% (see Fig. 3).

Thirdly, if the “normal” temperature at which the main sensor error is determined (usually this is room temperature), is not in the center of the temperature compensation range, then ignoring the nonlinearity of the temperature dependence of the error