Error compensation of pressure sensor

Reasonable error compensation of pressure sensors is the key to their application. Pressure sensors mainly have sensitivity error, offset error, hysteresis error, and linear error. This article will introduce the mechanisms of these four errors and their impact on test results. At the same time, it will introduce pressure calibration methods and application examples to improve measurement accuracy.

At present, there are a wide variety of sensors on the market, which allows design engineers to choose the pressure sensors required for the system. These sensors include both the most basic transformers and more complex high integration sensors with on-chip circuits. Due to these differences, design engineers must strive to compensate for measurement errors in pressure sensors, which is an important step in ensuring that the sensors meet design and application requirements. In some cases, compensation can also improve the overall performance of sensors in applications.

The concepts discussed in this article are applicable to the design and application of various pressure sensors, which have three categories:

1. Basic or uncompensated calibration;

2. There is calibration and temperature compensation;

3. It has calibration, compensation, and amplification.

Offset, range calibration, and temperature compensation can all be achieved through thin film resistor networks, which use laser correction during the packaging process. This sensor is usually used in conjunction with a microcontroller, and the embedded software of the microcontroller itself establishes the mathematical model of the sensor. After the microcontroller reads the output voltage, the model can convert the voltage into a pressure measurement value through the transformation of the analog-to-digital converter.

The simplest mathematical model for sensors is the transfer function. The model can be optimized throughout the entire calibration process, and its maturity will increase with the increase of calibration points.

From a metrological perspective, measurement error has a fairly strict definition: it characterizes the difference between measured pressure and actual pressure. However, it is usually not possible to directly obtain the actual pressure, but it can be estimated by using appropriate pressure standards. Metrologists usually use instruments with an accuracy at least 10 times higher than the measured equipment as measurement standards.

Due to the fact that uncalibrated systems can only convert output voltage to pressure using typical sensitivity and offset values.

This uncalibrated initial error consists of the following components:

1. Sensitivity error: The magnitude of the error generated is proportional to the pressure. If the sensitivity of the device is higher than the typical value, the sensitivity error will be an increasing function of pressure. If the sensitivity is lower than the typical value, the sensitivity error will be a decreasing function of pressure. The reason for this error is due to changes in the diffusion process.

2. Offset error: Due to the constant vertical offset throughout the entire pressure range, changes in transformer diffusion and laser adjustment correction will result in offset errors.

3. Lag error: In most cases, lag error can be completely ignored because silicon wafers have high mechanical stiffness. Generally, hysteresis error only needs to be considered in situations where there is a significant change in pressure.

4. Linear error: This is a factor that has a relatively small impact on the initial error, which is caused by the physical nonlinearity of the silicon wafer. However, for sensors with amplifiers, the nonlinearity of the amplifier should also be included. The linear error curve can be a concave curve or a convex curve.

Calibration can eliminate or greatly reduce these errors, while compensation techniques typically require determining the parameters of the actual transfer function of the system, rather than simply using typical values. Potentiometers, adjustable resistors, and other hardware can all be used in the compensation process, while software can more flexibly implement this error compensation work.

The one point calibration method can compensate for offset errors by eliminating drift at the zero point of the transfer function, and this type of calibration method is called automatic zeroing. Offset calibration is usually performed at zero pressure, especially in differential sensors, as differential pressure is typically 0 under nominal conditions. For pure sensors, offset calibration is more difficult because it either requires a pressure reading system to measure its calibrated pressure value under ambient atmospheric pressure conditions, or a pressure controller to obtain the desired pressure.

The zero pressure calibration of differential sensors is very accurate because the calibration pressure is strictly zero. On the other hand, the calibration accuracy when the pressure is not zero depends on the performance of the pressure controller or measurement system.

Select calibration pressure

The selection of calibration pressure is very important as it determines the pressure range that achieves the best accuracy. In fact, after calibration, the actual offset error is minimized at the calibration point and remains at a small value. Therefore, the calibration point must be selected based on the target pressure range, and the pressure range may not be consistent with the working range.

In order to convert the output voltage into a pressure value, typical sensitivity is usually used for single point calibration in mathematical models because the actual sensitivity is often unknown.

After performing offset calibration (PCAL=0), the error curve shows a vertical offset relative to the black curve representing the error before calibration.

This calibration method has stricter requirements and higher implementation costs compared to the one point calibration method. However, compared with the point calibration method, this method can significantly improve the accuracy of the system because it not only calibrates the offset, but also calibrates the sensitivity of the sensor. Therefore, in error calculation, actual sensitivity values can be used instead of atypical values.

Here, calibration is performed under conditions of 0-500 megapascals (full scale). Since the error at the calibration points is close to zero, it is particularly important to correctly set these points in order to obtain the minimum measurement error within the expected pressure range.

Some applications require high precision to be maintained throughout the entire pressure range. In these applications, the multi-point calibration method can be used to obtain the most ideal results. In the multi-point calibration method, not only offset and sensitivity errors are considered, but also most linear errors are taken into account. The mathematical model used here is exactly the same as the two-stage calibration for each calibration interval (between two calibration points).

Three point calibration

As mentioned earlier, linear error has a consistent form, and the error curve conforms to the curve of a quadratic equation, with predictable size and shape. This is especially true for sensors that do not use amplifiers, as the nonlinearity of the sensor is fundamentally based on mechanical reasons (caused by the thin film pressure of the silicon wafer).

The description of linear error characteristics can be obtained by calculating the average linear error of typical examples and determining the parameters of the polynomial function (a × 2+bx+c). The model obtained after determining a, b, and c is effective for sensors of the same type. This method can effectively compensate for linear errors without the need for a third calibration point.