Author: Paul Perrault, senior field application engineer, Mahdi Sadeghi, MEMS product application engineer, ADI company

Accelerometer is a very good sensor, which can detect the static and dynamic acceleration when the bridge begins to collapse under the action of gravity, showing a slight change in direction. These sensors include mobile application devices that can change the display direction when you tilt the mobile phone display, and tactical devices that are subject to export control and can help military vehicles or spacecraft navigate. However, like most sensors, it is one thing for the sensor to perform well in the laboratory or test bed, and quite another to maintain the same system level performance in the face of desolate and uncontrolled environmental conditions and temperature stress. Like human beings, when the accelerometer is subjected to unprecedented stress in its life cycle, the system will react and may fail due to the influence of these stresses.

After calibration, the tilt accuracy of high-precision tilt detection system can generally be better than 1 °。 Using market leading ultra-low noise and highly stable accelerometers, such as adxl354 or adxl355, the tilt accuracy can reach 0.005 by calibrating the observed error sources °。 However, this level of accuracy can be achieved only when the stress is properly reduced. For example, the compressive / tensile stress on the sensor may cause an offset of up to 20 mg, resulting in an inclination error of more than 1 °。

This paper discusses the performance index of high precision angle / tilt detection system using accelerometer. We first analyze the sensor design from a micro perspective to better understand the influence of micron level stress and strain. The analysis shows that if the overall mechanical and physical design method is not followed, some surprising results will appear. Finally, practical steps are introduced to help designers improve performance in demanding applications.

Design of adxl35x sensor

From the perspective of price and performance, MEMS based accelerometers are suitable for all kinds of applications from consumer products to military detection. Among the ADI product portfolio, the most outstanding low-noise accelerometers are adxl354 and adxl355, which support precision tilt detection, seismic imaging and other applications, as well as many emerging applications such as robot and platform stability. The market leading features of adxl355 give it unique advantages in high-precision tilt / angle detection applications, such as excellent noise, offset, repeatability and temperature dependent offset, as well as second-order effects such as vibration correction and cross axis sensitivity. This paper will take this kind of special sensor as an example of high precision accelerometer to discuss in detail; However, the principles discussed in this section are applicable to most triaxial MEMS accelerometers.

To better understand the design considerations that led to the excellent performance of the adxl355, let’s first review the internal structure of the sensor and explain why the triaxial response to environmental parameters (e.g., out of plane stress) varies. In many cases, the out of plane stress is caused by the temperature gradient on the z-axis of the sensor.


Figure 1. Sensor architecture of adxl355. For the X / y sensor, with the movement of the detection mass, the fixed finger is connected with the mass

The capacitance between the fingers changes. The mass of z-axis sensor is not balanced, so the z-axis acceleration can be detected out of plane.

Adxl35x series accelerometers include a spring mass system, which is similar to many other MEMS accelerometers. The mass moves in response to external acceleration (static acceleration (such as gravity) or dynamic acceleration (such as velocity change)) and its physical displacement is detected by conduction mechanism. The most common conduction mechanisms used in MEMS sensors include capacitive, piezoresistive, piezoelectric or magnetic. The adxl355 uses capacitance conduction mechanism to detect movement by capacitance change, which can be converted into voltage or current output by reading circuit. Although adxl355 adopts capacitance conduction mechanism for all triaxial sensors on silicon chip, X / y sensor and Z sensor adopt two completely different capacitance detection architectures. The X / y sensor is based on differential in-plane interdigitation, while the Z sensor is an out of plane parallel plate capacitance sensor, as shown in Figure 1.

If there is compressive stress or tensile stress on the sensor, the MEMS chip will warp. Because the detection mass is suspended above the substrate by the spring, it will not warp with the substrate, but the gap between the mass and the substrate will change. For the X / y sensor, because the displacement in the plane has the greatest influence on the change of interdigital capacitance, the gap is not in the direction of capacitance sensitivity, which is caused by the compensation effect of the edge electric field. However, for the z-sensor, the gap between the substrate and the detection mass is actually the detection gap. Therefore, it will have a direct impact on the z-sensor, because it effectively changes the detection gap of the z-sensor. In addition, the z-sensor is located in the center of the chip, so as long as the chip is subjected to any stress, the position will produce maximum warpage.

In addition to the physical stress, there is always a temperature gradient on the z-axis sensor because the heat transfer on the z-axis is asymmetric in most applications. In typical applications, sensors are soldered on printed circuit board (PCB), and the whole system is packaged. The heat transfer of x-axis and y-axis is mainly transferred through the solder joints around the package and to the symmetrical PCB. However, in the Z direction, due to the solder joint and convection at the top of the chip, the heat is transferred through the bottom, and the heat is transferred to the outside of the package through the air. Because of this mismatch, there will be a residual temperature gradient on the z-axis. As with physical compressive / tensile stresses, this causes a shift in the z-axis that is not caused by acceleration.

Review of data affected by environmental stress

The adxl354 (analog output) accelerometer can be connected to any analog data acquisition system to implement data analysis, while the adxl355 evaluation board is optimized and can be directly put into the customer system, thus simplifying the existing embedded system prototype design. In order to clarify the main idea of this paper, we use a small evaluation board eval-adxl35x. In order to record and analyze data, we connect eval-adxl35x to sdp-k1 microcontroller board and use mbed ® Environment. Mbed is suitable for arm ® Microcontroller board open source and free development environment, with an online compiler, can help you quickly build. When the sdp-k1 board is connected to the PC, it will be displayed as an external drive. To program the board, just drag and drop the binary files generated by the compiler into the sdp-k1 drive. 3, 4

Once the mbed system records data through UART, a basic test environment is formed. We can try adxl355 experiment and transfer the output to a simple port for recording data and further analysis. It should be noted that the mbed code records the register at 2 Hz regardless of the output data rate of the accelerometer. Faster recording speed can also be used in mbed, but this article will not elaborate.

A good initial data set helps to determine benchmark performance and verify the noise level that may occur in most of our subsequent data analysis. Panavise articulated vise 5 with suction cup device is used, so that when the device is adhered to the glass surface, a fairly stable working surface can be achieved by setting the workbench. With this configuration, the adxl355 board (fixed from the side) is as stable as the laboratory bench. More advanced power users may notice the risk of tipping over when installing this vise, but it is a simple and economical way to change direction according to gravity. As shown in Figure 2, after the adxl355 board is installed, a set of data is collected for 60 seconds for the first analysis.


Figure 2. Test setup using eval-adxl35x, sdp-k1 and panavise stents.


Figure 3. Adxl355 data without low-pass filter (register 0x28 = 0x00) is collected for more than 1 minute.

Take 120 data points and measure the standard deviation, showing that the noise is below 800 μ 1 mg. According to the typical performance specifications in the adxl355 data book, we see that the noise density listed is 25 µ g/√Hz。 With the default LPF setting, the bandwidth of the accelerometer is about 1000 Hz. Assuming a brick wall filter, the noise is about 25% µ g/√Hz × √1000 Hz = 791 µ g rms。 This initial data set passed the first sampling test. To be exact, the coefficients used in the conversion from noise spectral density to RMS noise should represent the fact that the digital LPF will not roll off indefinitely (that is, a brick wall filter). Some use 1.6 × The coefficients can achieve simple RC single pole 20 dB / octave roll off, but adxl355 digital low pass filter is not a single pole RC filter. In any case, assuming that the coefficient is between 1 and 1.6, we can at least correctly estimate the noise approximation.

Compared with the measured signal, the bandwidth of 1000 Hz is too wide for many precision detection applications. To help optimize the tradeoff between bandwidth and noise, the adxl355 uses an on-board digital low-pass filter. In the next test, we set the LPF to 4 Hz, which will reduce the noise by √ 1000 / √ 4 ≈ 16. The test is completed in the mbed environment using the simple structure shown in Figure 4, and the data is shown in Figure 5. After filtering, the noise is reduced as expected. As shown in Table 1.


Figure 4. Mbed code for configuring registers.


Figure 5. When LPF is set to 4 Hz (register 0x28 = 0x08), adxl355 data is collected for more than 1 minute.

Table 1. Expected and measured noise of adxl355

Table 1 shows that under the current setting, the noise of y-axis is higher than the expected theoretical value. After investigating the possible causes, we found that the vibration of the fan of additional laptops and other laboratory equipment may be noise on the y-axis. To verify this, we turn the vise so that the x-axis reaches the original position of the y-axis, and the result shows that the x-axis becomes the more noisy axis. The noise difference between the axes seems to be the instrument noise, not the difference of the noise level between the axes of the accelerometer itself. This type of test is actually the “initial” test of the low noise accelerometer, thus enhancing the confidence of further test.

In order to understand the impact of thermal shock on adxl355, we selected a hot air gun 7 and adjusted it to the cold air mode (actually several degrees higher than the room temperature) to apply heating stress to the accelerometer. We also use the adxl355 on-board temperature sensor to record the temperature. In this experiment, we use a vise to place adxl355 vertically, and use a hot air gun to blow air on the top of the package. We expect that the temperature coefficient will appear with the increase of chip temperature, but any thermal stress will appear almost immediately. In other words, if a single detection axis is sensitive to thermal stress, there may be large fluctuations in the accelerometer output. By deleting the average value when the data changes gently, it is easy to compare the three axes at the same time. The results are shown in Figure 6.


Figure 6. Thermal shock data of adxl355 when using hot air gun with cold air mode.

As can be seen from Figure 6, the slightly higher temperature air is blown onto the sealed ceramic package with a hot air gun. As a result, there is ~ 1500 on the z-axis μ The offset on the y-axis is much smaller than that on the y-axis µ g) There is almost no offset on the x-axis. Although many end-user products have a shell on the top of the PCB, which can disperse the thermal stress, we need to consider these types of fast transient stress. From this simple test, it can be seen that these stresses may show as offset errors.

Figure 7 shows the opposite polarity effect when the hot air gun is turned off.

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Figure 7. Thermal shock to adxl355 when the hot air gun is turned off at t = 240 seconds.

When the hot air gun is used in the heating environment, the effect is more obvious; That is, when the temperature impact is larger. The output temperature of weller hot air gun is about 400 ℃, so it should be separated for a certain distance to avoid damage due to overheating or thermal shock. In this test, the hot air gun blows out hot air at a distance of about 15 cm from adxl355, resulting in an immediate temperature rise of about 40 ℃ ° C. As shown in Figure 8.


Figure 8. Thermal shock of adxl355 when using hot air gun.

Although the intensity of thermal shock is quite large, it is still obvious that the reaction speed of z-axis is much faster than that of x-axis and y-axis during this experiment. Using the offset temperature coefficient in the data book, when the temperature is 40 ℃ offset, you will see about 100 ℃ µ g/ ° C × forty ° C = 4 mg, and the X and Y axes will eventually show this. However, we find that the 10 mg shift appears almost immediately on the z-axis, indicating that this effect is different from that caused by temperature. This is caused by the thermal stress / strain of the temperature difference on the sensor, which is most obvious on the z-axis because, as mentioned earlier, the sensor on the z-axis is more sensitive to the thermal stress than on the X and y-axis.

In the data book, the typical offset temperature coefficient (offset temperature coefficient) of adxl355 is ± one hundred µ g/ ° C。 We need to understand the test method used here, which is very important because the misalignment temperature coefficient is measured in an oven using an accelerometer. Within the temperature range of the sensor, the oven temperature rises slowly, and we measure the slope of the offset. A typical example is shown in Figure 9.

o4YBAGCrC46AHYH1AAMCun_ 1twU840.png

Figure 9. Temperature characteristics of adxl355 tested in an oven.

Two effects are shown. One is the offset temperature coefficient described and recorded in the data book. This is the oven with 5 ° C / min, but without heat preservation, at – 45 ° C to + 120 ° The average value of many products in the temperature range of C. This result can be obtained from a chart similar to figure 9, and it can be pointed out that the ° 18 mg, or about 109 µ g/ ° C. Slightly over 100 µ g/ ° C is within the range of typical values, but it is still within the range of minimum and maximum values specified in the data manual. However, consider the case shown on the right side of Figure 9, let the device be at 120 ° What about 15 minutes at C. When the equipment is at high temperature, the actual offset decreases and improves. In this case, the average is above 165 ° The temperature coefficient of maladjustment is about 60 µ g/ ° C。 The second effect is related to the thermal stress of temperature difference. When the mass of the sensor is stabilized in the whole temperature range of the silicon chip device, the stress decreases. The hot air gun tests shown in figures 6 to 8 also show this effect. Compared with the long-term misalignment temperature coefficient listed in the data book, this effect will appear in a shorter time range. It is very important to understand this. Due to the influence of overall thermokinetics, the heating rate is much slower than 5 ° The above findings are very valuable for many C / min systems.

Other factors affecting the stability of adxl355

After a deep understanding of the thermal stress in the design, another important aspect of inertial sensors needs to be understood, that is, their long-term stability or repeatability. Repeatability refers to the accuracy of continuous measurement for a long time under the same conditions. For example, in a period of time, the gravity field in the same direction at the same temperature is measured twice, and the matching degree is observed. For applications where maintenance calibration cannot be performed regularly, the repeatability and sensitivity of the offset are critical factors in evaluating the long-term stability of the sensor. Many sensor manufacturers do not describe or specify long-term stability in their data books. In ADI’s adxl355 data book, the repeatability is 10-year life prediction value, including high temperature working life test (HTOL) (TA = 150 ℃, vsupply = 3.6 V, 1000 hours), measurement temperature cycle (− 55 ℃ to + 125 ℃ and 1000 cycles), velocity random walk, measurement offset caused by broadband noise and temperature hysteresis. As shown in the data book, the adxl35x series has excellent repeatability, and the accuracy of the adxl355’s X / y sensor and Z sensor are ± 2 mg and ± 3 mg。

Under stable mechanical, environmental and inertial conditions, repeatability follows the square root law because it is related to the time of measurement. For example, to obtain the repeatability of the offset of the x-axis over a period of two and a half years (which may be a short period for the final product), you can use the following formula: ± 2 mg × √ (2.5 years / 10 years)= ± 1 mg。 Figure 10 shows the HTOL test results of 32 devices in 23 days: the offset is 0 G. The square root law can be clearly seen in this figure. It should also be emphasized that the performance of each device is different due to the process differences in the manufacturing process of MEMS sensors, and the performance of some devices is better than that of other devices.


Figure 10. Long term stability of adxl355 up to 500 hours.

Suggestions on mechanical system design

After the above analysis and discussion, it is obvious that the mechanical mounting surface and housing design can help improve the overall performance of adxl355 sensor, because they will affect the physical stress transmitted to the sensor. Generally speaking, mechanical installation, housing and sensors will form a second-order (or higher-order) system; Therefore, it will respond differently during resonance or overdamping. Mechanical support systems have modes (defined by resonance frequency and quality factor) that represent these second-order systems. In most cases, our goal is to understand these factors and minimize their impact on the sensing system. Therefore, the selected sensor package, all interfaces and materials should be able to avoid mechanical attenuation (due to overdamping) or amplification (due to resonance) within the bandwidth of the adxl355 application. In this paper, these specific design considerations are not discussed too much; However, a few utilities are briefly listed:

PCB, mounting and housing

  • The PCB is firmly bonded to the rigid substrate. Use multiple mounting screws and glue on the back of PCB to ensure firm support.
  • Place the sensor close to the mounting screw or fastener. If the volume of PCB is large (about a few inches), multiple mounting screws are used in the center of the board to avoid low-frequency vibration of PCB, which will affect the measurement results of accelerometer.
  • If the PCB is only mechanically supported by the groove / convex edge structure, a thicker PCB (recommended thickness greater than 2 mm) is used. When the PCB size is large, increase its thickness to maintain the rigidity of the system. Use finite element analysis (such as ANSYS or similar analysis) to determine the optimal PCB size and thickness for a specific design.
  • For some applications, such as structural health monitoring applications where sensors are measured for a long time, the long-term stability of sensors is crucial. When choosing packaging, PCB and adhesive materials, we should choose the products with the least performance degradation or mechanical characteristics change in a long time, so as to avoid additional stress to the sensor, resulting in offset.
  • Avoid assuming the natural frequency of the enclosure. It will be helpful to carry out natural vibration model calculation for simple shell and finite element analysis for complex shell design.
  • Welding the adxl355 and the circuit board together will produce stress, resulting in an offset of up to several mg. In order to reduce this effect, it is suggested that PCB pad pattern, heat conduction sheet and copper wire path should be symmetrically arranged. Strictly follow the welding guidelines provided in the adxl355 data book. We also found that in some cases, performing solder annealing or thermal cycling prior to calibration can help alleviate stress accumulation and help manage long-term stability issues.

Filling materials

Filling materials are widely used to fix electronic devices in the housing. If the sensor package is made of secondary molding plastic, such as connecting plate grid array (LGA), filling materials are not recommended, because their temperature coefficient (TC) does not match the shell material, which will cause the pressure to directly affect the sensor, resulting in offset. However, the adxl355 adopts hermetic ceramic package, which can effectively protect the sensor from TC. However, the pouring material may still form stress accumulation on the PCB, which is because the performance of the material will degrade with the passage of time, resulting in the micro warpage of the silicon chip and the formation of stress on the sensor. For applications that need to maintain stability for a long time, perfusion is generally recommended to be avoided. Low stress conformal coatings (e.g., C-type poly (p-xylene)) can provide some moisture barrier to replace pouring. eight

Air flow, heat transfer and heat balance

In order to achieve the best sensor performance, it is very important to design, place and use the detection system in the environment where the temperature stability is optimized. As shown in this paper, even small temperature changes may lead to unexpected consequences due to the thermal stress on the bare sensor. Here are some suggestions:

  • The sensor should be placed on the PCB to minimize the thermal gradient on the sensor. For example, linear regulators generate a lot of heat; Therefore, when they approach the sensor, they will generate thermal gradient on MEMS, and the thermal gradient will change with the current output of the regulator.
  • As far as possible, the sensor module should be deployed in the area away from the airflow (such as HVAC) to avoid frequent temperature fluctuations. If this is not possible, thermal isolation on the outside or inside of the package can be helpful and can be achieved by thermal insulation. Note that both conduction and convective heat paths need to be considered.
  • It is suggested that the thermal quality of the enclosure should be selected so that it can suppress the environmental thermal fluctuation in the application where the environmental thermal change cannot be avoided.


This paper describes how the performance of high-precision adxl355 accelerometer will decline without fully considering the environmental and mechanical effects. Through the overall design practice, while focusing on the system level configuration, keen engineers can obtain excellent sensor system performance. Many of us are under unprecedented life pressure, but it will never overwhelm us. What matters is how we deal with the pressure, and so is the accelerometer. It is very important to realize this.

reference material

1 Chris Murphy。“ Choosing the most suitable MEMS accelerometer for application — Part one. “

Simulation dialogue, Vol. 51, No. 4, October 2017.

2 Chris Murphy。“ Using accelerometers to measure tilt under conditions of temperature change and vibration. “《 Simulation dialogue, August 2017

3 sdp-k1 evaluation system. ADI company

4 mbed: sdp-k1 user guide. ADI company

5 panavise articulated bracket. PanaVise。

6 mbed code. ADI company

7 weller 6966c hot / cold air gun. Weller。

8 Parylene。 Wikipedia.

About the author

Mahdi Sadeghi is a MEMS product application engineer in ain Technology Department of ADI company. He received his PhD in electrical engineering from the University of Michigan at Ann Arbor in 2014. His doctoral dissertation, as well as his work as a researcher of ERC WIMS, is mainly to develop sensor microsystems for UAV and automatic vehicle platforms. He has experience in micro hydraulic sensors and actuators, micro fluid systems, inertial sensing system design for wearable devices, and sensing solutions for condition monitoring applications.

Paul Perrault is a senior field application engineer based in Calgary, Canada. He has worked in ADI company for 17 years, responsible for more than 100 kinds of CPU amplifier power supply design, as well as the design of Na sensor nodes and all current levels between nodes. He holds a Bachelor of Science Degree in electrical engineering from the University of Saskatchewan in Canada and a master’s degree in electrical engineering from Portland State University. In his spare time, he likes skiing in the countryside, climbing on the limestone of the Rocky Mountains, climbing on the local hills, and having a good time outdoors with his young family.

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