Optimizing high precision tilt/angle sensing: Establishing baseline performance - Embedded.com

Optimizing high precision tilt/angle sensing: Establishing baseline performance


In part one of this series, we reviewed the internal structure of a 3-axis high precision MEMS accelerometer. In this second article, we will review how to acquire a good starting dataset to establish baseline performance and validate what sort of noise levels to expect in subsequent data analyses.

While the analog output of an accelerometer could connect to any analog data acquisition system for data analysis, the manufacturers often provide evaluation boards optimized to be placed directly into customer systems for ease of prototyping with existing embedded systems. For illustrative purposes for this article, the small form factor evaluation board EVAL-ADXL35x was used. For data logging and analysis, the EVAL-ADXL35x was connected to an SDP-K1 microcontroller board and programmed using the Mbed environment. Mbed is an open-source and free development environment for ARM-based microcontroller boards. It has an online compiler and lets developers get started quickly. The SDP-K1 board, when connected to the PC, shows up as an external drive. To program the board, simply drag and drop the binary file generated by the compiler into the SDP-K1 drive.3, 4

Once the Mbed system is logging data through the UART, we now have a basic test environment for trying out accelerometer experiments and streaming the output to a simple terminal for data logging and further analysis. It’s important to note that regardless of the output data rate of the accelerometer, the Mbed code is only logging registers at 2 Hz. Logging faster than this is possible in Mbed, but is outside the scope of this article.

A good starting dataset helps to establish baseline performance and validate what sort of noise levels to expect in most of our subsequent data analyses. Using a PanaVise articulated vise arm5 that has a suction cup mount allows a reasonably stable work surface in a bench setup as it sticks to the glass work surface. The ADXL355 board (held from the side) is as stable as the lab benchtop in this configuration. More advanced power users may note that this vise mount would have some risk of tipping motion, but it is a simple and cost-effective method that allows changing orientation with respect to gravity. With the ADXL355 board placed in the mount as shown in Figure 1, a set of data for 60 seconds is captured for a first analysis.

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Figure 2. Test setup using an EVAL-ADXL35x, SDP-K1, and PanaVise mount. (Source: Analog Devices)

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Figure 2. ADXL355 data with no low-pass filter (register 0x28=0x00), taken over 1 minute. (Source: Analog Devices)

Taking the 120 data points and measuring a standard deviation shows noise in the range of 800 μg to 1.1 mg. From the ADXL355 typical performance specifications in the data sheet, we see the noise density listed as 25 µg/√Hz. With default low-pass filter (LPF) settings, the accelerometer has a bandwidth of about 1000 Hz. Noise would then be expected to be 25 µg/√Hz × √1000 Hz = 791 µg rms, assuming a brick-wall filter. This first dataset passes the first sniff test. To be accurate, the conversion from noise spectral density to rms noise should have a factor to represent the fact that the digital LPF does not have an infinite roll-off (that is, a brick-wall filter). Some use a 1.6× coefficient for a simple RC single-pole 20 dB/decade roll-off, but the ADXL355 digital low-pass filter is not a single-pole RC filter. In any case, assuming a coefficient between 1 and 1.6 at least gets us into the right approximation for noise expectations.

For many precision sensing applications, 1000 Hz is far too wide bandwidth for the signals being measured. In order to help optimize the trade space between bandwidth and noise, the ADXL355 has an on-board digital low-pass filter. For the next test, we set the LPF to be 4 Hz, which should have a net reduction of noise by a factor of √1000/√4 ≈ 16. This is done simply in the Mbed environment using the simple structure shown in Figure 3, while the data is shown in Figure 4.6 After filtering, the noise dropped demonstrably as expected. This is shown in Table 1 below.

Figure 3. Mbed code for configuring a register. (Source: Analog Devices)

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Figure 4. ADXL355 data with the LPF set to 4 Hz (register 0x28=0x08), taken over 1 minute. (Source: Analog Devices)

Table 1. Expected and Measured Noise of the ADXL355 (Source: Analog Devices)

Noise X Y Z
No Filter 791 923 791 1139 791 805
4 Hz Filter 50 58 50 185 50 63

Table 1 shows that noise in the y-axis with the present setup is higher than expected by theory. After investigating the probable causes, we noticed that additional laptop and other lab equipment fan vibration likely manifests itself in the y-axis as noise. To test this, the vise was rotated to place the x-axis into the position where the y-axis was for this testing and the higher noise axis did move to the x-axis. The noise difference between the axes then appears to be instrumentation noise and not an intrinsic difference in the noise levels across the axes of the accelerometer. This type of testing is effectively the “Hello World” test for a low noise accelerometer, so it gives confidence in further testing.

In order to get a sense of how much effect a thermal shock would have on the ADXL355, we took a hot air gun7 and put it into cooler air mode (practically a few degrees above room temperature) in order to apply thermal stresses to the accelerometer. The temperature is also logged using the ADXL355’s on-board temperature sensor. The experiment used the vise to place the ADXL355 vertically so that an air gun can blow air at the top of the package. The expected outcome of this experiment is that the temperature coefficient of the offset would show up as the die heats up, but any differential thermal stresses would appear almost instantly. In other words, if the individual axis of sensing is sensitive to differential thermal stress, one expects to see a bump in the accelerometer output. Removing the average value from the data when it was quiet allows an easy comparison of all three axes at the same time. The results are shown in Figure 5.

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Figure 5. ADXL355 thermal shock data using a hot air gun on cool setting. (Source: Analog Devices)

As can be seen in Figure 5, the air gun was blowing slightly warmer air onto the ceramic package, which is hermetically sealed to the environment. This results in a ~1500 μg shift in the z-axis, a much smaller amount of shift in the y-axis (maybe ~100 µg), and virtually no shift in the x-axis. While many end customer products have some enclosure on top of the PCB that distributes differential thermal stresses, it is important to consider these types of fast transient stresses, which can manifest themselves in an offset error as seen in this simple test.

Figure 6 shows the opposite polarity effect as the hot air gun is shut off.

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Figure 6. ADXL355 thermal shock with an air gun shutting off at t = 240 seconds. (Source: Analog Devices)

This effect is even more pronounced when the air gun is used in the heated setting; that is, when the temperature shock is larger in magnitude. The output from the Weller air gun is on the order of ~400°C, so it’s important to apply it at a distance to prevent damage from overheating or thermal shock. In this testing, the hot air was blown at approximately 15 cm from the ADXL355, which resulted in an almost instantaneous temperature shock of ~40°C, as shown in Figure 7.

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Figure 7. ADXL355 thermal shock with a hot air gun. (Source: Analog Devices)

Even though the amount of thermal shock is quite strong, it is still striking to see how much faster the z-axis responds in this experiment than the x and y axes. Using offset temperature coefficient from the data sheet, and with a 40°C shift in temperature, one would expect to observe about 100 µg/°C × 40 °C = 4 mg shift, which the x and y axes do eventually begin to show. However, noting an almost instant 10 mg shift in the z-axis shows that this is a different effect that is being dealt with rather than offset shift due to temperature. This is a result of differential thermal stress/strain on the sensor and is most obviously seen in the z-axis due to this sensor being more sensitive to differential stresses than the x and y, as described earlier in this article.

The typical temperature coefficient of the offset of the ADXL355 (offset tempco) is specified at ±100 µg/°C in the data sheet. It is important to understand the test methodology used here as the offset tempco is measured with the accelerometers in an oven. The oven is slowly ramped through the temperature range of the sensor, and the slopes of the offsets are measured. A typical example is shown in Figure 8.

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Figure 8. Oven-based temperature characterization of the ADXL355. (Source: Analog Devices)

There are two effects at play in this plot. One is the offset tempco as characterized and documented in the data sheet. This can be interpreted as the mean value of many parts from –45°C to +120°C as the oven ramps up the temperature at 5°C/min but without any soak time. This would be derived from plots similar to Figure 9 and would call out about 18 mg over 165°C, or about 109 µg/°C, which sits slightly outside the typical value of 100 µg/°C, but within the minimum and maximum range as specified in the data sheet. However, consider the right side of Figure 9 as the devices continue to soak at 120°C for about 15 minutes. As the devices sit at a hot temperature, the actual amount of offset shift drops and improves. In this case, the mean value is close to 10 mg over 165°C or about 60 µg/°C offset tempco. The second effect at play then is the differential thermal stress as the sensor proof mass stabilizes in temperature across the entire silicon device and the stress is then reduced. This is the effect that is seen in the air gun testing shown in Figure 6 through Figure 8 and it is important to understand this effect operates on a faster time scale than the longer-term offset tempcos as listed in the data sheet. This could be valuable for many systems, which, due to their overall thermal dynamics, will likely have much slower ramp than 5°C/min.

In part three of this series, we will explore other facts affecting stability and then offer mechanical system design recommendations to improve the overall performance of a 3-axis high precision MEMS accelerometer.


1 Chris Murphy. “Choosing the Most Suitable MEMs Accelerometer for Your Application—Part 1.” Analog Dialogue, Vol. 51, No. 4, October 2017.

2 Chris Murphy. “Accelerometer Tilt Measure Over Temperature and in the Presence of Vibration.” Analog Dialogue, August 2017.

3 SDP-K1 evaluation system. Analog Devices, Inc.

4 Mbed: User Guide for SDP-K1. Analog Devices, Inc.

5 PanaVise articulated arm mount. PanaVise.

6 Mbed code. Analog Devices, Inc.

7 Weller 6966C heating/cooling air gun. Weller.

8 Parylene. Wikipedia.

Paul Perrault is a senior staff field applications engineer based in Calgary, Canada. His experience over the last 17 years at Analog Devices varies from designing 100+ amp power supplies for CPUs to designing nA-level sensor nodes and all current levels in between. He holds a B.Sc. degree from the University of Saskatchewan and an M.Sc. degree from Portland State University, both in electrical engineering. In his spare time, he enjoys back-country skiing in hip-deep powder, rock climbing on Rockies’ limestone, scrambling and mountaineering in local hills, and spending time outdoors with his young family. He can be reached at paul.perrault@analog.com.
Mahdi Sadeghi is a MEMS product application engineer in the AIN Technology Group at Analog Devices. He received his Ph.D. in electrical engineering from the University of Michigan, Ann Arbor, in 2014. His Ph.D. thesis and work as a research fellow at the Engineering Research Center for Wireless Integrated Microsystems (ERC WIMS) focused on the development of sensing microsystems for unmanned air vehicles and autonomous mobile platforms. His experience includes microhydraulic sensors and actuators, microfluidic systems, inertial sensing system design for wearables, and sensing solutions for condition-based monitoring applications. He can be reached at mahdi.sadeghi@analog.com.

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