Optimizing high precision tilt/angle sensing: Accelerometer fundamentals

Accelerometers are marvelous sensors that enable the sensing of static and dynamic accelerations as varied as the orientation with respect to gravity to the subtle motions of bridges beginning to fail. These sensors range from cell phone-grade devices that change the orientation of your display when you tilt them to export-controlled, tactical-grade devices that help to navigate military vehicles or spacecraft.[1] However, as with most sensors, it’s one thing for the sensor to perform well in the lab or benchtop. It’s quite another to get that performance at the system level in the face of environmental and temperature stresses that are wild and uncontrolled. When accelerometers, like humans, experience unprecedented stress in their lifetime, the system may react and fail due to effects from these stresses.

High accuracy tilt sensing systems are generally calibrated to achieve tilt accuracies better than 1°. Utilizing market-leading ultralow noise and highly stable accelerometers, such as the ADXL354 or ADXL355, one can achieve tilt accuracy of 0.005° with proper calibration of observable error sources.[2] However, this level of accuracy can only be achieved if stresses are properly mitigated. For instance, compressive/tensile stresses on the sensor can cause offsets as large as 20 mg, and thus tilt inaccuracies over 1°.

This article series reviews the performance metrics of a high precision angle/tilt sensing system using accelerometers. We’ll start in this article with an understanding of the sensor design itself at the microscopic level in order to better understand the effects of stresses and strains down to the micron level. In a separate article, we’ll then cover some surprising results that can happen if a holistic mechanical and physical design approach is not followed. Finally, we’ll close this series with tangible steps designers can take to maximize performance in the most demanding applications.

Fundamentals of Sensor Design

MEMS-based accelerometers can run the gamut in price and performance from consumer products to military sensing. Today, the best performing low noise accelerometers enable applications like precision tilt sensing, seismic imaging, and many emerging applications in robotics and platform stabilization. Important capabilities for high precision tilt/angle sensing applications include excellent noise, offset, repeatability, and temperature-related offsets, as well as second-order effects like vibration rectification and cross-axis sensitivity.

To better understand the design considerations for a 3-axis high precision MEMS accelerometer to perform optimally, it is educative to first review the internal structure of such a sensor, which will clarify the reason the three axes produce different responses to environmental parameters (for example, out-of-plane stress). In many cases, this out-of-plane stress is caused by a temperature gradient across the z-axis of the sensor.

The accelerometer shown in Figure 1 consists of a spring mass system, similar to many other MEMS accelerometers. The mass moves in response to an external acceleration (static acceleration like gravity or dynamic acceleration like velocity changes) and its physical displacement is sensed by a transduction mechanism.

click for full size image

Figure 1. Sensor architecture of a 3-axis high precision MEMS accelerometer, specifically the ADXL355 from Analog Devices. For the X/Y sensor, as the proof mass moves, the capacitance between the anchored fingers and the fingers attached to the proof mass changes. The imbalance of mass on the z-axis sensor allows for out-of-plane sensing of z-axis acceleration. (Source: Analog Devices)

The most common transduction mechanisms in MEMS sensors are capacitive, piezoresistive, piezoelectric, or magnetic. An accelerometer like the ADXL355 utilizes a capacitive transduction mechanism, in that a movement is sensed by a change in capacitance that, through a readout circuit, is converted to voltage or current output. Although the ADXL355 utilizes the capacitive transduction mechanism for all three axes sensors on a silicon die, X/Y sensors and Z sensors have two fundamentally different capacitive sensing architectures. X/Y sensors are based on differential in-plane fingers, while a Z sensor is an out-of-plane, parallel plate capacitive sensor, as shown in Figure 1.

If there is either compressive or tensile stress on the sensor, the MEMS die warps. Since the proof mass is suspended over the substrate with springs, it does not warp in tandem with the substrate, and, therefore, there will be a change in the gap between the mass and the substrate. For X/Y sensors, the gap is not in the direction of capacitive sensitivity, as the in-plane displacement has the largest impact on the capacitance change for the fingers. This is due to the compensating effect of the fringe electric field. For the Z sensor, however, the gap between the substrate and the proof mass is indeed the sense gap. Therefore, it has direct impact on the Z sensor since it effectively changes the sensing gap for the Z sensor. Another exacerbating effect is that the Z sensor is located in the center of the die, where the warpage is maximized for any given stress on the die.

In addition to the physical stresses, temperature gradient across the z-axis sensor is common due to the heat transfer asymmetry in the z-axis in most applications. In a typical application, the sensor is soldered to a printed circuit board (PCB) and the entire system is within a package. The X and Y heat transfer is dominated by conduction through the solder joints in the perimeter of the package and to the PCB, which is symmetric. In z-direction, however, the heat transfer is through conduction at the bottom due to solder and convection on top of the die as heat moves through the air and out of the package. Due to this mismatch, there will be a residual differential temperature gradient across the z-axis. Just as with the physical compressive/tensile stress, this will yield an offset in the z-axis that is not induced by acceleration.

In the next article in this series, we 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.


^[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.

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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Original article: Optimizing high precision tilt/angle sensing: Accelerometer fundamentals
Author: Paul Perrault and Mahdi Sadeghi