MEMS accelerometer calibration optimizes accuracy for industrial applications

By Randy Carver and Mark Looney Analog Devices - October 27, 2007


MEMS inertial-sensors technology has been driven by automotive safety systems; as such, the technology has been applied to several high-volume applications. The large volumes associated with automotive safety systems have enabled substantial investment in MEMS manufacturing technology, packaging concepts, quality assurance systems, and innovative design approaches.

This has resulted in cost-effective, reliable solutions that are gaining interest in many other market segments as well. These include gaming consoles (Wii Remote) and a variety of mobile-handset applications.

In addition, MEMS sensors are finding their way into an increasing number of industrial applications, including workplace safety systems. Equipment position sensing, impact detection, and roll-over prevention for lift trucks are examples of workplace safety systems that benefit from MEMS accelerometers.

Workplace safety systems are tasked with detecting potentially dangerous operating conditions without impacting normal operation. One of the primary factors in this process is the accuracy of the sensing solution used to detect the dangerous operating conditions. As with most technology solutions, MEMS accelerometers have a trade-off relationship between cost and performance.

For applications such as automotive and commercial, adequate performance at the lowest cost possible is sufficient. But industrial applications, such as workplace safety systems, require higher accuracy. In such cases, reliability, convenience, and component costs of these solutions are critical.

With the introduction of higher integration and more accurate accelerometer products, system designers still have a need to understand how parts are calibrated; this allows them to decide whether to purchase this capability or develop their own calibration routines. This article outlines the calibration process used for a dual-axis accelerometer and highlights its most common error sources.

CALIBRATION " PURPOSE AND VALUE For many MEMS inertial sensor consumers, calibration provides opportunity to trade system cost for improved accuracy in their sensing solutions, as shown in Figure 1. While the relationship in this graph is generic, the performance goals are generally driven by end-system performance requirements that add value for the customer.

For example, greater accuracy means the roll-over prevention system does not need to overcompensate when determining the limits on a lift truck. Optimized accuracy levels can enable a crane to serve a larger area, or handle heavier loads, without the threat of tipping. The bottom line is that optimizing performance in safety sensing systems will add to the value to the overall solution.


The cost increase associated with calibration includes both direct material costs (ADC, microcomputer, extra PCB complexity, labor), and investment costs (calibration fixtures, R&D engineering) that can be amortized over the anticipated volume of systems produced. The obvious goal of any calibration process is to achieve valuable performance levels, while managing the associated costs.

The difference between a well-executed calibration process and a less-effective one is illustrated in the performance vs. cost curves shown in Figure 1. Diligence in identifying and mitigating risk will determine what a given level of performance improvement will cost. It only takes one mistake to move from blue to red!

Developing a MEMS calibration solution can broken down into four simple steps: 1. Establish performance goals. 2. Determine calibration requirements. 3. Design calibration process. 4. Implement correction formulas. Design goals
Establishing valuable performance goals for an accelerometer calibration sets the tone for the entire development process. First, these goals will guide sensor selection. Second, they will guide the analysis process, which will determine the behaviors that need correction, and, ultimately, the complexity of the calibration process. This is critical, because the temptation to ask for more than what is necessary can cause cost over-runs and schedule delays.

This, obviously, requires the developer to have an early understanding of how the accelerometer sensing system will affect the final system's performance goals. Although this early investment in time may seem inconvenient, it will likely lead to better performance and create opportunities for further innovation. This discussion highlights areas for consideration when the calibration must achieve a composite error of 1%.

Error sensitivity analysis A typical circuit for providing calibrated accelerometer performance looks like the diagram in Figure 2. The error analysis determines the impact each component will have on the overall system-accuracy goals. Each of these components will have behaviors that need to be considered. In addition to the MEMS accelerometer, the amplifiers, A/D, multiplexer, and passive components will exhibit their own offset, gain, noise, linearity, power supply and temperature dependent behaviors that need to be carefully considered and added to the sensor's performance.


Figure 2. Typical Calibrated Accelerometer Circuit

This section identifies the common threats to the stated performance goals, and shows how to quickly determine their impact, while avoiding a detailed circuit analysis. For simplicity, this sensitivity analysis focuses on a sensor's performance. The contribution of the remaining circuit elements will be assumed to be minimal for this discussion. The ideal equation for any linear sensor, including a MEMS accelerometer is


IEEE-STD-1293-1998, Appendix K, offers a comprehensive modeling approach for describing the error behaviors in a typical MEMS accelerometer. The following equations offer a simple relationship to describe the impact of many common errors:


The sensor signal conditioning circuit will contain several components that can influence this equation. Here is a partial list of common error sources in these types of components:

1. MEMS Accelerometer 2. Amplifier 3. Passive components 4. A/D

Each of these components will contribute to the sensitivity (gain), bias (offset), linearity, noise, power supply dependent behaviors, and temperature dependent behaviors. As the point of discussion here is calibration, the focus will be on the sensor. The principles illustrated can be applied to the rest of the circuit as well.

With composite error goal of 1% in mind, we can quickly review the specifications of the available MEMS sensors. For example, a leading accelerometer can be evaluated as follows:

Table 1. MEMS Accelerometer Sensitivity Analysis Parameter Performance Notes

Sensitivity +950mV/g to +1050mV/g Equates to 5%

Offset 30mg (typical)

100mg (maximum) 3% for 1g system

10% for 1g system

In this example, the calibration procedure must account, primarily, for bias and sensitivity, which both exceed the 1% composite error goal. Calibration Design
One reliable source of stimulus for low-g accelerometer calibration is gravity. The simplest means of using gravity is through the use of the industry standard tumble test, which has been documented in IEEE-STD-1293-1998. Tumble tests are used in applying an external stimulus varying between +1 g to the device under test (DUT).

This low stimulus level restricts the use of the tumble test to accelerometers with full-scale ranges of less than 20 g, based upon the need for the calibration stimulus to equal 5% or more of the full-scale range.

Beyond this range, linearity, resolution, noise and other range-dependent behaviors will become more influential and impede the process of achieving the desired accuracy levels. Restricting the full-scale range allows the basic 4-point tumble test to be used for calibration purposes, rather than the multi-point tumble test, which allows for the calculation of linearity errors.


Figure 3. Four-Point Tumble Illustration

A simplified diagram of the 4-point tumble test is shown within Figure 3. Here, the device under test (DUT) is vertical. The X-axis of the DUT is oriented along the horizontal axis for 0° inclination. The X-axis output of the DUT is recorded. The DUT is then rotated 90°, 180° and finally 270° with the output of the X-axis being recorded at each of the four measurement positions.

As the DUT is rotated, the X-axis sensor's output will be a sinusoidal function, with respect the incline angle, as shown in Figure 4. The difference between the actual and ideal curves is due to the accelerometer's offset and sensitivity errors. By taking data at each 90° increment, these behaviors can be characterized and isolated.

The offset of the overall sinusoid can be calculated by averaging the 0° and 180° points. Subtracting the 270° data point from the 90° data point provides a measure of the accelerometer output for the 1 g stimulus provided by gravity.


Figure 4. Four Point Tumble Data Output


These relationships depend on perfect alignment at the 0°, 90°, 180°, and 270° positions. They also depend on perfect vertical alignment for assurance of a full 1 g stimulus.

Measurement Sensitivity Since "perfection" is neither practical nor affordable, it is important to understand the sensitivity to each potential error that can be introduced by the calibration system itself. Determining the impact of each error influence will help mitigate risk against critical performance criteria.

Initial Alignment Angle Absolute angle refers to the starting position. This error in start position will impact the sensitivity, but not the offset. The impact of this behavior can be isolated from the other sensitivities and described by the following equation:


For a sensitivity error of 1%, the initial alignment error must be less than 8°. If the sensitivity error is more aggressive, say 0.1%, the initial alignment error must be less than 0.8°. The absolute angle has an equal, but opposite, effect on the acceleration measurements at 0° and 180°, so this alignment error does not affect the offset. This is one advantage of using a 4-point measurement approach. Once the actual offset is known, the initial alignment error can be calculated:


If the sensitivity accuracy goals require this, the calculated alignment error can be plugged back into the error equations above and used to scale the correction factors accordingly. This relationship relieves the pressure of having the initial starting point at exactly 0°. Relative Alignment Error
The relative alignment error is defined as the deviation from the ideal 90° step size between each measurement step. The offset calibration will experience greater sensitivity to this error. The offset error introduced by the alignment error can be calculated using the following relationship:


For an offset accuracy goal of 1%, or 10 mg for a 1 g range application, the alignment must be better than 0.57°. For an offset accuracy goal of 0.1%, or 1 mg, the relative alignment must be better than 0.057°. Although the initial alignment angle can be readily accounted for, the relative angle sensitivity requires strict positional control for high-accuracy calibration.

Off-Axis Tilt Off-axis tilt error is the amount of change in the axis of rotation, with respect to the horizon. If the rotational apparatus is perfectly vertical, then the axis of rotation is perfectly horizontal. Off-axis tilt will impact the sensitivity error in a manner that is very similar to the initial alignment impact.

Gravitational Acceleration Variation Caution is warranted here since the ideal 1 g external stimulus may not exactly be 1 g. It more accurately reflects twice the local gravity, which can vary from the ideal gravity based upon latitude, elevation above sea level, lunar-solar gravity fluctuations, and large nearby masses.

Mechanical Vibration Vibration of any kind can translate into linear acceleration and introduce errors into the calibration process. Mechanical isolation, using a granite block or air-isolated table structure, will help and digital filtering of the data can help remove some artifacts of vibration as well.

Accelerometer Sensitivities The two most common conditions that influence accelerometer behavior are power supply voltage and temperature. The four-point tumble can be used to characterize the accelerometer's behavior over anticipated supply and temperature ranges as well. The linear approximation approach requires that the four-point tumble data be taken at the extremes (minimum and maximum) for each parameter.

These data can be used to extrapolate incremental correction factors, based on accuracy requirements. If nonlinear behaviors are observed, more data points can be added, along with increasing the order of the curve fitting.

Power Supply Some accuracy requirements will drive the need to characterize the influence of power supply variation. If these behaviors need calibration attention, the same four-point tumble test can be used at different supply levels to gather the data required for the appropriate curve-fitting operation.

The complexity of the curve fit will be dependent on the accuracy goals and the nature of the errors themselves. The result will be a set of calibration coefficients for each power-supply condition.

Temperature In order to maintain a 1% error due to thermal variation, the temperature coefficients for sensitivity and offset should be considered.

Sensitivity = 0.3% (typical, "40°C to +125°C) Offset = 0.1mg/°C (typical)

For a quick estimate, these values can be doubled (2 assumption) and combined as follows:

Composite error for temperature:


If the maximum acceleration measurement level is 1g, then this ratio can be used to calculate how wide the temperature can vary, while maintaining the 1% composite thermal error goal:


The relative alignment error is defined as the deviation from the ideal 90° step size between each measurement step. The offset calibration will experience greater sensitivity to this error. The offset error introduced by the alignment error can be calculated using the following relationship:


For an offset accuracy goal of 1%, or 10 mg for a 1 g range application, the alignment must be better than 0.57°. For an offset accuracy goal of 0.1%, or 1 mg, the relative alignment must be better than 0.057°. Although the initial alignment angle can be readily accounted for, the relative angle sensitivity requires strict positional control for high-accuracy calibration.

Off-Axis Tilt Off-axis tilt error is the amount of change in the axis of rotation, with respect to the horizon. If the rotational apparatus is perfectly vertical, then the axis of rotation is perfectly horizontal. Off-axis tilt will impact the sensitivity error in a manner that is very similar to the initial alignment impact.

Gravitational Acceleration Variation Caution is warranted here since the ideal 1 g external stimulus may not exactly be 1 g. It more accurately reflects twice the local gravity, which can vary from the ideal gravity based upon latitude, elevation above sea level, lunar-solar gravity fluctuations, and large nearby masses.

Mechanical Vibration Vibration of any kind can translate into linear acceleration and introduce errors into the calibration process. Mechanical isolation, using a granite block or air-isolated table structure, will help and digital filtering of the data can help remove some artifacts of vibration as well.

Accelerometer Sensitivities The two most common conditions that influence accelerometer behavior are power supply voltage and temperature. The four-point tumble can be used to characterize the accelerometer's behavior over anticipated supply and temperature ranges as well. The linear approximation approach requires that the four-point tumble data be taken at the extremes (minimum and maximum) for each parameter.

These data can be used to extrapolate incremental correction factors, based on accuracy requirements. If nonlinear behaviors are observed, more data points can be added, along with increasing the order of the curve fitting.

Power Supply Some accuracy requirements will drive the need to characterize the influence of power supply variation. If these behaviors need calibration attention, the same four-point tumble test can be used at different supply levels to gather the data required for the appropriate curve-fitting operation. The complexity of the curve fit will be dependent on the accuracy goals and the nature of the errors themselves. The result will be a set of calibration coefficients for each power-supply condition.

Temperature In order to maintain a 1% error due to thermal variation, the temperature coefficients for sensitivity and offset should be considered.

Sensitivity = 0.3% (typical, "40°C to +125°C) Offset = 0.1mg/°C (typical)

For a quick estimate, these values can be doubled (2 assumption) and combined as follows:

Composite error for temperature:


If the maximum acceleration measurement level is 1g, then this ratio can be used to calculate how wide the temperature can vary, while maintaining the 1% composite thermal error goal:


Implementation
It is possible to apply correction factors calculated during this calibration process to many digital platforms. . Examples include micro-controllers (C), digital signal processors (DSP), field programmable gate arrays (FGPA), and other programmable logic devices. The processing resources required for the correction formulas might influence processor selection, but in many industrial systems, processors have other requirements that may be more demanding. The math required for the correction is relatively simple: (1) remove the offset/bias errors using an add operation and (2) remove the scale errors using a multiply operation.

While in service, industrial systems experience changes in operating conditions that can influence the bias and sensitivity behavior in MEMS accelerometers. The most common conditions that influence these behaviors are power supply voltage and ambient temperature. Power-supply voltages can change by as much as 10% and each industrial system will have its own temperature range requirements.

If these conditions cause greater variation than the system performance goals will allow, then the four-point tumble characterization will need to be performed over multiple conditions, to map the error behaviors and developer table of calibration coefficients. The final implementation of these coefficients will look like the diagram in Figure 5. The calibration tables in this case have three variables, including a set for an extra condition, which could be for frequency response or a variety of other conditions.


Figure 5. Calibration Signal Flow

CONCLUSION One of the most critical factors in deploying a calibrated accelerometer function is the establishment of valuable performance goals. Given the risk areas identified and discussed in this article, developers have an awareness that calibration is not free, but still have great opportunity to add value, if the end goal is clearly established.

Developing performance goals expands thinking beyond "engineering capability" into the realm of schedule risk (lost revenue), performance risk (failed customer expectations), and cost overruns (lost market share). Even a basic understanding of performance impact, along with the required investment for achieving that performance through calibration, will equip engineers to make better integration decisions, as they ponder the everlasting question of: make vs. purchase.

Is the assumed risk of developing a custom calibration system and process worth the anticipated improvements in either cost or performance, in comparison with an off-the-shelf solution, such as Analog Devices' ADIS16201 fully calibrated dual "axis, accelerometer/inclinometer? The principles illustrated within will help answer that question for each individual situation.

About the authors

Mark Looney is the iSensor Application Engineer for Analog Devices . He earned a MSEE from the University of Nevada in 1995. ( mark.looney@analog.com )

Randall Carver, P.E., is a staff design engineer at the Multichip Products Business Unit of Analog Devices in Greensboro, NC. He earnedi a BSEE degree from the University of Tennessee. ( randy.carver@analog.com )