Qualitative to quantitative sensor transition challenges

Examining several issues in light of current MEMS sensor design and use yields several directions to consider.

Dr David Hayner, Coherent Sensors -- EDN, November 22, 2011

The fall of the laptop

Consider an OEM’s plan to use a 3-axis accelerometer to measure the angular acceleration of a laptop. The concept is to use this information to determine if the laptop is falling, sliding or tipping off a table, prior to entering free-fall, and retract the head to protect the HDD (hard disk drive). This application of inertial sensors illustrates many of the challenges the MEMS vendor and OEMs will encounter as MEMS sensors are increasingly used in quantitative applications. To date, the vast majority of inertial MEMS sensor applications are qualitative in nature: portrait/landscape detection, gaming, tap/double tap, and even many auto uses. In these applications, the sensors are used to observe large scale events, not to measure and quantify. As MEMS sensors are increasingly used in quantitative applications, many new challenges will be encountered by both vendors and users.

The laptop example raises several issues:

• A single accelerometer could be aligned along a potential axis of rotation. There will always be the ambiguity of a set of acceptable linear accelerations “appearing” to be a critical set of rotations of the laptop. While a 3-axis gyro will not sense a fall, it will not confuse linear accelerations with specific sets of rotations. Perhaps the customer can work with changes in tilt vs time, but there is still the linear acceleration to rotation ambiguity. This ambiguity may be resolvable via the use of three or more 3-axis accelerometers or a 3-axis accelerometer, a 3-axis gyro and more sophisticated processing of all the signals.
• What are the bandwidths and dynamic ranges of signals critical to this function relative to the various disturbances? The device (the laptop) the sensors are there to protect is a potential source of interfering signals. Some of these are vibrations that may mask the signals critical to the tilt/rotation/fall detect functions. What sort of signals will the HDD, DVD/CD drive, keyboard or speakers generate and be sensed by the accelerometer? What sort of external signals will couple from the bus, train, aircraft or car the laptop is used in?
• How does the customer’s design and manufacturing process affect offsets, package stress, alignment, and mechanical and electrical coupling?

These questions, while not all strictly quantitative in nature, all drive towards a more precise understanding of the sensor and the totality of interactions with the product and the product’s environment. In this laptop example, a detailed understanding of disturbances and how they are transmitted to the sensor will be needed, the impact of these signals on the performance of the applications understood, and a host of design and manufacturing considerations taken into account by both the MEMS vendor and OEM user. The objective of this article is to examine several of these issues in light of current MEMS sensor design and use. From this, several directions will be identified that both the MEMS vendors as well as the user community will likely need to consider.

Just what is ODR?

MEMS sensor specs are full of references to ODR (output data rate). In many cases, a sensor’s bandwidth is specified as ODR/2 or ORD/4. Precisely, what is meant by these two statements? To the first statement, sensor data is placed in an output buffer at the rate specified by the ODR. Regarding the second, data bandwidth in the signal is equal to 0.5 or 0.25×ODR. While there may be information out to approximately ODR/2 or ODR/4, and this data may be an accurate measure of an inertial input, from a quantitative perspective, these implications are disingenuous. A typical assumption—and implication based on how bandwidth is specified as ODR/2—is data can be read from the sensor data buffer at rates less than the ODR rate of 400 Hz and the information content in the data, to a signal bandwidth of 200 Hz, is preserved. Figure 1 illustrates an example from a typical MEMS accelerometer driven with various mechanical oscillations.

The analog output MEMS sensor was originally sampled at 400 Hz with no significant anti-aliasing filter. A user reading data from the sensor at 400 Hz will accurately discern tones at 11 and 65 Hz. If the user reads data from the sensor at 100 Hz, however, the resulting data will represent a frequency response as illustrated in red in this figure. The 65-Hz tone is clearly aliased to 35 Hz in addition to other significant corruptions in the spectrum.

If the user wants to use data at 100-Hz SR (sample rate), the correct method is to read data from the sensor at 400 Hz, digitally filter (to anti-alias) and then decimate 4:1 to 100 Hz. Few sensor users have the ability to implement these techniques. Further, many appliance operating systems will not support user specified sample rates with guaranteed timing performance. Without this control, the data user does not know what they are getting and could not design an anti-aliasing system. The Android SensorManager spec simply states sensor data rates in terms of “as fast as possible,” “rate suitable for games,” etc. These are far from useful quantitative specifications.

Second, in stating a bandwidth, there is usually the implication of a 3-dB point followed by a specified roll-off of signal amplitude with frequency. This is typically at least first order (20 dB/decade), preferably higher. In stating bandwidth as ODR/2, it is impossible to have a 3-dB point. In stating bandwidth as ODR/4, what is the filter characteristic?

The Nyquist theorem states that the theoretical maximum represented frequency at a sample rate of X (Hz) is <X/2. Reality is quite a bit more severe. Perfect lowpass filters are quite rare. In fact, filters much beyond a second order (40 dB/decade) are uncommon in practice. Assuming a 400 Hz SR or ODR, (Nyquist = 200 Hz), a 20 Hz cutoff is required with a second order lowpass filter in order to realize 40 dB of attenuation of potentially aliasing signals by Nyquist. Using the typical MEMS specification convention, the corresponding signal bandwidth is ODR/20.

In order to realize a 20 Hz signal bandwidth and reduce aliasing, two options are: First, use a 20 Hz analog, second order lowpass filter on the analog continuous time output of the MEMS sensor, or second, oversample, digitally filter and decimate. In either case, die costs and/or power requirements are not moving in the direction desired in the large volume markets. The emphasis in MEMS sensor design to date has been on package size, bits, the ENOB (effective number of bits), SNR (signal-to-noise ratio), power and cost—not quantitative applications. A typical architecture common in the consumer MEMS industry is described and analyzed in the following sections. This architecture exacerbates quantitative value with additional aliasing problems.

Typical MEMS inertial sensor signal path

Illustrated in Figure 2 is a typical MEMS inertial sensor signal path. At a high level, the transfer function of the analog path, as illustrated in Figure 3, is a sinc² function followed by a 10 kHz lowpass anti-aliasing filter. A common view of this transfer function is that aliasing signals are attenuated before the ADC by a combination of the sinc² and anti-aliasing filters. In fact, the sinc² function and the anti-aliasing filter are both too little and too late.


To understand the process details, recall that aliasing is a result of the change from continuous time to discrete time. For a sampling rate, the highest unambiguously representable signal is <SR/2. The MEMS sensor is sampled by the switching in the C2V amplifier. The result is aliasing of raw sensor signals in the first step of the analog processing chain. The native mechanical bandwidth of MEMS sensors are typically in the 3-10 KHz range, with a second order roll-off after cut-off. Given the appliances in which MEMS sensors are typically employed, there is a great deal of potential signal energy in the 3-10 kHz range to be aliased.

Figure 4 provides the time and frequency response details for this sampling process. As a result of sampling at 4 kHz, all signals above 2 kHz are folded down into the 2-kHz passband. As a result of the finite time of the sampling interval, a sinc envelope function is generated. It is this envelope function generated by each of the sampling stages: C2V, gain stages and filtering that generate the sinc² or sinc³ transfer function of the sensor path. Recall that the sinc(x) function is sin(x)/(x). One derivation is via Fourier transforms of step functions in the frequency domain.

In Figure 4, folding frequencies are indicated by dashed vertical lines at multiples of 2 kHz. All frequency content above 2 kHz will be folded down. The critical interval is the frequency band out to about 30 kHz. Over this interval, the sinc function of the C2V amp only provides on the order of 1 dB of attenuation. There is virtually zero anti-aliasing filtering of the MEMS signal prior to sampling in the C2V amp. Vibrations, noise, good signals, bad signals: all the energy measured by the MEMS sensor between 2 kHz and 30 kHz is attenuated by at most 1.3 dB prior to folding into the passband.

The “anti-aliasing” filter illustrated in Figure 5 cannot fix the aliasing of the C2V stage. Arguments are made that this filter reduces noise folding or the impact of the averager/decimator. But with a cutoff of 10 kHz, this filter has little impact. In fact, simulations indicate that the AA filter can actually slightly degrade SNR.


Illustrated in figures 6 and 7 are Matlab/Simulink simulations of the C2V stage. The simulation of Figure 6 employed a sinusoid swept from 100 to 1000 Hz over a 1 second simulation. Sample rate modulated images of this signal are clearly indicated, together with the sinc roll-off. In Figure 7, tones at 2500 and 8200 Hz have been added to the swept input. The aliasing of these tones is clearly observable.



While this analysis was specific to a particular MEMS signal path architecture, the same arguments can be made for most sampled data front-ends in which anti-aliasing is not performed prior to any signal switching or sampling operations.

In the final step in the processing chain of Figure 2, the ADC output is “filtered” by an 8:1 averager and decimated to the ODR. The input to the ADC is effectively the signal illustrated in figures 6 or 7. Averaging filters are very inexpensive to implement and do provide some SNR improvement. The frequency responses of an 8:1 averaging filter and a second order Butterworth filter are illustrated in Figure 8. Anti-aliasing characteristics of the 8:1 averaging filter are poor. The result is continued folding of already aliased signals, and previously un-aliased signals, down into the 500-Hz wide-output passband.

Precision or accuracy

MEMS sensors have generally been designed more for precision and dynamic range than accuracy. Known performance over wide temperature ranges has been one driver. The ability of other system elements to account for, adapt to, or be insensitive to offsets and significant scale factor errors has enabled this approach. Cost has been a dominant concern, and accuracy is more expensive than dynamic range. In many of the current applications, dynamic range is more important. Quantitative applications will be much less forgiving. Take a simple navigation example using an accelerometer. Assume a perfect sensor, perfect 16-bit signal chain and ADC mapped into +/− 2Gs. Epsilon of less than 0.5 LSB is approximately 300 μm/sec² or approximately 31 μGs. Double integrate this undetectable acceleration for 10 minutes and the position uncertainty is 54 m!

Part of the precision problem stems from the use of voltage references as the internal measurement stick. With 5-25 ppm/°C of offset shift and 0.05% absolute accuracy, 12 bits of ENOB are about the limit. Somewhat independent of future precision requirements, substantial improvements in accuracy may well require a transition to architectures employing a time base as the internal measurement stick. Temperature-compensated oscillators can provide +/−1-ppm/year frequency stability over typical consumer and industrial application temperature ranges.

MEMS structures are critical to quantitative success. Structures which provide self-compensation over some fraction of the temperature range may be required. Open loop designs may need to transition to closed-loop systems in order to reduce noise and provide a more linear, and repeatable, measure. Typical wafer process variations can introduce large proof mass alignment offsets in accelerometers and large quadrature errors in gyros. Both of these limit precision and increase offsets. Compensation for these offsets, biases and interferers, often amplified by temperature effects, can be a limiting factor in device accuracy and performance over temperature. Closed-loop methods can reduce these impacts and provide a more consistent physical operating range for the device.

Disturbances and extraneous signals

In almost any practical implementation, there will be a variety of disturbance signals, both in and out of the baseband. With signal paths similar to that just described, the signal read from the MEMS sensor must be assumed to contain significant aliasing terms and is therefore of dubious quantitative quality. For the industry to address more sophisticated applications, four changes will be required. First, a more quantitatively accurate and consistent description of the data content generated by MEMS sensors is necessary. Second, this must be enabled by development of a non-aliasing and well-characterized signal path. The third critical part will be strategies to address and account for a variety of disturbances, including package stress. Fourth, the drivers of the operating systems that read these devices must provide a well-defined and time-base-driven sampling process.

Given a perfect MEMS sensor, only a small fraction of the quantitative challenge has been addressed. Handling of extraneous signals, managing their impact on the sensing device and accounting for, or designing around the residual’s impact on the application are typically the larger challenges. Extraneous signals manifest themselves in dramatic and simultaneously, sometimes subtle, ways. For instance, high frequency signals can be aliased and appear as an offset or a low frequency drift component. This section will review several of the potential sources, impacts and mitigation strategies for dealing with extraneous signals. In general, this article will not address sensor cross-coupling, g or g² sensitivity of gyros or related device aniso-sensitivities of either class of device.

A general process for assessing and quantifying the system and environmental impacts on the sensor system is outlined in the following paragraphs.

A first step is to quantify the signal requirements and sensitivities of the various applications relative to the sensor data required. Signal outputs from a sensor that is an interferer to one application may well be a critical signal component in another application. This spectrum allocation process often reveals contradictions or key sensitivities in the data required by the applications. This is a critical first step in the overall sensor selection, and design of the sensing structure, alignment and methods.

The second step is data collection on real platforms in functional, operational conditions with the sensors and all major elements represented in the structure as intended for final use. This step can be particularly time consuming. In addition to expected inputs, it is critical to include as many extraneous signals to the system as possible—both singularly and in combinations. Good customer use models are critical in driving this data collection effort to capture how users will employ the product and the environments it will be used in. Good policy includes using several standard classes of inputs not in the user model as a check on under-specification.

Next, nalysis of the sensor-generated data and comparison to the spectrum allocation maps will provide the means to determine appropriate mitigation strategies. Often conflicts are encountered at this stage. Once the sensors, the good signals and interfering signals are aligned with the applications, mitigation strategies can then be addressed. Again, conflicts may arise and iterations in the allocation, sensor selection, placement processes or applications may be required.

Finally, analysis of application performance relative to the disturbances must be completed. Is continuous operation required or can an application be switched off or be conditioned during certain periods of interference? Does the application need to operate effectively despite the presence of the interfering signal? Which interfering signals can be tolerated? What is the impact of a specific application failing given specific disturbances?

A stabilized platform example

A stabilized platform containing rate gyros could not be perfectly balanced. As a result, typical carriage inputs caused a low frequency roll component below the gyro threshold. An external vertical sensor and an angular resolver are added to the system to null the roll. In this case, there was a conflict in gyro specs. A gyro that could sense the low roll rate did not have the bandwidth required to meet residual rate specifications. This example illustrates several options. Change the mix, position, number or types of the sensors, and/or modify one or more applications to accommodate.

The types of disturbances encountered tend to be specific to the appliance and environment. An incomplete list of disturbance sources:

• Mechanical vibration: Typical sources are rotating machines, linear motors (speakers).
• Non-ideal motions: An example is a linear motor with unintentionally curved guides.
• Thermal: Thermal shocks; different CTEs can be significant. Temperature gradients across the sensor are often ignored (see sidebar: Thermal sensitivities).
• Shocks and impulses: These are short term, broadband energy inputs.
• Electrical: Switch mode power supplies, system clocks, power switching systems.
• Background Noise: Road noise, bearing noise, non-laminar fluid flows, audio signals.

There are several methods for eliminating, or at least mitigating, the effects of disturbances. Some of these include:

• Isolation at the source: Use of dampers, placement techniques, baffles, etc, to minimize coupling of disturbance signals to the sensors. Highly recommended.
• Electronic Filtering: Notch filters can be effective in eliminating the signals from rotating machines. More generally, adaptive filters can be effective in this scenario.
• Closed-loop designs for the sensor: Often recommended for dealing with large shocks or impulses with broadband signal structures.
• Algorithm Modifications and/or use of complementary inputs.
• Isolation at the sensor: Use sparingly. Signals that are disturbances to some applications may well be critical signals to other applications. Further, since most MEMS sensors are soldered onto PCBs, this can be difficult to achieve.
• Electrical signals: Decoupling circuits, sensor system design, shielding, board layout.

Continued fall of the laptop

In the laptop example at the beginning of this article, the data bandwidth on which this application will depend is relatively low frequency—tilt changes preceding a fall will likely occur in the sub-2-Hz range. For a 7200 RPM disk drive, the base rotational rate (120 Hz) may well fall into the sensor passband, but out of the application passband. As a result of the specific balance of the disks, bearing wear, etc, frequencies could be at various harmonics of 120 Hz and could be aliased into the application passband. While the tones from the HDD will likely be relatively stable in frequency, those from the ODD (optical disk drive) will not. Two things to consider: Are the disturbing signals large enough to make detection of signals relating to tilt difficult to resolve? Is one of the spindle frequencies at a value that can fold to near DC? In the first case, notch filters may well be the direction to take if the signals are large enough to impact operation of the required algorithms. In the second case, the customer may need to provide physical isolation of the HDD and/or ODD at the critical frequencies that alias to the application passband.

The head actuator may be another disturbance source. These impulses can couple in a variety of mechanisms and generate energy over a wide range of frequencies. These impulses are generally sufficiently short in time to possibly not impact the algorithms but testing will be required. If they do interfere, the likely best route is to mount the drive in such a way to minimize transmission of these signals into the rest of the system.

Speakers are a major challenge. They generate wideband signals, from device passband into aliasing frequencies; they can be large signals and they are transient. Many structures in the appliance can resonate or be a source of coupling of these signals to the sensor. In an interesting recent example, a consumer gyro, fixed in rotation and translation, was exposed to a speaker at approximately 1 ft. Coupling was strictly via compression waves in the air. Speaker volume was conversational speech. As the frequency input to the speaker was swept, signals in the 3.5 kHz to 4.5 kHz audio range were somehow coupled into the gyro mechanics and then aliased to the 8-25 Hz range. The amplitude of the aliased signal was +/−20 counts, or approximately 5 bits. The best solution may be to disable the speaker when certain functions are active. The second option is careful sensor placement and possible case and mechanical PCB design modifications.

Keyboards and keypads can generate low frequency inputs together with highly variable impulse structures. Mechanical decoupling can be difficult in small handheld devices but may be an option in the laptop example. Use of a gyro to detect the rotation prior to a fall then switching to the use of accelerometers to detect free fall may be an option. The user is not likely typing on the keyboard while the device is in free fall.

One concept is to add an airbag to each of these tablets, notebooks and smartphones. In the event of a fall, encase the device in a soft shell. One can only imagine the turmoil on the nerd-bird between Austin and San Jose after encountering some mid-air turbulence if disturbances are not handled adroitly.

Summary of current state

Despite the potential for aliasing, large and time varying offsets and scale factor changes, inexpensive MEMS sensors are enjoying huge success. They provide functionally useful measures of human, machine and environmental inputs. Consider an accelerometer used in a cell phone for detecting a “tap.” The input is a short-lived and complex set of accelerations dependent on a number of items—from how the user held the device, to what they tapped it with, to where they tapped it, to the detailed mechanical design of the cellphone. The app developer wants all of this variability to disappear. To maximize the detectability of the tap over as wide a range of variables as possible, a good strategy is to dump all the input energy input into the passband in a simple and repeatable manner. A heavily aliasing system will do this well. This argument can be extended to a wide range of useful functions. Application developers (and OS vendors) desire their software to be sensor and platform independent in order to maximize their revenue. The more all sensors mush inertial inputs in reasonably similar manners, the more the data looks the same independent of the sensor and platform (and unknown sample rate). In these cases, aliasing is less an enemy and, to some parties in the ecosystem, a friend. This simplistic approach will be seriously challenged by the needs of quantitative applications.

Recommendations

This article has reviewed several challenges in the migration of MEMS sensors from qualitative to quantitative applications. These include better understanding (and documentation) of the time dependence of output data from the sensors. In many cases, OSs will need to provide a more specific, controllable and precise interface to sensor data.

Front-end signal processing designs will need to significantly mitigate aliasing. Approaches include the use of anti-aliasing filters, possibly with package pins for external caps. A system employing a high oversampling rate followed by digital filtering and decimation is another option. These modifications will also significantly impact sensor bandwidth and SNR concerns. Alternate topologies could help provide the means to differentiate on precision vs accuracy. A large number of MEMS sensor architectures currently employ a voltage reference as the sole reference in the device. High performance inertial sensors typically employ very accurate time bases as the internal reference source.

In quantitative applications, effectively addressing various sources of disturbances is often 90% (or more) of the solution. This is not strictly a vendor or OEM challenge, but rather one that both will need to work together, more closely than likely accustomed, in order to solve these problems. OEMs will need to provide a great deal more information on the use case, device models, environments, etc than they are typically comfortable providing. MEMS sensor vendors will need to develop a much deeper understanding of the realities of how their sensors actually behave in practical applications, and provide this knowledge to their customers. There will be cultural and organizational challenges on both sides. From personal experience, ignore these at your peril.

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Author’s biography
David Hayner works for Coherent Sensors where he consults in MEMS sensor architecture, design and general sensor applications. He has developed servo solutions for products ranging from hard and optical disk drives, to diesel engine control, adaptive optical sensing systems and stabilization of imaging reconnaissance platforms. He has a PhD from the University of Illinois (Urbana, IL).

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