Sensors - June 2001 - A Micromachined Thermal Accelerometer

A Micromachined
Thermal Accelerometer

for Motion, Inclination, and Vibration Measurement

Thermal-based accelerometers offer designers a way to reduce system cost, size, and complexity.

A novel accelerometer based on thermal convection has only one moving element—a tiny bubble of heated air hermetically sealed inside the sensor package cavity. When an external force such as motion, inclination, or vibration is applied, the bubble moves in a manner analogous to the bubble in a spirit level. The change of state develops a signal that is amplified, conditioned, and output as either a ratiometric or an absolute voltage.

Photo 1. The package and die of a single-axis accelerometer can be seen in this cutaway view.

Physical Configuration
A shallow trench is micromachined into the sensor’s silicon substrate and an air cavity is formed in the top of the package (see Photo 1). A heater bar consisting of a silicon resistor is suspended across the trench. Two uniformly spaced thermocouples are positioned on either side of the heater. The configuration is, in fact, similar to that of a Wheatstone bridge. Any variation in temperature between the two thermocouples creates a differential signal that is amplified and otherwise conditioned according to the requirements of the application.

Operating Principle
Because the cool air around the bubble is denser than the warm air over the heating element, any change in the sensor’s motion and/or

Figure 1. In the unpowered (i.e., unheated) thermal sensor, no heated gas is developed. The X,Y axes are used here as a reference (A). The sensor components are shown in (B). Figures 1-4 by Clark Linehan, courtesy of Memsic Inc.

Figure 2. When the device is powered, but with no acceleration or tilt applied, the warm air produces a temperature gradient between the heater and the thermocouples forming the sensing elements. In this state, the temperataure on both sides of the X,Y profile is equal (A). The bubble of heated air is centered on the heater bar (B).

Figure 3. Acceleration causes the heated air to move in the same direction as the applied force, inducing a temperature differential, DT, between the thermocouples (A). An onchip differential amplifier develops a signal from the movement of the heated bubble, which moves in the direction of the acceleration (B).

Figure 4. As the acceleration increases, so does the temperature differential (A). Also, larger tilt angles have the same effect; the bubble can be seen moving farther to the right around the cavity and trench (B).

orientation causes the cooler air to force the heated bubble toward the end of the package cavity in the direction of acceleration. This movement creates a temperature differential in the vicinity of the two thermocouples. Amplifying this difference produces an output signal that characterizes both the nature (e.g., shock or tilt) and the direction of the applied force. The direction may be either horizontal (acceleration or deceleration, for [xample) or vertical (inclination/tilt angle relative to the Earth’s gravitational field).

The sensor’s operation is shown in Figures 1–4. The sequence begins with an unpowered sensor. Figure 1A is an X,Y chart of temperature vs. distance with the heater bar as a reference point and with no power applied (i.e., no heating). This corresponds to the sensor’s components in Figure 1B.

Powered Sensor (No Acceleration)
The temperature/distance profile in Figure 2A shows the peak temperature directly above the heater with no acceleration or tilt. This creates a bubble of heated air centered on the heater element (see Figure 2B). Per Figure 2A, both temperature sensors aÄe at the same temperature, and no differential signal is developed. However, the temperature gradient becomes paramount to the convection transfer when either acceleration or tilt is introduced.

Powered Sensor (Acceleration Applied)
Figure 3A illustrates the resultant temperature differential (°

t) as acceleration (deceleration) is applied. The asymmetrical temperature profile occurs as the cooler air forces the heated air in a left-to-right direction. The higher density cooler air in the cavity shifts the bubble and develops a temperature differential that affects the thermocouple resistances, and this imbalance (when amplified, etc.) produces a usable output signal proportional to acceleration or tilt (see Figure 3B).

Figures 4A and 4B represent a larger differential caused by a greater acceleration or tilt angle. Per Figure 4B, the bubble of heated air has been displaced farther to the right as the deceleration or gravitational forces are increased.

Signal Conditioning and Programmability
Onchip signal conditioning and programmable functions minimize the sensor’s parametric tolerances. Onchip programmability serves to tighten sensitivity, zero-g bias level, offset, and output, as well as to select a ratiometric or an absolute output. The device chosen for this discussion has an absolute value output. The ability to factory-program critical device parameters after packaging translates into customizing sensor characteristics to customer needs, but without the additional logistics, cost, and other concerns associated with handling and inventorying multiple devices. Tighter circuit parameters facilitate system designs and expedite product development and fabrication cycles when compared to board-level implementations.

Thermal Accelerometer Characteristics and Limits
Understanding the basics can be vital to incorporating these sensors into a new design. A listing of important sensor parameters is given in the sidebar, “Thermal Accelerometer Characteristics and Limits”.

Competing Accelerometer Technologies
Although the principles of convection sensing are not new, practical applications had to wait for the development of hybrid (bulk and surface) micromachining derived from submicron CMOS technology. Implementing signal conditioning circuitry on chip is feasible with thermal and capacitive sensors, but most others (especially older technologies) mandate board-level circuitry to provide basic amplification and other tasks. The benefits of mixed-signal (analog and digital) circuitry, programmability, and customization are evident to users of newer, smart sensors. Many older technologies involve discrete accelerometer elements in their overall design. These generally add cost and complexity, and adversely affect system dependability, size, and reliability.

TABLE 1
Comparison of Accelerometer Technologies
Basic Technology		Piezo- electric	Piezo Film	Liquid Tilt	Electro- mechanical Servo	Bulk Micro- machined	Surface Micro- machined	Thermal Bulk/Surface Micro- machined No Proof Mass
Cost Factor		High	Low	Low	Highest	High	Low	Lowest
Resolution		2.5 mg	2.5 mg	0.5 mg	20 µg	0.05 mg	0.25 mg	0.5 mg
Perfor- mance	DC/Tilt	No	No	Yes	Yes	Yes	Yes	Yes
Perfor- mance	Typ. freq.	20 kHz	20 kHz	10 kHz	20 kHz	400 kHz	400 kHz	100-150 kHz
Dual Axis		No	No	No	No	No	Yes	Yes
Integrated system		Board	Board	Board	Board	No	On chip	On chip
Onchip signal processing		No	No	No	No	No	Yes	Yes
Onchip program- mability		No	No	No	No	No	No	Yes
Mixed-signal expandability		No	No	No	No	No	No	Yes
Self-test capabilities		No	No	No	No	No	On demand	Yes (continuous)

It should be noted that the types listed as Yes under DC/Tilt can be used as inclinometers to measure tilt angle. Because these applications are becoming very important, more definitive discussion on tilt angle follows. Capacitive technology dominates impact sensing at present, but the escalating demand for lower cost sensors is focusing attention on newer thermal devices.

Essential Thermal Accelerometer Parameters
Deciding whether a thermal accelerometer/inclinometer is suitable for a given application entails an examination of several MEMS parameters, along with the specific design prerequisites. These include operating voltage range (plus tolerance), operating temperature range, frequency response, sensitivity, and zero-g level (offset).

Operating Voltage Range (Plus Tolerance). Although the supply voltage range is listed as 2.7–5.25 V (and some specifications allow a ±10% tolerance), exploiting a 5 V (<<5%) fixed regulator shrinks the zero-g level tolerance, some sensitivity variations, and the temperature output voltage. Data from a sampling of devices are shown in Table 2.

TABLE 2
Operating Voltage Range 1
Vs = 5 V, TA = 25ºC	Min.	Nominal	Max.	Average	Tolerance
Zero-g level (offset V)	0.981	1.000	1.009	0.9965	-1.9% to 0.9%
Sensitivity (@ 1 g)	45 mV	50 mV	55 mV	48.6 mV	±10%
Temperature output (V)	0.969	1.000	1.012	0.9968	43 mV

Repeating the process with another sample having a 4 V supply illustrates an upward shift in sensitivity, but the zero-g level and temperature output voltages were more consistent with the 5 V measurements (see Table 3).

TABLE 3
Operating Voltage Range 1
Vs = 4 V, TA = 25ºC	Min.	Nominal	Max.	Average	Tolerance
Zero-g level (offset V)	0.993	1.000	1.023	1.0076	-1.7% to 2.3%
Sensitivity (@ 1 g)	55.5 mV	60 mV	64.5 mV	58.4 mV	-4.9% to 10.5%
Temperature output (V)	0.977	1.000	1.022	0.9959	45 mV

Clearly, the offset voltage deviation is well within the specified ±5% (less than ±2%). In a high-resolution, low-g application, however, variations in the offset necessitate some calibration or compensation technique to null the circuit response.

More critical is the sensitivity, especially over temperature, and the temperature sensor (5 mV/K, ±5%) is vital to correcting for temperature variations.

Although the nominal for the temperature output voltage is 1.000 V, deviations in this output signal are listed to illustrate sensor stability and performance. System control circuitry must use this signal in conjunction with the analog output voltage to calibrate system response over temperature.

Operating Temperature Range. These sensors are specified for operation over a range of –40°C to 85°C, and are capable of operation from –65°C to 125°C. However, systems having limited or very restricted temperature excursions benefit from simplifying the calibration and control techniques for nulling the zero-g signal, linearizing the sensitivity, and compensating for temperature effects. These processes alleviate problems with the signal conversions and resultant calculations of the analog output voltage over temperature.

Frequency Response. The frequency response of thermal accelerometers is typically –3 dB at 40 Hz, but the rolloff is only second order and therefore provides a usable signal above 100 Hz. Adding an equalizer circuit will extend the usable frequency response to 160 Hz. The parameter depends on the thermal time constant of the temperature sensing. The movement of the heated bubble occurs instantaneously; consequentially, the sensor will display less attenuation of frequencies to ~160 Hz (i.e., ~9000 rpm) and satisfy most rotating applications.

Sensitivity. The sensitivity and zero-g level are critical to detecting small changes in the analog output signal. These parameters are very significant for tilt angle applications, particularly if the design demands accurate sensor signals well beyond ±45° inclination, but useful angular limits also involve the measurement circuitry (e.g., the resolution limits of A/D conversion).

Figure 5. A plot of sensor sensitivity against temperature, in conjunction with a formula (in text), provides a way to compensate and correct for sensitivity changes caused by temperature variations. Control circuitry can calculate the actual sensitivity and correlate it to measured g levels.

Figure 5 plots sensitivity over temperature and is predictable per the following formula:

S_i	= sensitivity at some initial temperature, T_i
S_f	= sensitivity at some final temperature, T_f

For broad temperature applications, a built-in temperature sensor can be used to correct this inherent sensitivity change; over a range of –40°C to 60°C, the sensitivity approximates 5 mV/°C. As shown in Figure 1, sensitivity decreases with temperature and is definitely nonlinear. Clearly, it is necessary to accurately determine the true requirements of the system design.

Zero-g Level (Offset). As previously noted, 1.00 V is the nominal for the analog output on an absolute device and the specified limits are ±5% (i.e., ±50 mV). Sampling recorded tighter tolerances, but these might not satisfy higher resolution design objectives. In many applications, techniques must therefore be provided to null the output to a known, stored value (calibrating the zero-g level), and then exploit this in conjunction with the temperature and sensitivity signals to compensate for normal unit-to-unit parametric variances and system temperature changes. Another device, not discussed in this article, develops a ratiometric output voltage that is directly related to the supply voltage (i.e., 0.37 • V_DD).

Figure 6. Output voltage A (analog) is an absolute level (nominally 1.0 V), as is T (temperature), and varies linearly with temperature. Both A_OUT and T_OUT are essential for calculating and correcting for temperature.

The analog signal is very stable (12 mV change from –40°C to 125°C, but only 2 mV from 0°C to 60°C). Over 0°C–60°C, the temperature signal is obviously linear and varies ~4.95 mV/°C. Developing a lookup table to store various data points, and using an EEPROM microcontroller to store the analog voltage, temperature output values, and sensitivity variations, is one technique designers should consider.

Another probable aspect of high resolution is the need to detect small incremental voltages. This is particularly evident in tilt angle/inclinometer applications where the maximum field is ±1 g and the nominal sensitivity is +50 mV/g (the Earth’s

Figure 7. In an illustration of the accelerometer's basic orientation relative to the Earth's surface, the X axis (parallel to the Earth) and tilt angles from this position are the most sensitive. An orientation along the Y axis (perpendicular to the Earth) develops the least sensitivity. Table 2 corroborates 0º as the preferred static position.

gravitational field strength is 1 g). The accuracy of a high-resolution design is dependent on creating specific lookup tables and associated calculations.

A/D Conversion
Although amplifying the analog output increases the signal to the A/D converter, any inherent noise and errors are also amplified (see Figure 7). Resolving the small incremental voltages listed in Table 4 involves a minimum of 14 (or even 16) bits. In theory, 14-bit converters resolve ~300 µV but make no provision for noise or error, nor is there any allowance for the lower gain (~33 mV/g) as the temperature increases to 85 C. A 16-bit A/D should be capable of resolving ~150 µV, but also is influenced by the noise/error issues.

TABLE 4
Sensor as Inclinometer (Angular Resolution) Absolute Value Device: V_OUT = 1.000 V @Zero g; V_DD = 5 V; T_A = 25°C; Earth’s Field is Sin
Tilt Angle	Earth's Field	V_OUT (NOM) @ 50 mV/g	V_OUT ( - 1º)
90º	1.000000	1.0500000	8.0 µV
89º	0.999847	1.049992	22.0 µV
88º	0.999391	1.049970	39.0 µV
87º	0.998630	1.049931	52.8 µV
86º	0.997564	1.049878	68.3 µV
85º	0.996195	1.049809	83.0 µV
84º	0.994522	1.049726	99.0 µV
83º	0.992546	1.049627	114.0 µV
82º	0.990268	1.049513	128.6 µV
81º	0.987688	1.049384	143.6 µV
80º	0.984808	1.049240	158.6 µV

10º	0.173648	1.008682	856 µV
9º	0.156434	1.007822	858 µV
8º	0.139173	1.006959	866 µV
7º	0.121869	1.006093	867 µV
6º	0.104528	1.005226	868 µV
5º	0.087155	1.004358	870 µV
4º	0.059756	1.003488	871 µV
3º	0.052336	1.002617	872 µV
2º	0.034899	1.001745	872 µV
1º	0.017452	1.000873	873 µV
0º	0.000000	1.000000	Ref

Another aspect is cost vs. complexity. At present, 10-bit A/D conversion is the resolution limit of most low-cost microcontrollers. Adding an amplifier state (10 × gain) between the analog output and A/D input increases the incremental signals, and may allow 10-bit conversion. However, loss of gain at temperatures >60 C means 10-bit resolution may prove troublesome. The 10 × gain is predicated on the higher gain (sensitivity) at –40 C (~1.9 × the 25 C value). Applications with restricted temperature ranges may allow boosting amplifier gain (slightly), but still retain the needed headroom.

Thermal Accelerometer Applications
Accelerometers are used to measure inertia, tilt, and vibration in a wide variety of markets, including appliances (washing machine balance), robotics (joystick control), impact/shock detection, safety (earthquake detection), automotive (alarms, active suspension), and antenna control (azimuth direction). The first three will serve as examples.

Washing Machine Vibration and Tilt. The appliance industry is moving toward smarter, more efficient machines. The imbalance and vibration that often occur during the spin cycle and cause the washer to shut down could be corrected by a restricted tilt angle sensor and a low-cost microcontroller.

Joystick Control of Robots. Joystick applications typically involve tilt angles (X,Y) and inertia. Depending on the accuracy requirements, high-resolution sensing may also be necessary. Because the range of the angular motion is more restricted and well above the noise floor, the analog signal can be significantly amplified (boosting the incremental voltage swing to the A/D), and low-cost microcontrollers with 10- to 12-bit conversion can be used. A dual-axis, single-chip accelerometer, op-amp, and microcontroller could offer a solution for designs that do not entail <1 incremental changes.

Figure 8. An oscilloscope plot shows a momentary impact of 7.0+ g's and a change in signal amplitude of ~360 mV. The peak duration is ~5 ms, and can be readily detected by various circuit techniques. Although the normal limit of the thermal sensors is ±10 g's, they will withstand levels of 50,000 g's without being damaged.

Impact/Shock Sensing. Multi-g shock (deceleration) may prove rather simple to detect. The analog output voltage shown in Figure 8 is referenced to ~1.0 V (zero-g offset) and spikes to ~1.35 V (~7 g impact). With a pulse duration >5 ms, detecting impacts of this magnitude may require only a comparator and a suitable voltage divider. For typical applications, the minimum sensitivity (per Figure 5) is ~33 (60°C) and impact forces >5 g may be detected without amplification or A/D conversion. Voltage swings of this or greater magnitude might completely preclude any concern for the ±50 mV offset; however, actual, individual g-level trip-points shift with device offset, sensitivity, and temperature. Obviously, this technique cannot afford tight tolerances for detecting impact/shock, but for less demanding designs it may offer the ultimate, lowest cost solution.

Summary
The new thermal accelerometers presented here offer an inexpensive, high-reliability alternative to competing technologies. The lack of any proof mass in these convection-based, single-chip smart sensors makes them robust and capable of surviving severe operating environments.

The bubble of heated air avoids the stiction problems associated with other technologies. The CMOS mixed-signal technology is capable of integrating smart circuit functions that many other competing technologies now lack.

Exploiting the sensor’s output signals may necessitate a variety of control techniques. System complexity is very dependent on resolution demands, temperature changes, and certain other factors.

Some applications can be solved with very simple, low-cost circuitry; others demand precision and stability that might necessitate high-resolution A/D conversion and/or lookup tables.

For Further Reading
Frank, R. 1996. Understanding Smart Sensors, Artech House, Norwood, MA.

Leung, A.M., Jones, I., et al. 1998. “Micromachined Accelerometer Based On Convection Heat Transfer,” IEEE publication 0-7803-4412-X.

Milanovich, V., Bowen, E., et al. 18 Nov. 1998. “Convection-based Accelerometer and Tilt Sensor Implemented in Standard CMOS,” Proc Intl Mech Eng Conf and Exp, MEMS Symposium, Anaheim, CA.

SIDEBAR:

Thermal Accelerometer Characteristics and Limits

Absolute Max. Ratings
Acceleration (any axis, 0.5 ms)	50,000 g
Supply Voltage, V_s	-0.3 to +7.0 V
Output short-circuit duration	Indefinite
Operating temperature	-55ºC to 125ºC

Recommended Operation
Measurement range	±10 g (typ.)
Nonlinearity (BFST)	±2% F.S.
Sensitivity (V_s - 5 V ±10%	50 mV/g (typ.)
Min.	45 mV/g
Max.	55 mV/g
Zero-g level @A_out, V_s ±10%	1.0 V (typ.)
Min.	0.95 V
Max.	1.05 V
Noise density	1.0 mg/Hz (typ.)
Max.	7.0 mg_rms
Frequency response (-3 dB bandwidth)	40 Hz (typ.)
Temperature sensor (scale factor)	5 mV/K (norm.)
Output drive capability	2.5 mA (typ.)
Operating voltage range, V_s	2.70-5.25 V
Quiescent supply current (V_s = 5 V)	2.7 mA (typ.)
V_s = 3 V	4.0 mA (max.)
Quiescent supply current (V_s = 3 V)	6.5 mA (typ.)
V_s = 3 V	7.0 mA (max.)
Turn-on time	400 ms (typ.)
Temperature range	-40ºC to 125ºC

Mike Bugnacki is Senior Staff Engineer and John Pyle is Senior Applications Engineer, Memsic Inc., 100 Burtt Rd., Andover, MA 01810; 978-623-8188, fax 978-623-9945, jpyle@memsic.com.

Paul Emerald is Motion Sensing Engineering Consultant, Memsic Inc., 7 Woodside Dr., Sterling, MA 01564; 978-422-6286; fantasmacinzento@aol.com.