A Micromachined Quartz Angular Rate Sensor for Automotive and Advanced Inertial Applications

Truly low-cost, highly producible inertial sensors with no known

Figure 1. A vibrating dual-ended quartz tuning fork and signal processing electronics constitute a complete gyroscope.
wearout have been a goal of the industry for many years. The concept of using a vibrating element to measure rotational velocity based on the Coriolis principle has also been around for a few decades. In fact, the idea arose from the observation that a certain species of fly uses a pair of vibrating antenna to stabilize its flight. This sensing technique was the inspiration behind the practical embodiment of BEI GyroChip.

The Coriolis Effect

The Coriolis effect is named for the French physicist and mathematician Gustave Gaspard de Coriolis (1792–1843). An assistant professor of mathematics at the École Polytechnique in Paris from 1816 to 1838, Coriolis is best remembered for his 1835 seminal paper, "Sur les équations du mouvement relatif des systèmes de corps," in which is demonstrated that the laws of motion could be used in a rotating frame of

Photo 1. BEI MotionPak and BEI GyroChip series angular rate sensors are offered in a variety of packages and specifications to satisfy a wide spectrum of applications.
reference if an extra force called the Coriolis acceleration is added to the equations of motion.

The rotating frame of reference is the rotating velocity of the Earth, and nearly 200 years later, physicists and mathematicians continue to try to explain in lay terms how the Coriolis effect works. A typical example of the Coriolis effect is that exhibited by wind patterns on Earth. Convection cells in the atmosphere set up a wind flow from the poles toward the equator (with a north-south orientation). The Earth's rotation, however, causes these linear flows to develop a sideways (orthogonal) component of motion. This "bends" the wind from a north-south to an east-west direction. It is the Coriolis effect that creates the east-west "trade winds," and which is responsible for the spiral of clouds observed in satellite photos. The basic formula defining the Coriolis effect is:

2 m (angular velocity) x (velocity in a rotating frame) (1)

Photo 2. The BEI GyroChip yaw sensor is a crucial component in automotive dynamic stability control systems. (Courtesy of GM MLCG.)

As applied to the motion of a particle P along a path in the lamina as the lamina, and thus the path, as well, moves, the total acceleration a P is given by:

a P = a P/path + a M + 2 x V P/path (2)


a P/path = acceleration of P relative to the path considered as fixed

a M = acceleration of point M, which is on the path and with which P coincides at the instant

V P/path = velocity of P relative to point M, which is on the path and with which P coincides at the instant; this velocity can only be tangential to the path along which P is moving in the body

= angular velocity of the path (or lamina)

2 x V P/path = Coriolis's component; its direction is obtained by visualizing the rotation in the plane of the lamina of V P/path through a right angle in the same sense as

Photo 4. BEI GyroChip technology plays a key role in the platform stabilization of the Longbow Apache helicopter (A) and the Sikorski S-92 HELIO stabilization systems (B)

The Coriolis force is one of three important classes of forces in physics that are called "fictitious." The other two are centrifugal force and the apparent force that is a consequence of motion in an accelerating reference frame. Yet those experiencing these forces cannot tell that they are fictitious in any sense. Indeed, the cornerstone of Einstein's theory of general relativity is the equivalence principle, which states that "fictitious forces cannot be distinguished in any way whatsoever from real forces, by any 'interior' experiment." Simply stated, this principle relies on experiments demonstrating equivalent forces measured outside the rotating frame of reference or, in this case, Earth.

In 1851, Jean Bernard Léon Foucault (1819–1868), a French physicist and geometrician, became the first to use the Foucault pendulum to experimentally determine the rotation of the Earth, and in doing so confirmed the presence of the Coriolis effect. His experiment is represented at the Smithsonian in Washington, DC. In 1852, Foucault went on to invent the modern gyroscope. Obviously, all this early experimentation was carried out without the benefit of today's satellite technology.

Principle of Operation

The BEI GyroChip family of products uses a vibrating quartz tuning fork to sense angular velocity [1]. By using the Coriolis effect, a rotational motion about the sensor's longitudinal axis produces a DC voltage proportional to the rate of rotation. The sensor consists of a microminiature double-ended quartz tuning fork and supporting structure, all fabricated chemically from a single wafer of monocrystalline piezoelectric quartz (similar to quartz watch crystals).

Photo 5. A triad of QRS11s provided the astronauts with an inertial reference during untethered spacewalks. (Courtesy of NASA.)

The use of piezoelectric quartz material simplifies the active element, resulting in exceptional stability over temperature and time. The drive tines, which constitute the active portion of the sensor, are driven by an oscillator circuit at a precise amplitude that causes the tines to move toward and away from one another at a high frequency (see Figure 1). Each tine will have a Coriolis force acting on it of:

F = 2 m i x V r      (3)


m = tine mass

V r = instantaneous radial velocity

i = input rate

This force is perpendicular to both the input rate and the instantaneous radial velocity. The two drives tines move in opposite directions; the resultant forces are perpendicular to the plane of the fork assembly and in opposite directions as well. This produces a torque that is proportional to the input rotational rate. Because the radial velocity is sinusoidal, the torque produced is also

Photo 6. The BEI GyroChip used in the Mars rover Sojourner was the first micromachined technology to operate on the Martian surface. (Courtesy of Jet Propulsion Laboratory.)
sinusoidal at the same frequency of the drive tines, and in phase with the radial velocity of the tine.

The pickup tines, being the sensing portion of the sensor, respond to the oscillating torque by moving into and out of plane, producing a signal at the pickup amplifier. After amplification, those signals are demodulated into a DC signal proportional to the sensor's rotation. The output signal of the BEI GyroChip reverses sign with the reversal of the input rate since the oscillating torque produced by the Coriolis effect reverses phase when the direction of rotation reverses.

The BEI GyroChip will generate a signal only with rotation about the axis of symmetry of the fork. That is the only motion that will, by Coriolis sensing, produce an oscillating torque at the frequency of the drive tines. This also means that the BEI GyroChip can truly sense a zero rate input.


Available in several models (see Photo 1), the gyroscopes are used in a wide variety of applications. The Automotive Quartz Rate Sensor (AQRS) is used to detect yaw for vehicle dynamic control systems and by General Motors on its StabiliTrak System (offered on certain models of Cadillacs and Corvettes) [2] and Continental Teves on its Electronic Stability Program (offered on many models of Mercedes, BMWs, Volkswagens, and other European automobiles). This advanced sensor package, together with other sensors, helps detect and correct deviations between the driver's intended course and the actual course of the vehicle. Such deviations are determined through the use of steering column sensors to measure intended course, and yaw rate sensors that measure the car's actual course by detecting the degree of vehicle spin or rotation. The stability control computer receives the inputs of these and other sensors and activates control efforts through the front brakes to help keep the car on its intended course (see Photo 2). Typical specifications of the AQRS are listed in Table 1.


 AQRS Performance Specifications

 Supply Voltage  +4.75 to + 5.25 VDC
 Power  < 0.15 W
 Volume/Weight  <200 cm 3 ; <0.15 kg
 S.F. Error/Linearity  <±3% F.S., <0.5%
 Bandwidth  >50 Hz
 Noise <0.01°/s/(check)Hz
 Bias Error  <±3°/s
 Turn-On Time  <1 s
 Operating Temp.  ·40°C to 85°C
 Vibration  1.5 g rms , 20·2000 Hz
 Shock  1 Meter Fall to Concrete
 EMC Protection  >100 V/M
Photo 7. Three QRS11s provided precise inertial reference and stabilization for NASA's autonomous EVA robotic camera (AERCam) Sprint.

A high-performance version of this quartz rate sensor, the QRS11, is used by the military and the aerospace industry in critical flight control systems such as those in the Maverick missile (see Photo 3) and in inertial subsystems that provide platform stabilization onboard the Apache Longbow helicopter and the Sikorsky S-92 HELIO stabilization system (see Photo 4). Typical specifications of the QRS11 are listed in Table 2.

A triad of the standard quartz rate sensors was used for the critical inertial reference unit in the SAFER (simplified aid for EVA rescue), an astronaut backpack (see Photo 5) designed for extra-vehicular activity on the 9 September 1994 STS-64 Space Shuttle/Space Station mission [3]. A cold gas propelled system in the SAFER is intended to provide an astronaut who "falls off" the spacecraft with the means to get back.

The autonomous Sojourner Mars rover (see Photo 6), deployed during the Pathfinder mission, used a standard, off-the-shelf quartz rate sensor as the inertial heading reference for traversing the planet's surface. The same model has been selected by the Jet Propulsion Laboratory for the next Mars mission with a roving vehicle. In the Sojourner application, the quartz rate sensor was followed by an A/D converter feeding the vehicle's central computer that handled the navigation (directional commands) tasks. The bias characteristics of the single rate (yaw) channel were corrected by a zeroing circuit that was switched on when the vehicle was not moving. The rover's tilt and its influence were compensated by a built-in inclinometer.

Three quartz rate sensors formed the inertial reference and stabilization unit of NASA's AERCam/Sprint "Satellite," a free-flying, cold gas thruster powered 35 cm diameter sphere carrying TV cameras (see Photo 7). Designed for use outside a spacecraft, the small, unobtrusive camera platform has a self-contained propulsion system that gives six-degree-of-freedom


 QRS11 Performance Specifications

    Standard  High
Input Voltage
Input Current
+/·5 VDC ±5 regulation
<70 mA (each supply)
Standard Ranges
Full Range Output
S.F. Calib.
S.F. Over Temp.
 ±50, 100, 200, 500,1000°/s ±2.5 VDC
< 1% of value
< 0.03/°C
Bias Calib. @ 22°C
Bias Variation over Temp.
Short-Term Bias Stability
Long-Term Bias Stability
g Sensitivity
Start-Up Time
Bandwidth (·90°)
Output Noise
Operating Life
<1 s
>60 Hz
<0.05% of Full Range
<0.04°/s <0.010°/s/(check)Hz
10 yr., typical
Operating Temperature
Vibration Operating
40°C to 80°C
8 g rms 20 Hz·2 kHz random
200 g
<60 g rms
Figure 2. Shipboard, land-based, and airborne antennas are being stabilized for accurate satellite pointing by means of the BEI GyroChip. (Courtesy of SeaTel, Inc.)
movement and an automatic attitude-hold capability. The vehicle moves at a rate of ~0.25 fps and is protected from impact damage by a cushioned housing. When the sphere was flown by radio control from the orbiter around the space shuttle in the November 1997 mission, the stability of the inertial reference system and resulting TV images were reported as "extremely precise" by the astronauts [4]. The quartz rate sensors in this sphere were standard off-the-shelf units.

For orbital applications, space radiation tests have been performed on the standard quartz rate sensor. These include total dose and heavy particle radiation:

1.9 x 10 6 particles/cm 2

krypton/xenon isotopes to an LET (linear energy transfer) of 111 MeV / (mg/cm 2 )

For the heavy particle testing, the metallic cover was removed from the sensor electronics to expose the ceramic SMT package containing the semiconductor chip on the PCB to artificial cosmic radiation. The sensor's output (bias) and input current were monitored, and no radiation effects were discerned during or after testing.

Photo 8. BEI GyroChip technology is used to enhance new-generation avionics and flight information systems for commercial and military aircraft.

The QRS11, BEI GyroChip II, and Horizon versions of the sensors are used for stabilizing shipboard satellite antenna systems and aircraft and land vehicle antennas as well (see Figure 2). They are also being incorporated into emerging technologies such as the newest generation of high-reliability, solid-state avionics and flight information systems (see Photo 8).

Inertial Measurement

The Global Positioning System (GPS) has reached a maturity that allows low-cost, accurate static position determination in a small, lightweight portable unit. When augmented with additional information provided by ground-based beacons and vehicle-mounted transponders, reliable relative position accuracy is a proven technique available for combat vehicles, automobiles, field robots, personnel, or other platforms [5].

In "field" applications, however, position data can be adversely affected by interference,

Figure 3. A six-degree-of-freedom inertial measurement unit consists of three gyroscopes, three accelerometers, and signal processing electronics.
breakdowns, and blackouts. GPS signals, for example, can be obscured by objects in the receiving operational environment or electronically jammed with countermeasures. There is also a geometric factor associated with the finite number of satellites in view, which could degrade the accuracy. Finally, several seconds can be required for computation of a new position update. The GPS is therefore limited in its ability to keep constant accurate track of the relative position of multiple high-velocity interacting objects--the "current" reading will always lag behind the objects' true positions.

One solution to these problems is an inertial measurement system (IMU) consisting of incremental angle sensors (gyroscopes) as shown in Figure 3. Because inertial sensors are self-contained, they cannot be jammed by external signals. Moreover, their position update rate is fast enough to keep accurate track of even very rapidly moving objects. The principal application shortfall of an IMU is that the position estimate error increases with time such that even typical fighter aircraft quality IMUs will be outside the typical GPS position accuracy in a minute or two. However, GPS and an IMU can be combined to take advantage of the GPS

Photo 9. The Boeing 777 (shown here) and 737 aircraft use quartz rate sensors in their flight stabilization systems. More than two million sensor operating hours have been logged in the B777 without a failure.
position accuracy and the IMU's rapid update capability and self-contained position sensing. To be practical in the "field," the IMU should be as portable as the GPS receiver, implying small size, light weight, low power, ruggedness, high reliability, low cost, and the necessary performance and production maturity to match that available in GPS technology. IMUs also provide the basis for position measurements where GPS is not available (e.g., indoor applications, other planets, or near the poles). In conjunction with a compass (which has low response time and problem at the poles) and inclinometers, the devices can provide position and orientation estimation for robotic applications.

A digital IMU is part of the Rockwell Collins Proline 21 avionics system, serving as the inertial sensor portion of the aircraft's attitude and heading reference system. The Boeing 777 and 737 airplanes use quartz rate sensors in their flight stabilization systems (see Photo 9). The sensors have accumulated more than 2 million operating hours in the B777 without a failure.

The MotionPak IMU, a solid-state six-degree-of-freedom system, is capable of measuring linear accelerations and angular rates in instrumentation, control, and field robotic applications [6]. The reliable, compact, and fully self-contained motion measurement package has been adapted by Carnegie Mellon University for integration into the Nomad robot. This autonomous mobile unit, designed to demonstrate developing technologies for lunar and planetary exploration, recently participated in a field experiment named Atacma Desert Trek (see Photo 10). Table 3 lists the performance specifications of the MotionPak.


Photo 10. Carnegie-Mellon University used a compass and data obtained from the MotionPak to derive the inertial heading and reference of the Nomad. (Courtesy of Carnegie-Mellon University.)

Until recently, there was no lightweight, inexpensive, reliable inertial sensor that could be used to directly measure rotational velocity. Traditional spinning wheel gyroscopes were heavy, consumed a lot of power, and, because they had moving mechanical parts, wore out after just a few thousand hours of operation.

Advances in micromachining of quartz crystals, combined with the miniaturization of electronics, have made it possible to produce a monolithic vibrating quartz sensor in a compact package for use in measuring angular velocity. The GryoChip is small and lightweight, consumes very little power, and since there is only one active part, extremely reliable. It has therefore found a wide spectrum of applications in the automotive, aerospace, defense, industrial, commercial, and medical industries.

BEI GyroChip and MotionPak are registered trademarks of BEI Technologies, Inc.


The authors wish to thank Brad Sage, Director of Business Development, Systron Donner Inertial Div., for providing quartz rate sensor application data; and Linet Aghassi for her help in preparing this article.


1. A.M. Madni et al. 3–10 Feb. 1996. "A Microelectromechanical Quartz Rotational Rate Sensor for Inertial Applications," Proc 1996 IEEE Aerospace Applications Conf, Aspen, CO, Vol. 3:315-332.

2. A.M. Madni et al. 9–12 Nov. 1997. "A Miniature Yaw Rate Sensor for Intelligent Chassis Control," Proc ITSC'97, IEEE Conf on Intelligent Transportation Systems, Boston, MA, Paper No. 0002.

3. "Rescue Device Shines in Untethered EVA Test." 26 Sept. 1994. Aviation Week:25.

4. "Columbia EVA Added to Aid Station." 8 Dec. 1997. Aviation Week:34.

5. "Global Positioning System (GPS) and Inertial Measurement Units (IMU) for Combat ID." Apr. 1995. Systron Donner Inertial Div. Internal Report.

6. A.M Madni et al. 12–16 Oct. 1998. "Solid-State Six Degree of Freedom Motion Sensor For Field Robotic Applications," Proc 1998 IEEE/RSF Intl. Conf on Intelligent Robots and Systems (IROS), Canada, Vol. 3:1389-1398.


MotionPak Performance

Input Supply Voltage
Input Power
 ±1 5 VDC
7 W



 Standard Ranges

Full-Scale Outputs

 50, 100, 200, 500°/s
±2.5 VDC
 1, 2, 5, 10 g's
±7.5 VDC
 S.F. Calibration  <1%  <1%
 S.F. Temp.
 <0.03%°C  <0.03%°C
 Bandwidth  >60 Hz  DC to >500 Hz
Linearity  <0.05% F.R.  <25 µg/g 2
 Bias (Factory Set)
Temp. Sensitivity
(over full temp.)
Long-Term (1 year)
g Sensitivity
from 22°C

<±12.5 mg
<100 µg/°C

<1000 µg


 Threshold/Resol. <0.004°/s* <10 µg

Operating Temp.
Storage Temp.
Vibrating Survival


-40°C to 80°C
-55°C to 100°C
2 g rms , 20·2 kHz random
(1 min. duration)
200 g peak


 32 oz (nominal)

 *Values indicated for 100°/s range.