Analog Devices AN668 Application Notes
AN-688
FREQUENCY (Hz)
PHASE ANGLE (Degrees)
2
–2
–6
–8
–10
0 10 9
0
0
–4
20 30 40 50 60 70 80
WITH 2kHz FILTER
–10
–8
–6
–4
–2
0
2
FREQUENCY (Hz)
PHASE ANGLE (Degrees)
0 40 60 80 10020
WITH 2kHz FILTER
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106 • Tel: 781/329-4700 • Fax: 781/326-8703 • www.analog.com
Phase and Frequency Response of i MEMS® Accelerometers and Gyros
by Harvey Weinberg
INTRODUCTION
Iner tial sensors are often used in applications where
phase and frequency response are critical to proper
system operation. This application note will discuss the
phase and frequency response of the Analog Devices
iMEMS accelerometers and gyroscopes (ADXLxxx and
ADXRSxxx series components).
GENERAL CONCEPTS
In general, the Analog Devices iMEMS inertial sensors frequency and phase response are dominated by their output
lter response. Since the output lter is generally dened
by external components specied by the user, phase and
frequency response can be tailored to the application. This
is the result of two architectural features:
• Open loop architecture—In general, no force feedback
is used on the sensor beam.
• Relatively high beam resonant frequency beams.
To illustrate this point, Figure 1 shows the phase response
from 5 Hz to 80 Hz of an ADXRS150 gyro set to 2 kHz
bandwidth. Figure 2 shows the phase response from
5 Hz to 100 Hz of an ADXL203 set to 2 kHz bandwidth.
In both cases, one can see that the phase response is
essentially at.
Figure 1. ADXRS150 Phase Response
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Figure 2. ADXL203 Phase Response
AN-688
–200
–180
–160
–140
–120
–100
–80
–60
–40
–20
0
FREQUENCY (Hz)
PHASE ANGLE (Degrees)
1 10 100 1k 10k
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
FREQUENCY (Hz)
PHASE ANGLE (Degrees)
1 10 100 1k
FIRST-ORDER FILTERS
All ADXL series low g (<20 g ) accelerometers use a
single - pole RC lter where the resistor is internal and
the capacitor is external. The user sets the bandwidth,
and indirectly the phase response, by his or her choice
of capacitor value. The phase response of a rst- order
(RC) system is dened as
Phase Response = –ARCTAN (wRC)
where
w = 2 pf
In general, one can assume that a rst-order lter has a
phase response of –45° at its –3 dB corner frequency.
Figure 3 shows the phase response for a 100 Hz rst-order
low-pass lter. All ADXLxxx series low g accelerometers,
i.e., the ADXL103/ADXL203, ADXL202E/ADXL210E, and
ADXL311, will respond identically.
The ADXRSxxx series gyros look like they would have
2-pole lter response (two cascaded single - pole lters),
but this is not the case. The rst pole is the RC lter
composed of the parallel combination of R
and C
. The purpose of this pole is to inhibit higher
MID
SEN1
, R
SEN2
amplitude clock artifacts from overloading the output
amplier, so the corner frequency is generally chosen to
be fairly high, 10 times the required overall bandwidth
(e.g., for a 40 Hz gyro response, one would set the rst
pole to 400 Hz). The effect of this pole on phase response
is, therefore, minimal (approximately –5°).
The second pole is normally used to set the actual bandwidth of the gyro. It is a classic single - pole RC lter (the
R is the internal R
external C
). The phase response for a 100 Hz band-
OUT
resistor of 180 k , and the C is the
OUT
width would be very similar to that of the single -pole
accelerometer shown in Figure 3.
SECOND-ORDER FILTERS
All ADXLxxx series high g (>20g ) accelerometers use
internal 2-pole switched capacitor Bessel lters. Since
the lter is totally internal, there is no adjustment or
modication that the user can do to modif y the phase
response.
In general, the phase response for a 2- pole Bessel lter
will be less than –10° below 25% of its –3 dB corner fre quency and –90° at its –3 dB corner frequency. The phase
response for a 400 Hz Bessel lter is shown in Figure 4.
AN04567–0–2/04(0)
,
Figure 4. 400 Hz Second-Order Low-Pass Filter
Phase Response
The user may, of course, add an ex ternal lter to any
of the high g accelerometers. In this case, the ex ternal
lter’s phase response will dominate that of the internal
lter, assuming that the external lter’s cut- of f frequen cy is much lower (more than 10 times lower) than that of
the internal 2- pole lter.
CONCLUSION
The phase response of the Analog Devices iMEMS inertial
sensors is essentially determined by the output lter.
Most devices have output lters whose corner frequency is determined by user supplied components, so the
user can tailor the phase response to their application.
Devices with internal lters can be simply modeled as
ideal lters.
Figure 3. 100 Hz First-Order Low-Pass Filter
Phase Response
© 2004 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners.
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