MEMSIC MXD2020E/FL Rev D
Page 6 of 8
11/14/2003
T2 (ms)
MEMSIC
Sample
Rate
Counter-
Clock
Rate
(MHz)
Counts
Per T2
Cycle
Counts
per g
Reso-
lution
(mg)
10.0
100
1.0
10000
2000
0.5
10.0
100
0.5
5000
1000
1.0
2.5
400
1.0
2500
500
2.0
2.5
400
0.5
1250
250
4.0
Table 2: Trade-Offs Between Microcontroller Counter Rate and
T2 Period.
USING THE ACCELEROMETER IN VERY LOW
POWER APPLICATIONS (BATTERY OPERATION)
In applications with power limitations, power cycling can
be used to extend the battery operating life. One important
consideration when power cycling is that the accelerometer
turn on time limits the frequency bandwidth of the
accelerations to be measured. For example, operating at
3.0V the turn on time is 40mS. To double the operating
time, a particular application may cycle power ON for
40mS, then OFF for 40mS, resulting in a measurement
period of 80mS, or a frequency of 12.5Hz. With a
frequency of measurements of 12.5Hz, accelerations
changes as high as 6.25Hz can be detected.
Power cycling can be used effectively in many inclinometry
applications, where inclination changes can be slow and
infrequent.
COMPENSATION FOR ZERO G OFFSET CHANGE
OVER TEMPERATURE
The compensation of offset is performed with the following
equation: Aoc = A + ( a + b * T + c * T * T)
where Aoc is the offset compensated acceleration, A is the
uncompensated acceleration, T is temperature and a, b, c
are constants characteristic to each accelerometer.
Computer programs are used to determine these constants.
The constants can be read from and written to the MCU
EEPROM via the RS-232. The constants a,b,c are normally
stored in the MCU EEPROM. To determine the values of
the constants, each accelerometer is taken to three different
temperatures, preferably evenly spread across the desired
temperature span. The zero g bias (A0, A1 and A2) and the
temperatures (T0, T1 and T2) are recorded at each
temperature. The data collected (A0, T0, A1, T1, A2, T2) is
used in a quadratic interpolation (or LaGrange polynomial)
to determine a, b and c as follows:
r0 = A0 / ( (T0-T1)*(T0-T2) )
r1 = A1 / ( (T1-T0)*(T1-T2) )
r2 = A2 / ( (T2-T0)*(T2-T1) )
a = r0 * T1 * T2 + r1 * T0 * T2 + r2 * T0 * T1
b = - r0 * (T1+T2) – r1 * (T0+T2) – r2 *(T0+T1)
c = r0 + r1 + r2
In many cases a computer is used to control the
temperature, communicate with the MCU, and to calculate
the constants. After calculating the constants, the computer
downloads the constants to EEPROM.
For a more detail discussion of temperature compensation
reference MEMSIC application note #AN-00MX-002
Microcontroller
MEMSIC
Accel
I/O
I/O
A/D
Ax
Ay
T
Figure 5: Zero g Offset Temperature Compensation Circuit
COMPENSATION FOR EXTENDING THE
FREQUENCY RESPONSE
The response of the thermal accelerometer is a function of
the internal gas physical properties, the natural convection
mechanism and the sensor electronics. Since the gas
properties of MEMSIC's mass produced accelerometer are
uniform, a digital filter can be used to equally compensate
all sensors. The compensating filter does not require
adjustment for individual accelerometers. The function of
the compensating filter is to apply gain in proportion with
the acceleration changes. The faster the acceleration
changes occur, the higher the gain that the filter applies.
For analog output accelerometers, the compensating filter
can be implemented with a circuit involving two op-amps
and some resistors and capacitors. For digital output
accelerometers, a digital filter is necessary.
In applications where high frequency accelerations need to
be measured, a DSP (digital signal processor) may be
necessary to implement the digital filter. DSP IC’s and
development tools are readily available from major IC
manufacturers.
However, if the bandwidth requirement is relatively low
(i.e. 100Hz), it is possible to implement a digital frequency
compensating filter with an 8 bit microcontroller. The
microcontroller will likely have to be capable of operating
at relatively high clock frequencies (20MHz).
CONVERTING THE DIGITAL OUTPUT TO AN
ANALOG OUTPUT
The PWM output can be easily converted into an analog
output by integration. A simple RC filter can do the
conversion. Note that that the impedance of the circuit
following the integrator must be much higher than the
impedance of the RC filter. Reference figure 6 for an
example.
1uF
DOUT
AOUT
10K
MEMSIC
Accel.
Figure 6: Converting the digital output to an analog voltage
