mxd2020e memsic, mxd2020e Datasheet - Page 6

• Manufacturer Part Number: mxd2020e
• Description: Ultra Low Noise, Low Offset Drift ?1 G Dual Axis Accelerometer With Digital Outputs
• Manufacturer: memsic

CHOOSING T2 AND COUNTER FREQUENCY
DESIGN TRADE-OFFS
The noise level is one determinant of accelerometer
resolution. The second relates to the measurement
resolution of the counter when decoding the duty cycle
output. The actual resolution of the acceleration signal is
limited by the time resolution of the counting devices used
to decode the duty cycle. The faster the counter clock, the
higher the resolution of the duty cycle and the shorter the
T2 period can be for a given resolution. Table 2 shows
some of the trade-offs. It is important to note that this is the
resolution due to the microprocessors’ counter. It is
probable that the accelerometer’s noise floor may set the
lower limit on the resolution.
Table 2: Trade-Offs Between Microcontroller Counter Rate and
T2 Period.
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
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:
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.
MEMSIC MXD2020E/F Rev H
T2 (ms)
10.0
10.0
2.5
2.5
constants
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
MEMSIC
Sample
Rate
100
100
400
400
characteristic
Counter-
(MHz)
Clock
Rate
1.0
0.5
1.0
0.5
to
Counts
Per T2
10000
Cycle
5000
2500
1250
each
accelerometer.
Counts
2000
1000
per g
500
250
Reso-
lution
(mg)
0.5
1.0
2.0
4.0
Page 6 of 8
For a more detail discussion of temperature compensation
reference MEMSIC application note #AN-00MX-002
Figure 4: 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 5 for an
example.
Figure 5: Converting the digital output to an analog voltage
MEMSIC
Accel.
MEMSIC
Accel
DOUT
10K
Ax
Ay
T
1uF
I/O
I/O
A/D
AOUT
Microcontroller
2/26/2007