Analog Devices AN604 Application Notes

AN-604

a

APPLICATION NOTE

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Using the ADXL202 Duty Cycle Output

by Harvey Weinberg

Calculation of the Acceleration Output

Acceleration experienced by the ADXL202 may be calcu­lated using the following formula:

Acceleration in

As outlined in the data sheet, the nominal duty cycle
output of the ADXL202 is 50% at 0
cycle change per
from the duty cycle:

If the 0 g duty cycle output of the ADXL202 is other than
50%, and/or the duty cycle changes more or less than

12.5% per
rate. In practice, the 0
ADXL202 vary somewhat from device to device (see the
data sheet for details). So this formula can only be
used for low accuracy measurements. For higher
accuracy measurements, the actual offset and scale val­ues must be substituted.

()

Acceleration in

g

, the acceleration calculation will be inaccu-

Duty Cycle Duty Cycle at

g

=

g

. Therefore to calculate acceleration

()

g =

g

output and the sensitivity of the

–

Duty Cycle per

g

and 12.5% duty

TT

()–%

12 50

.%

12 5

g

0

g

In addition, the result of this equation would be a num­ber in the range of ±2 for an ADXL202. In general, it is
inconvenient to use real numbers in calculations with a
small microcontroller since floating point mathematics
would be required to get meaningful results. A preferred
method for calculation of acceleration with a small
microcontroller using fixed point math is included in
this application note, along with two simple methods of
calibration to find the actual offset and scale values.

This application note outlines methods to decode the duty
cycle output, conversion from duty cycle to acceleration
(or tilt angle), and calibration of the ADXL202. These meth­ods are geared toward use with 8-bit microcontrollers
having limited computational capability.

Decoding the Output

The most direct way to decode the duty cycle output is
shown in Figure 1. A counter is started at the rising edge
of the X output (Ta = 0). The count at the falling edge
(Tb) is recorded, and the timer is stopped at the next ris­ing edge of the X output (Tc). This process is then
repeated for the Y output (Td, Te, and Tf).

REV. 0

T1

T2

X

OUT

Ta

Y

OUT

Figure 1. Basic Decode Technique for the ADXL202

Tb

Tc

Td

T2

T1

Te

© Analog Devices, Inc., 2002

Tf

AN-604

While this technique is very easy to understand, you can
only acquire one sample of acceleration from both axes
every three cycles (i.e., 3 ⫻ T2) since you must wait for
the next rising edge of X

after Tf.

OUT

Note that while T2 is nominally constant, it does change
over temperature and contains some jitter. For systems
that do not require resolutions of better than 100 m
T2 may be measured only once. For more accurate
measurements, several T2 measurements should
be made and averaged. The average should be
updated periodically to account for T2 drift over
temperature.

T1

T2

X

OUT

Ta

Tb Te

An Improved PWM Decode Scheme

Since the duty cycle modulator (DCM) uses the same tri­angle wave reference for the X and Y channels, the
midpoints of the T1 of each period must be coincident. This
is illustrated in Figure 2. Here it is shown that even
though the X and Y duty cycle outputs are different,

g

,

the midpoints of T1 are synchronized. Therefore, an
improved PWM decode technique can be used to speed up
the data acquisition time. Figure 2 shows the sequence of
events. A counter is started at the rising edge of the X out­put (Ta = 0). The count at the falling edge of the X output
(Tb) is recorded. Then the counts at the rising and falling
edges of the Y output (Tc and Td) are recorded. A flow chart
outlining this method of calibration is shown in Figure 3.

Y

OUT

T1

Tg

Tc

T2

Tf

Td

Figure 2. High Speed Decoding Technique for the ADXL202

By definition:T1x = Tb – Ta = Tb (if the counter is zero at Ta)

T1y

= Td –

T2x

= T2y = Te – Ta = Tg –

Tc

Tf

Since the midpoints of the high states of the X and Y duty cycle signals are coincident:

T

2 = [Td – ((Td – Tc)/2)] – [(Tb – Ta)/2]

T

2 = [Td – ((Td – Tc)/2)] – [Tb/2] (if the counter is zero at Ta)

The advantages of this system of decoding are:

1. One sample of acceleration from both axes can be acquired every two

2.

T

2 is only calculated once for both the X and Y signals.

T

2 cycles.

–2–

REV. 0

START TIMER AT Ta

RECORD TIME AT Tb

RECORD TIME AT Tc

RECORD TIME AT Td

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T1x = Tb

T1y = Td – Tc

T2 = [Td –

((Td – Tc)/2)] – [(Tb – Ta )/ 2 ) ]

DONE

Figure 3. Flow Chart for High Speed Decoding Technique for the ADXL202

REV. 0

–3–