–10–

ADXL150/ADXL250

REV. 0

DEVICE BANDWIDTH VS. MEASUREMENT

RESOLUTION

Although an accelerometer is usually specified according to its

full-scale g level, the limiting resolution of the device, i.e., its

minimum discernible input level, is extremely important when

measuring low g accelerations.

3dB BANDWIDTH – Hz

100m

g

1m

g

10m

g

10

1k

100

660m

g

66m

g

6.6m

g

Figure 19. ADXL150/ADXL250 Noise Level vs. 3 dB

Bandwidth (Using a “Brickwall” Filter)

The limiting resolution is predominantly set by the measure-

ment noise “floor,” which includes the ambient background

noise and the noise of the ADXL150/ADXL250 itself. The level

of the noise floor varies directly with the bandwidth of the mea-

surement. As the measurement bandwidth is reduced, the noise

floor drops, improving the signal-to-noise ratio of the measure-

ment and increasing its resolution.

The bandwidth of the accelerometer can be easily reduced by

adding low-pass or bandpass filtering. Figure 19 shows the

typical noise vs. bandwidth characteristic of the ADXL150/

ADXL250.

The output noise of the ADXL150/ADXL250 scales with the

square root of the measurement bandwidth. With a single pole

roll-off, the equivalent rms noise bandwidth is

π divided by 2 or

approximately 1.6 times the 3 dB bandwidth. For example, the

typical rms noise of the ADXL150 using a 100 Hz one pole post

filter is:

Noise rms

Because the ADXL150/ADXL250’s noise is, for all practical

purposes, Gaussian in amplitude distribution, the highest noise

amplitudes have the smallest (yet nonzero) probability. Peak-

to-peak noise is therefore difficult to measure and can only be

estimated due to its statistical nature. Table I is useful for esti-

mating the probabilities of exceeding various peak values, given

the rms value.

Table I.

Nominal Peak-to-

% of Time that Noise Will Exceed

Peak Value

Nominal Peak-to-Peak Value

2.0

× rms

32%

4.0

× rms

4.6%

6.0

× rms

0.27%

6.6

× rms

0.1%

8.0

× rms

0.006%

RMS and peak-to-peak noise (for 0.1% uncertainty) for various

bandwidths are estimated in Figure 19. As shown by the figure,

device noise drops dramatically as the operating bandwidth is

reduced. For example, when operated in a 1 kHz bandwidth,

the ADXL150/ADXL250 typically have an rms noise level of

32 mg. When the device bandwidth is rolled off to 100 Hz, the

noise level is reduced to approximately 10 mg.

Alternatively, the signal-to-noise ratio may be improved consid-

erably by using a microprocessor to perform multiple measure-

ments and then to compute the average signal level.

Low-Pass Filtering

The bandwidth of the accelerometer can easily be reduced by using

post filtering. Figure 20 shows how the buffer amplifier can be

connected to provide 1-pole post filtering, zero g offset trimming,

and output scaling. The table provides practical component values

Cf

R2

1M

RT

200k

0

g TRIM

SCALE

FACTOR

TRIM

(OPTIONAL)

R3

100k

0.1 F

R1a

75k

0.1 F

2

SELF-TEST

25k

5k

ADXL150

GAIN

AMP

OFFSET

NULL

COM

C1

0.1 F

BUFFER

AMP

DEMODULATOR

SENSOR

TP

(DO NOT CONNECT)

14

9

10

7

5

CLOCK

OP196

3

4

6

2

8

7

2

R1b

50k

EXT

AMP

GAIN

R3

VALUE

F.S.

RANGE

DESIRED

OUTPUT

SCALE FACTOR

Cf ( F)

100Hz

Cf ( F)

30Hz

Cf ( F)

10Hz

0.0082

0.0056

0.0033

0.0015

0.027

0.022

0.010

0.0056

0.082

0.056

0.033

0.015

76mV/

g

25

g

2.0

200k

100mV/

g

20

g

2.6

261k

200mV/

g

10

g

5.3

536k

400mV/

g

5

g

10.5

1M

Figure 20. One-Pole Post Filter Circuit with SF and Zero g Offset Trims