MPXM2102AS datasheet(335/670 Pages) MOTOROLA

335 / 670 page

AN935

3–189

Motorola Sensor Device Data

www.motorola.com/semiconductors

PRESSURE (torr)

Figure 1. MPX12 Linearity Analysis Raw Data

5.0

SPAN (mV)

Figure 2. MPX10 Series Span versus Linearity

4.0

3.0

2.0

1.0

–1.0

COMPENSATION FOR NONLINEARITY

The nonlinearity error shown in Figure 1 arises from the

assumption that the output voltage changes with respect to

pressure in the following manner:

Vout =Voff + sens*P

[1]

where Voff = output voltage at zero pressure

differential

sens = sensitivity of the device

P = applied pressure

It is obvious that the true output does not follow this simple

straight line equation. Therefore, if an expression could be

determined with additional higher order terms that more

closely described the output behavior, increased accuracies

would be possible. The output expression would then become

Vout = Voff +(B0+B1*P+B2*P2+B3*P3 +. . .)

[2]

where B0, B1, B2, B3, etc. are sensitivity coefficients. In

order to determine the sensitivity coefficients given in equation

[2] for the MPX10 series of pressure transducers, a polynomial

regression analysis was performed on data taken from 139

devices with full scale spans ranging from 30 to 730 mV. It was

found that second order terms are sufficient to give excellent

agreement with experimental data. The calculated regression

coefficients were typically 0.999999+ with the worst case

being 0.99999.

However, these sensitivity coefficients

demonstrated a strong correlation with the full scale span of

the device for which they were calculated. The correlation of

B0, B1, and B2 with full scale span is shown in Figures 3

through 5.

0.5

SPAN (mV)

0.4

0.3

0.2

0.1

– 0.1

– 0.2

– 0.3

– 0.4

– 0.5

Figure 3. MPX10 Linearity Analysis —

Correlation of B0 Vout = B0 + B1 (P) + B2 (P)2

B0 = 0.1045 – 0.00295*(SPAN)

1.1

SPAN (mV)

Figure 4. MPX10 Linearity Analysis —

Correlation of B1 Vout = B0 + B1 (P) + B2 (P)2

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

B1 = 0.2055 + 1.598E – 3*(SPAN)

+ 1.723E – 4*(SPAN)2

0.0030

SPAN (mV)

Figure 5. MPX10 Linearity Analysis —

Correlation of B2 Vout = B0 + B1 (P) + B2 (P)2

0.0025

0.0020

0.0015

0.0010

0.0005

B2 = –1.293E – 13*(SPAN)5.68

In order to simplify the determination of these coefficients

for the user, further regression analysis was performed so that

expressions could be given for each coefficient as a function

of full scale span. This would then allow the user to do a single

pressure measurement, a series of calculations, and

analytically arrive at the equation of the line that describes the

output behavior of the transducer. Nonlinearity errors were

then calculated by comparing experimental data with the

values calculated using equation [2] and the sensitivity

coefficients given by the regression analysis. The resulting

errors are shown in Figures 6 through 9 at various pressure

points. While using this technique has been successful in

reducing the errors due to nonlinearity, the considerable

spread and large number of devices that showed errors >1%

indicate this technique was not as successful as desired.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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