MPXM2102AS datasheet(533/670 Pages) MOTOROLA

533 / 670 page

AN1660

3–387

Motorola Sensor Device Data

www.motorola.com/semiconductors

Figure 3. MPX5000 Series PSPICE Compound Coefficient Model

NOTES:

* TEMPERATURE SENSITIVE

* * TEMPERATURE & PRESSURE SENSITIVE

RS2

350

RS3

350

RS7

675

RS10

RS9

1350

RS6

1000MEG

RS1

350

RS4

350

RS5

750

RS11

RS8

1000MEG

RS17

112K

RS16

500

V(1,0)

RS13

265.5

RS12

10K

ES3

G=100,000

–

ES1

G=100,000

–

ES2

G=100,000

–

RS14

112K

RS15

500

ES4

–

STIMULUS

The last section of these models is labeled STIMULUS. Bias

voltage, pressure, and temperature are applied here. Nominal

bias voltage (VCC) is 3.0 volts for Uncompensated sensors,

10.0 volts for MPX2000 sensors, and 5.0 volts for MPX5000

sensors. Pressure is selected on the second line. It is effective

when the * on line 4 is removed to command a temperature

sweep. Line 3 calls for a sweep of pressure and temperature.

An * placed in front of Line 3 allows the temperature sweep on

line 4 to be selected.

COMPOUND COEFFICIENTS

Applying temperature coefficients to variables such as

resistance is an essential part of modeling. The linear

approach, that is usually used, is based upon the assumption

that changes are small, and can be modeled with a linear

approximation. Using temperature coefficient of resistance as

(TCR) as an example, the linear expression takes the form:

(2)

R(Temp) = R25(1 ) TCR(Temp – 25))

Provided that the TCR in equation (2) is 100 parts per million

per degree Celsius or less this approach works quite well. With

sensor TCR’s of several thousand parts per million per degree

Celsius, however, the small change assumption does not

hold. To accurately model changes of this magnitude, the

mathematical expression has to describe a physical process

where a unit change in temperature produces a constant per-

centage change in resistance. For example, a 1% per degree

TCR applied to a 1 K Ohm resistor should add 10 ohms to the

resistor’s value going from 25 to 26 degrees. At 70 degrees,

where the resistor has increased to 2006 Ohms, going from 70

to 71 degrees should add 20.06 Ohms to its value. The error

in the linear expression comes from that fact that it adds 10

ohms to the resistor’s value at all temperatures.

A physical process whereby a unit change in temperature

produces a constant percentage change in resistance is easi-

ly modeled by borrowing an expression from finance. Com-

pound interest is a direct analog of temperature coefficients.

With compound interest, a unit change in time produces a

constant percentage change in the value of a financial instru-

ment. It can be described by the expression:

(3)

Future Value = Present Value (1

) i)n

where i is the interest rate and n is the number of periods.

Substituting R25 for Present Value, R(Temp) for Future Value,

TCR for i, and (Temp – 25) for n yields:

(4)

R(Temp) = R25(1 ) TCR)(Temp *25)

Equation (4) works quite well, provided that TCR is constant

over temperature. When modeling semiconductor resistors, it

is also necessary to account for variable TCR’s. At cold, the

TCR for p type resistors changes with temperature. These

changes are modeled using TABLE functions that have 3 val-

ues for TCR. Results of this modeling technique versus actual

measurements and a linear model are summarized in Table 1.

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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