3–387
Motorola Sensor Device Data
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Figure 3. MPX5000 Series PSPICE Compound Coefficient Model
6
5
14
3
7
**
**
**
**
*
*
NOTES:
* TEMPERATURE SENSITIVE
**TEMPERATURE & PRESSURE SENSITIVE
0
8
11
13
12
10
9
2
4
1
RS2
350
RS3
350
RS7
675
RS10
RS9
1350
RS6
1000MEG
RS1
350
RS4
350
RS5
750
RS11
1K
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
RS15
RS14
112K
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:
TCR)(Temp
(4)
R(Temp) = R25(1
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.
25)
F
Freescale Semiconductor, Inc.
n
.