6

O

6

(1.8639

V

2.1962 10

3.88 10

)

T

1481.96





u

u







LMT88

www.ti.com

SNIS175A – MARCH 2013 – REVISED JANUARY 2015

Typical Applications (continued)

Solving for T:

where

•

equation that can be used to calculate the temperature of the LMT88.

(6)

An alternative to the quadratic equation a second order transfer function can be determined using "least squares"

method:

T = (

where

•

(7)

A linear transfer function can be used over a limited temperature range by calculating a slope and offset that give

best results over that range. A linear transfer function can be calculated from the parabolic transfer function of

the LMT88. The slope of the linear transfer function can be calculated using the following equation:

m =

−7.76 × 10

where

•

T is the middle of the temperature range of interest and m is in V/°C. For example for the temperature range of

(8)

T = 35°C

(9)

and

m =

−11.77 mV/°C

(10)

The offset of the linear transfer function can be calculated using the following equation:

where

•

•

(11)

Using this procedure, the best fit linear transfer function for many popular temperature ranges was calculated in

Table 3. As shown in Table 3, the error that is introduced by the linear transfer function increases with wider

temperature ranges.

Table 3. First Order Equations Optimized for Different Temperature Ranges

TEMPERATURE RANGE

MAXIMUM DEVIATION OF LINEAR EQUATION

LINEAR EQUATION

FROM PARABOLIC EQUATION (°C)

−55

130

±1.41

−40

110

±0.93

−30

100

±0.70

-40

85

±0.65

−10

65

±0.23

35

45

±0.004

20

30

±0.004

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