LM20

SNIS106Q – DECEMBER 1999 – REVISED JANUARY 2015

www.ti.com

Typical Applications (continued)

(6)

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

squares method:

T = (

−2.3654×VO

2) + (−78.154×V

O ) + 153.857

where

•

T is temperature express in °C and VO is the output voltage expressed in volts.

(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 LM20. The slope of the linear transfer function can be calculated using the Equation 8 equation:

m =

−7.76 × 10

−6× T − 0.0115,

where

•

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

(8)

For example for the temperature range of TMIN = −30 to TMAX = 100°C:

T = 35°C

(9)

and

m =

−11.77 mV/°C

(10)

The offset of the linear transfer function can be calculated using the Equation 11 equation:

b = (VOP(TMAX) + VOP(T) − m × (TMAX+T))/2

where

•

VOP(TMAX) is the calculated output voltage at TMAX using the parabolic transfer function for VO

•

VOP(T) is the calculated output voltage at T using the parabolic transfer function for VO.

(11)

The best fit linear transfer function for many popular temperature ranges was calculated in Table 3. As shown in

Table 3, the error 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

Linear Equation

Equation from Parabolic Equation (°C)

Tmin (°C)

Tmax (°C)

−55

130

VO = −11.79 mV/°C × T + 1.8528 V

±1.41

−40

110

VO = −11.77 mV/°C × T + 1.8577 V

±0.93

−30

100

VO = −11.77 mV/°C × T + 1.8605 V

±0.70

-40

85

VO = −11.67 mV/°C × T + 1.8583 V

±0.65

−10

65

VO = −11.71 mV/°C × T + 1.8641 V

±0.23

35

45

VO = −11.81 mV/°C × T + 1.8701 V

±0.004

20

30

VO = –11.69 mV/°C × T + 1.8663 V

±0.004

12

Submit Documentation Feedback

Copyright © 1999–2015, Texas Instruments Incorporated

Product Folder Links: LM20