AN897 datasheet(7/16 Pages) MICROCHIP

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 2004 Microchip Technology Inc.

DS00897B-page 7

AN897

PIECE-WISE LINEAR INTERPOLATION TABLE

Each of the three gains uses a piece-wise linear inter-

polation table [9] to convert ADC codes to estimated

temperature. Within each table, the ADC’s codes were

divided into 64 segments, with 16 codes per segment.

The tables only include those ADC codes at the end

points between segments. Table 3 shows the extreme

valid table entries for each of the three tables.

TABLE 3:

INTERPOLATION TABLE END

POINTS.

Values of TTH and RTH beyond the specified tempera-

ture range of the thermistor (-40°C to +150°C) are

estimates only; they are not supported by actual data.

The thermistor self-heating error correction has been

included in Table 3.

The table’s entries go outside of -40°C to +150°C to

ensure proper functioning of the piece-wise linear

interpolation table when the reading overflows. In this

algorithm (Appendix A.2.6 “Firmware for the Signal

Analysis PICtail Daughter Board”), the table values

outside the valid range take on the nearest valid value.

This means that when G = 1 and ADC code > 960, the

table returns a value of -43.5°C. When G = 32 and

ADC code < 208, the table returns a value of 150.9°C.

The other table entries beyond the end points in Table 3

(e.g., near gain-change points) are zero because the

hysteresis algorithm will prevent them from being read.

This approach has been used for readability.

Digital Error Analysis

Figure 17 shows the estimated interpolation error for

the interpolation table. Changing the PGA’s gain takes

full advantage of the ADC’s resolution. The accuracy of

this piece-wise linear interpolation table is 0.034°C

over the -40°C to +150°C temperature range. The

improved ADC temperature resolution makes this

design’s piece-wise linear interpolation table behave

much better than the first design’s.

FIGURE 17:

Piece-wise Linear

Interpolation Error, Design # 2.

The digital roundoff error will be roughly proportional to

the ADC temperature resolution curve’s envelope (see

Figure 13). If the roundoff error is much less than the

ADC resolution, this error will have little impact.

The total digital error includes both the piece-wise lin-

ear interpolation error and round-off error.

DESIGN COMPARISON

Figure 18 shows the thermistor’s specified accuracy. It

contributes the same error to both designs.

FIGURE 18:

Thermistor Accuracy.

Figure 19 compares the ADC temperature resolution

between the first and second design. The second

design is better because changing the PGA’s gain

helps improve the ADC temperature resolution.

Gain

(V/V)

ADC Code

(LSb)

TTH

(°C)

RTH

(

Ω)

VOUT

(V)

960

-43.5

420k

4.688

112

51.2

3.44k

0.547

960

49.2

3.72k

4.688

224

94.9

787

1.094

960

92.6

845

4.688

208

150.9

179

1.016

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

-50

-25

100

125

150

Thermistor Temperature (°C)

Design # 2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

-50

-25

100

125

150

Thermistor Temperature (°C)

BC Components

# 2322 640 55103

10 k

Ω @ +25°C

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