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–5–
A/D Converter Performance
As measured on the bench (using a precision reference
voltage generator in place of the AD22100), this A/D
circuit delivered 14-bit resolution, less than 1 LSB of
“flicker,” and approximately 0.03% integral linearity
error. The integral linearity could be improved via the
use of a comparator with better CMRR, but this level of
performance was judged adequate for this application.
The converter’s worst nonlinearities occur at the
extreme ends of the input range where the pulse train
density is either very high or very low. This happens be-
cause the ripple caused by the pulse train cannot be ad-
equately suppressed by the fixed pole of the RC filter. In
this particular application, this nonlinearity results in er-
rors of a few tenths of a degree when the input is near
–50°C or +150°C (the specified operating range for the
AD22100).
Calibration and Scaling
Despite the ratiometric characteristic of both the A/D
converter and the AD22100 sensor, this circuit requires
calibration. An ideal implementation of this A/D archi-
tecture
shouldn’t
require calibration; for example, an
input of exactly one-half the supply voltage should re-
sult in a perfect 50% pulse train density, which should
result in an output of 8096 counts (one half of 16,384 it-
erations of the conversion loop).
Unfortunately, in the real world there are error sources
that result in a less than perfect transfer function. The
input offset voltage of the comparator causes a corre-
sponding offset error at the output. Slew rate limitations
and other error sources in the hex inverter circuit can
also cause gain errors. Consequently, it is necessary to
calibrate the A/D for accurate operation.
The A/D output must also be scaled for use in most ap-
plications. We must compensate for the 0 °C offset term
(1.375 volts, or 27.5% of the power supply voltage), as
well as deal with the gain of the sensor (22.5 mV/ °C).
In this application, we are assuming that the user re-
quires a signed binary integer output with a resolution
of 0.1°C; this implies that the output must be 03E8H
(1000 counts) when the sensor is at 100 °C, and 0 counts
when the sensor is at 0 °C.
The normal method of calibration for analog circuits is
the use of trim potentiometers. Since this circuit already
includes a microcontroller, we can eliminate trim poten-
tiometers in favor of electronic digital calibration. Fur-
thermore, we can combine the scaling and calibration
into a pair of simple procedures.
The side benefit of electronic calibration is a significant
improvement of accuracy in temperature measurement.
Without electronic calibration, the accuracy of the
AD22100 is fairly good. The error of the least expensive
grade is typically ±0.5°C at 25°C, rising to ±0.75 over its
specified temperature range. However, an examination
of the typical maximum performance plot of the
AD22100 (see Figure 6) reveals that most of the errors
are caused by simple gain and offset errors, not by sen-
sor nonlinearity. If we could correct for these terms, the
resulting accuracy would be significantly improved. Ex-
amination of actual AD22100 factory evaluation data
shows that the nonlinearity of the sensor between 0 °C
and 100 °C is just a few tenths of a degree; if the sensor
were actually calibrated at 0 °C and 100°C,
the overall
accuracy could be considerably improved over the data
sheet specifications!
4
3
2
1
0
–3
–4 –50 TEMPERATURE – °C
–25 0 25 50 75 100 125 150
ERROR – °C
–1
–2
MAXIMUM ERROR
TYPICAL ERROR
MAXIMUM ERROR
Figure 6. Typical AD22100 Performance
Calibration at 0 °C and 100°C is convenient, as well. If no
controlled temperature chamber is available, a fairly
close approximation to these temperatures can be
achieved with ice water and boiling water (although
altitude and contaminants might degrade the accuracy
somewhat).
The mathematics of calibration and scaling are most
easily understood by referring to the graph in Figure 7.
Prior to calibration and scaling, the natural output of the
converter is an unsigned 14-bit integer (represented by
the trace labeled “A” on the graph). If we were to as-
sume a perfect converter, operating at 5 volts, then the
numerical values for this trace would be 11,878 counts
at 100 °C (3.625 V/5 V times 16,384), and 4,506 counts at
0°C (1.375 V/5 V times 16,384). The theoretical zero
crossing of this trace occurs at –61.111 °C.