3–208
Motorola Sensor Device Data
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PURPOSE
This paper describes a simple method to gain more than
8–bits of resolution with an 8–bit A/D. The electronic design is
relatively simple and uses standard components.
PRINCIPLE
Consider a requirement to measure pressure up to
200 kPa. Using a pressure sensor and an amplifier, this
pressure can be converted to an analog voltage output. This
analog voltage can then be converted to a digital value and
used by the microprocessor as shown in Figure 1.
If we assume for this circuit that 200 kPa results in a +4.5 V
output, the sensitivity of our system is:/
S
4.5 V 200kPa
0.0225 V kPa
22.5 mV kPa
(1)
or
S
If an 8–bit A/D is used with 0 and 5 Volt low and high
references, respectively, then the resolution would be:
S
5V
2
8
–1
5V 255
(2)
0.01961 V
19.60 mV per bit
or
Rv
This corresponds to a pressure resolution of:
R
P
5V
0.871 kPa per bit
19.60 mV bit)
22.5 mV kPa
(3)
Assume a resolution of at least 0.1 kPa/bit is needed. This
would require an A/D with at least 12 bits ( 212 = 4096 steps).
One can artificially increase the A/D resolution as described
below.
Refer to Figure 1 and assume a pressure of 124 kPa is to
be measured. With this system, the input signal to the A/D
should read (assuming no offset voltage error):
V
m
(measured)
4.5 (Papp) x (S)
(124 kPa) x 22.5 mV kPa
2790 mV,
(4)
where Papp is the pressure applied to the sensor.
Due to the resolution of the A/D, the microprocessor
receives the following conversion:
M
(2790 mV)
142.35
142 (truncated to integer)
19.60 mVbit
(5)
The calculated voltage for this stored value is:
V
c
(calculated)
(142 count) x 19.60mV
count)
2783 mV
(6)
The microprocessor will output the stored value M to the
D/A. The corresponding voltage at the analog output of the
D/A, for an 8–bit D/A with same references, will be 2783 mV.
The calculated pressure corresponding to this voltage
would be:
P
c
(calculated)
(2783 mV)
123.7 kPa
22.5 mV kPa
(7)
Thus, the error would be:
E
Papp–Pc
124 kPa–123.7 kPa
0.3 kPa
(8)
This is greater than the 0.1 kPa resolution requirement.
Figure 1. Block Diagram
+V
G
A/D
MPU
OUTPUT
CIRCUITRY
Vm
M
Pc
SEMICONDUCTOR APPLICATION NOTE
REV 1
F
Freescale Semiconductor, Inc.
n
.