AN1100 Analog to Digital Converter Resolution Extension Using a Pressure Sensor

Freescale Semiconductor
Application Note
AN1100
Rev 3, 05/2005
Analog to Digital Converter Resolution
Extension Using a Pressure Sensor
PURPOSE
This paper describes a simple method to gain more than 8bits of resolution with an 8-bit A/D. The electronic design is
relatively simple and uses standard components.
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):
Vm(measured)
Principle
Consider a requirement to measure pressure up to
200kPa. 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 +4.5V
output, the sensitivity of our system is:/
S
or
S
=
=
=
4.5 V/200kPa
0.0225 V/kPa
22.5 mV/kPa
(1)
If an 8-bit A/D is used with 0 and 5 Volt low and high
references, respectively, then the resolution would be:
S
or
=
=
Rv =
5 V/(28 – 1 = 5V/255)
0.01961 V
19.60 mV per bit
(2)
Rp =
=
5 V/(19.60 mV/bit) / (22.5 mV/kPa)
0.871 kPa per bit
(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.
M
=
=
=
(2790 mV) / (19.60 mV/bit)
142.35
142 (truncated to integer)
VM
A/D
= (142 count) × (19.60mV/count) (6)
= 2783 mV
Vc(calculated)
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:
= (2783 mV) / (22.5 mV/kPa)
= 123.7 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.
M
Figure 1. Figure Block Diagram
© Freescale Semiconductor, Inc., 2005. All rights reserved.
(5)
The calculated voltage for this stored value is:
+V
G
(4)
where Papp is the pressure applied to the sensor.
Due to the resolution of the A/D, the microprocessor
receives the following conversion:
Pc(calculated)
This corresponds to a pressure resolution of:
= 4.5 (Papp) × (S)
= (124 kPa) × (22.5 mV/kPa)
= 2790 mV,
MPU
PC
Output
Circuitry
+V
VM
G
M
A/D
Σ
-
Control
C
D
G
Control
Output
Circuitry
MPU
VC
D/A
M
Analog Circuitry
Figure 2. Expanded Block Diagram
Figure 2 shows the block diagram of a system that can be
used to reduce the inaccuracies caused by the limited A/D
resolution. The microprocessor would use the stored value M,
as described above, to cause a D/A to output the
corresponding voltage, Vc. Vc is subtracted from the
measured voltage, Vm, using a differential amplifier, and the
resulting voltage is amplified. Assuming a gain, G, of 10 for the
amplifier, the output would be:
D
=
=
=
(Vm–Vc) × G
(2790 mV – 2783 mV) × 10
70 mV
(9)
=
=
=
Expanded Voltage = Vc + ((C × R)/G)
= 2783 + ((3 × 19.60)/10)
= 2789 mV,
NOTE: R is resolution of 8-bit d/A
(11)
Corresponding Pressure=
=
=
2789 mV/
22.5 mV/kPa
123.9 kPa
(12)
Actual – Measured
124 kPa – 123.9 kPa
0.1 kPa
(13)
Thus the error is:
The microprocessor will receive the following count from
the A/D:
C
The microprocessor then computes the actual pressure
with the following equations:
70mV/(19.60 mV/count)
3.6
3 full counts
(10)
Pressure Error
=
=
=
Figure 3 and Figure 4 together provide a more detailed
description of the analog portion of this system.
+V
R4
+V
R3
R2
R1
R5
+
R8
A1
+
-
A2
-
R6
NOTE: R7 = R2, R1 = R6
R7
VM (To Second Stage)
R9
R10
Figure 3. First Stage - Differential Amplifier, Offset Adjust and Gain Adjust
AN1100
2
Sensors
Freescale Semiconductor
Vm
R11
+
Vm
(From
First
Stage)
R15
+
A3
R12
-
-
R14
R16
R17
R13
NOTE: R14 = R12, R11 = R13
D
A4
From D/A
VC
Figure 4. Second Stage - Difference Amplifier and Gains
FIRST STAGE (FIGURE 3)
The first stage consists of the pressure sensor; in this case
the MPX2200 is used. This sensor typically gives a full scale
span output of 40 mV at 200 kPa. The sensor output (VS) is
connected to the inputs of amplifier A1 (1/4 of the MC33079,
a Quad Operational Amplifier). The gain, G1, of this amplifier
is R7/R6. The sensor has a typical zero pressure offset
voltage of 1 mV. Figure 3 shows offset compensation circuitry
if it is needed. A1 output is fed to the non-inverting input of A2
amplifier (1/4 of a MC33079) whose gain, G2, is 1+R10/R9. G2
should be set to yield 4.5 volts out with full-rated pressure.
THE SECOND STAGE (FIGURE 4)
The output from A2 (Vm = G1 x G2 x Vs) is connected to
the non-inverting input of amplifier A3 (1/4 of a MC33079) and
to the A/D where its corresponding (digital) value is stored by
the microprocessor. The output of A3 is the amplified
difference between Vm, and the digitized/calculated voltage
Vc. Amplifier A4 (1/4 of a MC33079) provides additional gain
for an amplified difference output for the desired resolution.
This difference output, D, is given by:
D
=
G3 =
(Vm Vc) × G3
(
(R14/R13) 1 +
R17
R16
where G3 is the gain associated with amplifiers A3 and A4.
The theoretical resolution is limited only by the accuracy of
the programmable power supply. The microprocessor used
has an integrated A/D. The accuracy of this A/D is directly
related to the reference voltage source stability, which can be
self-calibrated by the microprocessor. Vexpanded is the system
output that is the sum of the voltage due to the count and the
voltage due to the difference between the count voltage and
the measured voltage. This is given by the following relation:
therefore,
Vexpanded
=
Vc + D/G3
PVexpanded
=
Vexpanded/S.
Pexpanded is the value of pressure (in units of kPa) that
results from this improved-resolution system. This value can
be output to a display or used for further processing in a
control system.
CONCLUSION
This circuit provides an easy way to have high resolution
using inexpensive microprocessors and converters.
)
AN1100
Sensors
Freescale Semiconductor
3
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AN1100
Rev. 3
05/2005
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