At low elevations, a square meter on the earth’s surface has greater weight above it than at higher altitudes. This is due to the
mass of water vapor and air that sits upon it. Imagine cubes of air and water vapor stacked from the ground to space. At the low
altitude there is more cubic mass above, while higher altitudes will have less of these stacked above it.
Air and water vapor will compress more at sea level and the air is significantly denser than at high altitude. The density is not
uniform with altitude, and thus the pressure is not either. The reason for altitude’s non-linear relationship is that air has infinite
compressibility. It disproportionately compresses more as weight is placed upon it. Hence the graph of Pressure vs. Altitude seen
in Figure 6.
The simplified mathematical equation used to calculate altimetry in Table 3 is:
–h
------------------
7990m
ph = p0 ⋅ e
(eq. 1)
(eq. 2)
p0
------
h = 18400m ⋅ log
ph
Assuming p0 = 101.3 kPa
ph - Pressure at height h
po - Initial Pressure point at sea level or 101.3 kPa
Calculations for a 24-bit ADC
First: Figuring out how the 24-bit ADC translates to counts, followed by pressure and altitude.
Table 4.
ADC Resolution
8-bit
Range of ADC Counts
0 to 255
12-bit
0 to 4095
16-bit
0 to 65,535
18-bit
0 to 262,143
0 to 16,777,215
24-bit
24-bit ADC LTC2442 reference voltage is 4.1 V (temperature and voltage stable shunt).
MPXM2102A has a 16.4 mV span @ 4.1 V supply.
Output is gained x 98.8 by instrumentation amplifier.
Span of differential amplified signal is now 1.62 V.
Low pressure end of 0 kPa input is approximately 0 V seen at the differential amplifier output.
Conversely the higher end of the pressure reading at 100 kPa is = 1.62 V.
SPAN of MPXM2102A after Differential Instrumentation Amplifier is now 1.62 V.
The 24-bit ADC would have a resolution of 4.1V/16777215 counts or 0.244 V per an ADC count. Since the differential span of
the sensor is 1.62 V after the amplifier, the span of 0 to 100 kPa can be seen as a ADC value of 0 counts to 6629045 counts.
This makes each ADC count equivalent to 0.0000151 kPa or 0.0151 Pa. The LTC2442’s value was shortened to a 18-bit
conversion to minimize the baseline noise seen on the ADC output.
For an 18-bit ADC conversion, 4.1V/262143 equals a resolution of 15.6 V per a single ADC count. Since the differential span
of the sensor is 1.62 V after the amplifier, the span of 0 to 100 kPa can be seen as a ADC value of 0 counts to 103846 counts.
This makes each ADC count for the pressure span equivalent to 0.000963 kPa or 0.963 Pa.
AN3956
Sensors
Freescale Semiconductor
12
FREESCALE [ Freescale ]
