## Introduction

The MPX4115A from Motorola provide a voltage proportional to the absolute pressure with a transfer function of:

**V**_{out} = V_{S} x (0.009 x (P – 0.095))± (Pressure Error x Temp. Factor x 0.009 x V_{S})

The values V_{out} and V_{S} are read directly using a 10 bit ADV using the DS2438 slave device. The transfer function is then used to calculate the presssure P in kPa.

However for meteorological purposes the atmospheric pressure is usually presented in hPa (1hPa = 1mb = 0.1kPa) and normalised to sea-level values to facilitate comparison between stations at differing altitudes. Furthermore, to improve the sensitivity and resolution the output of the MPX4115A is offset by fixed voltage and the result multiplied by 10 using an INA122 intstrumentation amplifier.

## Altitude Correction

Atmospheric pressure is conventially reported as the eqivalent pressure at sea level. However in South Africa as the greater portion of the land mass has an elevation of over 900 metres whilst the area below 500 metres consists merely of a narrow fringe around the coast, the actual solution adopted is the construction of bi-level charts, viz. 850-mb surface contour analysis for the plateau and sea-level isobars for coastal areas. Thus, for stations at an elevation above 500 gpm, pressure is reported at the nearest 100 gpm or 1250 gpm levels. The pressures at these levels are then reduced to the 850-mb
surface. As there is no direct method of determining the virtual temperature of the column between these
levels and the 850-mb surface for the appropriate stations, empirical methods are resorted to as the only
alternative.

As an initial estimate the calibration of pressure sensor will be done based on a normalisation to sea-level and then modified if necessary following comparison with local meteorological stations.

### Normalisation to sea-level

Normaly the Laplace formula is used for normalisation:-

But for a home weather station the simpler Babinet gives close correspondence up to 1000 metres and results within 1% to considerably greater heights

For an altitude of 1675m (Benoni South Africa) the Babinet equation gives a correction factor of **0.82326**. Therefore the standard atmospheric pressure of **101.325kPa** will be read as **83.417kPa** at this altitude.

## Transfer function

Because we are using an INA122P Instrumentation Amplifier with a fixed gain of 10X we need to determine an offset voltage that will place the standard atmospheric pressure in the middle of our measurement range. The transfer function for the INA122P is:

**V**_{o} = 10 * (V_{in} - Offset)

Where **V**_{o} is the output in Volts and **V**_{in} is the transfer function of the MPX4115 i.e.

**V**_{o} = 10 * (V_{S} x (0.009 x P – 0.095) - Offset)

At a standard pressure of **83.417kPa** (101.3kPa at sea-level) and a supply voltage **V**_{S} of 5V the final output **V**_{o}
should be 5V

Rearranging we get

**Offset = V**_{s}(0.009 P - 0.095) - 0.5

Substituting and solving for the Offset we get a value of **2.778**for a supply voltage of 5V (for supply voltages of 4.93V and 4.97V the offsets are
2.731 and 2.758 respectively).

The transfer function for the atmospheric pressure sensor becomes:-

**V**_{o} = V_{S} x (0.009 P – 0.095)) - 27.78)

Re-arranging we obtain :-

With a supply voltage of 5V this provides a range of 72.3 to 94.51 kPa (87.8 to 114.8kPa at sea-level) and a resolution of 0.022 kPa.

For absolute pressure in kpA then **P = 2.222 V**_{0} + 72.3086

For normalised pressure in kPa then **P = 2.699 V**_{0} + 87.832

## Calibration

Calibration is accomplished by monitoring your pressure and comparing it with a known calibrated
reference source. You can use another calibrated barometer or a nearby online weather
station such as the National Weather Service at www. nws . noaa . gov /. I use the nearby
international airport Synop Information for FAJS (68368) in Johannesburg International Airport, South Africa

Start by adjusting the intercept. When the reference station indicates a pressure near mid-scale
(101 kPa), adjust the software offset until your weather station matches. Then, over time,
monitor the pressure extremes to determine if the gain needs adjustment. When the reference
station indicates high pressure (at least 102kPa), check your barometer. If your pressure
reads lower, you will need to increase the gain. Conversely, if the reference station is reporting a
high pressure, and yours reads higher, you will need to reduce the gain.
In either case, divide the reference pressure by your reading to get a correction factor. Then
multiply the correction factor by the present value of gain to get your new
gain. If you tweak the gain, you'll also have to re-adjust-the offset. Repeat this
process until you are satisfied with the calibration.