Pressure - temperature correction of pressure

Let us consider a pressure sensor integrated on the RBRconcerto³ C.T.D. The pressure reading from Channel-3, without correction for the effect of temperature on the sensor, is given by a cubic polynomial:

$//<![CDATA[ \begin{array}{l}Praw = c_0 + c_1 \cdot R + c_2 \cdot R^2 + c_3 \cdot R^3\end{array} //]]>$

where R is the normalized voltage ratio from Channel-3 monitoring pressure, c0...c3 are the core coefficients of the cubic polynomial equation, and Praw is the uncorrected pressure output, reported in dbar for RBR instruments.

The equation which accounts for residual temperature sensitivity of the pressure sensor is:

$//<![CDATA[ \begin{array}{l}Pcorr = Pcal + \dfrac{(Praw - Pcal) - Kp_1 \cdot (T - Tcal) - Kp_2 \cdot (T - Tcal)^2 - Kp_3 \cdot (T - Tcal)^3}{1 + Kp_4 \cdot (T - Tcal)}\end{array} //]]>$

Casting this into the form used by the logger would yield:

$//<![CDATA[ \begin{array}{l}Pcorr = x_0 + \dfrac{(Praw - x_0) - x_1 \cdot (value(n_0) - x_5) - x_2 \cdot (value(n_0) - x_5)^2 - x_3 \cdot (value(n_0) - x_5)^3}{1 + x_4 \cdot (value(n_0) - x_5)}\end{array} //]]>$

where

• Praw is the cubic polynomial in R, as before,
• x0 is the calibration pressure 'Pcal' in dbar,
• x1 ,   x2, x3, x4    correspond directly to the constants "Kp1" through "Kp4",
• x5 is the calibration temperature "Tcal" in °C,
• n0    is the index of the temperature channel, in this example 2,
• value( n0 ) is the final output value of the temperature channel in °C,
• Pcorr is the corrected output in dbar.