Introduction

pH probes provide a voltage that is a direct relation to the solution’s pH and temperature:

• pH probe’s output is measured in mV.
• the result is always mV = 0 for a pH = 7, for all temperatures.
• The reading is linear in relation to the solution’s acidity.
• The slope of the reading is linear in relation to the temperature.
• at 0 degC the slope is 54.20 mV/pH
• at 25 degC the slope is 59.16 mV/pH
• at 100 degC the slope is 74.04 mV/pH

Calculating pH

If X is the slope of the pH reading for a given temperature, then the pH is given by:

pH = 7.0 – V/X With V the measured voltage of the probe in mV.

And X is given by:

X = 0.1984 * T + 54.20 With T in degrees Celcius.

Measuring temperature

Temperature is measured using an RTD (Resistance Thermal Device). Its resistance is given by the following quadratic equation:

Rt = R0*( 1 + A*T + B*T*T)

With:

R0 = 1000

A = 0.0039083

B = -0.0000005775

Using a linear approximation for estimating the temperature using the thermal resistance.

Rt = 1000 * ( 1 + 0.0039083 * T ) Which gives;

T = ( Rt – 1000 ) / 3.9083

The max temperature approximation error is 1.5 degrees C.

Sensitivity of the result to the different parameters

The biggest variation of the pH in relation to the measured voltage will be where X is the smallest, i.e at 0 degrees Celcius:

A variation of the measured voltage by 1mV will change the pH value by at most 0.000018

The biggest variation of the pH in relation to the measured temperature will be where X is again the smallest, i.e between 0 and 1 degree Celcius, and at the highest measured voltages, i.e -500mV

A variation of the measured temperature by 1.5 degree Celcius will change the pH value at most by 0.06

Calibrating a pH probe and electronics

The electronics and probe will introduce errors in the form of drift of the reference and slopes. To correct this, calibration is needed and is done in the following manner:

On a regular basis, the system will be calibrated using solutions at known pH.

As the solutions are at a known pH, the expected measured valued are known, and therefor can be used in comparison with the actual measured values to infer a calibration correction.

Method:

The correction will be a linear function: transforming a measured voltage into an expected voltage.

V = a * v + b With V = expected voltage and v = measured voltage.

The two buffers used will have a pH of 7.0 and 4.0, the current temperature is important for calculating the expected voltage for the pH = 4 solution.

If vph4 and vph7 are the measured values at the current temperature tcur , then we have:

a * vph7 + b = 0

a * vph4 + b = 3.0 * ( 0.1984 * tcur + 54.20)

a = 3.0 * ( 0.1984 * tcur + 54.20) / (vph4 – vph7)

b = – a * vph7

Note: once a and b are calculated, then the expected voltage in the range -600 mV to 700 mV will be calculated using the formula: V = a*v + b, with v being the measured value, no matter what the electronic circuit or measuring range or number system is used.

Effectively calculating pH

It is assumed that the following data is known:

• a calibration data
• b calibration data
• Rt measured resistance off temperature probe.
• Vp measured voltage off pH probe.

1st step: calculate theoretical voltage of the probe.

V = a * Vp + b

2nd step: calculate temperature.

T = ( Rt – 1000 ) / 3.9083

3rd step: calculate temperature correction

X = 0.1984 * T + 54.20

4th step: calculate pH

pH = 7.0 – V/X