Sensor Output Signal

The measuring signal, which is the electron flow between anode and cathode, is mathematically expressed by:

Where:
I = measured signal (A • s)
n = number of electrons released by the chemical reaction (n = 4)
F = Faraday constant (9.649 × 10⁴ As/mol^-1)
P_M = oxygen permeability of the membrane (cm²)
P_O2 = partial pressure of oxygen (mol/cm³)
b = membrane thickness (cm)
A = area of cathode tip (cm²)

The equation shows that the measured signal is directly proportional to the partial pressure of oxygen and not to the oxygen concentration. If the measured value must be expressed in ppm, ppb, or mg/l, then the sample fluid temperature, the barometric pressure, and the oxygen solubility of the measured media must be known. A separate temperature probe can be used, but most oxygen sensors have a built-in temperature probe. A solubility table for oxygen in water is normally included in the software of modern dissolved oxygen meters, and even a barometric pressure sensor is incorporated into some sensor devices.

The membrane’s permeability is also temperature dependent. The oxygen permeability of the membrane increases strongly with rising temperature, which allows more oxygen to diffuse into the electrolyte of the oxygen probe, even though the oxygen partial pressure has not changed. This would result in false measuring results if not compensated for with a temperature measurement near the membrane.

The temperature dependency of the oxygen diffusion P_M is explained by:

Where:
P_M = oxygen permeability of the membrane (m²)
P_Stp = oxygen permeability at standard temperature and pressure (m²)
E = initiation energy (J/mol)
R = gas constant (J • K^-1 • mol^-1)
T = absolute temperature (K)

The measuring current increases exponentially when the temperature of the membrane rises. The temperature dependency of the membrane is normally given as the “membrane temperature coefficient” and can be compensated for by a compensation circuit and a temperature probe.