Capacitive distance sensor - humidity influence?

We are using a capacitive sensor to measure displacement (from here: https://www.micro-epsilon.com/displacement-position-sensors/capacitive-sensor/?sLang=en). However, we seem to notice a significant dependence on the humidity of the air on the result (temperature in the room is controlled and almost constant, humidity varies over the year from about 20%-50%).

The obvious cause would be a humidity dependence of the relative permittivity. However, I cannot seem to find any data of this dependence (except some for the static case). On the other hand, this surely has been measured.

So the question is: Is there data available for the humidity dependence of the relatve permittivity of air at frequencies from 20 Hz to e.g. 10 kHz?

• There are capacitive humidity sensors for air. They work on the same principle as your displacement sensor. I think you are going to have to account for air humidity when using your displacement sensor.
– JRE
Jan 22 '21 at 11:47

At around 20 °C, water has a relative electrical permittivity of about 80. Air is 1 so, any water content could be a significant factor in altering the capacitance measured. Given that capacitance is proportional to permittivity there should be a fairly direct link.

I guess all you have to do is calculate the percentage presence of water in a given "air" volume for a certain level of humidity. For instance, wiki states this: -

A parcel of air near saturation may contain 28 g (0.99 oz) of water per cubic metre of air at 30 °C (86 °F)

And, this document pretty much shows the same thing (ignore the red lines). At 30 °C and 100% RH, the water content is around 25 g per cubic metre: - So, using the above example, 1 cubic metre contains 28 g of water or, as a volume that's 28 ml. And, there's 1,000,000 ml in 1 cubic metre so, as a volume percentage, 28 mg of water per cubic metre is 0.0028%.

Given that the permittivity of water is 80, then the capacitance could increase by 80 x 0.0028% = 0.224%.

But, you may also attract condensation onto your sensor and that will surely make the capacitance sensor read a much higher value.

Is there data available for the humidity dependence of the relative permittivity of air at frequencies from 20 Hz to e.g. 10 kHz?

This graph from here suggests that you won't get a change in dielectric permittivity of water until you are in the GHz region: - And this graph shows that the dielectric permittivity of water is constant down to 1 MHz. I think it's reasonable to assume that it will stay constant down to DC: - And this graph from here pretty much nails it down to about 10 Hz: - • (a) So this means I can add relative permittivity with the appropriate volume fraction? 28g=28ml would be for a liquid though, not for vapour? (b) Is there data on how that would depend on frequency? Jan 22 '21 at 11:13
• 28 g would still translate to a percentage of water as a gas in one cubic metre. As for frequency I don't understand your question? Do you mean how often? @Toffomat Jan 22 '21 at 11:18
• If you want specific help re the sensor, please link the exact data sheet for the device you are using rather than the ambiguous link in your question. Jan 22 '21 at 11:21
• (a) But weight-wise, 28 g of water per m^3 would be more like 2.2% (1m^3 of air is about 1220 g). (b) Re frequency: The permittivity is frequency dependent. But maybe that's negligible in the range from static to some 10 kHz (?) Jan 22 '21 at 11:27
• Well, 28g/m^3 is about 2.2% by weight. But anyway, your answer indeed helps, thank you! Jan 22 '21 at 12:13