I am trying to build a sensor that will have maximum sensitivity (in the form of capacitance change) to the dielectric environment immediately outside the shell of the sensor. I am envisioning a plastic cylinder with the two capacitive plates inside the wall in the form of two identical cylindrical rings separated by a gap. I want the free-air capacitance between the plates to be approximately 10 pF, and capacitance when the probe is immersed in a high-dielectric environment to be as high as possible.

Anybody have any clues as to the appropriate formulas to approximate the free-air capacitance? Is my proposed geometry appropriate? How do I pick the optimal size (diameter/length) of the rings and their separation distance?

Thanks for any and all help on this!

- Michael

 

In reality the capacitance will probably only change by a factor of εr - the relative permittivity. Fringing may be slightly different in the two cases (in air or dielectric) but I can't imagine why it would be.

So if εr=3 then you'll have 30pF rather than 10pF.

http://www.davidpace.com/physics/em-topics/capacitance-cylinders.htm

also see this calculator

http://www.ajdesigner.com/phpcapacitor/cylindrical_capacitor_equation.php

 

When immersed, will the fluid be between the two plates?

What fluids are you working with? Some may be more conductive than anything like a dielectric.

 

The cylindrical rings will be insulated from the target media by the plastic cylinder they are installed within. I am trying to get the fringe field to project as much as possible through and beyond the plastic cylinder into the surrounding material. My initial target for this beastie is dry-to-moist sandy soil, and I am going to use the change in dielectric properties within the fringe field to estimate the moisture content of the soil.

The equations referenced above are for co-axial electrodes. To envision what I am proposing, take a single cylindrical electrode (say a section of copper pipe), and remove a ring-shaped slice from the center, leaving two aligned, identical, ring-shaped electrodes. From the idealized perspective of one electrode, the other electrode appears as a pure circle with no area. All the field lines connecting the two electrodes would have to exit at right angles to the cylindrical surfaces, curve through the surrounding space, and connect with the other electrode in a symmetrical fashion (hence the enhanced fringe effect).

Can anybody point me to a closed-form solution for calculating the free-air capacitance of two electrodes in my proposed geometry? All the reference equations I have been able to dig up are for classical capacitor geometries which minimize/ignore fringe effects.

If I can find a reference solution I can morph it into my actual dimensions as needed. In particular, I don't know how to optimize the separation distance between the rings. If only I could do a finite-element simulation it would be cake, but that is beyond my competence...

- Michael