Someone asked in the signal analyzers forum about measuring permittivity with a coaxial probe. Clearly that was the wrong place, and had some silly title.
(A read of How To Ask Questions The Smart Way might be useful!)
This is my response to that.
The topic of coaxial probes is complicated, and of interest to me too. The problem is any papers I find on the topic seem to be littered with maths I can't follow. Dr. Dunsmore gave an interesting reference of Dave Blackman's Ph.D. - I will have to look at that at some point.
There's also an interesting Ph.D. thesis by Philip G. Bartley, with the title
CHARACTERIZATION AND CALIBATION OF AN ARBITRARILY SHAPED PERMITTIVITY MEASUREMENT PROBE
(He seems to have missed the "R" out of calibration). I stuck a copy on my website
Dr. Bartley's work must have been done in collaboration with Agilent, as Dave Blackham is mentioned, all the pictures show HP/Agilent kit. Also Shelley Begley is mentioned, who I believe is a materials expert at Keysight. (I can't recall her surname, but I met a Shelley at Keysight offices in the UK. She was a materials expert. It seems highly likely it was the same Shelly, but I'm not 100% sure.)
There are a few interesting things about that Dr. Bartley's Ph..D.
- There's not tons of maths - in fact, some really important equations are not included.
- It works for any shape of probe - not just the "simple" coaxial one. For example, if a coaxial probe was modified to be shaped like a hypodermic needle.
The method works on training fuzzy logic and neural networks with solutions of known permittivity. The known values of Er used for training are made by mixing chemicals like water and methanol in a way where Er can be determined. The problem is Bartley never gives any simple equation of the form
Er=f(percentage of water, percentage of methanol)
Instead the reader is expected to obtain the information for a huge volume of data in some NIST document, which is laid out in a very confusing way. I did intend contacting Dr. Bartley about that, hoping he could provide the necessary information in simple way, but never got around to it. The work is interesting, and for a Ph.D. thesis, refreshing easy reading.
I'm sure the coaxial probe will be the subject of many more Ph.Ds. That one was interesting, but spoiled by the lack of any information about how much of each chemical one needs for a specific permittivity.