It is a very interesting subject...
I think the link in the first post doesn't work but here's a link to David Knight's stuff on inductor resonance.
http://g3ynh.info/zdocs/magnetics/ap.../self-res.html
It's a while since I last read his work on this and the latest version of his paper is now over 100 pages long. I think his work dates back a long time. I think it may go back over 10 years at least because I remember seeing the interesting Trio TS430S transmitter experiments he did. I think the last time I read this paper it was much shorter.
This evening I skimmed over the latest version of his paper here:
http://g3ynh.info/zdocs/magnetics/ap...s/self-res.pdf
There's loads of interesting info there and lots of extracts from other researchers' work. However, I think it has become quite bloated now and it doesn't flow very well. I think there is room for a more focussed document that just shows the reader how to model an inductor up through two or more resonance modes. I also notice that this latest version does have graphs to show that the resonance modes aren't always at exact multiples of the first resonance. Anyone with access to basic/modern test gear can do a few simple experiments and spot this in less than an afternoon.
I did a lot of study work of my own many years ago at work on this subject for the reasons I gave earlier. This culminated in various attempts to model and understand what is going on within the inductor itself. I was mainly interested in quite small inductors that go on a PCB and I found that the 'black box' s parameter model of a solenoid is the best one to use in a simulator as it is so versatile and accurate. This was followed by my own (complex) transmission line model.
It generally models the first two or three resonance modes quite well.
I didn't need to adopt any of the complex equations given by the various contributor's to David's paper and just derived my own, based on simple observations and the application of some basic transmission line theory. So it was all very crude but it seemed to give fairly good results for both free space and 'in circuit' use. Note that my research work spanned up into the microwave bands as I was testing for resonances up from VHF into the GHz region. I was working with much smaller inductors
