Rap 'n Tap
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From: Josh K
Date: 6/11/00
Time: 5:13:14 AM
Remote Name: 207.57.42.172
Kevin,
it's not that the different formulas can't all be right. None of them are exactly right, but all of them are pretty good approximations. It's very difficult to calculate inductance to high accuracy even for a simple one-layer solenoid. Among other complications, it's hard to work out the effects of spacing between the wires and the simple fact that the coil has two ends (instead of extending infinity). For practical purposes the formulas we all know and love have been worked out - with great labor - to deal with these effects approximately, and they are accurate to a few per cent.
Because they're approximations, they are valid only for certain ranges of the parameters (length/diameter ratio, winding thickness, etc.) Unfortunately, these ranges aren't usually given with the formulas.
The measured inductance of a coil will vary with frequency. One reason is the distributed capacitance: the coil is not a pure inductance but a rather complicated RLC combination, so what you see across its terminals depends on frequency.
An interesting book on coils is "The Theory And Design Of Inductance Coils" by V.G. Welsby. I bought it hoping to find the magic formula. He actually spends very little time working out an inductance formula from first principles, and for the simplest possible ideal case. The rest of the book makes it clear why it's not practical to attempt refinements of that idealized formula. It's an interesting account of all the real-world complications we have to deal with, even with our simple-looking coils.