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Registered Member #1845
Joined: Fri Dec 05 2008, 05:38AM
Location: California
Posts: 211
Task: You are given a 15 foot long length of 22 gauge wire. You will connect this to a 100KHz AC source. How would you orient the wire to make it have the most inductance possible. (No iron cores allowed, you can only bend the wire into turns.)
I was wondering about this today. I couldn't decide whether the lenth of wire would have more inductance if it had, say 5 huge turns, or 35 smaller turns.
If I had to take a guess at it, I would think that one should wind the wire in a multilayered solenoid coil, with many small turns on each layer, rather than several turns with a huge diameter.
I guess I could plug some number into one of those inductance calculators, but I don't really trust them to give me accurate answers.
Registered Member #2099
Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
Not a trivial problem, but I agree with your inclination to use many small turns.
For cases like your examples, where the coil is practically a thin ring, the product of loop radius and turns count is constant. Inductance goes up as the SQUARE of increased turns count, and as a slower function (logarithm) of increased loop radius.
[edit] For a single layer solenoid, the optimum is a stubby cylinder with length a bit less than its radius. See
What I didn't have time to find (during break from day job) was a similar reference I once saw, that found the optimum for a multilayer coil with a rectangular winding cross-section. It's called a "Somebody" coil, but I don't remember the name, and it was stubby & thick.
[edit again] Don't let my boss know, but you want a Brooks coil. Ideally the winding cross section is a circle, to optimize the average coupling between turns, but a pretty close approximation is square cross section with thickness & length about 1.5 times the mean radius. So Steve, if you make one of these out of your specified piece of wire, what L/R time constant will you get?
Registered Member #2099
Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
Oops. It's not part of the original task, but since Steve specified 100 kHz somebody should figure (or measure) the capacitance and self-resonant frequency of a Brooks coil wound with the specified piece of wire.
Registered Member #29
Joined: Fri Feb 03 2006, 09:00AM
Location: Hasselt, Belgium
Posts: 500
You want to maximise the mutual coupling between all the turns as well as the total flux per unit current enclosed by the coil (inductance equation: L*I = N*phi).
I would recommend a coil wound in the form of a toroid with the toroid diameter about the same as the winding diameter.... (This is a guess, mind you... no calculations today!) This is based on the fact that the toroid configuration has very low flux leakage wrt other coil geometries, hence inter-winding coupling should be quite high...
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Inductance question
This is based on the fact that the toroid configuration has very low flux leakage wrt other coil geometries, hence inter-winding coupling should be quite high...