inductanceinductor
Inductors come in many types e.g. cylindrical (single and multi layer), spiral (single layer and stacked), toroidal (single and multi layer), and probably others.
For an air core inductor, assuming the same wire pitch and including the volume enclosed by the coils, is there a particular shape/layering method that gives the best inductance per unit volume?
Assume a that the current is low enough that thermal issues are not a concern, i.e. it is a tuning inductor and not a power inductor.
I've used a two terminal oscillator, with the inductor in parallel with a suitable capacitor, with a scope or counter to measure the oscillation frequency. I once checked an inductor on a very expensive inductance meter at work, and the values were identical. The source-coupled oscillator using two FETs is ideal for this application, or the LM311:
I would think there would be a slight difference but very little and that would depend a lot on the operating frequency. Two quotes gleaned from Google and appear to be reliable sources:
"Litz wire is used to make inductors and transformers, especially for high frequency applications where the skin effect is more pronounced and proximity effect can be an even more severe problem. Litz wire is one kind of stranded wire, but, in this case, the reason for its use is not the usual one of avoiding complete wire breakage due to material fatigue."
"Litz wire conductors are beneficial for reducing A.C. losses in high frequency winding"
So this is just to make a point that Litz wire is used to improve effeciency, this would be especially so in SMPS like computer PSU's where the transformers operate at high frequencies. It's not used for inductance reasons as far as I am aware and probably makes little difference.
Best Answer
For best Q, it is a cylindrical coil of (length) Diameter/Length=2
Turns will be spaced apart.
This is simply the optimum point. If you make it longer, then the same copper would add inductance faster by increasing D. If you make it shorter you lose mutual coupling faster. See. Note that one thing this graph tells you is that flat coils are not the solution.
Note it is Q you want. Best inductance/volume, just means bazillions of turns of very fine wire, and unusable RF performance.
There are plenty of other constraints that can act. - Self resonance inter-turn / interlayer C becomes an issue with air core coils. Modern radios use ferrite to keep N down. Before ferrite you see basket weave, cotton covered wire, spaced turn coils to keep the C down. - skin effect: litz wire is used in medium frequencies to reduce effective R
Internal capacitance can be thought of as C which is bypassing the L - and thus removing it. turn-turn C is limited effect, because dV between turns is low. But if you wind a second layer of windings, like a solenoid/relay/transformer, then dV between ends is very high, and so a lot more current flows through interlayer C, than inter-turn C. So multilayer coils are undesireable. (Before you say What about the little IF coils in radios - if the size is very small for the frequency, because you are using ferrite, then the C is too small to matter, and you can wind however suits you
When your constraint is size, and as radios became more complex, more coils = less space, it does become the constraint, then you have to choose non-optimum, like multilayer windings. Now you wind like a ball of string, with the windings criss-crossing to keep the wire gap high.
Perhaps another perspective is:
For a given size, you can keep adding layers. As you add each layer, the inductance will go up. At some point the self-C dominates, and the inductance starts to go down again.