# Is there an inductor type that has the best inductance per unit volume?

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.

• Depends on SRF , fill factor , winding pattern and wire type Apr 18, 2018 at 21:33
• Wire gauge affects Q, which is the efficiency of the inductor vs. its DC resistance, so wire gauge plays a role. With the right wire gauge, Q is at maximum without adding un-needed weight.
– user105652
Apr 18, 2018 at 21:34
• When in doubt, use some multivariate calculus to define a surface area :) Notice that the equations for inductors with different shapes utilize some type of pattern to come up with equations that are related to the object's shape.
– user103380
Apr 18, 2018 at 21:35
• Best or highest inductance? Best or highest Q? Best or highest SRF? Best or lowest resistance? Apr 19, 2018 at 7:46
• I meant best in the sense of highest value, not highest in some other parameter specifically related to inductors such as Q or SRF. Apr 19, 2018 at 11:17

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.

• So a single layer cylindrical coil of optimal length has more inductance/volume than a set of stacked spirals that can fit in the same volume? Apr 18, 2018 at 21:51
• Single layer coils have a well defined solution for best Q. As you add constraints I don't think there is such a simple rule. Apr 18, 2018 at 22:17