It sounds a little like it's not fully clear what parameters are held constant and which are varied in this discussion.
For a fixed core size and flux density but a variable gap, the largest gap length (lowest Al value) gives the highest energy storage capability at saturation. However, for a fixed inductance a larger gap would require more turns, which means you'll have higher copper losses at a certain current.
For this reason, there is a limit to the longest useful gap, although if the peak current is much higher than the RMS current, things will be different. Put in a huge gap and a certain core will store lots of energy, but it won't work for continuous duty.
So you'd usually not want to gap the core more than neccessary because copper loss would be higher if you did. In the case of the LI² - Al curves, the manufacturer has presented this information as the Al you should use for a certain energy storage to get the lowest copper loss.
If you don't have those curves and want to determine what is needed you could calculate it from scratch. I'd start with determining the amount of linked flux (flux times turns, often denoted by capital greek Psi) which needs to be supported, and this is given by inductance times desired saturation current:
Psi = N * Phi = L * I
where
Phi = B * A (flux equals flux density times cross sectional area)
The
minimum number of turns for a certain saturation current on a fixed core, fixed saturation flux density, fixed inductance and variable gap length (or variable Al value equivalently) can then be calculated. Yes, it is actually a
minimum number when parameters are fixed and varied in this manner. This can be seen by rearranging the equation above:
B = Phi / Ae = (L * I) / (N * A)
As L, I and A are fixed, B increases with decreased N so you'd want to make sure that
N > (L * I) / (Amin * Bsat)
Actually, given that everything is given except the number of turns and the gap length, specifying the minimum number of turns at this point is the same as specifying the maximum allowable Al value. (minimum required gap length)
Now you can determine if the turns will fit given a realistic current density, or alternatively make them fit by choosing thin enough wire and see if it gets too hot. (either by experiment or calculation) This is the lower Al limit (maximum gap limit) in the energy curves.
If you don't require an optimal design, the previously presented method of winding as many turns as you can on a variable-gap core works to get maximum inductance for a certain current by selecting the wire to give allowable temperature rise (or current density by rule of thumb, for example).
If you have considerable AC losses things get more difficult of course, but the bulk core losses will be lower for a fixed core size and inductance if you choose a large gap and a large number of turns. The same AC voltage over higher number of turns gives a lower AC flux density.
One thing that can be useful to keep in mind I think is that if you have a fixed AC voltage then core loss is only dependent on the number of turns for a fixed core and not the inductance and gap length, at least as a first order approximation. Increasing the number of turns decreases the core loss in this case, typically at the expense of increased copper loss. This also applies to cores where you can't change the gap, including powder toroids. Sometimes optimizing inductor losses and size can be more important than having a certain inductance.
Copper losses (eddy currents) from the gap fringing field I find more difficult to make general statements about as all dependencies are interlinked and scaling exponents are unintuitive. It also makes all the difference exactly which parameters you hold constant and which you vary. These losses can sadly be significant in many cases, especially if there are many layers of thick wire...
Home
Help
Search
Login
Register
