Paul said:
What is this "gap" to which everyone is referring? The spacing between
turns or something else?
It is the space between UU, EE, pot, PQ, RM or other two piece ferrite
or stacked laminated cores. The energy in inductors made with high
permeability material resides mostly in the field that passes through
the gap, as does the saturation resistance during high amp turns
operation. The core essentially couples the turns (carries most of
the same field around all the turns) and focuses it through the air
gap. If you design an inductor for some peak current and at the
current it reaches some specific flux, and you wish to change that
inductor to a higher inductance at the same current, you have to
increase the gap size, first, to keep the flux the same at the higher
amp turns. But increasing the gap lowers the AsubL value (inductance
per sqrt turn) so you also need more turns than what it would have
taken if the gap had not been enlarged. So under this constraint, the
inductance is no longer proportional to the turns squared.
A more useful constraint might be that the total amp turns remain
constant and the gap remains constant (also fixed peak flux) as you
change the inductance by filling the window to the same extent with
different wire sizes. Since the core geometry is constant,
inductance proportional to turns squared holds. But the current
capability goes down as the inductance goes up. Double the number of
turns, and the current capability goes down by half, while the
inductance goes up by a factor of 4. The resistance also goes up by a
factor of 4 (twice as long a wire with half the cross sectional area
for the same coil cross section). So the resistive losses at full
current stay the same.
Going through the range of inductances possible for a given pregapped
core using this rule shows the normal optimum use of the core as an
energy storage inductor. If your required product of square root of
inductance times current (which is essentially a constant for a fixed
gap and fill factor) is more than any example for a given gapped core,
you need a larger core. If your product is smaller, you are wasting a
bit of the core's capability (which you may want to do to lower
losses).
If you put a spacer between the halves of an ungapped core pair (or
add space to a pregapped set), you get a different product of square
root inductance times current for each gap, but there is a best gap
for any combination (from a total loss standpoint) for any combination
of DC and various frequencies of AC current. For large, high
frequency AC applications, larger gaps are better from a core los
standpoint because of the lower flux swings and the lower hysterisis
losses. For DC current, the core losses are zero, so the smaller gap
lowers the number of turns, allowing fatter copper and lower resistive
losses. You just have to worry about saturation and inductance
tolerance.