martin manning wrote: ↑Sun Apr 20, 2025 2:21 pm
From
https://www.aikenamps.com/index.php/out ... -explained
"The leakage inductance is proportional to the square of the number of turns, so you must decrease the number of turns to reduce the leakage inductance, but this is at odds with the need to increase the number of turns for good low frequency response. In addition, the flux density may be exceeded if you reduce the number of turns. Different winding techniques, such as interleaving, can help reduce the amount of leakage inductance, and improve the high frequency response."
This is mildly misleading. Leakage inductance is indeed proportional to the square of the number of turns, as is primary and secondary inductances. In an inductor winding, doubling the number of turns increases the inductance by a factor of four. But decreasing turns to decrease leakage is not a formula to decrease leakage inductance per se. In the Golden Age of hifi tube amps, the figure of merit was the the ratio of primary inductance (and hence bass response) to leakage inductance, not the magnitudes.
Helmholtz is correct. At a given impedance level, the primary inductance determines the bass cutoff. The treble cutoff is determined by the combination of leakage inductance and parasitic capacitances.
Leakage inductance is determined literally by the magnetic flux/field lines that leak out of a winding and does not couple through any core to another winding. It therefore acts like an inductance in series with the nominal primary winding that does not cause anything to appear on a nominal secondary. If you wind two coils and set them a meter apart on a table, they will have some flux that couples both coils, and a LOT that does not. So driving one coil will let you sense some of that drive in the second coil, but not very much. The amount you can sense in the second coil goes up and down as the square of the distance between them. The inductance you sense driving the first coil is nearly the entire isolated inductance of the first coil.
As you move the coils closer, more and more of the magnetic field from the first coil gets into the middle of the second coil, so you can sense more in the second coil. As you move the second coil literally inside the first coil, the second coil can pick up most of the first coil's drive.
But not all of it. The second (now inner) coil misses some of it because some of the first coil's flux sneaks between the two of them in a cylinder on the inside. We try to fix this by inserting iron into the middle of the two coils. Iron "conducts" magnetic field about 8 to 10 thousand times better than air or vacuum or any other non-magnetic material. Inserting iron in the middle of the two coils makes the magnetic field get "short circuited" into the iron by a factor of thousands. This rapidly leads to the iron enclosed coils we think of as transformers.
But magnetic fields are sneaky. Even with two concentric coils, some of the flux can sneak between the layers of one coil, and between the layers of the second. This rapidly leads to interleaving. By winding one layer of the first coil, one layer of the second, a second layer of the first coil, a second layer of the second coil, we can force vastly more of the M-field to be inside coils of the secondary. The ultimate is reached with bi- (and tri-, quad-, penta-...) filar winding. Two wires are wound literally side by side in a coil. This makes the smallest possible spaces and cracks for the field to sneak out of. It's used in special cases, but because it's a screaming pain to wind, it's used sparingly. It's expensive.
The received wisdom here is that the relative minimization of leakage inductance is how well and intimately you can intermix the primary and secondary windings. Multifilar winding to some degree is how you reduce the relative effect to the best possible degree. Interleaving, winding one or a few layers of primary, then secondary, then primary, then... is the way it's done in practice. I had to go through the math description of magnetic leakage as a green-eared engineerling. Compared to 1:1 interleaving (that is one primary, one secondary) leakage inductance goes down by the square of the number of interfaces between sections.
So yes, leakage goes up by the square of turns, but the turns is fixed by impedance considerations and bass response needs. Leakage inductance is minimized as much as possible by interleaveing in as many degrees as possible, economic, and practical
"It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so"
Mark Twain