Gap question, and Real Data

[Tim Williams]

In general, for small air gaps, is A_L * I_sat constant when
increasing the air gap?
I know stored energy goes up, because energy goes as I^2. But I don't
need that here.

In other news, I've measured the largest cores I have on hand...

Powdered iron (yellow, one side white): 178nH/T^2, >200At saturation
2" o.d. blue or green toroid: 3.3uH/T^2, 20 or 10At saturation
respectively
Big flyback core (black ferrite, like 4" tall, 1" dia. limbs): 6uH/
T^2, 20At saturation

The latter looks like it could actually work, since about 7 turns of
1/4" copper tubing would get me 300uH inductance (secondary). At
10kHz, that's 18.47 ohms X_L, which would draw 2.7A at 50Vrms. 2.7A *
7T = 18.9 At, which is just shy of saturation. Maybe it'll saturate
noticably on the peaks, or on startup transients, but 10kHz is a
design minimum, too (it will run at 20kHz most of the time, and can
start as high as 50kHz easily enough).

Now, that's a real core, with a fairly long magnetic path and cross-
section of maybe a square inch (give or take.. I'll measure it in more
detail some time). That's about equivalent to the largest toroid
Amidon sells (although that has maybe half the path length and no
gaps, which might get a higher A_L * I_sat product, I don't know). It
does look like I'll need a fairly large toroid either way, probably 4
or 5" across, maybe 6. I don't think it has to be ankle sized, but a
few square inches cross section would be a good start. It still
appears to be special order, or at least non-Amidon-stocked material.

Tim

 

[[email protected]]

In general, for small air gaps, is A_L * I_sat constant when
increasing the air gap?
I know stored energy goes up, because energy goes as I^2.  But I don't
need that here.

In other news, I've measured the largest cores I have on hand...

Powdered iron (yellow, one side white): 178nH/T^2, >200At saturation
2" o.d. blue or green toroid: 3.3uH/T^2, 20 or 10At saturation
respectively
Big flyback core (black ferrite, like 4" tall, 1" dia. limbs): 6uH/
T^2, 20At saturation

The latter looks like it could actually work, since about 7 turns of
1/4" copper tubing would get me 300uH inductance (secondary).  At
10kHz, that's 18.47 ohms X_L, which would draw 2.7A at 50Vrms.  2.7A *
7T = 18.9 At, which is just shy of saturation.  Maybe it'll saturate
noticably on the peaks, or on startup transients, but 10kHz is a
design minimum, too (it will run at 20kHz most of the time, and can
start as high as 50kHz easily enough).

Now, that's a real core, with a fairly long magnetic path and cross-
section of maybe a square inch (give or take.. I'll measure it in more
detail some time).  That's about equivalent to the largest toroid
Amidon sells (although that has maybe half the path length and no
gaps, which might get a higher A_L * I_sat product, I don't know).  It
does look like I'll need a fairly large toroid either way, probably 4
or 5" across, maybe 6.  I don't think it has to be ankle sized, but a
few square inches cross section would be a good start.  It still
appears to be special order, or at least non-Amidon-stocked material.

Tim

Hello Tim,

For a coil or primary winding of a transformer you can use:

B=L·I/(n*A),
B = flux density in T, I = current through coil or magnetizing current
for the transformer primary, n=number of turns, A=core cross section.

When you make a transformer and there is only AC, the flux density in
the core will not increase when you load the secondary winding.

Based on a sine wave voltage (no DC through the windings):

B = U/(2*pi*f*n*A),
B = peak flux in T, U = peak voltage of sine wave, f = frequency, n =
number of turns, A = cross section of core.

All SI basic units.

For a transformer without DC, an air gap is mostly not required. Only
in case of energy storage you can use an air gap.

Energy in air gap = 0.5*Vol*u*H^2 = 0.5*vol*B^2/u
Energy in J, Vol = volume of air gap, H = magnetizing field strength
(in A/m), u = permeability (not relative permeability) in H/m. E in
air gap must be greater then 0.5*L*I^2.

Hope this helps a bit in selecting the right core and number of turns

Best regards,

Wim
PA3DJS
www.tetech.nl
don't forget to remove a, b and c for the PM.