Hello again,
I have a couple formulas i'll present for your use.
I also have a new calculator on the way which was originally
intended for the EE course as i dont like the way most
available free calculators are set up. It doesnt do
everything yet, but it does quite a lot so i'll be
releasing one version in a day or two or three...
that way folks will be able to enter things in and get
quick answers to problems like these.
For example:
Calculate_L(N,Ae,Mu,Length,Height)
(or something similar)
will calculate the inductance from the toroid core
with a number of turns N. You'll have to enter in
the dimensions but that's all.
But before we get to the formulas, i just want to
stress that these calculations are not that important, really,
because the small toroid saturates for a short time
and it stops because the ic chip turns the transistor
off, so it's not quite the same as most switchers that
use a linear inductor. Not that you cant use a linear
inductor instead...it's been done with success...but
you'll have to try a few or else talk so someone who
found inductors that work well with this circuit.
I found some that worked but the efficiency wasnt as
high as with the hand wound coil on the small toroid.
That said, here's the formula for inductance:
L = 1.26*N*N*mu*Ae*1e-8 /(gap*mu+ml)
where
L is inductance in Henries
N is the number of turns
mu is the permeability of the core (typically 10 to 25000)
Ae is the area of the core in square cm
gap is the length of the gap (single gap in toroid) in cm
ml is the average (mean) magnetic path of the core in cm
Since your toroid will not have a gap, this reduces to:
L = 1.26*N*N*mu*Ae*1e-8 /(ml)
If you want to know about the saturation, you'll have to
look at the manufacturer's data sheet on the type of
material the core is made from. You'll find some level
of flux (B) that will represent the max allowing some
temperature rise. You can use the following formula
to determine if the inductor will saturate...
Bdc=1.26*Idc*N*mu/(gap*mu+ml)
where
Bdc is the flux due to the dc current in gausses
Idc is the dc current in amps
N is the number of turns (wire goes through the center)
mu is the core material's permeability
gap is the gap length in cm
ml is the mean magnetic path in cm
With a gap of zero this reduces to:
Bdc=1.26*Idc*N*mu/(ml)
After looking at the magnetic data you'll determine that
there is some max B (which we'll call Bmax) where the
core is saturated enough to be called in saturation.
Then, you can determine if the level of Bdc goes over Bmax
or not by simply comparing Bdc to Bmax. If Bdc is greater
than Bmax then it saturates.
If instead AL is given, you can calculate Bdc from:
Bdc=N*Idc*AL/(10*Ae)
where everything is the same as above, and
AL is the value of inductance (L) for 1000 turns on the core.
By examining the above formulas and doing a few calculations
we can show that it is true that a core with lower mu will
be harder to saturate, but it's also true that it will take
more turns to produce a given value of inductance.
Same with adding a small air gap.
Ok, now that we're done talking about the calculations
I'd just like to remind anyone who's interested that
the small toroid will most likely always saturate, but
that's not always a problem in a circuit that senses
inductor current directly (as with the Zetex 300 chip).
Take care,
Al
