Jamie said:
Hi,
I am trying to calculate the max number of turns that I can
use in a transformer at a given current using the formula from this
page:
http://info.ee.surrey.ac.uk/Workshop/advice/coils/#turn
N = Bsat*le / (μ*I)
where:
N = turns
Bsat = saturation flux density (Tesla)
le = effective length (meters)
u = permeability (Henries/meter)
I = current (Amps)
for the transformer I have:
Bsat = 0.37 Tesla
le = 99 * 10-3 meters (99mm)
ui = 2200
I = 10amps
N = 0.37 * 99 * 10-3 / (1.257 * 10-6 * 2200) * 10
N = 1.3turns
The number of turns should be higher for the
transformer I am using, an EE "E64 15 50" core.
35G material from Iskra. (
www.iskra-feriti.si)
I think I have made a mistake with the permeability
but am not sure.
Also this formula doesn't seem to take into account the
cross sectional area of the transformer, which should
increase the allowable number of turns at the given
current.
Also the 35G material has an Al of about ~10000n
cheers,
Jamie
Nope, thats right. You have implicitly taken Ae into account by using
Bsat = Phi_sat/Ae.
What are you trying to make - a choke, or a transformer? the calculation
method is slightly different (although all the maths is the same).
BTW, 370mT might work at 20C, but at 100C the choke will well and truly
saturate - Bsat DECREASES with increasing temperature. I inherited a UPS
design once that suffered from this particular problem.....
It sounds like you want a choke, and you want to bang 10A thru it. Given
that its a planar core, its probably an output choke for a forward
converter, or maybe a buck choke.
what you have discovered is that ferrites dont make very good
high-current chokes, unless you stick in an air gap.
(unless, of course, 1T and about 10uH is OK, along with saturating)
Initially, ignore the permeability, and use the maximum MMF,
Hsat = NI/le
for 35G material (3F3), Hsat = 50 - 70 A/m
(its a gradual curve, which means you get to pick "saturated")
say Hsat = 70A/m = N*10A/0.1m so N = 0.7T
Wow, this is a lot lower than your 1.3T. BECAUSE mu_i falls off with
increasing H......
[and mu_is all over the show with temperature, peaking just below the
Curie temperature (200C), above which it drops to 1]
ignoring the practical difficulties associated with winding 0.7T (and
the reduced permeability), we end up with L = 4.9uH and E = 245uJ
OK, so now what?
Well, when you add an air gap, the BH curve shears over - more H before
it saturates.
originally, you had Ho = (NoIo)/le
when you add an air gap, this becomes:
H = Ho*[1+(mu_i*Ae*lgap)/(Agap*le)]
and if Agap = Ae (it does if we ignore fringing flux) this gives:
H = Ho*[1+(mu_i*lgap)/le]
So, if Io stays the same, we can write:
H = N*Io/le = (No*Io/le)*[1+(mu_i*lgap)/le]
i.e.
N = No*[1+(mu_i*lgap)/le]
so now you can pick some arbitrary number of turns N, and work out how
big a gap you *NEED* to prevent the core saturating
(this is a terrible way to do it, but its a tutorial....)
say you want 4T and mu_i = 2200. We already calculated No = 0.7T so:
4 = 0.7*[1+2200*lg/0.099]
lg = (4/0.7 - 1)*0.099/2200 = 0.2mm
Alas by bunging in an air gap, the effective permebaility is reduced.
For an air gap bigger than about 0.1mm, its a reasonable approximation
to say ALL of the energy is stored in the air gap itself. So we can
calculate the inductance as:
Lgapped = mu_0*N^2*Ae/lg
Ae = 10.2mm x 50.3mm = 500mm^2
Lgapped = 1.257e-6*16*500e-6/0.2e-3 = 50uH
and E = 2.5mJ
So although the effective permeability went down, the total inductance
went up, and there is now 10x more energy stored in the choke c.f. the
0.7T winding. Pluis of course you can actually wind a 4T winding, which
your production guys will appreciate
There is enough information here for you to derive a closed-form
solution for lg & N, given I and the desired L. I'll leave that as an
exercise for you
alternatively, whack up a quick spreadsheet, MathCad etc, and bang some
numbers in until you are happy with the result. Dont make your gap too
small, there are finite manufacturing tolerances - the guy I use gives
+/- 0.05mm, so 0.05mm gas are a BAD idea.
When designing a transformer, the procedure is different. We can just
use the transformer equation, V = N*dPhi/dt
Phi = B*Ae
V = N*dB*Ae/dt
for square wave, dB = Bsat, dt = Ton so:
Vin*Ton/(N*Ae) = Bsat
which can be solved for N (use min Vin, Max Ton)
Then calculate L = N^2*Al
If you need a precise value of L (eg flyback), this result is probably
too high, so introduce a gap to reduce L to the required amount. If its
too low, the core is too small.
Note that the transformer equation is often written V = 4.44*N*B*Ae*f
this is confusing, because it assumes sinusoidal operation:
B = Bpk*sin(wt)
and dB/dt = w*Bpk*cos(wt) which has the maximum value w*Bpk
and w = 2*pi*f
giving Vpk = 2*pi*f*N*Bpk
then just to confuse you, they use V = Vrms = Vpk/sqrt(2)
Vrms = sqrt(2)*pi*N*Bpk*f = 4.44*N*Bpk*f
Voila!
(personally I hate formulae with magic numbers)
HTH
Cheers
Terry
