Genome said:
[snip]
Thanks for any thoughts and discussion.
Paul
You need the following sums
L = uoueN^2Ae/Le
B = uoueNI/Le
H = NI/Le
dI = VinTon/L
You are not allowed to use one sum without thinking about how it might
affect another one. You avoid that sort of sophistry by using all the
sums to find your answer.
The B field don't depend on the core.
Choice 1) Do Sums.
Choice 2) Use sophistry to prove it does.
Subsequently
Choice 1) Problem Solved.
Choice 2) Invoke 'Ad Hominem' Attack strategy.
A gap affects ue. There is something about permeance and reluctance which
is something like conductance and resistance. The gap appears in series
with things so/but you get the answer by adding the reluctances.
Unfortunately designing magnetic components is hard because there are too
many variables to play with.
N = LI/BAe
Works
But then you might need
AwAe = LIpkIrms/BpkJK
To get a first guess at what the size of your core should be. J and K are
the guesses.... and then Bpk ignores the core loss so you might adjust
something else for another guess. J ignores the winding losses so.....
you might have to guess again.
Do you trust the software?
Leakage inductance has nothing to do with uncoupled flux. It's down to
energy stored in the field(s) between the windings, series term.
If you want to control stuff then you might control the coupling of the
flux and that is a parallel thing.
DNA
I don't think I need to go through all that calculation, especially when I
am using off the shelf components (but I appreciate the information). The
actual circuit performance and waveforms closely match what I see in
LTspice. I was just surprised that the toroidal inductor rated at higher
current did not produce as much output power. It may be that the smaller
inductor (Sumida CDR127/LD100) may have more effective gap and thus allow
higher current than the larger toroid (Miller 2101-H-RC). I have ordered 8
pieces of the board, and will soon be able to test them. They are designed
so I can use either the on-board SMT inductor, or an external toroid, or
both in parallel.
Basically, I can predict the maximum current in the inductor, and hence the
energy stored, vs frequency. Using LTspice with a 61 ohm load, I found that
at 200 kHz and 70% duty cycle the maximum inductor current with 12 VDC at
10 uH is 4.4A (Energy = 97 uW-sec * 0.2 = 19.4 W), and I get 40 volts (26.2
W). At 100 kHz, I can get 48 volts (37.7W) with a maximum inductor current
of 8 A (32 W). The actual inductor current in the first case, which is
running in continuous mode, includes a DC component of 650 mA from the 12
volt source. Adding that gives a power contribution from the battery of 7.8
watts in the first case and 9.4 watts in the second.
The maximum output will be generated when the inductor starts charging
again after its energy has been discharged into the output capacitor, so
there will be no "dead time". With 12 volts, the inductor charges to 8.4 A
in 7 uSec, and it takes 3 uSec to charge the output capacitor, for 70% duty
cycle. The output is about 48 VDC into 61 ohms, or 38 watts. I calculate
the average input power to be about 70% of sqrt(8.4*8.4/2) * 12 V = 35.3
watts, plus the 780mA * 12V = 9.4W from the battery, or 44.7. I'm guessing
at this, but the simulator measured input watts to be 43, so I'm close.
This is 82% efficiency.
I'm running simulations in LTspice, and I think they are pretty much
correct, but I am still a little puzzled. In the continuous mode operation
at 200 kHz, I can see the DC component through the inductor as a 388 mA
minimum current. I get input power of 28.77 W and output of 25.77 W or
89.5% efficiency. In the discontinuous mode at 100 kHz, I get 38.7 watts
out, 43.1 watts in, and 89.8% efficiency. However, I have a hard time
grasping how it can output 38.7 watts when there is almost no inductor
current (It's actually negative) 10% of the time, and peak energy of 320
uW-Sec at 100 kHz or 32 watts. Maybe I'm simplifying the calculation too
much. The true power is probably the integral of the peak energy
(0.5*I^2*L) over the entire waveform, times frequency. OK, when I do that,
I get an average of about 98 uJ, but a peak of 316 uJ = 31.6 W.
BTW, a good reference for transformers, inductors, and other AC devices is:
http://www.ibiblio.org/obp/electricCircuits/AC/AC_9.html
The entire series is very good.
Paul
