# Big DC to DC converter toroid?

Discussion in 'Electronic Design' started by BobG, Jan 31, 2007.

1. ### BobGGuest

If I wanted to build a 15KHz 15KW DC to DC converter to hump 48 or 96V
at a couple hundred amps up two or three times to run a motor, could
someone tell me about how big the cross section of a ferrite toroid
would have to be? Gauss? All I know so far is magnetics get smaller
with increasing freq, and core cross section has to do with power....

2. ### Terry GivenGuest

a couple of things:

- you have several different bits of magnetics. A transformer, and
(it'll be buck derived) some form of choke (which will be on the HV side
no doubt).

- the transformer cross-section is chosen to keep the peak flux density
below saturation, then low enough to keep losses down. At 15kHz, you
will be saturation limited, so peak flux density can go up to 250mT
(2500G) for ferrite, no worries.

- the relevant equation is:

Vin*Ton = Np*Bpp*Ae

Np = no of turns on primary

Vin = primary voltage (V)

Ton = on time (s)

Ae = core cross-sectional area (m^2)

Bpp = peak-to-peak flux density (T)

you can vandalise the units if you wish, but MKS is easiest.

In theory you can let Bpp = 2*Bpeak = 500mT. BUT unless you have peak
current-mode control, you can run into problems when you first start up,
as Binitial = 0T. Once its running, B either starts at -Bpeak then ramps
up to +Bpeak, or vice-versa, hence Bpp = 2*Bpeak

Assuming you have PCMC and can let Bpp = 500mT, you can then calculate
Np*Ae:

Np*Ae = 48V*0.5/(15kHz*0.5T) = 3.2E-3 for 48V.

For one turn, this requires Ae = 3200mm^2. thats a big toroid.

for 10T, Ae = 320mm^2. you can get toroids this big, easily.

The real problem for the transformer is the winding resistance. 15kW/48V
= 313A, so 1mOhm will dissipate 98W or so.

As you increase frequency Np*Ae goes down, so for the same core fewer
turns are required. If you fill up the winding volume (or at least use a
constant amount) then the resistance is proportional to the square of
the number of turns. Fewer turns = more copper *and* shorter, so
resistance drops. So going to say 30kHz will give you 5T on a 320mm^2
core, and the resistance will be 4x less than at 15kHz.

(If you have multiple layers, this doesnt work, proximity effect buggers
everything up).

BUT as you increase F, core loss goes up. At some point core loss gets
high enough that you have to start decreasing Bpeak. You still win, but
by less (and less and less as f keeps getting higher).

with modern ferrites you can be saturation-limited up to around 100kHz
or so.

FWIW I have a 2500W dc-dc toroid I designed sitting on my desk that runs
from 16V - 32Vdc, and the overall transformer is 50mm OD x 25mm high. it
runs cool, too.

Cheers
Terry

3. ### Paul E. SchoenGuest

You might consider doing this at a lower frequency with a steel core
toroid. I made a prototype for this type application from a nominal 500 VA
toroid that is only about 3" dia and 2" thick. It should work up to about 2
kHz (30x), with an output power of 15 kVA. It had about 0.2 V/turn at 60
Hz, so it should be 6 V/t at 2 KHz. You will probably want 360 VDC (for 240
VAC motor), or 720 VDC for a 480 VAC motor. The hard part will be getting
10 to 20 turns of wire rated at 150 to 300 amps through the hole. The
secondary will be about 50-100 turns of #11-#14 for 20-40 amps.

Paul

4. ### JoergGuest

A regular 50/60Hz core at 2kHz? Must have been a high quality core. Did
it get hot?

5. ### Paul E. SchoenGuest

I did not build the prototype for full power, and I would probably not be
able to test it if I did. I would need 350 amps at 48 volts for 15 kW
output. However, I did an LTSpice simulation, which produces 17 kW at 706
VDC with 95% efficiency. Of course, this depends on many factors, and I
have modeled a nearly ideal output transformer. A well-constructed tape
wound toroid may be efficient enough to work at 2 kHz. It will also work at
1 kHz, with a core twice as large. I think it is worth a try. My ASCII file
follows:

Paul

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6. ### JoergGuest

That one word you used (well-constructed) is exactly the point. With
regular EI cores it's the same, some are great, almost good enough for a
decent audio transformer. Then there are others which are, as Archie
Bunker would have put it, lousay. But the difference won't show much in
SPICE, it'll show during extended full load testing.

[...]

7. ### JohnGuest

Core cross section is not all there is to it. The power handling capability
of a core at a given frequency is a function of its AcAw product where Ac is
the core area and Aw is the window area. Obviously, the higher the
frequency, the greater the power handling ability. But, then again, the
higher the frequency, the greater the core and copper losses.

You can write the equation for the power handling capability of a core based
on its core area. You can also write the equation for the power handling
capability of a core based on its window area. Solving the two equations
simultaneously gives the power handling capability of the core. In the
process of writing the equations, you will discover that you need some more
information. It turns out that you will either need to specify temperature
rise or regulation. For transformers smaller than a certain size, it is
regulation that dominates the requirement. For transformers larger than that
certain size, it is temperature rise that is the dominating requirement. In
your case, your requirement will be determined by temperature rise of the
transformer.

To be more exact, it is the geometry and dimensions of the transformer that
determines its capability. For a given core, it will have a certain surface
area and volume when filled with wire. The temperature rise will be a
function of the surface area divided by the watts per cubic inch of loss.
There is a section in The Radiotron Designer's Handbook by RCA that
discusses transformer design and it starts off, as I recall, with a
temperature rise requirement. I believe that book is now online.

If you have a starting point (such as Terry Given's post - last paragraph),
you might be able to ratio his power-handling capacity to your requirement
if he can give you his AcAw product (don't forget to include the effects of
frequency). Otherwise, you will need to think deeply for a long time, read
the book, and write your own equations. Or, you can experiment. If your job
is to design things, maybe you need to do the math. OTOH, if this is a
one-shot project, experimentation may be the answer.

In any case, I wish you luck with your project.

Cheers,
John