Carl,
** Youre certainly wrong all right Manfred.
The slight size difference is not enough to make much difference
especially when only about 1/2 the turns the core is capable of for a
pratical SB-220 conversion using stranded #14 are used and well spaced.
Let's do a real, practical design, to find out how much difference there
is. The exercise might be illustrative to people actually still building
tube amps and considering the use of toroids.
My assumptions will be these:
- 1500W output power
- 2500V plate voltage under full load
- Loaded Q of 12 (it's open to discussion whether this is the best choice)
- 50 Ohm antenna
Under these conditions the plate load resistance is 2083 ohm. For a Pi
matching section with 2083 ohm input, 50 ohm output, and Q=12, at
1850kHz, we get an inductance value of 16.8uH.
First let's try a single T-200-2. That core has an Al value of 12nH per
turns squared. It would require 37 turns to produce 16.8uH.
There will be 2031 volt RMS applied to the inductor, and 10.4 amperes of
RF current flowing through it.
With 2031V and 37 turns, and the core having 1.33 cm^2 of cross area,
the flux density will be 50.2 millitesla. This is about 5 times higher
than the maximum value recommended by Amidon as a guideline, at this
frequency! So for CCS it's certainly not workable, but let's look a bit
further to find out how bad it really is. Perhaps it's usable for
typical ICAS?
Amidon publishes a loss chart for type 2 material. 50mT at 1.85MHz is
far off that chart! Extrapolating, the volumetric loss turns out to be
roughly 20 watts per cubic centimeter. With the core having a volume of
17.25cm^3, the core loss under a steady carrier would be 345 watts!
In typical SSB transmission, the average amplitude is only about one
half the peak amplitude (one quarter of the peak power). Core loss
changes roughly with the square of amplitude too, so during SSB
transmission the core loss would be about 86W. With 50% TX, and short
exchanges, that would be 43W average dissipation. In still air, that
results in a temperature rise of about 240 degrees Celsius above the
ambient. Definitely unuseable! But with a lot of airflow, maybe it would
be workable for light duty, but it would still be a very lossy, lousy
tank coil!!!
Excuse me for not writing down every step of the calculations. I used an
online tool, quickly googled up, to calculate the Pi values, then used
plain math to calculate voltage and current, and then used the 1995
Amidon catalog along with a few of the equations on my own "transformers
and coils" page to calculate everything else.
Note that the above shows ONLY the core loss. The wire also contributes
some loss, which hasn't been considered. Using thick wire, the core loss
dominates far and wide in this case.
Now let's see what happens if we swap the T-200-2 for a T-225-2 core.
Its Al value is the same, so we still need the same 37 turns. But its
cross area is 13.2% larger, so the resulting flux density is 13.2%
lower. That would be 44.4mT. The resulting volumetric loss would be
"only" 15.6W/cm^3. But this core has a volume of 22cm^3, so that the
total core loss would be 343W, almost the same as the 345W of the
smaller core. So in this regard indeed we don't gain anything!
But now let's see the heating. This core has 42% more area. That results
in a heat rise of only 178 degrees Celsius in still air. Still far too
much to use without forced air cooling, even in light duty, but still a
lot better than the 240 degrees of heat riseof the smaller core!
So, there's the advantage of the bigger core.
Another advantage is that with the lower flux density, it will cause
less distortion.
When using a pair of T200-2 or a single T200-2A the pair will run cooler.
Certainly. Let's calculate what happens when using a pair of T-200-2
cores, stacked.
The stacked pair will give about 23nH per turns squared. So we need only
27 turns. We get 2.66cm^2 of cross area. That leads to a flux density of
34.4mT.
At that flux density, core loss is about 9W/cm^2. Note that I'm looking
up these values on a chart, extrapolating outside it, so these are NOT
precise at all. Take them with care!
Anyway, at 9W/cm^2, and a total volume of 34.5cm^3, the total core loss
is now 310W. Still whopping high!
Assuming the same reduction of dissipation due to low duty cycle, as I
did for the other cores, we now need to dissipate 39W.
The dissipation area does not double by stacking cores, since the core
sides touching each other are lost for dissipation. So we now have about
90cm^2 of dissipation area. This leads to a heat rise of 157 degrees
Celsius. So this is better than any of the previous solutions, but still
far from being good.
Let's play a bit more: What happens if we take the two T-200-2 cores,
wind them separately, and connect them in series?
We now need 8.4uH per core. This leads to 26 turns per core. Each coil
will see half the total voltage. That leads to 35.7mT of flux density.
So it's much the same as stacking the cores, except that by separating
the cores we get some more dissipation surface. That helps some, but not
dramatically.
So, the big question is now: What can be do, to make a low loss tank
coil, on a toroid?
Keeping the circuit design the same, and not having any lower loss core
material at hand, the only thing we can do is using a significantly
larger core. But then the toroidal coil is not much smaller than an air
coil... Anyway, let's try it. Let's try a T-400-2 core.
That core has 18nH per turns squared, so we need 31 turns on it. The
cross area is 3.66cm^2, so that the flux density ends up being 22.1mT.
There we get about 1.8W/cm^3 of volumetric loss. This big core has a
volume of 91cm^3, so that we still get 164W of total core loss - not
brilliant at all! Again assuming our low duty cycle, we would have 20.5W
avergae dissipation in the core, and given its large thermal mass, our
longest continuous transmission can be longer too than with the smaller
cores.
At about 190cm^2 of dissipation surface, in still air this core would
heat up by only 49 degrees. So, this large core would actually allow
fanless operation, at least in low duty cycle use.
What else can we do?
An easy trick is to just use a lower loaded Q of the Pi tank! At a Q of
7, about the lowest we can use, we need 26.7uH. Taking again the single
T-200-2 core as a minimal solution attempt, we end up with 47 turns on
it. That leads to 39.6mT flux density. That falls between the single
T-225-2 and the pair of T-200-2 cores. You can work out the rest yourself...
And the harmonic suppression of a Pi tank with a Q of just 7 might not
be good enough. Which leads to more calculations, considering a Pi-L tank.
As you can see, using this kind of powdered iron toroids is a rather
lossy compromise. We can reduce the core loss by going to even lower
permeability cores, but then we get close to air coils.
An attractive option could be using very low permability ferrite cores.
"Very low permability" in ferrite means still higher permeability than
plain normal powdered iron! So, such cores would need to be airgapped.
Ferrite offers a much better ratio of permeability to loss than powdered
iron does. The result MIGHT be compact, relatively low loss tank coils -
if you can find proper ferrite cores!
OK, Carl, I concede that the difference between those cores isn't
significant, considering that they all are lousy/lossy in this application!
So... peace! OK? ;-)
If anyone wants the detail of how I calculated or where I looked up
something, let me know. If I had included every detail here, the post
would have been way too long.
Manfred
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