On Fri, 28 Feb 2003 12:49:39 EST MorgusMagnificen@aol.com writes:
Hi Eric,
> In response to offline requests and suggestions, here is the detailed
> calculation for the toroidal coil. I would like to proceed by making a
very
> clear statement of the problem to be analyzed - many of the disputes
that
> occur here are a simple result of fuzzy or missing assumptions that
should
> always precede any analysis of a model.
Certainly true in this venue... proceed to fuzzy assumptions...
> In a typical tank circuit, PI, PI-L or even parallel-link coupled,
there will
> be a significant high RF voltage across the coil. It's peak-to-peak
value is
> typically in the range of VCC. For a 4KVDC amp this results in a peak
of 2KV
> and and RMS of about 1400V.
Say WHAT!!?
A typical tube amplifier with a 4KVDC plate supply should exhibit
something in the vicinity of 3.5 KV peak RF voltage with an RMS figure of
about 2.5KV.
Though these errors have little to do with the following analysis...
> These values are all somewhat approximate and
> depend upon the details of the amp and its operating mode. I do not
want this
> analysis to be at all dependent on those unknowns, for sake of
simplicity and
> generality. I am just going to state the problem in terms of RMS
voltage
> across the coil. For purposes of evaluating the coil and/or the ferrite
> material from which it is made, the coil voltage is the only variable
> parameter.
The core in question is a powdered iron unit, not a ferrite... If you
can't read that in the catalog then, the rest of this will be futile...
> The question is simply stated: For a given voltage across the coil,
> what power will it dissipate due to RF losses (I am going to neglect
the
> ohmic wire losses - by comparison, they are negligible). My
calculations
> will show the exact values, limited only by the accuracy of the mfrs.
data My
> introductory estimate of the actual RF voltage is only used as a
guideline in
> knowing where on the data curves to look for answers (more on this
> shortly.)
An Amidon catalog, a Micrometals catalog, and a couple of articles
will come in handy...
> The calculation to be performed here is basic EM field theory, which I
will
> review as succinctly as possible. This calculation must find the peak
value
> of B (the magnetic flux density) during an RF cycle, given the RMS
voltage
> across the coil. With B(pk) known, the power loss is simply read off of
> l data from mfr. This graph specifically gives us the power loss per
> unit volume of core material (mw/cm(cube) ) and we multiply this by the
> volume of the core, known from its geometry.
>
> The core in question is a MM T400-2 which has the following physical
> parameters:
> OD=4.0 ID=2.25 Ht=.65 area=3.46cm(sq.) VOL=86.4cm(cube)
> A-sub-L=18nH.
Bob Bloom, W6YUY, listed the coil in question in his August 1985 Ham
Radio article (pp29-36) as using a T-400-2A Amidon (Micrometals) iron
powder core.
I have an Amidon catalog circa 1970 that lists it as a T-400A-2...
maybe the numbers were changed by someone at some point. The core in
question is: 4" OD, 2.25" ID, 7.43 cm? Ae
My 1990 Micrometals catalog lists it as T-400-2D
I have the core here... I do know how big it is...
>
> The manufacturers data for power loss is only listed for freq. up to
2.5MHZ,
> so I am going to assume a 2.5MHZ tank circuit.
That's kind of irrelevant, unless we are going to try and build
something for WWV.
> Using a typical PINET
>
> calculation I arrive at a target L of 11.5uH (assuming 2000 ohm
Rplate). To achieve this
> inductance we use 25 turns of wire on the T400-2 core:
And this isn't the question at hand either... from the original
posting:
>>> The Swan runs 2500vdc on the plate at about 800ma max.
That would be about a 1700 ohm load in Class B. With an RMS voltage
in the vicinity of 1500V.
> L=25*25*18=11250nH=11.25uH
>
> The next step is to determine the peak flux, and here it gets as bad as
it's
> gonna. In a rigorous calculation, which would have to calculate the
peak flux
> by finding the time-integral of the voltage across the coil (Faraday's
> law/Maxwell's second ea.) Rather than marching out the dreaded integral
signs
> here, I will use the fact that this problem has been solved so many
times
> that its generic answer is also an EE101 formula. It is known as the
> 'transformer' equation, the same one that is used to design the primary
of a
> power transformer (same problem -different frequency). I repeat that
> equation here in my favorite units;
>
> B(pk)=V*22.5/(N * f(MHZ) *A(cm-sq) )
>
> V is the RMS voltage across the coil terminals, N is the number of
> turns, A is the cross section area of the core. Plugging in the numbers
for
> our case:
> B(pk)=V*22.5/(25 * 2.5 *3.56) = V * .104
Using the real core as wound with 20 turns, at a real frequency of 1.8
Mhz and the real operating voltage...
B(pk) = 1500 * 22.5 / (20 * 7.43 * 1.8) = 126 Gauss
> We are almost there now. Lets pick a voltage, say 500V. This gives
> us a peak flux of 500 * .104 = 50Gauss (there is no need for more
than 2 SF
> of accuracy here)
>
> Looking in the mfrs data book for their type-2 material, we find that
at
> 2.5mhz and a peak flux of 50G. the power loss is 160mw/cm(cube). For
> our core this results in:
>
> P(core)=160 * 86.4 = 13,700mw=13.7Watts.
Using the formula from the Micrometals catalog for the loss at the
actual frequency and other real conditions...
Core loss = 8.86 * 10^-10 * F^1.14 * B ^2.19 = 476 mw/cm^3
> This is the final answer - 13.7 Watts loss at 2.5MHZ with 500VRMS
applied. I
> repeated this for several power levels relavent to kw amplifiers, with
the
> following results. I state the results in the format
VoltsRF/B(pk)/k/P,
> where k is the data read from the mfrs graph (unless you have their
> data book, you will have to trust me on this one):
>
> 500/50/160/13.7
> 1000/104/680/58.75
> 1500/156/1600/138.2
> 2000/208/3000/259
Using the true power and volume numbers...
476 mw/cm^3 * 171cm^3 ... The power answer is 81 watts.
Keep in mind that this figure is for single tone operation. The real
loss in SSB operation would be considerably less -- say half that number.
>
> There has been some confusion about what the core WC6W had for sale
actually
> is, and I cannot answer that. He stated it as a T400-2A,
Look in an old Amidon catalog... distributors get to play with the
numbers as they will...
>but there is no such core listed in the Micrometals catalog. They do
list a T-400-2D
> which is the double height version of the T400-2, so I repeated all of
these
> calculations for that core.
I'm not going to do this a 2nd time...
> There was a surprise in the results, which are as follows. The
> calculations are similar, but the area doubles, the volume doubles, and
> A-sub-L doubles. To accommodate the latter, I decreased the turns count
to 18
> to maintain a constant inductance value of 11.5 uH. Here are the
> results:
>
> 500/36/80/13
> 1000/72/360/62
> 1500/108/850/147
> 2000/144/1500/259
>
> I would like to re-iterate that these calculations were for f=2.5MHZ,
forced
> by lack of more data from the mfr.
The manufacturer shows the formulas that generated the graphs you
used right on the graphs in their 1990 catalog.
>One thing is for certai, however, the
> losses increase very rapidly with frequency.
It does NOT work that way!!!!!!!!!
While it is true that the core losses increase as the frequency
increases...
one must also note that the number of turns on the core, in this
application, decrease as the square root of the frequency
so, with both of those terms (# of turns, frequency) in the
denominator of the flux equation,
the flux density decreases faster than the losses increase,
even when the frequency term in the core loss equation is considered!
This situation is also apparent from the table of allowable flux
numbers shown on page 17 of the April 1989 Amidon catalog.
Therefore, the lowest frequency of operation is the limiting condition
and requires the most core which is why I used 1.8 Mhz for the true
calculations.
> At 3.5MHZ, the above loss figures could possibly double, even after
decreasing N to scale up
> the PINet. In other words, these results are seriously optimistic for
80M,
> somewaht pessimistic for 160.
>
> These calculations show that this core, or its alternate, would produce
an
> enormous amount of heat/loss at voltages above 500-1000. On that basis
alone
> I can't see its use in typical amplifiers.
Depends what typical is... The core/coil as described is adequate for
a low voltage (2000-2500V) kilowatt amplifer as described in Bob's
article or the Swan query that started this thread.
If typical is a 4CX5000 at 5-6KV then, the answer is no.
Incidentally, there is also some prior art in the ham journals: "The
Whole of the Doughnut" by E.L. Klein, W4BRS in the June 1967 issue of 73
Magazine.
A careful study of both this article, Bob's later article and the
numbers will show that this is a possible solution when space is the
prime factor. There are tradeoffs.
One final point -- Both articles specify separate air (core) coils for
28 MHz so, the IRON POWDER core isn't even involved at the highest
frequency and with the air core coil providing a considerable portion of
the inductance for 24MHz, 21MHz, 18MHz and even as low as 14 Mhz
operation, the core losses are considerably reduced.
> Here is another dirty,little secret. This RF saturation effect is
really
> another form of distortion, when viewed as a circuit element. I
predict,
> without yet having made the calculations (which are possible but quite
> involved) that this could also be a significant factor in rejecting
this
> core.
Both the Micrometals and Amidon catalogs make the point that at these
frequencies the cores are being operated no where near saturation, which
is in the neighborhood of 2000 gauss for the type 2 material -- the
limiting factor in this application is strictly heating.
> The first person who finds a significant flaw in this analysis, as
alleged by
> WC6W, will receive from me a reward consisting of a steak dinner at a
> restaurant in his area.
The Encounter at LAX?
73 & Good evening,
Marv WC6W
>
> 73
> Eric von Valtier K8LV
>
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>
>
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