Hi Dave, Peter,
> I'm looking for information on applying toroidal inductors in the
> plate tank circuit of a (large, 4-1000 based) tube HF amp. Are there
> special considerations in estimating core size and material type to
> avoid saturation, or other electrical considerations?
There are many consideration, but saturation is NOT one of them. The
tank inductor in a classical tube amplifier sees no DC, and at HF all
magnetic materials in existence will melt down or otherwise degrade from
loss far before they saturate. So you need to design the inductor such
that the magnetic flux stays below a critical level set by loss, and
that will "automatically" result in a level far below saturation.
> You need to use powered iron cores.
That's right (except for the typo of the "d" going amiss in "powdered").
While some ferrites have lower loss, they are not stable enough for a
relatively high Q application like this. Also, many ferrites are more
touchy than powdered iron when it comes to heat tolerance, due to a
lower Curie temperature.
> The limitation is the voltage across the windings.
Yes. And there are two things here to get it right.
First is to understand the ratio between flux density and the other
parameters. Flux density is directly proportional to applied voltage,
and inversely proportional to frequency, number of turns, and cross
section of the core. For sine waves, like we have in an amp, and using
metric units, we get the very simple relationship:
Flux density [Tesla] = Volts / (turns * Hz * cross section [m2] * 4.44)
The 4.44 factor in this formula is given by 2 * 2 * 1.11, where one of
the two's stands for the fact that you have two half cycles in each
cycle, the other two is for the fact that you will magnetize the
material in both polarities, and the 1.11 reflects the difference
between the RMS value and the average value of a sine wave. So this
equation gives the peak value of magnetic flux density. The peak-to-peak
value instead, which is used in some data sheets, is of course twice as
So, for example, if you have 4000 volts RMS across your tank coil, at
3.8 MHz, the core has 5 square centimeters of cross section, and you
have 100 turns, then the flux density would be:
4000 / (100 * 3800000 * .0005 * 4.44) = .0047 Tesla, or 4.7mT,
which might be fine with some powdered iron mixes, but not with others.
And this brings us to the second thing you need to care for: How much
flux density a given core will take, at a given frequency, for a given
amount of loss. This is a figure you have to take from graphs or
equations in the data sheets provided by the manufacturers of the cores.
Typically these data sheets also give the heat rise for a given core
size at a given amount of total core loss, and also they tell what's the
maximum temperature the material can safely work at. So you need to
consider the ambient temperature inside your amp housing, see how much
headroom you have from there to the core's limiting temperature, and
that gives the acceptable heat rise, which in turn gives the acceptable
In this you can apply factors for intermittent service, if you like, but
you should also consider the loss of the wire, which might contribute a
very significant amount of heat. This wire loss is calculated from the
current going through the wire (in turn calculated from the applied
voltage and the reactance of the coil at the frequency considered), from
wire diameter, skin depth at the given frequency, and resistivity of the
wire material (at the worst case temperature!).
Once these things are clear, you need to start some juggling with core
sizes and number of turns, until you arrive at a combination that
provides the correct inductance and also will tolerate the applied
voltage without excessive loss in the core.
And of course you need to repeat the calculations for each band. Which
brings me to a side note: It's not good to short out turns on higher
bands, like many designers do with air coils. The toroids couple all the
turns excessively well for that. If you short turns, a really big loss
results. So you need to switch bands by switching in or out entire
coils, each with its own core. Typically you would use toroids for the
lower bands only, and air cored coils for the higher ones.
All the above might sound a bit overwhelming when you first read it, but
it is nothing terribly difficult, once you put numbers into it and start
understanding the matter.
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