I'm with you up to this point, Tom, but here, you're mistaken. An
effective common mode choke is dominantly resistive in the frequency range
where it is to be used. The reactive component of the choke can be
cancelled a length of feedline that is capacitive at the operating
frequency, which increases the dissipation and makes the choke
ineffective. The key to not having it fry is to make the Z high enough
that the common mode current is small.
It works the way I said. I run into this ALL the time. It is a constant
headache for high power or high impedance circuits.
The choke has a certain equivalent parallel impedance. The voltage across
the resistive part of that impedance makes heat. If we have a perfectly
balanced load from a perfectly unbalanced source, the common mode voltage
across the isolating choke is half of the voltage across the load terminals.
If we assume the load is 1000 ohms and power 1kW, voltage is P^2 over 1000 =
1000 volts. In an ideal condition 500 volts would be across the "isolation
turn" a simple choke represents.
If that choke is 10,000 j0, a very difficult task in the real worldat
higher frequencies, we have 500 volts across 10k of resistance, or 25 watts
dissipation. It is difficult to have enough CM resistance at high enough
load impedances or voltages, even if the load is perfectly balanced.
(That is why ferrite core plate chokes are not in common use in amplifier
with a few thousand volts or more. We can't make impedance high enough to
not cause too much core heat.)
Furthermore, the common mode circuit is NOT a simple voltage divider when
the choke is added to the feedline of an antenna. Rather, it is part of an
antenna system that includes the "intentional" antenna and the
"unintentional" antenna (the feedline), and it is the lengths of those
components, and the position of the choke, that will determine the voltage
across the choke and the resulting current. To find the dissipation, we
must add the equivalent circuit of the choke to an NEC model of the
antenna with the choke and the feedline (as a single wire), including it's
connection to ground. NEC will tell us the current in the choke, and I
squared R is the dissipation. An antenna with severe imbalance can easily
fry a very good choke at high power.
I certain agree there are many variables, but it is best to start with a
simple model. Just to be clear, an antenna example with PERFECT balance can
be a major issue with choke heating. This is why there is no such thing as a
universal "one thing fits all" solution or "one thing causes all the
problems". There are several things involved.
Because there are multiple variables working to create a wide range of end
results, any discussion has to be clearly defined. I chose a simple ideal
case of a perfectly unbalanced source feeding a perfectly balanced load of a
certain resistive impedance and power.
This is an age old problem. It is a problem in higher voltage solid state
amplifiers, as well as antenna baluns.
The worse answer to give people is "it depends on many things", but that is
often the only correct answer. One size will not fit all.
73 Tom
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