You can measure the complex impedance of a ferrite core quite easily and
with moderate accuracy using an antenna analyzer. From that reading and
a low frequency impedance measurement, you could calculate the complex
permeability. However, you can find graphs of the values for common
ferrite types at http://www.conformity.com/040spotlight.pdf and other
web sources. But it's not obvious to me why you'd need to calculate or
measure the complex permeability -- all you need to do is measure the
impedance of a short wire with the core slipped over it. When you slip
the core over the antenna, it'll behave just as though an impedance of
that value was inserted in series with the antenna wire at that point.

Different types of ferrites are quite different at HF. Low frequency
ferrites like the Fair-Rite 70 series are primarily resistive at HF, and
would simply add loss to an antenna like adding a series resistor. High
frequency types like the 60 series are inductive with reasonable Q
through the HF range so would behave pretty much like a series inductor
of moderate Q. Type 43, probably the most common type now available, has
a Q on the order of 1 at HF, so it also would primarily just add loss to
an antenna.

But hey, if you use one of the lossy ferrites you'll end up with an
antenna that's really broadband and quiet. That's what we all want,
isn't it?

Roy Lewallen, W7EL

Tom Donaly wrote:

Balanis, in his book _Antenna Theory, Analysis and Design_, has
a short section dealing with this. Define a parameter
Q = (mu - 1)ln(b/a), where mu is complex permeability of
the ferrite, a is the radius of the conducting wire, and b is
the radius of the conducting wire plus the ferrite. According to
Balanis, increasing the real part of Q "a. increases the peak input
admittance b. increases the electrical length (lowers the resonant
frequency c. narrows the bandwidth." In order to use this formula,
you have to know the complex permeability of the ferrite coating.
I don't know how you'd measure that. Maybe Richard Clark knows.
It would be fun to try. I wouldn't pin any hopes on it being
practical, though, since it doesn't seem to be in general use anywhere.
73,
Tom Donaly, KA6RUH