This thread started with Prof. Baker mentioning the fact that mu(r) of
stainless steel may reduce skin depth on HF wire antennas and hence
efficiency.
NEC2 typically assumes mu(r) of 1 when using load type 5 which would
result in an error in the computed efficiency if mu(r) of some
material is larger than 1.
We have been working on a different problem where we actually are
trying to use permeable materials to suppress currents on conductors
and it was my opinion that mu(r) of a metal such as stainless steel
will be close to 1 at HF frequencies as result of the classical eddy
current and gyromagnetic limiting frequencies. Prof Excell mentions a
reference (which unfortunately a cannot lay my hands on) which
indicates ferromagnetic properties up to a few hundred megahertz. A
few other readers also seem to be of the opinion that the
ferromagnetic properties of stainless steel is significant at HF/VHF
frequencies.
I had a careful look at this issue, since it may affect some of the
work we are currently involved with. We wish to use the complex
permeability to suppress currents on conductors and for this
application one certainly do not get much permeability from stainless
steel. I do believe that I was wrong in concluding that one hence will
see no effect on skin depth as well. Profs Baker and Excell are
correct and that some high frequency permeability may indeed affect
conductor skin depth at HF/VHF frequencies and above. I shall try to
clear up some of the confusion I may have caused below (and would like
some more feedback since not everything is that clear to me yet):
My main reference have been: "Soft Magnetic Materials" Editted by
Richard Boll and published by Heyden & Son Ltd. This is a textbook
sponsored by the Vacuumschmelze (VAC) GmbH, Hanau, who manufactures
metal alloy magnetic materials.
They define two limiting frequencies associated with permeable
metals. The classical eddy current limiting frequency, fw, which is
related to the thickness of the metal (or sheet thickness for
laminated materials). This is given by:
fw = (1000*rho)/(mui*d^2)
where fw is in kHz, rho is in ohm mm^2/m, d is the material thickness
in mm, and mui is the permeability at 4 mA/cm (close to initial
permeability). This equation yields very low values of limiting
frequencies for high conductivity materials such as stainless steel
unless extremely thin laminations are used. I do believe, from a more
detailed look, that this effect will reduce the "bulk permeability",
for instance when using the material as a core of an inductor etc, but
will should not reduce the localized permeability which will affect
skin depth. The gyromagnetic limiting frequency (discussed in detail
below) will have to be taken into account for skin depth calculations
but yields much higher limiting frequencies.
The gyromagnetic limiting frequency gives an upper frequency limit
independent of the sheet thickness and purely a function of the
material and the applied field strength.
To quote from my source "It has been shown that the measured limiting
frequency does not - as would be expected from classical theory -
continue to increase with decreasing sheet thickness, but reaches and
upper limit. This limiting value is cuased by the damping and inertia
of the electron spin which impose an upper limit on the speed of the
magnetization processes. A limiting frequency fg is thus reached
(limiting in the sense that it is the frequency at which the real part
and imaginary part of the permeability as a ratio of the initial
permeability have reached a values of 0.5), which was termed the
gyromagnetic limiting frequency and is indepenednt of the sheet
thickness.... The gyromagnetic limiting frequency fg depends on the
ratio of the saturation flux density to the initial permeability
(Bs/mui).. The gyromagnetic limiting frequency fomula valid both for
metals and ferrites is:
fg = 10000*k*Bs/mui where k is a value between 0.8 and 1.9.
where fg is in MHz, Bs is the saturation flux density in T, mui is the
relative initial permeability.
Assuming mui of about 1000 and Bs of 2T this gives fg = 20 MHz (not
kHz as indicated in my first reply!). This would imply that one will
still observe a permeability of 500 at 20 MHz using the rough values
here - which may certainly affect skin depth and hence antenna
efficieny at HF frequencies.
I hope that the above clears up some of the issues and I will
appreciate feedback from anybody with relevant experience/information
Andre Fourie
Tel: Intl + 27 11 4030380
Fax: Intl + 27 11 4030381
Website: http://www.poynting.co.za
email: fourie_at_poynting.co.za
Papermail: Dr APC Fourie, PO Box 318, Wits, 2050, South Africa
Received on Wed Dec 17 1997 - 12:52:13 EST
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