In , Frank Gilliland
wrote:
In , lancer wrote:
snip
Chrome has about the same conductivity that Stainless does, or at
least from the info I found. 3-15% for Stainless, 19% for chrome,
relative to copper.
For a conductor 102" long with a diameter of 0.625", the following metals have
the following AC resistance at 27 MHz:
Chromium .0194 ohms
Copper .00711 ohms
S. Steel .0451 ohms
By golly, I made -another- mistake in my math, which is not such a suprise. But
when I was double-checking my work this time I ran across something that
everyone should find VERY significant. So from the beginning.....
S = Skin depth in meters = sqrt(2/(2*pi*f*u*q)), where
q = conductivity of conductor (mhos/m), and
u = 4piE07 * relative permeability of medium
This is what's interesting. Stainless steel comes in many varieties. Some of
them aren't even steel but use the term because they are used for the same
applications. Regardless, some stainless steel is ferromagnetic and some is not.
The nonferromagnetic steel will have a relative permeability close to that of
copper, or 1 for all practical purposes. OTOH, ferromagnetic steel will have a
relative permeability much higher, and the value of 500 was used in the
calculations below.
AC resistance in ohms = l / (q * S * 2 * pi * r), where
l = length of conductor (in meters)
r = radius of conductor (in meters)
Note that there are two different listings for the conductivity of chromium. The
first value is based on the information that it is 55% of the conductivity of
copper, and the second value (as well as the values for copper and stainless
steel) is based upon CRC's HC&P:
Cu Cr #1 Cr #2 S.S. S.S. (ferro)
Conductivity: 5.80E07 3.19E07 .769E07 .166E07 .166E07
Skin depth: 12.7E-06 17.1E-06 34.9E-06 75.2E-06 3.36E-06
AC resistance: .0705 ohms .0952 ohms .194 ohms .161 ohms 9.31 ohms!!!
Notice that the differences in the resistance are all insignificant except for
the ferromagnetic stainless steel. This is because of it's high relative
permeability. Now when I realized this issue I put a magnet to my whip it
doesn't stick. So I went to the shop this morning and checked a number of SS
whips of different lengths. Some were magnetic and some were not. The magnetic
whips are now all in a pile for other uses.
So even old farts like me can learn something new. From now on I'll recommend to
everyone to check an antenna with a magnet before buying it, because that's what
I intend to do myself.
Now, back to the X-terminator. Comparing the difference in radiation efficiency
with regards to length and polarization, the 102" whip has 102" that are
vertical. Everything is sent vertically polarized. Nothing is wasted in
horizontal polarization. OTOH, the X-terminator has 9.5" vertical, followed by
74" of coil, then 3.75" vertical, 41.23" of coil, 5.5" vertical, and 32" of
(gasp!) stainless steel. So you have a total of 166" of conductor, with 50.75"
of it radiating the desired vertically polarized radiation, but 115" of it
dumping horizontal hash. Let's disregard for the moment that 32" (or 63%) of the
vertical total is made of that infamous stainless steel, and forget the extra
overall resistance due to the additional length of conductor needed to wind the
coils. Let's concentrate instead on the fact that the coils consume 69% of the
total 'wire' in this antenna. Now if the current distribution was even
throughout the length of the antenna, that would mean the coils are radiating
69% of the power as multi-phasic mush. But that's not the case, as the coils are
positioned near the base of the antenna, where the antenna's current
distribution is the greatest. That means the coils are radiating -more- than if
the current was evenly distributed, and therefore -more- than 69%! And that
means the efficiency of the X-terminator is less than 31%!!!
And if that isn't bad enough, let's take a look at an el-cheapo 102" stainless
steel whip of -magnetic- persuasion. If the whip has an AC resistance of 9.31
ohms, and the input impedance is an ideal 50 ohms, that translates into a loss
of only 19%. If the input impedance is 36.5 ohms, the wire diameter is 0.25",
and accounting for power reflected back to the radio due to mismatch, loss is
still well below 30%. Both scenarios are a -hell- of a lot better than the 69%
waste caused by the X-terminator's loading coils, and we didn't even go into
absorbtion, reflection, hysteresis and eddy current losses caused from the
vehicle roof right below those coils!!!
So yes, stainless steel -is- more resistive than chromium. But the difference is
not significant. So I'll say it again -- there is no way that this antenna will
outperform an unloaded 102" whip whether it's made of fiberglass, stainless
steel OR ferromagnetic steel!
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