Yes, the Q as determined by simply taking X/R decreases as you approach
1/4 wavelength, but what you really need to do is resonate it with a
capacitance and look at the Z as a function of frequency when you do
that. I mean, it IS a resonator if it's 1/4 wave long: it would look
like Q=0 there if you take X/R, but of course it's not. If you simply
want _inductance_ (i.e. a loading coil), do NOT make the stub close to
1/4 wave long. It's just the same as trying to use a coil for
inductance up near its self-resonance.
Also, a point that was in my mind when I originally posted, but failed
to put well into writing then, is that as frequency increases, the Q of
a solenoid coil will increase about as the square root of
frequency...and the size stays the same. But the stub's Q also
increases as the square root of frequency, while it's size (length) is
directly proportional to 1/freq, and it's shrinking in size.
And thanks for the cross-check on my numbers, Owen. I hacked it pretty
quickly, and may have missed a cog somewhere, though I think the
numbers are reasonably close. I suppose one of Reg's programs will
give you stub impedance, too. -- I think I see why my numbers may be
a bit different than what you got; I'll check on it as I have time,
though the difference isn't enough to worry me--the trends are still
the same.
Cheers,
Tom
Owen Duffy wrote:
On 16 Apr 2006 15:44:06 -0700, "K7ITM" wrote:
OK, I gotta take issue with the part that says,
" A transmission line, even a very good one, generally has a Q of
someplace around 20-75. The definition of Q I am using is reactance
over ESR. Say you need a reactance of 400 ohms to resonate an antenna.
Linear or stub loading would add a series resistance of 5 to 20 ohms as
loss resistance at that point in the system.
"
I know that transmission line Q varies all over the place: it's much
more reasonable to use it in a resonator at high frequencies than low,
and line construction makes a big difference too. To back this up with
numbers, I just ran some calcs (actually put together a little Scilab
program to run them for me) on four different lines: (a) is RG-8/RG-213
type line with solid poly dielectric, (b) is 75 ohm air insulated coax
in an 0.5" ID copper tube, (c) is balanced two-wire line made with
12AWG (~2mm) wire spaced 2" (~5cm) on centers), and (d) is two 0.625"
OD copper tubes spaced 3" on center.
For a 1/8 wave section of line shorted at the far end, the calculated
impedances and Qs a
line a, 10MHz: 0.622+j50, Q=80
line a, 100MHz: 0.197+j50, Q=254
line a, 1000MHz: 0.0622+j50, Q=800
I tried these numbers in the line loss calculator at
http://www.vk1od.net/tl/tllce.php using Belden 8267 of 2.475m length
for 0.125 wavelengths and Zload=0.0000000001. The input Z I got was a
little higher at 0.88+j50 (probably slightly different approximation
of Zo used in the calcs), yeilding a Q of 57. The Q is quite dependent
on line length, decreasing as length increases towards a quarter wave.
I suspect this is not a good method of analysing behaviour when the
line elements are field coupled to other radiator elements, the
currents in each leg are not necessarily equal and opposite.
Owen
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