Robert Lay W9DMK wrote:
..For your 1/4WL open stub on 10.6 MHz, with a stub impedance of 0.57 ohms,
I calculate total losses of about 0.2 dB.
I hope I'm not misinterpreting your values - I assume that you are
starting with a theoretical open circuit and a theoretical RG-8 line
and calculating a theoretical impedance seen looking into that line of
0.57 + j 0. From that you then calculate a theoretical 0.2 dB. When I
say calculate, I assume that you may instead by using a nomogram.
Not using a nomogram but everything is 100% theoretical. It doesn't
matter what line is being used as long as it's Z0 is 50 ohms. Matched
line loss didn't enter into my calculations. It's only total loss.
Anyway, based on all of that being the situation up to but not
including the loss figure, when I take the 0.57 + j0 and calculate the
SWR as 87.7 I get a loss more like .05 dB, theoretically, so I'm not
sure in what ways we are coming up with these numbers.
Is that the additional loss due to SWR or the total loss? My theoretical
loss is total loss and the matched line loss need not be known. The
measured resistance of the resonant stub is all one needs to know besides
Z0.
I can explain
exactly how I got mine, which was via measurements followed by a
theoretical cacluation of loss based on the two SWR's formula which is
built into all Smith Charts.
I can't remember where the following formula came from. I think it
was from an RF guru at Intel, but I can't be sure. I have a hand-
written notebook of useful formulas covering 25 years but I didn't
record where they all came from.
The formula for theoretical TOTAL losses in a *resonant* stub:
Total loss = 10*log{[(Z0-R)/(Z0+R)]^2}
where R is the measured resistance of the resonant stub and Z0
is the characteristic impedance of the stub material. You can
see the [(Z0-R)/(Z0+R)]^2 term is akin to a virtual rho^2 at
the mouth of the stub. Since rho^2 = Pref/Pfor, the losses in
the stub are equivalent to the losses in an equivalent resistance
equal to the measured virtual resistance at the mouth of the stub.
--
73, Cecil
http://www.qsl.net/w5dxp