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November 26th 04, 04:38 PM

(Robert Lay W9DMK) wrote:
Yes, I believe it does - that is, it makes perfect sense to have a low
resistance and to have a near zero reactive component. What does not
make sense is that the high SWR is supposed to produce outrageous
losses. I don't see values that I can interpret as high losses - quite
the opposite. Maybe I just don't interpret it correctly, but I would
expect it to be several ohms - not 0.57 ohms.

Hi Bob, I'm still at my relatives' house posting through Google. I'll
expand on this when I get back to my computer.

Those equations in The ARRL Antenna Book (15th Edition) make an assumption
that may or may not be true - I don't know. What they are assuming is that
the losses are due to the additional power associated with high SWR. In
general, if the forward power is 100w for the matched case and the sum
of the forward and reflected power is 300w for the unmatched case, the
losses will be three times higher for the unmatched case. That seems a
reasonable assumption. However, rho at the shorted or open end of a stub
is equal to |1| so rho^2 will be equal to 1. That puts (1-rho^2) = 0 in
the denominator of the equation and makes the addditional losses undefined.

In fact, and this is where it gets ridiculous, the examples in the
ARRL Antenna Book would lead me to believe that the above quarter wave
line would exhibit 20 dB of total losses. In order to get those
numbers the SWR at the load of say 8000 would have to decrease to
1.01:1 at the source end in order to account for 20 dB in losses. (See
the example on page 24-9 of the 17th Edition.)

Here's an example. Assume 100w is delivered to the load for both the
matched and unmatched conditions. Assume 3dB matched line loss in the
transmission line. Assume an SWR of 5.83:1 (rho=0.707) at the load for
the mismatched condition.

Forward 200w------------3dB loss-------------Matched Load 100w

Forward 400w------------3dB loss-------------Mismatched Load 100w
Reflected 50w both Forward 200w
directions Reflected 100w

The equations gives an additional loss of 5.44dB. This is based on an
assumption that the losses are directly proportional to forward power
plus reflected power.

Remember that at the mouth of the stub, the impedance is equal to
(Vf + Vr)/(If + Ir) so, knowing the Z0, that should allow you to
calculate those four values existing at the mouth of the stub. From
that, you can calculate the total losses. More when I get back.
--
73, Cecil, W5DXP