John Ferrell wrote:

I am absorbing this, but slowly.

I have understood that a "matched line" would indicate the same SWR at
every point you might measure it with a directional coupler.

A matched line is one which is terminated with its characteristic
impedance. The SWR on a matched line is 1:1 at all points along the line.

The Swr
we are discussing is that which we can measure with a directional
coupler, is it not?

Yes and no. To measure the SWR requires an SWR meter or directional
coupler which is designed for the particular characteristic impedance of
the line. If a directional coupler is the proper impedance, it can be
used to calculate the SWR from the forward and reverse powers. If it
isn't, it can't.

The SWR on a mis-matched line will vary with the position you choose
to measure it.

No, it won't, unless it has loss. If it has loss, the SWR will be
greatest at the load and will monotonically decrease toward the source.

This can be indicated by varying the transmission line
length to get an acceptable match for the system. This will satisfy
the need to match a transmitter for a given frequency. A directional
coupler placed at different places on the line will still indicate a
non uniform SWR. Any feed line losses due to insulation or radiation
are effectively hidden from the transmitter end.

It appears that you're assuming that what you measure with an SWR meter
or calculate from directional coupler readings is the SWR. Unless the
coupler or meter is designed for the Z0 of the line, it isn't. If the
coupler or meter isn't of the proper impedance for the line, you'll get
different readings as you move along the line. Those readings aren't,
however, the line's SWR.

. . .

Roy Lewallen, W7EL