In article
,
Keith Dysart wrote:

In another thread, "Calculating a (fictitious) phase shift;
was : Loading Colis", David Ryeburn has provided the
arithmetic for the general case which includes the
following expression:
-j*(Z_2)*cot(alpha + beta) = -j*(Z_1)*cot(alpha)

"alpha" is the length of the open line
"beta" is the "phase shift" at the joint

Yes.

"Z_2" is the impedance of the open line
"Z_1" is the impedance of the driven line

Backwards. Z_1 is the characteristic impedance of the open-circuited line
(100 ohms, in some of the examples previously discussed). Z_2 is the
characteristic impedance of line from the junction point back to the source
(600 ohms, in those examples).

But beta is dependant not only on the two
impedances, but also on the length of the
open line.

There are no simple relationships here.

It does not seem to be a concept that is
particularly useful for the solving of problems.

I couldn't agree more. The angle alpha + beta is useful; the angle beta is
not. But I thought I would provide the formulas in an attempt to set things
straight.

In article
.
Keith Dysart wrote:

There are many ways to create the impedances
for matching, each with different advantages. As
you point out, one of the benefits of using two
different impedance lines is a reduction in material,
though, you could go all the way to just using
a lumped capacitor and save even more.

Agreed. I've always liked capacitors better than transmission line segments.
It takes a pretty crummy capacitor to have as low a Q as a transmission line
section is likely to have. Even inductors are often better than transmission
line segments. But W5DXP was trying to explain how a loaded mobile antenna
worked (using transmission line concepts).

However, loaded mobile antennas presumably radiate, at least a little, and
my analysis (and W5DXP's discussion of angle lengths of transmission lines
and "phase shift" at their junction) is for *LOSSLESS* transmission lines.
This makes me wonder.

David, ex-W8EZE

--
David Ryeburn

To send e-mail, use "ca" instead of "caz".