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

Looks like you haven't thought it through. If one
wants to create a shortened dual-Z0 stub with
equal lengths of each section of Z0High and Z0Low,
here is the corresponding chart for different
ratios of Z0High/Z0Low.

http://www.w5dxp.com/DualZ0.gif

As an example, one can create an electrical 1/4WL
stub that is 1/3 the normal physical length by
using 600 ohm line and 50 ohm line.
--
73, Cecil http://www.w5dxp.com

On Dec 13, 5:57 am, Cecil Moore wrote:
It does not seem to be a concept that is
particularly useful for the solving of problems.

Looks like you haven't thought it through. If one
wants to create a shortened dual-Z0 stub with
equal lengths of each section of Z0High and Z0Low,
here is the corresponding chart for different
ratios of Z0High/Z0Low.

http://www.w5dxp.com/DualZ0.gif

As an example, one can create an electrical 1/4WL
stub that is 1/3 the normal physical length by
using 600 ohm line and 50 ohm line.

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.

This reality, however, does not demonstrate any
value for the *concept* of phase shift at a
discontinuity. For the concept to be useful it
should facilitate understanding or problem
solving. As far as I can tell, you always solve
the problem in the conventional way (change
the angle on the Smith chart, un-normalize
the impedance, re-normalize the impedance
to the new Z0, measure the angle to get to
the desired impedance) and then work out
the "phase shift" at the discontinuity. It sure
looks like additional work that adds no value
since the important and useful information
has already been derived before computing the
"phase shift".

As such, I declare it "not particularly useful".

....Keith

Keith Dysart wrote:
This reality, however, does not demonstrate any
value for the *concept* of phase shift at a
discontinuity.

It may indeed have little value for stubs. But
for loaded mobile antennas the value is obvious.

The value is that it explains the phase shift
through a loading coil in a loaded mobile
antenna and the phase shift at the coil to
stinger junction. Using dual-Z0 transmission
line stubs we are ready to understand loaded
mobile antennas, the phase shift through the
loading coil, and the "missing degrees" at the
coil to stinger junction.

According to Dr. Corum, my 75m Texas Bugcatcher
coil has a Z0 of ~4000 and a VF of ~0.02.

The stinger has a Z0 in the ballpark of 400 ohms
and a VF close to 1.0

Knowing what we know about a dual-Z0 1/4WL stub,
we can now use that knowledge to analyze a base-
loaded mobile antenna with coil and stinger.

---Z0=4000 ohm coil---+---10 deg 400 ohm stinger

Now it's a piece of cake. How many degrees of
loading coil do we need to make the configuration
90 electrical degrees long?

Arctan((400/4000)*cot(10)) = ~30 degrees

What is the impedance at the coil to stinger
junction?

400*cot(10) = ~ -j2300 ohms

What is the phase shift at the coil to stinger
junction?

90 - 30 - 10 = ~50 degrees

I stumbled upon the dual-Z0 stub idea in trying to
understand the phase shifts and delays in a loaded
mobile antenna. The same general principles apply.
Using traveling-wave current to measure the delay
through my Texas Bugcatcher coil agreed within 15%
with these calculated values.

One side said the coil had to make up the missing 80
degrees of antenna that necessarily had to be there
with a 10 degree stinger. This side did not understand
the phase shift at the coil to stinger junction.

The other side said the coil, like a lumped inductor,
has ~zero phase shift through it. This side did not
understand the limitations of the lumped circuit
model.

The delay through a coil is what it measures and
calculates to be within a certain accuracy. It is not
80 degrees and it is not ~zero degrees.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:

...
400*cot(10) = ~ -j2300 ohms
...

I am in the middle of a brain fog/block.

I am attempting to get an equation to obtain the cotangent of x (or 10
in the above.) I HAVE DONE THIS BEFORE-got something wrong here ...

(1/tan(10)) = 5.67128

and (400*(1/tan(10)) = 2268.51273

There is no "built in" cotan function on my ti-86, ti-83, etc.

Help me out Cecil, anyone?

Regards,
JS

John Smith wrote:
There is no "built in" cotan function on my ti-86, ti-83, etc.

Poor guy - why can't you do cotangent functions in
your head? :-)

Help me out Cecil, anyone?

How about:

cot(x) = tan(90-x)

cot(10) = tan(80) = 5.67
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:

...
Poor guy - why can't you do cotangent functions in
your head? :-)
...

Cecil:

The extremly difficult will take me a couple of minutes ...

The impossible takes just a bit more time. :-)

I AM NOT A GURU! yanno? LOL

Regards,
JS

Cecil Moore wrote:
John Smith wrote:
There is no "built in" cotan function on my ti-86, ti-83, etc.

Poor guy - why can't you do cotangent functions in
your head? :-)

Help me out Cecil, anyone?

How about:

cot(x) = tan(90-x)

cot(10) = tan(80) = 5.67

Geesh, I had it, but sure didn't look right ... a walk around the block
and letting things go put all back to right ...

CoT(10) = (1/tan(10))

damn ... moments like these are humbling ...

Sometimes my progress forward is "inversely proportional" to the energy
I apply ... ;-)

Regards,
JS

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

Looks like you haven't thought it through. If one
wants to create a shortened dual-Z0 stub with
equal lengths of each section of Z0High and Z0Low,
here is the corresponding chart for different
ratios of Z0High/Z0Low.

http://www.w5dxp.com/DualZ0.gif

As an example, one can create an electrical 1/4WL
stub that is 1/3 the normal physical length by
using 600 ohm line and 50 ohm line.

Cecil,

So how do you make that 12:1 connection, say 50 ohm coax to 600 ohm open
line? Do you s'pose the connection bits add any phase shift all by
themselves? Do you have a model for that extra phase shift?

8-)

73,
Gene
W4SZ