On Wed, 12 Dec 2007 13:19:27 -0800 (PST), wrote:

On Dec 12, 11:00 am, Richard Clark wrote:
On Wed, 12 Dec 2007 07:21:21 -0600, Cecil Moore
wrote:

Double the frequency and see what happens.

Hi Dan,

The Lottery Commission is asking to re-examine your Ticket. Not to
worry, winners WILL be notified at a later date. All that is asked is
that you be patient as some have been waiting longer than you.

73's
Richard Clark, KB7QHC

Those white floating things are way, way off in the distance and
nowhere near to approaching us. The chairs for the band remain in
place, folded up. The angle of the deck is 0 degrees horizontal.

Keel's finally settled into the mud, I see.

73's
Richard Clark, KB7QHC

On Dec 12, 8:44 pm, "AI4QJ" wrote:
"Cecil Moore" wrote in message

. net...





wrote:
Although we know that the 200 ohm line is longer, there is no
indication that the length of the 600 ohm line must or must not
change.

The phase shift at the impedance discontinuity depends
upon the *ratio of Z0High/Z0Low*. The following two
examples have the same phase shift at the impedance
discontinuity.

Z0High Z0Low

---43.4 deg 600 ohm line---+---10 deg 100 ohm line---open

---43.4 deg 300 ohm line---+---10 deg 50 ohm line---open

So how long does the 600 ohm line have to be in the following
example for the stub to exhibit 1/4WL of electrical length?

---??? deg 600 ohm line---+---10 deg 50 ohm line---open

Based on what you say above, Zo high/Zo low = 6 resul;ts in 37 degrees.
Then for phase shift, (Zo high/Zo low)*37 deg = 6*D where D = phase shift.

If the above ratio is literally true, then in the above example, 12*37deg/6
= 74 degrees and length of the 600 ohm line = 90-74-10 = 6 degrees.

However, I would like to find a reference for the math showing the
characteristic impedance ratio relationship with phase shift. I am reluctant
to accepting formulas without seeing them derived at least once.

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

It can be seen, as noted by Cecil, that beta
will be the same if the impedances of the two
lines are scaled proportionally.

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.

....Keith

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

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

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

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".

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