I have previously presented my thoughts about the
similarity between dual-Z0 stubs and base-loaded
mobile antennas. Here is an article on the subject
of "Dual-Z0 Stubs" that is directly applicable
to base-loaded mobile antennas.

If we can shorten a stub by using two Z0s, why
can't we shorten an antenna by using two Z0s?

http://www.w5dxp.com/shrtstub.htm
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:
I have previously presented my thoughts about the
similarity between dual-Z0 stubs and base-loaded
mobile antennas. Here is an article on the subject
of "Dual-Z0 Stubs" that is directly applicable
to base-loaded mobile antennas.

If we can shorten a stub by using two Z0s, why
can't we shorten an antenna by using two Z0s?

http://www.w5dxp.com/shrtstub.htm

Congratulations, Cecil, you've just re-invented the electrical
analog of the Helmholtz resonator. Your analysis would be a lot
simpler if you'd first characterized each stub with T parameters
and then multiplied them together to get a two port you could use
to find the conditions for the resonance of the entire stub. You
could then use the differential calculus to find out what the
criteria was for the shortest overall stub. (It's true, both lengths
have to be the same.) If you want to take a stab at using your
discovery to deal with antennas, why don't you use two "dual Z0
stubs together to make a folded dipole. You could even do that in
EZNEC. Applying this to your favorite loaded dipole is a stretch,
but that probably won't stop you from trying.
73,
Tom Donaly, KA6RUH

(P.S. Where did you learn about "dual Z0" stubs?)

On Apr 24, 8:28*pm, "Tom Donaly" wrote:
If you want to take a stab at using your
discovery to deal with antennas, why don't you use two "dual Z0
stubs together to make a folded dipole. You could even do that in
EZNEC.

Tom,

How would that work in a folded dipole? Surely it's not the
differential mode "stub" you're trying to shorten - it's the common-
mode radiator.

Steve G3TXQ

steveeh131047 wrote:
On Apr 24, 8:28 pm, "Tom Donaly" wrote:
If you want to take a stab at using your
discovery to deal with antennas, why don't you use two "dual Z0
stubs together to make a folded dipole. You could even do that in
EZNEC.

Tom,

How would that work in a folded dipole? Surely it's not the
differential mode "stub" you're trying to shorten - it's the common-
mode radiator.

Steve G3TXQ

Hi Steve,
I have no idea what Cecil will find if he tries his
theory on this. However, according to Cecil's favorite text, a
folded dipole's behavior can be analyzed by assuming that its
current "is decomposed into two distinct modes: a transmission
line mode and an antenna mode." (From Balanis, _Antenna Theory_)
You've got EZNEC; you can try this, too. It won't cost you anything,
and, if nothing else, you might get the satisfaction of telling me
how wrong I am.
73,
Tom Donaly, KA6RUH

On Apr 24, 9:26*pm, "Tom Donaly" wrote:
However, according to Cecil's favorite text, a
folded dipole's behavior can be analyzed by assuming that its
current "is decomposed into two distinct modes: a transmission
line mode and an antenna mode." (From Balanis, _Antenna Theory_)
You've got EZNEC; you can try this, too. It won't cost you anything,
and, if nothing else, you might get the satisfaction of telling me
how wrong I am.

Tom: I was unaware of "Cecil's favourite text" and did my own work on
the folded dipole some time ago:
http://www.karinya.net/g3txq/folded_dipole/

I too found that you can resolve the currents between the two wires
into a common-mode radiating component and a differential-mode stub
component. My particular interest was in situations where the velocity
factors of the two modes is very different - for example if you use
zip cord for the construction - and discovering where you then need to
place the stub shorting links for minimum effect on the feedpoint
impedance.

I was disappointed to see that recent editions of the ARRL Antenna
Book don't recognise this effect, but earlier editions do. I have also
found that Cebik's analysis of the topic is incomplete, as a result of
which he reaches the wrong conclusion about shorting link position. I
wrote to ARRL about it some time ago, suggesting they re-instate the
original text, but they seem disinclined to respond.

Without modelling it, my guess is that a ""dual Zo" approach will
require the shorting links to be placed much closer to the centre of
the antenna, but it will do nothing for the overall length required
for common-mode resonance. After all, what you require of the stubs is
that they be very high impedance across the feedpoint, and with "dual
Zo" that would require them to be much shorter.

Now, if you can think of some way of forming a large discontinuity in
the COMMON-MODE Zo we may be onto a "breakthrough"

Steve G3TXQ

Tom Donaly wrote:
(P.S. Where did you learn about "dual Z0" stubs?)

While I was figuring out why Roy's "measurements"
were very accurate but virtually meaningless.

In an ideal stub, the current doesn't change phase
from end to end. An antenna is more like an ideal
stub than most people realize.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:
Tom Donaly wrote:
(P.S. Where did you learn about "dual Z0" stubs?)

While I was figuring out why Roy's "measurements"
were very accurate but virtually meaningless.

This is, of course, referring to Roy's "measurements"
of the "delay" through a 75m mobile loading coil as
being close to zero since there was "no measurable phase
shift" - as if the phase shift had anything to do with
the delay in a standing wave antenna. Hint: It doesn't!

Any person with a modicum of mathematics skill can
look at the following equation and know that there
is no phase shift relative to x in 1/4WL of wire or
coil.

Itot = Imax*cos(kx)*cos(wt)

Since Roy has known these details for more than
five years, I can only assume that he knows that
he is wrong but refuses to admit it - hoping that
his guru status will continue to promote his
old wives' tale.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Cecil Moore wrote:

Any person with a modicum of mathematics skill can
look at the following equation and know that there
is no phase shift relative to x in 1/4WL of wire or
coil.

To the extent that 'a modicum of mathematics skill' is
like 'a little knowledge', I suppose anything is possible.

Itot = Imax*cos(kx)*cos(wt)

Noting the linear variables and constants in there, and the absence of
anything that would change abruptly at certain particular values of x,
what would the expression for a standing wave on a shortened coil loaded
90 degree monopole have to look like?

ac6xg

"To convert from units of current to units of mass simply multiply the
superposition trig identity by mass (and ignore the factor of 2): Mtot =
Mmax*cos(kx)*cos(wt). Try it with any units you like!"

Jim Kelley wrote:
Cecil Moore wrote:
Itot = Imax*cos(kx)*cos(wt)

Noting the linear variables and constants in there, and the absence of
anything that would change abruptly at certain particular values of x,
what would the expression for a standing wave on a shortened coil loaded
90 degree monopole have to look like?

Ideally, it would be of the form:

For x = 0 to top of coil,
Itot = k1*cos(k2*x)cos(wt)

For x = bottom of stinger to top of stinger,
Itot = k3*cos(k4*x)*cos(wt)

where k1-k4 are constants

Note: The above is a conceptual simplification as it
ignores the current "bulge" in a real-world loading
coil.

Note that at the coil/stinger junction:

Itot = k1*cos(k2*x)*cos(wt) = k3*cos(k4*x)*cos(wt)

- as required by the laws of physics. Remember, it is
always implied that we are considering only the real
part of the phasor. Thus a current phasor can undergo
an abrupt amplitude and phase shift without changing
the real value.

10*cos(0) = 14.14*cos(45) = 10

The above phasor has abruptly rotated its phase by
45 degrees and increased its amplitude by 41% with
no violation of the laws of physics.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Tom Donaly wrote:
... why don't you use two "dual Z0
stubs together to make a folded dipole.

I had not thought of that before but I will now. TNX!

I will need to cause the current to be common-mode
rather than differential mode but it might work.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com