Antonio Vernucci wrote:
. . .
Under the assumption that dielectric loss is negligible, a permittivity
2.26 time higher than that of air results in a lower inner conductor
diameter, for a given outer diameter cable and a given impedance. . .

Yes, and this is why foamed dielectric cable has lower loss than solid
dielectric cable. Not because of lower dielectric loss (at least below a
few GHz), but because it has a larger center conductor for the same
impedance and outside diameter.

Roy Lewallen, W7EL

"Roy Lewallen" wrote in message
...
Antonio Vernucci wrote:
. . .
Under the assumption that dielectric loss is negligible, a permittivity
2.26 time higher than that of air results in a lower inner conductor
diameter, for a given outer diameter cable and a given impedance. . .

Yes, and this is why foamed dielectric cable has lower loss than solid
dielectric cable. Not because of lower dielectric loss (at least below a
few GHz), but because it has a larger center conductor for the same
impedance and outside diameter.

Roy Lewallen, W7EL


You've got it ... spread the word to all those amateurs who are hung up on
(negligible) dielectric loss!

Chris

christofire wrote:
"Cecil Moore" wrote in message
Moral: There is nothing magic about 50 ohms.

Actually, there is something 'magic' about 50 ohms.

It appears that you are using a different definition of
magic from the one I was using soI'll say the same thing
in different words:

There is nothing supernatural about 50 ohms.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Antonio Vernucci wrote:
Reading here and there that the signals of the on-going DX-expedition to
Glorioso Island are generally very low, I got the curiosity to simulate
the so-called "spiderbeam" antenna they are using (sized for the
10-meter band) on EZ-NEC.

Doing that, I obtained an unexpected result. The simulated antenna shows
a clear SWR minimum at 29.0 MHz where impedance is 76 + j32 ohm.

I then checked SWR across the 24 - 34 MHz range with the following results:

- going up in range 29 - 34 MHz, the reactance steadily increases (+334
ohm at 34 MHz)

- going down in range 29 - 24 MHz, the reactance remains positive and
steadily increases up to 28.5 MHz, after which it starts to decrease,
until it becomes 0 ohm at 27 MHz, and negative below that frequency. At
27 MHz impedance is 9 + j0 ohm (hence it is the resonant point).

I knew that the resonant point does not precisely coincide with the
minimum SWR point, but I would not have suspected such a big difference
(2 MHz shift at 29 MHz!).

Any comment?

Tony I0JX
Rome, Italy

Check the Alt Z0 option button at the upper left of the SWR display.
What happens to the minimum SWR frequency? Then change the Alt SWR Z0
value in the main window to some other value, say 300 ohm. What effect
does that have?

Interesting, isn't it?

Roy Lewallen

Check the Alt Z0 option button at the upper left of the SWR display. What
happens to the minimum SWR frequency? Then change the Alt SWR Z0 value in the
main window to some other value, say 300 ohm. What effect does that have?

Interesting, isn't it?

Roy Lewallen

Yes, changing the Alt Z0 makes a dramatic effect, and setting it to 9 ohm
obviously causes the minimum SWR point to shift from 29 to to 27 MHz (reaching
1:1).

Interesting to note that, using a 75-ohm cable, one can get a perfect match to
the simulated spiderbeam antenna in two possible ways:

- either cancelling the antenna reactance using a -32 ohm series-capacitor. One
then gets a (nearly) perfect match at 29 MHz, where antenna impedance is 76 +
j32 ohm

- or using a 9:75-ratio transformer. One then gets a perfect match at 27 MHz
(where impedance is 9 + j0 ohm)

Another interesting observation is that, at 29 MHz (i.e. where the antenna
impedance is 76 + j32 ohm and the SWR on a 75-ohm cable shows the minimum value
of 1.95) one can find a cable length at which the impedance appears to be purely
resistive and equal to 1.95*75 = 146 ohm (or 75/1.95 = 38.5 ohm). This fact is
deceiving as, seeing a purely resistive impedance, one could be led to
concluding that the real antenna resonant frequency is 29 MHz, whilst in reality
it resonates at 27 MHz (although knowing what is the real antenna resonant
frequency may not be so important).

I raised the above arguments just as a confirmation of the fact that
understanding what to do before attempting to adjust antennas is not that easy.

73

Tony I0JX

Antonio Vernucci wrote:
. . .
Another interesting observation is that, at 29 MHz (i.e. where the
antenna impedance is 76 + j32 ohm and the SWR on a 75-ohm cable shows
the minimum value of 1.95) one can find a cable length at which the
impedance appears to be purely resistive and equal to 1.95*75 = 146 ohm
(or 75/1.95 = 38.5 ohm). This fact is deceiving as, seeing a purely
resistive impedance, one could be led to concluding that the real
antenna resonant frequency is 29 MHz, whilst in reality it resonates at
27 MHz (although knowing what is the real antenna resonant frequency may
not be so important).
. . .

No one with a basic understanding of transmission lines would think that
the frequency at which resonance occurs (X = 0) at the input end is the
same frequency at which the load is resonant, except for two special
cases -- if the line Z0 equals the load resistance at the load's
resonant frequency, or the line is an integral number of quarter
wavelengths long at the load's resonant frequency. And, as you imply,
the resonant frequency of the antenna itself has no significance.
Transmission lines have been used for over a hundred years for impedance
matching, transforming a load of complex impedance into a purely
resistive impedance of a desired value.

I raised the above arguments just as a confirmation of the fact that
understanding what to do before attempting to adjust antennas is not
that easy.

The way to begin is to gain a basic understanding of how transmission
lines transform impedances. The ARRL Antenna Book is a good resource. If
a person's knowledge is limited to only vague understandings of SWR and
resonance, antennas and transmission lines will be a constant source of
mysterious and unexpected results.

Roy Lewallen, W7EL

"Antonio Vernucci" wrote in
:

....
I raised the above arguments just as a confirmation of the fact that
understanding what to do before attempting to adjust antennas is not
that easy.

Well, it was easier until people that don't understand the fundamentals
of transmission lines got access to instruments that measure R and X, and
used their new found capability to prop up the "resonant antennas work
better" myth.

For many common ham antenna *systems* (eg a length coax feed to a centre
fed, approximately half wave dipole using an effective balun), system
efficiency is best when transmission line losses are least, and
minimising line VSWR is a good first cut for best efficiency. Having done
that, an ATU at the tx to transform the load to that required by the tx
so that it can deliver its rated power with specification linearity may
be needed.

If you drill down on the resonance myth, its greatest validity is that
for some types of antenna systems (including the one described above),
resonance delivers a low VSWR, approximately the minimum VSWR, and in
those systems leads to approximately lowest line loss, resulting in best
efficiency. Nothing to do with the 'technical' explanation that I heard
the other day that a "resonance antenna fairly sucks the energy out of
the transmitter". It is a course a fallacy that resonant antennas
naturally "work better", or that resonance is a necessary condition for
high efficiency.

It is pointed out to me from time to time that the article that I
referred you to earlier is way above the head of the average MFJ259B
user, but it is my contention that you cannot realise much of the
potential of the MFJ259B or the like without understanding transmission
lines. VNAs are the new wave of instruments with potential exceeding
typical user's desire for understanding.

Owen

"Antonio Vernucci" wrote in
:

....
I knew that the resonant point does not precisely coincide with the
minimum SWR point, but I would not have suspected such a big
difference (2 MHz shift at 29 MHz!).

Any comment?

VSWR is not defined in terms of the conditions for resonance.

The characteristic of some kinds of antennas (including half wave dipoles
and quarter wave monopoles over ground) with resonant impedance near 50
ohms is that the R component of feedpoint Z varies slowly with frequency
around resonance (X=0) and X varies relatively quickly with frequency
around resonance. Because of this, in the region of resonance (X=0), X
tends to dominate VSWR(50) and the VSWR(50) minimum will be quite close
to where X=0.

Whilst many folk equipped with MFJ259Bs or the like, and with less
understanding, tune such an antenna for X=0, it is likely that the higher
priority for system efficiency is to tune for VSWR minimum. Worse, they
often do it at the source end of some length of transmission line.

I canvass the issues in the article "In pursuit of dipole resonance with
an MFJ259B" at http://vk1od.net/blog/?p=680 , you may find it
interesting.

Owen


Tony I0JX
Rome, Italy

My post below is not exactly on target for the thread, but I believe
useful. It's Sec 11.3 from Chapter 11 of Reflections, the whole of
which is available on my web page at www. w2du.com.
The title of the Sec is "A Reader Self-test and Minimum-SWR
Resistance."

Sec 11.3 A Reader Self-Test and Minimum-SWR Resistance

" Everyone knows that when a 50-ohm transmission line is terminated
with a pure resistance of 50 ohms, the magnitude of the reflection
coefficient,, rho , is 0, and the SWR is 1:1. Right? Of course! With
that in mind, here is a little exercise to test your intuitive skill.
If we insert a reactance of 50 ohm in series with the 50-ohm
resistance, the load becomes Z = 50 + j50. The SWR will be 2.618:1.
Now for the question. With this 50-ohm reactance in the load, is the
SWR already at its minimum value with the 50-ohm resistance, or will
some other value of resistance in the load reduce the SWR below
2.618:1? You say the SWR is already the lowest with the 50-ohm
resistance, because, after all, the line impedance, ZC, is 50 ohms?
Sorry, wrong. With reactance in the load, the minimum SWR always
occurs when the resistance component of the load is greater than ZC.
In fact, the more the reactance, the higher the resistance required
for to obtain minimum SWR. For any specific value of reactance in the
load there is one specific value of resistance that produces the
lowest SWR. I call this resistance the "minimum-SWR resistance."
Finding the value of this resistance is easy. First you normalize the
reactance, X, by dividing it by the line impedance, ZC. The normalized
value of X is represented by the lower case x. Thus x = XC / ZC. Then
we solve for the normalized value of resistance r, from Eq 5-1, which
is repeated here.

r = sqrt (x^2 - 1) Eq 5-1

Let's try it on the example above. The normalized value of 50 ohms
of reactance X, is x = 1. Substituting in Eq 5-1, r = sqrt 2 = 1.414.
So the true value of the minimum-SWR resistance is 1.414 x 50 =
70.7ohms. While the 50-ohm resistance yields a 2.618:1 SWR, the
70.7-ohm resistance in series with the 50-ohm reactance yields an SWR
of 2.414:1. Not a great deal smaller, but still smaller than with the
50-ohm resistance.

So let's try a more dramatic example, this time with a 100-ohm
reactance, which has a normalized value x = 2.0. With a 50-ohm
resistance, the SWR is now 5.828:1. However, with the normalized
minimum-SWR resistance, r = sqrt 5 = 2.236. Multiplying by 50, we get
R = 111.8 ohms. With this larger resistance in series with the 100-ohm
reactance, the SWR is reduced from 5.828:1 to 4.236:1. The results of
this exercise didn't turn out quite the way you expected, did it?"

For further proof of this concept I suggest reviewing the remainder of
this Sec using the Smith Chart, available from my web page.

Walt, W2DU

On Sun, 20 Sep 2009 22:41:29 -0400, Walter Maxwell
wrote:

My post below is not exactly on target for the thread, but I believe
useful. It's Sec 11.3 from Chapter 11 of Reflections, the whole of
which is available on my web page at www. w2du.com.
The title of the Sec is "A Reader Self-test and Minimum-SWR
Resistance."

Sec 11.3 A Reader Self-Test and Minimum-SWR Resistance

" Everyone knows that when a 50-ohm transmission line is terminated
with a pure resistance of 50 ohms, the magnitude of the reflection
coefficient,, rho , is 0, and the SWR is 1:1. Right? Of course! With
that in mind, here is a little exercise to test your intuitive skill.
If we insert a reactance of 50 ohm in series with the 50-ohm
resistance, the load becomes Z = 50 + j50. The SWR will be 2.618:1.
Now for the question. With this 50-ohm reactance in the load, is the
SWR already at its minimum value with the 50-ohm resistance, or will
some other value of resistance in the load reduce the SWR below
2.618:1? You say the SWR is already the lowest with the 50-ohm
resistance, because, after all, the line impedance, ZC, is 50 ohms?
Sorry, wrong. With reactance in the load, the minimum SWR always
occurs when the resistance component of the load is greater than ZC.
In fact, the more the reactance, the higher the resistance required
for to obtain minimum SWR. For any specific value of reactance in the
load there is one specific value of resistance that produces the
lowest SWR. I call this resistance the "minimum-SWR resistance."
Finding the value of this resistance is easy. First you normalize the
reactance, X, by dividing it by the line impedance, ZC. The normalized
value of X is represented by the lower case x. Thus x = XC / ZC. Then
we solve for the normalized value of resistance r, from Eq 5-1, which
is repeated here.

r = sqrt (x^2 + 1) Eq 5-1

Let's try it on the example above. The normalized value of 50 ohms
of reactance X, is x = 1. Substituting in Eq 5-1, r = sqrt 2 = 1.414.
So the true value of the minimum-SWR resistance is 1.414 x 50 =
70.7ohms. While the 50-ohm resistance yields a 2.618:1 SWR, the
70.7-ohm resistance in series with the 50-ohm reactance yields an SWR
of 2.414:1. Not a great deal smaller, but still smaller than with the
50-ohm resistance.

So let's try a more dramatic example, this time with a 100-ohm
reactance, which has a normalized value x = 2.0. With a 50-ohm
resistance, the SWR is now 5.828:1. However, with the normalized
minimum-SWR resistance, r = sqrt 5 = 2.236. Multiplying by 50, we get
R = 111.8 ohms. With this larger resistance in series with the 100-ohm
reactance, the SWR is reduced from 5.828:1 to 4.236:1. The results of
this exercise didn't turn out quite the way you expected, did it?"

For further proof of this concept I suggest reviewing the remainder of
this Sec using the Smith Chart, available from my web page.

Walt, W2DU