Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

"Antonio Vernucci" wrote in message
.. .
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


that is not surprising for an antenna that has a very low or very high
impedance at the resonant point. The SWR depends on the magnitude of the
impedances not the angle, so you could have a minimum SWR with a big
reactance and small real component.

Resaonance and minimum SWR
 

On Sat, 19 Sep 2009 18:03:25 +0200, "Antonio Vernucci"
wrote:

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?

Hi Tony,

What did you expect it to be?

73's
Richard Clark, KB7QHC

Resaonance and minimum SWR
 

Antonio Vernucci wrote:
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!).

There's a thread over on eHam.net dealing with this same subject.
Many complex antennas exhibit this effect to a certain extent. The
reason is obvious. Our SWR meters are calibrated for 50 ohms and
an antenna may be resonant with a e.g. 9+j0 ohm feedpoint impedance.

That's a 50 ohm SWR of 5.6:1 where almost 1/2 of the RF is rejected
at the antenna when 50 ohm coax is being used. If the 50 ohm SWR
drops below 5.6:1 somewhere else it necessarily must exhibit a
higher resistance and reactance than exists at the 9 ohm antenna
feedpoint.

Moral: There is nothing magic about 50 ohms. If you were using
a transmission line with a Z0 of 9 ohms with a 9 ohm SWR meter,
you wouldn't notice anything worth reporting.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com

Resaonance and minimum SWR
 

Dave wrote:

. . .The SWR depends on the magnitude of
the impedances not the angle, so you could have a minimum SWR with a big
reactance and small real component.

That's not true. For example, impedances of 50 + j0, 35.36 + j35.36, and
0 + j50 ohms all have the same magnitude (50 ohms), but a 50 ohm cable
connected to loads of those impedances will have SWRs of 1, 2.41, and
infinity respectively.

Correct formulas for calculating SWR can be found in the ARRL Antenna
Book, the ARRL Handbook, or any respectable transmission line text.
Incorrect ones can, I'm sure, be found on the Web and elsewhere.

Roy Lewallen, W7EL

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

"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

Resaonance and minimum SWR
 

"Cecil Moore" wrote in message
...
Antonio Vernucci wrote:
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!).

There's a thread over on eHam.net dealing with this same subject.
Many complex antennas exhibit this effect to a certain extent. The
reason is obvious. Our SWR meters are calibrated for 50 ohms and
an antenna may be resonant with a e.g. 9+j0 ohm feedpoint impedance.

That's a 50 ohm SWR of 5.6:1 where almost 1/2 of the RF is rejected
at the antenna when 50 ohm coax is being used. If the 50 ohm SWR
drops below 5.6:1 somewhere else it necessarily must exhibit a
higher resistance and reactance than exists at the 9 ohm antenna
feedpoint.

Moral: There is nothing magic about 50 ohms. If you were using
a transmission line with a Z0 of 9 ohms with a 9 ohm SWR meter,
you wouldn't notice anything worth reporting.
--
73, Cecil, IEEE, OOTC, http://www.w5dxp.com


Actually, there is something 'magic' about 50 ohms. An air-dielectric
co-axial cable has minimum loss per metre when its characteristic impedance
is 76.7 ohms and the relative permittivity of polythene is 2.26 so a
polythene-dielectric co-axial cable has lowest loss when its characteristic
impedance is 76.7/SQRT(2.26) = 51 ohms, which is most often rounded down to
50. This is on the basis that the conductor loss greatly exceeds the
dielectric loss, which is true over most of the frequency range for which
solid polythene dielectric is appropriate.

Maximum power handling, for a polythene-dielectric cable, occurs at a much
lower impedance: 30/SQRT(2.26) = 20 ohms.

Chris

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

Actually, there is something 'magic' about 50 ohms. An air-dielectric
co-axial cable has minimum loss per metre when its characteristic impedance is
76.7 ohms

I presume that the 76.7-0hm figure comes from a trade-off beween RF current and
conductor resistance. In other words, increasing the impedance value, the RF
current would become lower (for a given RF power), but the inner conductor
resistance would become higher because of the lower diameter needed to obtain
the higher impedance value (for a given outer diameter cable). And viceversa.


and the relative permittivity of polythene is 2.26 so a polythene-dielectric
co-axial cable has lowest loss when its characteristic impedance is
76.7/SQRT(2.26) = 51 ohms, which is most often rounded down to 50.

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. Probably, lowering impedance
from 75 to about 50 ohm, the loss advantage one experiences thanks to the higher
inner conductor diameter needed for the lower impedance value is higher than the
loss disadvantage caused by the higher RF current (for a given RF power).

Maximum power handling, for a polythene-dielectric cable, occurs at a much
lower impedance: 30/SQRT(2.26) = 20 ohms.

I do not succeed to understand that statement. Maximum power handling is bound
to maximum temperature which is in turn bound to dissipated power. If 50 ohm is
the impedance at which minimum loss occurs (for a given RF power), why lowering
impedance to 20 ohm should result in a loss reduction. In the equation
30/SQRT(2.26) = 20 ohms, which is meaning of the figure 30?

I wonder whether you could indicate us a reference where all those trade-offs
are mathematically discussed.

73

Tony I0JX

Resaonance and minimum SWR
 

On Sun, 20 Sep 2009 17:48:51 +0200, "Antonio Vernucci"
wrote:

I wonder whether you could indicate us a reference where all those trade-offs
are mathematically discussed.

This should help:
http://www.microwaves101.com/encyclopedia/why50ohms.cfm


--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558

Resaonance and minimum SWR
 

This should help:
http://www.microwaves101.com/encyclopedia/why50ohms.cfm


Yes, very helpful. Thanks

Tony I0JX

Resaonance and minimum SWR
 

"Jeff Liebermann" wrote in message
...
On Sun, 20 Sep 2009 17:48:51 +0200, "Antonio Vernucci"
wrote:

I wonder whether you could indicate us a reference where all those
trade-offs
are mathematically discussed.

This should help:
http://www.microwaves101.com/encyclopedia/why50ohms.cfm


--
Jeff Liebermann
150 Felker St #D http://www.LearnByDestroying.com
Santa Cruz CA 95060 http://802.11junk.com
Skype: JeffLiebermann AE6KS 831-336-2558


Thanks Jeff, that reference does help but it gets a bit confused over
matters of relative permittivity, Er.

Some time ago (2005), in my work, I derived the whole lot from almost first
principles. It turns out that the series conductor loss (as opposed to the
shunt dielectric loss) is proportional to (1+p)/ln(p), where p is the ratio
of the inside diameter of the outer conductor (D) to the outside diameter of
the inner conductor, and to SQRT(Er). The minimum value of this loss is
found by differentiating the function of p with respect to p and that's what
gives the 76.7 ohms value for Er = 1 (it also involves a constant for copper
conductors, the root frequency and 1/D). The result scales with SQRT(Er)
for polythene.

I should have stated the _peak_ power handling because the 30 ohms (air)
value results from combination of the expression for the electric field
strength and the expression for the characteristic impedance (along the
lines of P = V^2/R). Minimising the field strength gives the greatest
resistance to dielectric breakdown, but a different value of p results when
the impedance is taken into account at the same time. Again, the result
scales with SQRT(Er).

The application for all this was analogue to digital terrestrial television
switch over - the digital signals have much greater peak-to-mean ratios than
the analogue ones, so flashover in air-spaced feeders is a potential power
limitation.

Chris

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

"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

Resaonance and minimum SWR
 

"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

Resaonance and minimum SWR
 

christofire wrote:

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

Chris

I've been doing what I can. I pointed it out on this newsgroup on Sept.
12, 1998, and repeat it whenever the opportunity arises.

Roy Lewallen, W7EL

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

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

Resaonance and minimum SWR
 

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

Sorry, I goofed on Eq. 5-1. The corrected eq is r = sqrt (x^2 + 1).

Walt, W2DU

Resaonance and minimum SWR
 

Walter Maxwell wrote in
:

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!

Well, it for a distortionless 50 ohm line.

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?

Continuing on the distortionless example, if you visualise this on a
Smith chart, for any constant X and R independently variable, the value
of R for minimum VSWR will be such that the tangent to the reactance
circle is also a tangent to the VSWR circle at that point (R,X), and R
for minimum VSWR will always be greater than Ro for Xl0.

However, Zo for practical cables is not real, not quite.

Owen

Resaonance and minimum SWR
 

christofire wrote:

"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!

It isn't the amateurs so much as the advertising. Marketing departments
highlight the foam dielectric because it's more obvious, and pretty soon
even the manufacturers are believing their own publicity.

As for the 50-ohm impedance, the reasons why it became an industry
standard are interesting but purely historical. The reason for using it
now is almost exclusively because it *is* an industry standard.


--

73 from Ian GM3SEK 'In Practice' columnist for RadCom (RSGB)
http://www.ifwtech.co.uk/g3sek

Resaonance and minimum SWR
 

On Sep 21, 1:32*am, Ian White GM3SEK wrote:
christofire wrote:

"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!

It isn't the amateurs so much as the advertising. Marketing departments
highlight the foam dielectric because it's more obvious, and pretty soon
even the manufacturers are believing their own publicity.

As for the 50-ohm impedance, the reasons why it became an industry
standard are interesting but purely historical. The reason for using it
now is almost exclusively because it *is* an industry standard.

--

73 from Ian GM3SEK * * * * 'In Practice' columnist for RadCom (RSGB)http://www.ifwtech.co.uk/g3sek

Resonance means little. It is like reverse engineering where it is
assumed or understood that the transmission line will be 50 ohms! The
point to remember is that the less the resistive component that one
measures at the antenna the more the power is shifting over from the
resistive loss to the radiative resistance and nothing more. For
matching there is an advantage when the load is totally resistive
because the matching becomes less complicated. Obviously as more
energy is shifted over to radiative purposes it is more difficult to
feed as we do not know how to switch power transmission from a
parallel line to a singular line. But the fact remains, the less the
resistive losses the more power goes to radiation which is exactly
what you are trying to achieve.

Resaonance and minimum SWR
 

Art Unwin wrote:
Resonance means little.

snip a bit

The point to remember is that the less the resistive component that one
measures at the antenna the more the power is shifting over from the
resistive loss to the radiative resistance and nothing more.

It is truly amazing the things that come from his keyboard. This one
statement proves he understands nothing.

And he contradicted his previous stand on resonance, too! 2 in one blow.

tom
K0TAR