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Old September 4th 05, 12:55 AM
hasan schiers
 
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Owen,

Wire is laying on the ground, insulated, as it doesn't make any difference
and lasts longer. 66' is 1/4 wave at 80m which is always a safe starting
point. I probably could shorten them and do more. I intend to put in at
least 8 more for a total of 16.

I found out why the input Z was going up as I put more radials in...I was
measuring at the end of 55' of LMR-400 (as opposed to the measurements I
took when I was outside originally tuning the antenna.), and that was acting
as a 1/4 wave transformer.

I just went outside and connected through an 18 inch jumper to the MFJ-269
and got the following measurements:

2:1 VSWR Low freq Point: 3460 khz
2:1 VSWR Hi freq Point: 3801 khz
2:1 VSWR Bandwidth: 341 khz
Fo (Resonant freq) = 3560 khz, 40 ohms resistive, 0 ohms reactance

3500 32,9 1.6
3550 38,0 1.0
3600 44,9 1.2
3650 52,19 1.4
3700 57,30 1.6
3750 63,35 1.8
3800 69,39 2.0

Above table: freq, R,+/- j, VSWR, all taken from the MFJ-269

If the radiation resistance is 26 ohms and I measure 38 ohms feed impedance
at resonance, then apparently I have 12 ohms of ground loss, for an
efficiency of:

26/(26+12) or 26/38 = 68%

At least, that's where I'm at for the moment. Time for another 8 radials.

That 1/4 wave transformer (55' of LMR-400 between feedpoint and shack) that
Tom, W8JI, pointed out, makes a big difference in my confusion...at least it
all makes sense now.

73,

....hasan, N0AN
"Owen Duffy" wrote in message
news
On Sat, 3 Sep 2005 09:27:52 -0500, "hasan schiers"
wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest
data:


Radials 2:1 Fo 2:1 BW Z VSWR @ Fo


Hassan,

Where are the radials (above ground, buried, how far)?

I think you told us that they radial wire is insulated, is that
correct?

Why did you choose 66' long radials?

Owen
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Old September 5th 05, 12:20 AM
Owen Duffy
 
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On Sat, 3 Sep 2005 17:55:17 -0500, "hasan schiers"
wrote:

Owen,

Wire is laying on the ground, insulated, as it doesn't make any difference
and lasts longer. 66' is 1/4 wave at 80m which is always a safe starting
point.


It is in free space. Lying on the ground isn't free space.

Were the radials buried, depending on the ground, 66' might be more in
the vicinity of an electrical half wave. Suspended a short distance
above the ground might be close to an electrical quarter wave. Yours
will be somewhere between depending on the installation variables.

It would be interesting to measure the impedance and find the
resonance of a pair of opposite radials.

Owen
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Old September 4th 05, 01:49 AM
Owen Duffy
 
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On Sat, 3 Sep 2005 09:27:52 -0500, "hasan schiers"
wrote:

Question: Where was I taking my measurements.

I started out at the actual feedpoint...then put in about 55' of LMR-400,
and started a new set of measurements in the shack. Here is the latest data:

Radials 2:1 Fo 2:1 BW Z VSWR @ Fo
0 3340 3522 3920 580 36,0 1.3


Ok, you have figured out the coax transforms the impedance. If indeed
the Z at the generator end of the coax was 36+j0 (ie it was resonant
at that point), then I make the load Z ~ 62-j5.

This will confuse your efforts to infer an effective ground system
impedance, and losses.

Another point to consider, instruments like you are using (in my
experience) are more accurate near to 50+j0, and you may get better
results by bulking up the feedpoint Z with a known fixed resistor to
exploit the better measurement accuracy around 50+j0.

Owen
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Old September 4th 05, 02:12 AM
Owen Duffy
 
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On Sat, 03 Sep 2005 23:49:14 GMT, Owen Duffy wrote:


Ok, you have figured out the coax transforms the impedance. If indeed
the Z at the generator end of the coax was 36+j0 (ie it was resonant
at that point), then I make the load Z ~ 62-j5.


Sorry that should have been 69-j7 (above calc was for one of your
other figures, 40+j0).

Owen
--
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Old September 3rd 05, 04:36 PM
hasan schiers
 
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OK, here is my summary table for up to 8 radials, 66 feet long, insulated
wire, laying on the ground: (all measurements at the shack end of 55' of
LMR-400 coax, buried)

Radials 2:1 Fo 2:1 BW Z VSWR @ Fo
0 3340 3522 3920 580 36,0 1.3
2 3354 3524 3774 420 45,0 1.0
4 3419 3533 3741 322 60,1 1.2
8 3445 3550 3742 297 65,4 1.3

The formatting is bad, but in order, left to right:

Number of Radials
Lower 2:1 vswr point
Resonant Freq point
Upper 2:1 point
Bandwidth in kilohertz
Impedance as shown on the MFJ 269 at resonance.

I'm a bit confused by the rising feedpoint impedance with increased radial
numbers, but the narrowing down of the bandwidth indicates decreased losses.
It also indicates (since it continues to decrease), that I should add
another 8 radials to see if I begin approaching the asymptote (sp?). The
rate of change is slowing quite a bit.

Any input as to explanations and the data are most welcome.

....hasan, N0AN

p.s. Performance seems quite good for a VERY limited sample. A w6 this
morning was 2 to 3 S-units stronger on the inverted L than on the 45' high
Carolina Windom 80. An LU6 was coming in S9 with an S5 noise level, and
responded with a 59+ signal report on the first call. A sampling of other
signals prior to or shortly after sunrise is showing a clear superiority of
the inverted L with 8 radials over the CW 80, at distances 1500 km. Less
than that distance and either antenna could have the upper hand until one
gets to within the state of Iowa. I'll have to do more measurements to get a
firm idea as to where the cross-over point is between the two antennas.
"hasan schiers" wrote in message
...
45' high, 25.8 sloping wire at the top, 29 feet high at the far end. #12
THHN Insulated copper wire, stranded.

Predicted Radiation Resistance: 25.8 ohms, very good ground (rich
pastoral, midwest).

With no radials, I get a flat 50 ohm match at 3595 khz. Obviously this
would indicate ground losses of approximately 25 ohms, if I'm thinking
about this right. Also, predicted efficiency would then be 50 %
(25/(25+25), indicating a 3 dB loss. Forgetting about fresnel region
losses, this seems to be better than I had expected. 2:1 vswr bandwidth is
very broad....broader than what I get with EZnec 4.x with a 25 ohm load in
the base.

This means one of two things to me:

Either my ground losses are much higher than the 25 ohms I'm indirectly
calculating, or I have made some sort of conceptual error in thinking
about what the implications are of a 25 or 26 ohm feedpoint. All my
references point toward a 25 ohm radiation resistance for my 42' vertical
x 25.8 ft inverted L (with sloping top wire instead of flat top wire).
What is wrong with my logic here? If the R(rad) is 25 ohms, and I measure
a flat VSWR (on two other meters) at 3600 khz, then isn't the remaining 25
ohms, ground loss?

I also show about 37 ohms resistance and 0 ohms reactance at 3600 khz with
my MFJ-269, which is really confusing, in that if I have 25 ohms for Rrad,
then I have 13 ohms of ground losses. Further, 37 ohms is around 1.3 to 1.
So I have two other vswr meters showing 1:1 at 3600, and the MFJ showing
37 ohms. This is a pretty large percentage difference.

I would be inclined to believe the 25.8 ohms predicted by both EZnec 4 and
the Low Band DX'rs Handbook. In any case, I'll put out 4 radials tomorrow
morning and repeat all my measurements, looking for narrowing bandwidth
and lowered input Z as my ground losses decrease.

Ultimately, I'm going to put down 16, 66' radials, in steps of four,
taking measurements of input Z (mfj-269) and vswr bandwidth for 2:1, at
0,4,8 and 16 radials. I'll report what happens as I go along.

Anywho, without any radials at all there are quite a few distant signals
on 80m this evening, that are consistently louder on the newly installed
inverted L, than on my Carolina Windom at 45'. Most signals as one pans
the band, are louder (at 2 hours after sunset) on the C. Windom than on
the radial-less inverted L, but ones from several states away are equal or
better on the radial-less inverted L. Both seem to make good sense at
this point. I sure will be interested to see the effects of 4 and then 8
and on up radials, but that is going to take a few days, because I don't
want to make radial changes unless I have access to low angle signals,
which only happens at night or just before sunrise.

Tomorrow is radial day. I will be laying out 4 radials 65' long to begin
with. I have resistance and reactance measurements every 50 khz as a
baseline, before installing radials. 4 in the early morning, 4 more just
before sunset, then 4 more the next morning, and the final 4 the next
evening. #14 THHN stranded insulated copper wire for the radials, btw.

Depending on what I end up seeing for "effect" I'll go to 24 or 32 radials
by winter....but only if the improvement is both measurable and
"observable on the air"...radials are a pain in the rear (or more
accurately, the knees) to put in.

What fun!

...hasan, N0AN





  #6   Report Post  
Old September 3rd 05, 04:47 PM
Wes Stewart
 
Posts: n/a
Default

On Fri, 2 Sep 2005 23:29:17 -0500, "hasan schiers"
wrote:

45' high, 25.8 sloping wire at the top, 29 feet high at the far end. #12
THHN Insulated copper wire, stranded.

Predicted Radiation Resistance: 25.8 ohms, very good ground (rich pastoral,
midwest).

With no radials, I get a flat 50 ohm match at 3595 khz. Obviously this would
indicate ground losses of approximately 25 ohms, if I'm thinking about this
right. Also, predicted efficiency would then be 50 % (25/(25+25), indicating
a 3 dB loss. Forgetting about fresnel region losses, this seems to be better
than I had expected. 2:1 vswr bandwidth is very broad....broader than what I
get with EZnec 4.x with a 25 ohm load in the base.

This means one of two things to me:

Either my ground losses are much higher than the 25 ohms I'm indirectly
calculating, or I have made some sort of conceptual error in thinking about
what the implications are of a 25 or 26 ohm feedpoint. All my references
point toward a 25 ohm radiation resistance for my 42' vertical x 25.8 ft
inverted L (with sloping top wire instead of flat top wire). What is wrong
with my logic here? If the R(rad) is 25 ohms, and I measure a flat VSWR (on
two other meters) at 3600 khz, then isn't the remaining 25 ohms, ground
loss?

I also show about 37 ohms resistance and 0 ohms reactance at 3600 khz with
my MFJ-269, which is really confusing, in that if I have 25 ohms for Rrad,
then I have 13 ohms of ground losses. Further, 37 ohms is around 1.3 to 1.
So I have two other vswr meters showing 1:1 at 3600, and the MFJ showing 37
ohms. This is a pretty large percentage difference.

I would be inclined to believe the 25.8 ohms predicted by both EZnec 4 and
the Low Band DX'rs Handbook. In any case, I'll put out 4 radials tomorrow
morning and repeat all my measurements, looking for narrowing bandwidth and
lowered input Z as my ground losses decrease.

Ultimately, I'm going to put down 16, 66' radials, in steps of four, taking
measurements of input Z (mfj-269) and vswr bandwidth for 2:1, at 0,4,8 and
16 radials. I'll report what happens as I go along.

Anywho, without any radials at all there are quite a few distant signals on
80m this evening, that are consistently louder on the newly installed
inverted L, than on my Carolina Windom at 45'. Most signals as one pans the
band, are louder (at 2 hours after sunset) on the C. Windom than on the
radial-less inverted L, but ones from several states away are equal or
better on the radial-less inverted L. Both seem to make good sense at this
point. I sure will be interested to see the effects of 4 and then 8 and on
up radials, but that is going to take a few days, because I don't want to
make radial changes unless I have access to low angle signals, which only
happens at night or just before sunrise.

Tomorrow is radial day. I will be laying out 4 radials 65' long to begin
with. I have resistance and reactance measurements every 50 khz as a
baseline, before installing radials. 4 in the early morning, 4 more just
before sunset, then 4 more the next morning, and the final 4 the next
evening. #14 THHN stranded insulated copper wire for the radials, btw.

Depending on what I end up seeing for "effect" I'll go to 24 or 32 radials
by winter....but only if the improvement is both measurable and "observable
on the air"...radials are a pain in the rear (or more accurately, the knees)
to put in.

What fun!


Indeed.

Unfortunately, I believe that you are at the mercy of your
instrumentation. I doubt that you can make meaningful measurements of
the differences resulting from the addition of a few radials at a
time.

The fact that you can't get correlation between measurements made on
the -same- antenna with different instruments is a problem. Until you
have two clocks that read the same, you don't know what time it is.
  #7   Report Post  
Old September 3rd 05, 04:50 PM
hasan schiers
 
Posts: n/a
Default

I do have correlation now. The vswr meters and the mfj all read the same
resonant frequency now, Wes. See my post that shows the data for 0,2,4,8
radials. While a given absolute value might be in error (a certainty due to
inexpensive instruments), the trend is sound for bandwidth, but a bit
strange for feedpoint impedance. (BW is narrowing but input Z is going up,
with increasing numbers of radials.)

Ideas?

73,

....hasan, N0AN
"Wes Stewart" wrote in message
...
On Fri, 2 Sep 2005 23:29:17 -0500, "hasan schiers"
wrote:

45' high, 25.8 sloping wire at the top, 29 feet high at the far end. #12
THHN Insulated copper wire, stranded.

Predicted Radiation Resistance: 25.8 ohms, very good ground (rich
pastoral,
midwest).

With no radials, I get a flat 50 ohm match at 3595 khz. Obviously this
would
indicate ground losses of approximately 25 ohms, if I'm thinking about
this
right. Also, predicted efficiency would then be 50 % (25/(25+25),
indicating
a 3 dB loss. Forgetting about fresnel region losses, this seems to be
better
than I had expected. 2:1 vswr bandwidth is very broad....broader than what
I
get with EZnec 4.x with a 25 ohm load in the base.

This means one of two things to me:

Either my ground losses are much higher than the 25 ohms I'm indirectly
calculating, or I have made some sort of conceptual error in thinking
about
what the implications are of a 25 or 26 ohm feedpoint. All my references
point toward a 25 ohm radiation resistance for my 42' vertical x 25.8 ft
inverted L (with sloping top wire instead of flat top wire). What is wrong
with my logic here? If the R(rad) is 25 ohms, and I measure a flat VSWR
(on
two other meters) at 3600 khz, then isn't the remaining 25 ohms, ground
loss?

I also show about 37 ohms resistance and 0 ohms reactance at 3600 khz with
my MFJ-269, which is really confusing, in that if I have 25 ohms for Rrad,
then I have 13 ohms of ground losses. Further, 37 ohms is around 1.3 to 1.
So I have two other vswr meters showing 1:1 at 3600, and the MFJ showing
37
ohms. This is a pretty large percentage difference.

I would be inclined to believe the 25.8 ohms predicted by both EZnec 4 and
the Low Band DX'rs Handbook. In any case, I'll put out 4 radials tomorrow
morning and repeat all my measurements, looking for narrowing bandwidth
and
lowered input Z as my ground losses decrease.

Ultimately, I'm going to put down 16, 66' radials, in steps of four,
taking
measurements of input Z (mfj-269) and vswr bandwidth for 2:1, at 0,4,8 and
16 radials. I'll report what happens as I go along.

Anywho, without any radials at all there are quite a few distant signals
on
80m this evening, that are consistently louder on the newly installed
inverted L, than on my Carolina Windom at 45'. Most signals as one pans
the
band, are louder (at 2 hours after sunset) on the C. Windom than on the
radial-less inverted L, but ones from several states away are equal or
better on the radial-less inverted L. Both seem to make good sense at
this
point. I sure will be interested to see the effects of 4 and then 8 and on
up radials, but that is going to take a few days, because I don't want to
make radial changes unless I have access to low angle signals, which only
happens at night or just before sunrise.

Tomorrow is radial day. I will be laying out 4 radials 65' long to begin
with. I have resistance and reactance measurements every 50 khz as a
baseline, before installing radials. 4 in the early morning, 4 more just
before sunset, then 4 more the next morning, and the final 4 the next
evening. #14 THHN stranded insulated copper wire for the radials, btw.

Depending on what I end up seeing for "effect" I'll go to 24 or 32 radials
by winter....but only if the improvement is both measurable and
"observable
on the air"...radials are a pain in the rear (or more accurately, the
knees)
to put in.

What fun!


Indeed.

Unfortunately, I believe that you are at the mercy of your
instrumentation. I doubt that you can make meaningful measurements of
the differences resulting from the addition of a few radials at a
time.

The fact that you can't get correlation between measurements made on
the -same- antenna with different instruments is a problem. Until you
have two clocks that read the same, you don't know what time it is.



  #8   Report Post  
Old September 4th 05, 02:51 AM
Wes Stewart
 
Posts: n/a
Default

On Sat, 3 Sep 2005 09:50:43 -0500, "hasan schiers"
wrote:

I do have correlation now. The vswr meters and the mfj all read the same
resonant frequency now, Wes. See my post that shows the data for 0,2,4,8
radials. While a given absolute value might be in error (a certainty due to
inexpensive instruments), the trend is sound for bandwidth, but a bit
strange for feedpoint impedance. (BW is narrowing but input Z is going up,
with increasing numbers of radials.)

Ideas?


Well, I think that you're expecting the thing to behave just like a
monopole but it's not a monopole.

When I model your configuration (except for insulation) I get a
resonant freq of 3.573 MHz and R = 23.3 ohm over a Mininec Pastoral
ground.

Making it a full height monopole it must be 67' high and the feedpoint
R = 37.

I believe that I read elsewhere that you are taking data at the input
end of a coax line. Unless you have characterized the line and are
backing out its effects you are going to remain mystified.

Also it you have any other antennas in the area that can be an issue.

I'm a believer in modeling but unless -everything- is accounted for,
reality and the model won't correlate.

For example, I have a Cushcraft AV-80 vertical that I've used as a
test bed. This is a 2" diameter, 36' high pipe with four 3' top hat
wires. Cushcraft supplied a base-loading coil, which is not used.
The antenna is ground-mounted on a 16" square aluminum plate with
sixteen 50' radials. Installing radials at this location is a
"sticky" proposition and the soil is best characterized as sand
(decomposed granite actually).

I have measured the base impedance with both an HP8405 Vector
Voltmeter and coax bridge that was calibrated with an open-short-load
(OSL) method as well as a much faster N2PK vector network analyzer,
calibrated the same way. All measurements were taken at the base of
the antenna. This is an on again off again project (currently off)
with the goal of determining the effectiveness of the radial field.

The data are very repeatable and believed to be correct; however, I
cannot construct a model that replicates the physical antenna. For
example the curve on the Smith chart of the measured data has a little
bump in it and the resonant frequency is slightly off from the model.
The "bump" isn't a full-blown resonance loop, but it looks like it's
trying. Here is a plot from 1.5 to 15 MHz. The resonant freq is 5.5
MHz.

http://users.triconet.org/wesandlinda/Vertical_Z.gif

As you can see from the photo, there several other "verticals" in the
vicinity as well as my 45' foot tower with beam and wire dipoles 90'
away.

http://users.triconet.org/wesandlinda/Vertical_4.jpg




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Old September 4th 05, 03:19 AM
hasan schiers
 
Posts: n/a
Default

Yep! A question remains for modelling. Is the value for Source Data in EZnec
4.x directly correlated to the Rrad? My EZnec model (a modified ARRL
Inverted L with radials), shows:

Frequency = 3.6 MHz

Source 1 Voltage = 25.65 V. at 4.18 deg.
Current = 1 A. at 0.0 deg.
Impedance = 25.58 + J 1.872 ohms
Power = 25.58 watts
SWR (50 ohm system) = 1.958 (25 ohm system) = 1.081

Is that 25.58 ohms the same 25 ohms from the graph of Devoldere's book, or
is it simply a coincidence?

I have attached my *.ez file, if it makes it through the usenet group.


From my other more recent posts on the topic, you can see that I went back
out to the feedpoint with an 18" jumper and remeasured and the results are
quite "traditional".

If one can believe the graph in the latest version of Devoldere's "Low-Band
DXing", an inverted L like mine withe a .16 wavelength vertical portion and
the horizontal or vee'd portion making of the remainder to achieve
resonance, the Rrad should be about 25 ohms. Since the Z at resonance at the
feedpoint with 8 radials 66 feet long shows 38 ohms, it would appear I have
something like 13 ohms of ground return loss. This would represent an
efficiency of 67% or a loss of 1.7 dB. I'm thinking another 8 radials should
get me closer to about 1 dB of loss, at which point, I think I'll be tired
of cutting slits in the lawn. vbg

I did use an on-line TLE calculator to correct for the 55' of LMR-400, and
doing that yielded readings virtually identical to those I measured at the
feedpoint through my 18" jumper.

So, all in all, things worked as they should What got me confused was not
considering that I had a quarter wave transformer after I moved into the
shack to measure, and it was inverting my readings. Made me real queasy
there for a while.

Thanks to all for taking the time to provide ideas and answers. Tom and a
few others caught the 1/4 wave transformer problem...and after all, that was
my real question. I had no doubt that I was seeing an improvment in
efficiency by adding radials (as the 2:1 BW was steadily decreasing with
increasing radials)...I just couldn't get my head around the 60 ohm, ever
increasing values of Z in the shack. All I can say now is, "DUH!"

The sun has set....it's time to make instant switching comparisons between
my 45' high dipole and the new Inverted L. Last night and this morning it
appeared (although I didn't have a lot of data points yet), that stations
1500 km were much stronger on the inverted L than they were on the dipole,
including a 59+ report from an LU early this morning.

Thanks again, Wes (and all the others who commented). It has been fun
working through the process. Now it's time to chase DX.

....hasan, N0AN
"Wes Stewart" wrote in message
...
On Sat, 3 Sep 2005 09:50:43 -0500, "hasan schiers"
wrote:

I do have correlation now. The vswr meters and the mfj all read the same
resonant frequency now, Wes. See my post that shows the data for 0,2,4,8
radials. While a given absolute value might be in error (a certainty due
to
inexpensive instruments), the trend is sound for bandwidth, but a bit
strange for feedpoint impedance. (BW is narrowing but input Z is going up,
with increasing numbers of radials.)

Ideas?


Well, I think that you're expecting the thing to behave just like a
monopole but it's not a monopole.

When I model your configuration (except for insulation) I get a
resonant freq of 3.573 MHz and R = 23.3 ohm over a Mininec Pastoral
ground.

Making it a full height monopole it must be 67' high and the feedpoint
R = 37.

I believe that I read elsewhere that you are taking data at the input
end of a coax line. Unless you have characterized the line and are
backing out its effects you are going to remain mystified.

Also it you have any other antennas in the area that can be an issue.

I'm a believer in modeling but unless -everything- is accounted for,
reality and the model won't correlate.

For example, I have a Cushcraft AV-80 vertical that I've used as a
test bed. This is a 2" diameter, 36' high pipe with four 3' top hat
wires. Cushcraft supplied a base-loading coil, which is not used.
The antenna is ground-mounted on a 16" square aluminum plate with
sixteen 50' radials. Installing radials at this location is a
"sticky" proposition and the soil is best characterized as sand
(decomposed granite actually).

I have measured the base impedance with both an HP8405 Vector
Voltmeter and coax bridge that was calibrated with an open-short-load
(OSL) method as well as a much faster N2PK vector network analyzer,
calibrated the same way. All measurements were taken at the base of
the antenna. This is an on again off again project (currently off)
with the goal of determining the effectiveness of the radial field.

The data are very repeatable and believed to be correct; however, I
cannot construct a model that replicates the physical antenna. For
example the curve on the Smith chart of the measured data has a little
bump in it and the resonant frequency is slightly off from the model.
The "bump" isn't a full-blown resonance loop, but it looks like it's
trying. Here is a plot from 1.5 to 15 MHz. The resonant freq is 5.5
MHz.

http://users.triconet.org/wesandlinda/Vertical_Z.gif

As you can see from the photo, there several other "verticals" in the
vicinity as well as my 45' foot tower with beam and wire dipoles 90'
away.

http://users.triconet.org/wesandlinda/Vertical_4.jpg








  #10   Report Post  
Old September 4th 05, 05:16 PM
Wes Stewart
 
Posts: n/a
Default

On Sat, 3 Sep 2005 20:19:04 -0500, "hasan schiers"
wrote:

Yep! A question remains for modelling. Is the value for Source Data in EZnec
4.x directly correlated to the Rrad? My EZnec model (a modified ARRL
Inverted L with radials), shows:

Frequency = 3.6 MHz

Source 1 Voltage = 25.65 V. at 4.18 deg.
Current = 1 A. at 0.0 deg.
Impedance = 25.58 + J 1.872 ohms
Power = 25.58 watts
SWR (50 ohm system) = 1.958 (25 ohm system) = 1.081

Is that 25.58 ohms the same 25 ohms from the graph of Devoldere's book, or
is it simply a coincidence?


Without looking at the book I would say yes. If you put 1 A into a Z
and 25.65 V @ 4.18 degree develops then that Z = 25.58 +j1.872


I have attached my *.ez file, if it makes it through the usenet group.


It did.



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