On Thu, 13 Jan 2005, Alexander S. Yurkov wrote:
years ago. Unfortunely I have forgot where is my writings with this
formulas. Somewere they are but it is dificult to find them in my 'pile
up' of different papers:-) I'll try to find. Also this formulas may be
posible to find in archive of this list.
Here they are:
From [email protected] Thu Jan 13 19:20:35 2005
Date: Mon, 20 May 2002 13:34:15 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: more acurate formula for ground loss
Hi, Group!
I have derived more acurate formula for ground loss then previous one.
This formula show previous formula is extremely aproximate.
Factor of number units was losssed...
New formula is derived for such a configuration. T or inverted L
antenna is assumed. Height of horisontal part of antenna is H.
It lenght is l. Conterpoise is up (!!!) from the ground on heght
of h. h can not be less then wire radius. Conterpose length is l also.
H<<l is assumed. s is ground conductivity, pi = 3.14159... Unfortunely it
is very complex to describe conterpoise length not equal to antenna
horisontal part length. It is posible but formulas is extremely long and
complex. May by I'll can simplificate it in future.
For such a condition ground loss resistance R is:
R = R0 * ln( ((H+h)^2) / (4*H*h) )
where
R0 = 1/(pi*s*l)
ln - natural logarithm.
It seems to me than this formula is acurate if there is no enviroment
losses. Unfortunely I can not describe enviroment loss yet.
For h<<H formula can be simpificated:
R = R0 * ln( H/(4h) )
In previous formula logarithm factor was lossed, sorry.
May be if conterpoise is up from the ground it is posible to decrease
ground loss compared to case when conterpoise lie on the ground or is
burred. I have analyse this by this formula. I found that there is optimal
conterpoise heght h if coil loss resistanse is taken in consideration.
Attention, coil loss resistance is worth for this analyse!
Unfortunely this can be done only if enviroment losses is neglet.
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
From [email protected] Thu Jan 13 19:21:09 2005
Date: Mon, 20 May 2002 13:45:00 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: Forgot to notice...
I forgot to notice. Conterpoise is under horisontal part of antenna
assumed. Wires is parallel.
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
From [email protected] Thu Jan 13 19:21:26 2005
Date: Mon, 20 May 2002 14:28:36 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: more exectly...
On Mon, 20 May 2002, Alexander S. Yurkov wrote:
May be if conterpoise is up from the ground it is posible to decrease
ground loss compared to case when conterpoise lie on the ground or is
burred.
More exectly: "... to increase antenna effectivity...".
If h is increased R is decreased truely, but "antenna radiation height"
H-h is decreased also. But R is decreasing more quickly...
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
From [email protected] Thu Jan 13 19:21:38 2005
Date: Mon, 20 May 2002 22:38:26 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: Re: LF: more acurate formula for ground loss
Hi John and Group!
On Mon, 20 May 2002, john sexton wrote:
Hi Sasha,
Putting in the same antenna details as before,
the new formula gives 38 ohms, still too low by a factor of over 2,
but much better than with the first formula.
I just compare the formula to NEC-2 (Sommerfeld ground) modeling and get
such a result:
H=20m, l=100m, s=1mSm/m
h Rin Rrad Rg Rg formula/NEC
m NEC NEC formula
0.5 6.67 0.13 6.54 7.47 1.14
1 4.97 0.12 4.85 5.43 1.12
2 3.31 0.11 3.20 3.52 1.10
3 2.42 0.10 2.32 2.51 1.08
4 1.83 0.08 1.75 1.87 1.07
It seems differences is due to not enought segmentation in modeling (1
meter of segment length). I can't do better segmentation because of my
computer is not so good...
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
From [email protected] Thu Jan 13 19:22:15 2005
Date: Tue, 21 May 2002 10:35:38 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: Re: LF: more acurate formula for ground loss
Hi John and Group.
On Mon, 20 May 2002, john sexton wrote:
Putting in the same antenna details as before, the new formula gives 38 ohms,
still too low by a factor of over 2, but much better than with the first
formula.
May be 93 - 38 = 55 ohms is enviroment loss. And if make conterpoise up
from the ground about 1 or 2 meters, ground loss reduces from 38 to about
5omhs. So total loss will be 55+5=60 omhs. But it is the matter of
experiment...
It seems very interesting and worth to do 'pure' experiment in field
far from trees and buildings when no enviroment losses present and when
conterpoise is up from the ground and conterpoise length is equal to
antenna length. NEC-2 confirms the formula but this is only computer
modeling, not real measurement!
If it will be no problem to estimate ground loss itself then it will be
posible to separate ground and enviroment losses when doing experiments.
So experimental study of enviroment losses itself will be possible and
ways to reduce enviroment loss will become more obvious. Now we do not
know what part of total loss is ground loss and what is enviroment loss
itself.
However in order to do this since my earth wires are actually buried I used
a value of h = .0005 (1mm diam. wire) the minimum value permitted with your
formula.
It seems reasonable.
My generalised mirror reflection theory can be used for burred conterpoise
also I hope. It is only matter of time. Now I want to ensure this
theory for simple conditions. Complex conditions is a next step.
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
From [email protected] Thu Jan 13 19:22:36 2005
Date: Wed, 22 May 2002 12:06:09 +0000 (GMT)
From: "Alexander S. Yurkov" <[email protected]>
To: [email protected]
Subject: Burred conterpoise
Hi, Group!
I have just derived formula for ground loss when conterpoise is burred.
Configuration is the same then conterpoise is elevated. But now
h is conterpoise depth. Also wire radius r appears in the formula.
Ground loss resistance for this case is:
R = 0.5*R0*ln( (H+h)^4/(8*H^2*r*h)
If H>>h then it can be simplifired:
R= 0.5*R0*ln( H^2/(8*r*h) )
As for elevated conterpoise it should be h>r here.
It seems interesting then if h=r (conterpoise is lie on ground surface)
formulas for elevated and burred conterpoise yeld approximately the same.
Some difference is not suprisely because this is the limit when formulas
works.
Also it seems very interesting and worth that antenna ground loss
resistance is NOT EQUAL to such a ground system resistance (on DC for
example). Groung system (horisontal burred wire) resistance is:
R = 0.5*R0*ln( l^2/(2*r*h) )
It is not very suprisely if note then E-field lines is essentialy
different for ground system and antenna with burred conterpoise.
If it is an antenna E-field lines starts on conterpoise and goes to
antenna. If it is a 'pure' ground system E-field lines starts on the
conterpoise and goes to infinity. Another field configuration yelds
another resistance.
It seems to me extremely worth then formulas show the conderpoise wich
lie on soil surface is the extremely bad case. To reduce losses
conterpoise should be elevated or burred to adequate depth. To elevate is
better...
73 de RA9MB/Alex
http://www.qsl.net/ra9mb
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