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Date: Sat, 25 May 2002 21:51:19 +0000 (GMT)
From: "Alexander S. Yurkov" <fitec@omskcity.com>
To: rsgb_lf_group@blacksheep.org
Subject: LF: Ground loss for different length
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Hi Group.

Previosly I have sent the formula for estimation of LF antenna ground
loss if conterpoise length is equal to antenna length.

If conterpoise length is not equal to antenna length situation became more
complex as follows. If lengthes are equal then in the case H<<l carge
distribution on each wire is obviosly homogenios. Generaly it is not so
if lengthes is not equal. 

But NEC-2 modeling show linear curent distribution in each wire if
lengthes is not equal. If curent is distributed  linearly then charge
is homogenious because dq/dt + div J = 0

Thus seems reasonable to derive formula for LF antenna ground loss
resistance in assumption of gomogenious charge distribution even if
conterpoise length is not equal to antenna length. Now I have derived it
only for elevated conterpoise. The formula is:


R=(1/(pi*s) * [(1/la)*ln( (H+h)/(2*H) ) + (1/lc)*ln( (H+h)/(2*h) )]

where
la - antenna length,
lc - conterpoise length.
Other notations are the same then previously.

If lc=la then the formula obviously became the same then previous one.

The formula show if conterpoise length tends to infinity then R tends
to constant. So it is no reason make contrpoise length grater then
determed by:

(1/la)*ln( (H+h)/(2*H) ) >> (1/lc)*ln( (H+h)/(2*h) )


Also NEC-2 modeling show not big variation (not more 20 percent) of R if
conterpoise wire is not parallel to antenna wire. So the formula seems can
be used for any conterpoise direction.


73 de RA9MB/Alex
http://www.qsl.net/ra9mb