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Re: LF: modeling a loop

To: [email protected]
Subject: Re: LF: modeling a loop
From: Rik Strobbe <[email protected]>
Date: Fri, 05 Jun 2009 09:39:23 +0200
In-reply-to: <[email protected]>
References: <[email protected]> <[email protected]> <[email protected]>
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Dear Peter,

thanks for your interesting mail.

One question regarding the general formula for radiation resistance:

In other places I found Rrad = 160*Pi^2*(Heff/lambda)^2 = 1579*(Heff/lambda)^2
whereas Zo*(2/3)*pi*(heff/lambda)^2 = 790*(Heff/lambda)^2

So there is a difference of a factor 2 (what looks very much like the perfect ground vs free space difference)

73, Rik  ON7YD

At 02:43 5/06/2009, you wrote:
Rik Strobbe wrote:


When I model a 11m high and 22m long lazy-L antenna (using MMANA-GAL) the modeling result seem to agree with theory: 0.027 Ohm at 137kHz and 0.359 Ohm at 502kHz.
But when I model a 10.5m high and 22m long loop, 0.5m above ground:
- 0.0013 Ohm at 137kHz and 0.033 Ohm at 502kHz, a ratio of only 25 instead of the expected 180 - very different from the theoretical values: 0.00007 Ohm at 137kHz and 0.013 Ohm at 502kHz - modeling in free space at 502kHz confirms the theoretical 0.013 Ohm, but at 137kHz even in free space it is 0.0012 Ohm. If the claim that loop losses are not affected by the ground I would expect that the radiation resistance is not affected either.

I guess MMANA-GAL is not suited for modeling very small loops, is there other software that can scope with this ? Before going into the effort of putting op the loop I would like to have an idea of what to expect.

73, Rik  ON7YD - OR7T

Dear Rick, LF group,
years before reading your present post i have found ,among others, your review article concerning LF antennae (btw, it was , and still is, a wonderful piece of useful work done upon this subject) In this article there was a formula giving a theoretical estimate of a radiation resistance of a small loop. the term 'small' will be considered later.. over the past few years there were some (internet) reports about poor performance about mmana especially when the 'real ground' option has been switched on. your present post confirms this issue but which is more important and brings my attention is the ' free space' performance in the case of low frequencies.
so i decided to check out the  'theory'  behind the  formula  of
rad.res. of  small loops

from the very, very basic consideration of electromagnetic radiation
one arrives with Johnson-Nyquist
formula concernig the noise of carriers in a resistive medium i,e "antenna' which states that rad.res = Z(0)(2/3)pi(heff/lambda)^2 where Z(0) is an impedance of a free space (377ohm) but which can be alternatively presented as 4pi10^-7 c where heff is an effective height of an antenna and c ,velocity of light which , due to the units is 3 times 10^8 m/s)
the so called 'effective height ' is a proprtionality factor between
voltage induced in the antenna  due to the electric field .
In the case of a SMALL loop ( constant current ) simple considerations due to the Farady law lead to its effective height as 2piA/lambda , A is loop area ( single turn loop , air ). Simple math and we arrive to rad .res.as 320pi^4A^2/lambda^4
as it is in your review. Rick, i did this 'check' because :
a)  some aspects of my job are loosely connected with  electromagnetism
b)  i like this sort of  ' brain recreation'   - 'play' with formulas, hi
c) I simply wanted to 'confirm' this expression as being derived from the 'principles' i.e maxwell equations etcc.. and , first of all what assumptions, simplifications were made in order to get this. it seems that this expression is strongly supported by 'principles' and considerations are ok. let us go back to mmana performance .. your mmana modelling the loop at 502 kHz in a free space is consistent with theoretical estimate while 137 kHz case gives discrepancy. Considering only the theoretical expression of rad.res it just should be the opposite ! the loop is 'smaller' at 137 or 'bigger' at 502 in terms of a wavelength :) Therefore, it must be some sort of intrinsic error in mmana performance when going to lower frequencies due rather to the method and not to the 'physics' . mmana is based on the "method of moments" and may be it is the segmentation issue which comes into play in the case of lower frequencies - those DM1, DM2 parameters etc..
I must admit i've never played with these parameters  - usually i  was
opening one of the existing antennae files
in the  samples  subdirectories and was using it as a starting point
for  changing the geometries etc.. (but for HF so far..)

                                                 yours, peter, sq7mpj
qth: lodz , jo91rs




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