Date: Fri, 05 Jun 2009 09:39:23 +0200
To: rsgb_lf_group@blacksheep.org
From: Rik Strobbe <rik.strobbe@fys.kuleuven.be>
In-Reply-To: <4A286A4B.8090700@toya.net.pl>
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Subject: Re: LF: modeling a loop 
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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
>