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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