Dear
Markus (and LF Group)
Thank you very much for your very useful comments.
I have a few further comments.
(a)
On item 3. below: It is
useful to note that reflection at the walls of a waveguide and on the surface
of a real earth depend on the polarisation of the wave (and the angle of
incidence). Also there is a useful analogy with the voltage and current waves
reflected at the end of an open-circuit, short-circuit, or imperfectly matched,
transmission line. When we consider these reflection boundary conditions we
find that mu defined as B/H is not equal to mu(0) just above a conducting or
high permeability material ( just as you say). Above a dielectric material the
difference between mu and mu(0) is indeed negligible. However then the
difference in epsilon (defined as D/E) is large. We therefore have to consider mu
and epsilon separately initially, and then combine them together progressively
as we move away from the boundary surface. The ‘local’ impedance is
usefully defined as Zl = (mu/epsilon)^0.5 and is not in general 377 ohms until ‘free-space’
is reached, away from the boundary. I wish this was better explained in the
books! Actually the EMC engineers appear to have a better understanding of
this than the antenna engineers.
(b)
Item 5 really is the heart
of the matter. This discrepancy and disagreement between the two theoretical
approaches has existed mainly unnoticed, and certainly unresolved, for about
fifty years - since Chu (and Wheeler) presented the well known ‘Q is
inversely proportional to volume’ assertion that you quote. I have gone
on record as challenging, and continue to challenge, the Chu assertion. The
mathematics for this is impeccable but the ‘physics’ and physical assumptions
are not. My objections include: no consideration of (analytic) continuity of
the fields at the boundary of the sphere containing the antenna; no proof that
the Chu assertion excludes the possibility of additional antenna radiation modes
for which the Chu assertion does not apply; no consideration of the effects on
the large (magnetic and electric) displacement currents in the space surrounding
the sphere containing the physical antenna or the possibility (/probability) that
such currents themselves radiate; and the sometimes large discrepancies between
predicted and measured (loop) antenna efficiency results. I therefore strongly
defend the ‘antenna capture cross-section related to antenna pattern and defining
the antenna limiting Q’ view against the Chu-Wheeler (and Kraus electric
dipole) formulas for antenna Q and radiation efficiency.
(c)
I agree that earth
reflections can double the radiation resistance under the right assumptions. However
some surfaces and wave polarisation can actually halve the observed radiation
resistance. The philosophical question then is whether the ground under the
antenna is actually itself radiating or just reflecting.
(d)
A further point is that
some antennas close to ground, but not necessarily conductively connected to it,
can launch strong ground waves and this in general will appear as an additional
increase in radiation resistance at the antenna terminals.
In conclusion the story (or is it saga?) of
small (loop) antennas is not yet finished. We also have to remember that field detectors
are ‘reciprocal’ devices and are themselves small antennas. In my
view there is considerably more to be found out on all these, particularly when
used in a real environment just above ground. .
73 and regards to all.
Mike – G3LHZ
-----Original Message-----
From: owner-[email protected]
[mailto:owner-[email protected]]
On Behalf Of [email protected]
Sent: 16
March 2005 23:19
To: [email protected]
Subject: Re: LF: Untuned and tuned
loops
Dear Mike and LF Group,
thank you for your inspiring comments. I would like to add in a few remarks;
hope they will not be regarded as too theoretical...
>> 1. My strong support for what Jim
has said. The immediate environment always affects all field
measurements, not just magnetic field measurements.
The good side for loop measurements is that the magnetic field is much less
influenced by conducting or dielectric surroundings than the electric field. It
is easy for a tree or stone wall to shunt E to ground, whereas distorting H
requires a significant current flow, which can only be supported by a large
sheet of metal or a nearby wire loop. A nonresonant short pole has no effect at
all. And this is "the secret" why TX loops work so well in forested
terrain.
>> 2. Marcus’s formula is correct
for free-space and it is in all the books. Wire loss is not an issue for a
typical open-circuit loop
The formula connecting U to B is just an embodyment of Maxwell's
rot E = -dB/dt ,
it should very generally give the correct answer for B and (excluding
ferromagnetic cores) also H. It's true even for an electrically loaded
loop (see 4. below). However the often-used relationship between the magnetic
and electric field (E/H = Zo = 377ohm) is restricted to the undisturbed far
field zone.
>> 3. In an ‘environment’
near real ground, buildings etc., the ‘physics’ insists that such a
loop gives an open circuit voltage proportional to B = mu * H. The
presence of the environment means that mu is not equal to the free-space value
of mu(0).
Yes, but this difference is mostly neglegible. Though our environments may have
a lot of dielectric and or conducting objects around, they are hardly magnetic,
and µr = 1 is an excellent approximation in almost any situation. At RF, even a
steel wall looks like a short circuit (due to the eddy currents) rather than a
"magnetic wall", which would have high surface impedance. The
exeption of course are nonconducting ferromagnetics, like ferrites.
>> 4. The current in a short-circuit
lossless loop is directly proportional to the H field and it does not depend on
the area. This is not in ‘the antenna books’, but it is in
some physics books dealing with super-conductivity.
The short-circuit current does depend on the effective length of the magnetic
flux lines. For the schoolbook case of a long cylindrical coil (n turns,
arbitrary core material), we have
U = - n area j omega µ H, L = n^2 µ area / length,
n I = n U / (j omega L), = - H / length ,
easily memorized by the unit "amps per meter" for H. For a
"short" ring coil however, the magnetic length is a function of both
the wire and loop diameters.
The original induction rule is still correct in the short circuit case, as the
current creates a secondary field such that the total flux and the (averaged) H
passing through the loop area is indeed nulled.
>> 5. ...What the system Q ends up
being does not matter for this proof. Some may have noticed however that
it is a matter of considerable (unnecessary) dispute, as reported in the pages
of RadCom. However loop (or any antenna) losses do matter, because the
cross-section area of an antenna is reduced in proportion to its
(in)efficiency. This point is in most of the antenna books.
After real conductor losses have been minimised and factored out we find
practical outdoor Qs of 100 to 350. In a screened room the loop Q can
exceed 600.
This raises a fundamental issue on the efficiency limit of a small antenna. For
a magnetic antenna represented by a cylinder coil in free space, we would get
Rrad = Zo/(6pi) * area^2 * (2pi/lambda)^4
X = omega L = 2pi / lambda * c * µo * area / length,
and using Zo/c = µo we get a radiation Q-factor
Qrad = X / Rrad = 3/(2pi)^2 * lambda^3 / volume.
For an electrical antenna represented by a plate capacitor, we have
Rrad = Zo/(6pi) * height^2 * (2pi/lambda)^2
X = 1/omega/C = height / (omega*epsilon*area) ,
and with 1/Zo/c = epsilon we again get the very same value
Qrad = 3/(2pi)^2 * lambda^3 / volume.
If we have a lossy antenna confined in a small volume, with a given
Q<<Qrad we get a maximum possible efficiency of
eta = Q/Qrad = 13.2 * Q * volume / lambda^3,
no matter whether it is an electric or magnetic antenna! The energy storage is
necessary to support a reactive dipole field (r^-3) between the physical
antenna volume and the radiation zone, beginning at a distance lambda/2pi
("CFA"-promoters will disagree here...).
Above earth, the radiation resistances and efficiencies for both types of
antenna is doubled, which is plausible if we include the image antenna volume
below ground. Somewhat surprisingly, this still holds true for loops above
weakly conducting ground, as long as the skin depth (a few 10m at LF) is still
small compared to a freespace wavelength.
For a thin wire antenna, the "width" of the effective volume is not given
by the wire diameter itself but by the capacitance of the wire. For the rule-of
thumb 5 pF/m wire, we would have to use approximately half the height of the
wire times its length as the effective cross section. My TX antenna (220pF at
10 m above ground, Q = 200) has an effective volume of 2483m^3 and an
efficiency of 0.093%
So much for now, it has become late...
73 and good night
Markus, DF6NM
