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From: "James Moritz" <james.moritz@btopenworld.com>
To: <rsgb_lf_group@blacksheep.org>
Date: Fri, 25 Jul 2008 12:44:09 +0100
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Subject: LF: Re: Posting problem / Loop Conundrum
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Dear LF Group,

It seems that I can only make postings to the LF reflector from one of the
two PCs I have connected to the broadband modem. The one that works is an
old machine with Win98 - the one that doesn't is Vista, although the e-mail
message settings are the same on both PCs as far as I can tell, and sending
e-mail to other destinations does not seem to be a problem. Does anyone know
why this could be? All info gratefully received...

This is what I tried to send a couple of days ago re G4JNT's "loop
conundrum":

Dear Andy, LF Group,

> Now, I take two identical such loops and mount then on the same centre
> line but at right angles to eachother so there should be no coupling
> between them, whatsoever.   Now, I connect the two loops in series and
> resonate the combination with a single capacitor of half the original
> value.   The resulting radiation pattern should have the nulls filled
> in, and be a reasonable approximation to omnidirectional in azimuth.
>
> BUT...
> What is the resulting change in efficiency?
>

Here is my attempt to analyse this. According to the (Kraus) textbook, the E
field at a long distance from a small loop is:

120*pi^2*I*sin(theta)*A/(r*lambda^2),

where I is current, r distance and A loop area. In other words, the E field
(and the H field) are proportional to the sine of the azimuth angle theta,
relative to the axis of the loop. A second loop at right angles to the
first, with identical area and current would give the same E field as above,
except that sin(theta) becomes sin(theta + pi/2) due to the rotation. With
both loops present, the two fields will be superimposed - as IK1ODO says, at
a long distance the E field will be entirely vertical for both antennas, and
have the same phase because the distance is the same, so the field vectors
for each antenna will always be in the same direction and simply add
algebraically to give the total E field for the composite antenna:

120*pi^2*I*[sin(theta) + sin(theta + pi/2)]*A/(r*lambda^2)

a bit of fiddling with trig identities makes this equal to:

sqrt(2)*120*pi^2*I*sin(theta + pi/4)*A/(r*lambda^2)

So this is the same pattern as the single loop, except that the magnitude is
increased by sqrt(2), and the angle is slewed through pi/4, i.e. 45 degrees.
A very similar result occurs for the H field. So I agree with G4OKW. Since
the power density is proportional to E^2, the power density is twice as
great, and so the total radiated power will also be twice as much. So
argument 1 is OK, twice as much power in, twice as much radiated:

> Argument 1:
> Two identical loops = two times the loss R,  but also two times the
> radiation resistance (since they don't couple) so net efficiency
> remains the same.
>
> Argument 2 :
> Chu-Harrington relates efficiency / Q / bandwidth / volume enclosed.
> Therefore, as the enclosed volume has increased, the effciency ought
> to rise.
>
In my reading of the Chu et al limitations on antennas, the "volume"
considered is always a sphere which is just big enough to fully enclose the
antenna - in this case, you could add the extra loop without increasing the
size of the sphere, so the limit would stay the same. There is also a "shape
factor" which reaches 1 only for some theoretically optimum, and probably
un-realisable, antenna, with real antennas such as small loops having some
value less than 1. So there is only an upper limit on efficiency, real
antennas might be better or worse below this limit.

To get a pattern without nulls, you have to have a phase shift between the
loop currents - as has been pointed out, when the phase shift is 90 degrees,
you get an omnidirectional pattern. This has been implemented (for receive)
in DF6NM's directional spectrogram set-up. If the phases of the currents in
the two loops stay the same and the amplitudes vary, there will always be
angles where the fields of the loops cancel, giving nulls, and the pattern
will be that of a single loop skewed from the physical direction of the
actual loops. This is the principle behind the Bellini-Tosi type of LF/MF
direction finder with two loops with their signals summed in a "goniometer"
to give an electrically-steerable null. It is also why you will get sharp
nulls with small loops even when they are bent and twisted into funny
shapes, or with multi-turn "box" loops with thickness as well as area, or
soccer balls for that matter :-)

Cheers, Jim Moritz
73 de M0BMU