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Re: LF: Loop discussion

To: <[email protected]>
Subject: Re: LF: Loop discussion
From: "James Moritz" <[email protected]>
Date: Thu, 23 Jul 2009 18:40:01 +0100
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Dear Alberto, LF Group,

To give a sensible answer, you have to look at the numbers specific to your antenna and requirements. For example, suppose you want to use a broadband loop as you have described on 136kHz. I reckon the noise floor under quiet band conditions is about 1uV/m in 300Hz bandwidth at 136k. The figures I have to hand are for a 1m x 1m loop element made of 15mm copper water pipe, so let us use that as a basis.
The EMF induced in the loop is 2.1e-8 x fNAE, where f is Hz, N is number of
turns, A is m^2, and E is field strength in V/m. The 1uV/m band noise will
therefore produce an EMF of approx 2.9nV in the single-turn loop. Let us
follow Roelof's example and use a 1:30 step-up transformer. The EMF at the
secondary will therefore be 86nV. This is quite small, but we can use a low
noise amplifier - a J310 as used in the high impedance "Mini-whip" design
has an input noise voltage density of about 1.2nV/sqrt Hz, so contributes
21nV noise in 300Hz BW, about 12dB below the band noise level, so there is
some margin to allow additional noise from other sources.
The other thing we need to worry about is the thermal noise contributed by
the loss resistance of the loop and transformer. Suppose we want this to be
at least 6dB below the band noise level, i.e. 43nV at the transformer
secondary. The thermal noise EMF of a resistance is sqrt(4kTBR), so the
maximum resistance we can have is Vn^2 / 4kTB, where k is Boltzmann's
constant 1.38E-23, T is absolute temperature (say 300K), B is bandwidth of
300Hz - R works out to 372ohms. The impedance at the transformer secondary
will be the overall loss resistance of loop and transformer, in series with
the transformed inductive reactance of the loop (assuming that the
transformer winding inductance is high enough to have negligible effect).
The 1m^2 single turn loop has L of about 3.4uH, so with a 1:30 transformer,
the inductance at the secondary will be 900 times this, 3.06mH. This has a
reactance at 136k of 2.6kohms, so the minimum permissible Q of the
loop/transformer combination is 2.6k/372, i.e. about 7.
This is not very high. My prototype loop was made of 4 x 1m lengths of tube
with 4 x 90 degree elbows, so 8 solder joints, plus various hardware and
bits of wire connecting the resonating capacitors. The unloaded Q at 136k
was about 120 (and it seems the capacitors actually contributed
significantly to the loss), so the loop itself is probably not an issue, or
the addition of a few turns of wire as the transformer primary. I suspect
the transformer would be a greater contributor to the resistance due to
losses in the ferrite core , but provided the inductance of the primary was
several times larger than the loop inductance, it should be quite easy to
achieve an overall Q greater than 7. You also want to make the transformer
inductance high in order to minimise its shunting effect on the loop - this
would further reduce the already low voltage at the transformer secondary.
The impedance at the transformer secondary is kilohms, so a high input
impedance preamp is needed, whose noise figure is not seriously degraded by
the high source impedance, such as a JFET. A mini-whip-type buffer meets
this requirement, but with unity voltage gain, the output voltage is still
very low, so a sensitive receiver or further gain would be needed. Most
amateur type rigs used for receive on 136k would need 20 - 40dB additional
gain due to their poor sensitivity. An issue with a wideband design like
this is that the transformer would probably resonate somewhere in the 100s
of kilohertz range, which would put a sharp peak in the loop response at
that frequency - if this is in the broadcast band, it would probably be a
good idea to add a damping R-C combination to reduce the chances of strong
overloading broadcast signals. Some selectivity would be desirable in any
case, if the loop was used with a high gain preamp. Of course, if you
resonate the loop at the operating frequency, you can get quite a lot of
voltage gain "for free", but the bandwidth will be much smaller.
So it looks like this particular design is feasible and the loop
construction not very critical. I have not tried this particular
configuration (my loops need to incorporate some selectivity to be viable,
due to the 10s of volts/metre from the broadcast stations), but I used a
similar approach with the bandpass loops and several other designs, and got
more or less what was expected, so it should work OK.
Cheers, Jim Moritz
73 de M0BMU

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