RadioBanter - Loop Antenna at ~60 kHz

El 06-11-14 10:37, rickman escribió:
On 11/6/2014 2:23 AM, Jeff Liebermann wrote:
On Wed, 05 Nov 2014 20:50:31 -0500, rickman wrote:

Not sure why you can't discuss this in the right thread of this group.
I've posted my reply to your post in the loop antenna thread.

Because I prefaced my comments by mentioning that a 60 KHz loop is on
my "agenda". I guess that's a bit vague. What I meant to say was
that I'm not very well read on the technology involved, a total clutz
with LTspice, and I haven't built another loop so I can measure how it
acts. In other words, I'm not ready to discuss it (unless you can
tolerate my guesswork).

I'm happy bouncing things off you. I did some reading on this back a
year or so ago and feel like I got a lot, but not enough to really
optimize it for my application. One thing I was missing was an
understanding of the radiation resistance which I now have a formula
for and can include in my LTspice simulation when I get to it.

I don't quite have a feel for radiation resistance in terms of its
effect on the receive antenna, but I'm sure that will come once I look
at the equations. I expect it will be small, hopefully small compared
to the wire resistance.

One thing that gave me fits early on is the calculation of the loop
inductance. Seems there are a lot of equations out there and most of
the sources don't talk about where they got them or what they assume.
I finally got one from Lundin that seems pretty good and covers the
widest range of coils I might be using.

First, I'm not sure what you are talking about connecting high
impedance
antennas to condensation and salt fog. If you are transmitting, then
maybe you could get such high voltages as to attract microscopic
objects, but this is a receiver design.

Well, a 33:1 turns ratio is a 1000:1 impedance ratio. Using 75 ohms
as the coax cable and the characteristic impedance, that's 75K ohms.

Forget 75 ohms. There is no cable. The antenna connects directly to
the receiver circuit through the transformer. The characteristics of
the antenna are defined by the inductance of the loop and the
resonance with the tuning capacitor and the Q.

In general, board leakage and conduction problems start around 100K
(depending on trace spacing etc), so I suspect you can make it work,
at least on the bench.

100k? I will be using up to 10 Megohm parts but even that is not very
sensitive to board leakage unless you leave a lot of rosin on the
board and it collects dust for a few years.

However, in the typical marine atmosphere,
with ionic crud in the water, there will be leakage issues. I don't
recall the typical sheet resistivity for a standing salt water puddle
on a PCB, but I suspect it will be a problem.

I won't be in salt spray, it will be in my living room. Still, any
aquatic electronics would be in a sealed enclosure.

Of course, you can
conformal coat the board, hermetically seal the package, wax dip it,
or pot the antenna amplifier in epoxy to avoid the problem. However,
the favored method is to design with low impedances and not create new
problems with conformal coatings and sealed boxes.

There are also some PCB layout tricks that will help. For example,
here's part of a book on PCB design issues:
http://www.analog.com/library/analogdialogue/archives/43-09/edch%2012%20pc%20issues.pdf

See Pg 12-15 to 12-19 on "Static PCB Effects" with examples of PCB
guard patterns.

I am familiar with guarding, but that is not going to be needed with
an antenna. The voltage will be very low level even when the Q is
optimized, so no appreciable leakage currents.

Incidentally, my unofficial test for decent design was to immerse the
radio in a bucket of genuine San Francisco Bay salt water. If the
board continued to operate normally, it passes. If not, I get to
spend the evening with the bucket and a megohmmeter looking for the
culprit.

If you're building this loop as an academic exercise, you can probably
ignore all the aforementioned comments on PCB leakage. However, if
you're going to sell it, think carefully about such environment
problems.

I don't think it will ever see duty on a sea vessel.

Also, the antenna is not high impedance, just the input to the
receiver.
The transformer I am looking at is a high turns ratio current sensor.
It spans the right frequency range and is a nice compact package easy
to mount on a PCB.

Why not just make it a 40 KHz tuned xformer? You get the same
impedance transformation with the added bonus of additional bandwidth
reduction (increased Q) to eliminate as much atmospheric and man made
noise as possible. It's also much less lossy than a broadband
xformer.

What would that entail?

My main concern is lowering the Q because of the loading from the
receiver input, especially with the change in impedance as reflected
through the transformer.

Well, you're stuck with matching the loop to the receiver input
anyway, so there's no way around that with passive components. You
can insert an emitter follower to do the impedance transformation.

You aren't in tune with this design. The goal is to minimize power.
There won't be a preamp of any kind unless absolutely required.

Incidentally, the typical loaded Q for such loops seems to be around
100. Some claim 200 or more, but for small loops, 100 seems to be the
target. At 40 KHz, that's a -3dB bandwidth of 200 Hz, which is rather
wide for a 1Hz wide WWVB signal. You could probably increase the Q
somewhat, mostly be reducing the resistive losses, but that might
create drift and tuning accuracy problems. Higher Q is possible, but
I suspect will require a much more rigid and beefy design.

There is only so much that can be done to increase Q. The wire I am
using in the antenna is already pushing the skin effect at 1 mm
diameter. If I am reading the equations correctly increasing the
number of turns on the loop does increase Q. I am currently looking at
8 turns (50 feet of RG-6) and may increase it to 100 feet (16 turns).
But I've already built a support and 16 turns will be hard to add
without a redesign.

I think when I simulated it, I found the max
signal strength came with a 25 or 33:1 turns ratio because with higher
turns ratios the Q was spoiled enough to bring the voltage down at the
receiver input.

This simulation didn't include the effect of the radiation resistance,
so I will need to add that in. I expect this will lower the Q as a
starting point which means the affect from the receiver input loading
will not be as significant, possibly making a higher turns ratio in
the
transformer more useful.

I can't comment on that without seeing the design. Actually, I'm not
sure seeing the design will help as I need to do some more reading
before I can understand exactly how it works.

The equations are pretty simply once I found them (and could trust I
had the right ones).

Lundin's formula for inductance of a solenoid
L = N^2 * a * Correction Factor * μ0

N is the number of turns
a is the loop radius in meters
the correction factor based on the coil shape is a bit complex but
comes to 3.3 ballpark with the loop shape used.
μ0 is the permeability of free space

Depending on what is in your "Correction Factor", I would expect a^2
isntead of "a" (coil radius). I also expected to see the length of the
coil in the formula.

He is the effective height of the antenna, an expression of the
effectiveness of the antenna in converting the field into a voltage.

He = 2pi * N * A / λ, ignoring the orientation factor cos θ.

N is the number of turns
A is the loop area in meters^2
λ is the wavelength of the 60 kHz signal

Inductance and frequency get the reactance which when compared to the
total loss resistance yields the Q.

Multiply the effective height by the field strength (on the east coast
it's ~100 uV from WWVB) to get the antenna voltage. Someone was trying
to get me to use an equation based on the magnetic field but I believe
once you combine the equations you get the same calculation.

That someone was me, and you are right, results should be the same.

Multiply by Q and the transformer ratio and you have the voltage at
the receiver input.

Wire resistance goes up with the product of N and a, or in other words
the length of the cable. The loop inductance goes up with N^2 and a.
Effective height goes up with N and a squared (area). So a bigger loop
will get a larger signal but the same Q. Adding turns will get a
larger signal *and* a higher Q. Obviously the size of the loop has an
upper limit based on practicality, but more turns gets improved
performance with less impact on the size.

More turns (that is more copper/copper area) give higher Q, but there
are other effects that will cause deviation from this reasoning. I
still can't draw on a piece of paper what you have in mind, however
you may search for coil/inductor design and Q factor together with
names of researchers/experimenters (Medhurst, Nagaoka, Wheeler, Corum,
etc).

If you are able to make an LC circuit with Q say over 10.000 (10k),
radiation resistance will have some influence. When discussing Q1000,
size around 2 feet, forget radiation resistance, resistive loss
dominates.

--
Wim
PA3DJS
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