On 3/8/2013 4:20 PM, Tim Williams wrote:

It may sound like hyperbole, but it's mathematically sound. The midpoint
theorem, for example, guarantees that, between two points, you must've hit
some point inbetween, somewhere, as long as the function is continuous.
More usefully, functions arising in electronics are often one-to-one, so
it's not only true that you are guaranteed midpoints, but you'll find them
in order, too.

If you aren't looking at the extreme cases, you aren't doing your job.
Whatever's left inbetween can simply be interpolated!

The point here being, an antenna which doesn't couple into free space
obviously has a crappy SNR. The signal level can be anything, it doesn't
matter. The signal need not be small, because internal losses generate
thermal noise. With sufficient Q, you can push that thermal noise up to
your receiver threshold (which you said is an ADC) and detect signal.
It'll be bandlimited, ~60kHz noise, a useless signal, but present
nonetheless.

In general, antennas which do couple strongly to free space have low Qs.
A 1/2 wave resonant dipole has a Q of only 1 or 2, so bothering to call it
resonant is actually kind of weak. This is similarly true for a large
loop, which of course would be highly impractical here. So there must be
some middle case where SNR is reasonably unaffected, which will be the
best choice antenna.

I was warned a long time ago to be wary of people speaking in
"glittering generalities". You seem to insist on using terms without
giving a mathematical basis. How about if we use some math?

V = (2 * pi * A * N * E * cos(theta)) / lambda

V is the voltage on the antenna,
A is the loop area,
N is the number of turns,
E is the field strength,
theta is the rotation angle of the antenna and the transmitter (just
consider this term to be 1,
lamba is the wavelength (c/f)

This is multiplied by the Q factor when resonated by a capacitor. So
higher Q, higher signal.

Where in here do you think I am having a problem?


Since atmospheric noise dominates, the antenna can stand to be pretty
small.

You are making assumptions that don't hold true in my design.


Raw volts don't matter, you can always throw more amplifiers at it (as
long as they don't corrupt the SNR also!).

Maybe you didn't read my other posts. I am not using an amplifier. I
am running the antenna and coupler output directly into a digital input.

You hadn't mentioned that before...

You didn't ask.


The receiver input is high impedance, approximately 10 MOhms with a low
capacitance between the differential inputs of not more than 10 pF.

Any ESR? Example, the ATmega series 10 bit ADC specifies, I think, around
10pF + 10k ESR (somewhat depending on how many mux switches it's going
through to get there).

FET input resistance. I will double check that though.


Your description of what is happening is very terse and full of
shortened terms that I don't understand.

I could write a book on the subject to explore it in detail, but there are
many available already, and there are too many holes in my knowledge to
really be worth it, plus this is Usenet, you get what you pay for. I was
hoping you'd Google in the blanks.

I thought I was doing well, but you seem to be telling me I am making
mistakes, but I can't figure out what they might be.


What do you mean "line up that
10p resonance with the operating frequency"? I assume you are referring
to the 10 pF input capacitance. How does this get "lined up" with
anything?

There's yet another theorem in networks that has to do with matching.

A resonant tank's impedance varies wildly with frequency. But it will
always be resistive at resonance. If you connect this to another network,
which has a resistive input impedance at the same frequency, you don't
care what the L and C are, it will simply work -- old fashioned resistor
divider action!

You *do* have to worry about L and C and reactance and bandwidth to solve
for the frequency response and stuff, but you can at least approximate
that with Q factor (i.e., how much loss is draining power out of the
system).

So if your ADC input is exactly 10p + 10M, you could resonate it with 0.7H
(well...), which has a resonant impedance of 264k, and thus a reasonable Q
of 38. (The real world typically bitchslaps the theorist at this point,
as 0.7H chokes with10pF parasitic capacitance and Q 38 at 60kHz don't
exist.) If the capacitance's ESR is less than 6.9kohms (i.e., 264k / 38),
it won't have significant effect.

You can couple to this tank via parallel or series. If you did series,
the input impedance would be 264k / 38, or 6.9k, not horrible; going from
the 0.78 ohm loop to this in a single transformer requires a 1:100 CT,
which works fine at 60kHz. (This CT would require high inductance, so as
to avoid skewing results, but that's typical of a CT. An amorphous core
CT would probably suffice. So at least that part is physically
realizable.) Note the irony of coupling a current loop to a current loop,
where in both cases, the CT looks like a small impedance relative to the
loop it's within. That's simply how huge the impedance at the ADC is.

Since all these resistances are matched, the power transfer theorem holds,
and you're pushing as much voltage and power into the ADC as possible.
The bandwidth is about 1.6kHz, so the thermal noise floor is around 5uV at
the ADC. A received power of 1nW will generate 0.1V, which is probably a
reasonable figure. The SNR of the receiver is limited by quantization
noise for14 bits, thermal for14 bits. A 16 bit converter wouldn't be
too expensive at this sample rate (note it's the analog sample-and-hold
speed which limits direct conversion performance; a sigma-delta, running
at 100Hz, with no S&H, won't see jack).

When you talk about reactances canceling, that sounds a lot like a tuned
circuit at resonance. That is what I *am* doing and where this thread
started. One problem with that is the lack of precision or stability of
the parasitic capacitance. Any idea how to deal with that?

Considering theoretical 0.7H chokes aren't commercially available, you
might swamp it with more C, which stabilizes the value, and requires less
L to resonate. Rub: resonant impedance is lower, so the Q of the
components must be higher in order to achieve the same performance. Even
with a Q of 200, you still need over 0.25H, which is just as unlikely a
combination. Well, if you really wanted to try, maybe a gapped
ferrite-cored inductor could be made. Still, the only practical choice
seems to be lower signal level.

So ultimately, the question is, how little signal can you tolerate before
you need an amplifier? How many bits of conversion, how much sample rate
can you afford before a linear amplifier becomes cheaper on the power
budget?

Have you looked at the simulation data I had posted? I think you are
describing exactly the circuit we are simulating which I believe is an
accurate representation of the circuit I plan to build. Is that not
correct?

It's getting closer, but with adjustments (to the transformer inductance)
to make the resonances line up (same frequencies). Plus whatever
compromise you need to make on gain.

We are still having communications difficulties. You keep talking in
terms I can't relate to. I don't need you to write a book, but I do
need you to communicate clearly.

I am using a 1 bit ADC. Don't assume that I am doing what you have done
in the past.

--

Rick