On 11/6/2014 9:48 AM, Wimpie wrote:
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:

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.

It is not "my" correction factor, it is Lundin's. It is based on the
ratio of loop diameter to coil length and the formula I used applies for
diameters larger than the coil length. Here is the note in my spread
sheet...
Lundin's Formula for 2ab, Proc IEEE, Vol 73, No. 9, Sept 1985
If you google it I'm sure you can dig up all sorts of references.

Of all the many inductance formulas I found none used the area rather
than coil radius (not squared). Here is one for a single loop from
http://www.ece.mcmaster.ca/faculty/n...s/L12_Loop.pdf

The inductance of a single circular loop of radius a made of wire of
radius b is
L = μ a (ln(8a/b)-2)

Notice the 'a' factor (loop radius) is not squared.

When I did my research, Lundin's formula appeared to be the one that
gave the best results over the largest range of coil diameter to length.
It was also fairly simple to program in a spreadsheet. There is even
one web page I found that discusses some of the attempts to do better
which actually failed for various reasons. I found this very interesting.
http://www.g3ynh.info/zdocs/magnetics/part_2.html


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).

I have found most of those although more when looking for inductance
formula rather than Q formula.


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.

Ok, that is what I expected. Still, I want to add radiation resistance
to my simulation just for completeness. It shouldn't be hard. It is
just a bit more math to type in.

If I get a Q of 10,000 (10k) I don't think the design would be usable.
A degree or two of temperature drift and it would be out of tune. I
would like to see a Q of over 100 though.

--

Rick