On 10/20/2015 10:41 AM, amdx wrote:
On 10/20/2015 3:03 AM, rickman wrote:
On 10/19/2015 7:55 PM, amdx wrote:
On 10/19/2015 2:14 PM, rickman wrote:

To be a bit simplistic, the amount of signal captured is proportional
to the loop area; the number of turns has little to no effect on that.

I'm pretty sure that is not correct. The signal strength is
proportional to the number of turns *and* the loop area. I will
have to
dig out my notes on this, but some factors (like Q) even out with
various changes in antenna parameters such as number of turns, loop
size, etc. But signal strength is proportional to the area of the loop
and the number of turns.

From
http://www.lz1aq.signacor.com/docs/f..._loop_engl.htm


E = 2pi w S µR e / λ
λ is the wavelength in meters
w - the number of ML turns;
S – is the area of the windings in m2;
μR is the effective magnetic permeability of the ferrite rod SML.
μR is
always less than the permeability of the material used and depends from
the size, geometry and the way the windings are constructed. μR = 1 for
aerial loops.

The product:
А = w μR S (3)
is called effective area of the SML.


Correct me if I'm wrong,
A 1 meter square loop with 5 turns would equal 5 square meters.
A = 5 sq. meters.

A 2.23 meter x 2.23 meter 1 turn loop would equal 5 square meters.
A = 5 sq. meters.

A 5 meter x 5 meter 1 turn loop with a series inductor would equal 25
sq. meters.
A = 25 Sq. meters.

A 5 times increase in A (S) means about a 7db increase in signal
strength. (minus losses caused by series inductor)

Does that all seem right?

I forgot to include the following definitions.
Е – is the voltage between antenna terminals in uV;
е – is the intensity of electromagnetic wave in uV/m.

Not sure where you are going with this. For the purpose of calculating
the received signal strength of an antenna without factoring in
resonance, the area is just the area of one loop (S = pi r^2), not the
loop area times the number of turns. The number of turns (w) is
multiplied by the loop area in the formula along with the relative
permeability of the core material to get the effective area. Is that
what you mean?

Yes. I was getting at the point, a loop single turn loop of 2.23
meters square will have the same E as a 1 meter square loop with 5 turns.
Just some idea to consider when it comes to construction.

Un-resonated E is not the only issue and often the size of the loop is
limited because of the application. There are many tradeoffs involved
in a receiving loop. Here are some shorthands that may help in seeing
the issues. The starting point of L being proportional to r rather than
rln(r) or the complex details of the inductance formula, which is an
approximation I don't believe affects the results too much.

L ∝ r * N² (if you see a funny symbol after the N, it's N squared)

l ∝ r * N (that's wire length, not inductance)

R ∝ l (resistance rather than radius)

Q ∝ N (this is important to the result)

E ∝ r² * N * Q

E ∝ r² * N²

E ∝ l²

Once you take Q into account, the voltage from an antenna is primarily a
function of the length of wire used rather than the other details. Of
course the initial approximation has some impact on the results, but
this points out that most of the issues involved in trading off size for
turns is icing on the cake rather than the steak and potatoes. How do
you like that metaphor?

If you are Q limited (too much Q can narrow the bandwidth too much) then
the above relations don't apply and E ∝ the total area or r² * N as you
wrote.

Making the inductance more accurate using

L ∝ r * ln(r) * N² gives

Q ∝ ln(r) * N

E ∝ r² * N * Q

E ∝ r² * ln(r) * N²

E ∝ l² * ln(r)

So a larger loop will give some better performance than more turns, but
not hugely so. In the end convenience and practicality will have to
limit the size of the loop with little degradation to performance. I
just added this and have not reviewed it extensively, so please correct
me if I've made an error.


The post that Jim made explicitly stated, "the number of
turns has little to no effect on that", with "that" meaning "the amount
of signal captured", or E in the above formula. That is the point I was
correcting.

For equal capture area, a single turn loop uses less than 1/2 the wire
of a 5 turn loop. However you do lose inductance.

That is a *key* factor since Q is usually involved.


So why do you feel the need to include a series inductor with the 25 m^2
1 turn loop?


My thoughts are for a AMBCB loop, generally a 240uH loop and a 365pf
cap. So I need the extra inductance to resonate it in the AM broadcast
Band.

You added the inductor for the 25 Sq. meters loop, but not the 5 sq.
meters loops. That is my point. They would all need the inductor I
think, no? Why not more turns to raise the inductance?


If you want to exercise some of the math for this, try the page here and
tell me if the example about half way down the page was done correctly.
I get a different value for the radiation resistance and I'm pretty
sure the skin effect was not done correctly for the AC resistance.

http://sidstation.loudet.org/antenna-theory-en.xhtml

I'm a good constructor, but as much as I'd like to, I can't help you
with the math.

I'm not looking for help, I'm pointing out an error in a web page. I
don't like trusting any one resource. Heck, I've seen errors propagated
across many web sites before as one borrows from another without
checking. That's largely why I'm here and in a number of Yahoo groups.
I want to get the straight skinny on things before I build mine. I'm
in no hurry to get things built. Measure twice (or twenty times) and
cut once.

The Yahoo groups are more oriented to transmitting loops which is also
very interesting. Seems to be a lot of experience, but sometimes
lacking in true understanding. Not sure which is more important, I'm
still short on both, lol.

--

Rick