Coupling between tuned circuits 3

[doneirik]

Hello

I have two resonant circuits (tuned to the same frequency) that are magnetically coupled to each other via two coils placed paralell to each other. (energy and data is transferred from one circuit to another)

Now, I know that the coupling between the two can be overcoupled, undercoupled or critically coupled, and that maximum powetransfer occurrs as the circuits are critically coupled.

If I have understood correctly, the coupling type is determined exclusively by geometrical factors, i.e. distance between the two coils and their orientation and size with respect to each other. For two paralell, fixed sized coils, there should therefore be an optimal distance between the coils that gives two critically coupled circuits.

I am not sure how to calculte this distance. Do anyone have a tip or maybe a link to some good material on this subject.

regards
donE

 

[VEBill]

This topic is often covered in the ARRL (amateur radio) Handbook. Also, RSGB might have something as well.

There's likely something on the

http://www as

well. If I find anything, I'll post it.

 

[fsmyth]

0.12443" +/- 0.002" <big smiley>

Seriously, there is not a single distance for all cases.
Since maximum gain at resonance (critical coupling) occurs
when kQ = 1, and k = M/(L1L2)e-2 = X/(AB)e-2, where
k=coefficient of coupling,
M=mutual coupling,
X=coupling reactance at resonant frequency (fo)
A=reactance of first circuit (at fo)
B=reactance of similar element of second circuit (at fo),
it follows that there will be an optimum distance determined
by the frequency and coil loading, largely affected by the
selectivity desired, along with the coupling medium.
I've only dealt with this to any extent in tuned R.F.
circuits, usually with relatively high Q on both sides.

Liz gives a pretty good treatment:

http://www.du.edu/~etuttle/electron/elect34.htm

Another from a slightly different angle:

http://www.frontiernet.net/~jadale/Loop.htm

If you are talking about air-cores, surf around the
Tesla coil sites; they absolutely have to deal with
proper distances.


<als>

 

[Warpspeed]

It very much depends on the Q of each of the tuned circuits. Very high Q circuits will require less relative coupling to become over coupled.

I doubt very much if it can be worked out easily from first principles, but a simple practical test will soon tell you where you are as far as coupling coefficient goes.

 

[itsmoked]

Excuse me, but what the heck is over coupling? It would seem to me that one could have total coupling or something less but "over" coupling?

 

[Warpspeed]

No it can be overcoupled, that is the correct term.

Critical coupling is where you get maximum energy transfer between two resonant tuned circuits tuned to EXACTLY the same frequency, but the circuit still peaks at the one exact same centre frequency.

Increasing the coupling even more (overcoupling) will then create a double hump in the frequency domain. It is the classical way to build a bandpass filter with a reasonably flat passband and steep skirts.

 

[itsmoked]

Okay so it isn't really better or worse coupling but rather beter or worse coupled system Q?

 

[fsmyth]

The terms 'better' or 'worse' don't really apply.
Use 'more' or 'less', or 'tight' and 'loose'.
The tighter the coupling, the more each side of the
circuit affects the other (i.e., more 'mutual' coupling).
If you have a stiff signal source, you can tolerate a
tighter coupling. The overall Q is the square root of
the product of the Q on each side, and is equal to
2 times the freq. delta divided by the center freq.
(i.e., the bandwidth divided by the center freq.).
Selectivity depends on the amount of coupling.
There can be more than 2 coupled circuits.

These are just general points; one book I have takes
2 pages just to set circuit conditions, followed by
4 pages of exceptions, followed by 3 pages of formulae,
followed by 6 pages of graphs,..... and that is just
on selectivity. Phase relationships have their own chapter.
This is really hard to explain without LaTeX.

<als>

 

[fsmyth]

Here, try this:

http://home.hetnet.nl/~dick-kleijer/enkoppelfactor.htm

If you want to know more, use his index.
<als>

 

[fsmyth]

Even better; here he has scope capture pics showing the
effects of varied coupling:

http://home.hetnet.nl/~dick-kleijer/en2kringtest.htm

<als>

 

[itsmoked]

Thanks warp.
And
Thanks fsmyth! Now I get it. Nice clear links those.

 

[nbucska]

If not aircore, the core geometry is most critical

For several types of filters with odd number of tuned
circuits often the paired TC-s are coupled over-crytically
giving 2 humps, which is corrected to flat by the odd TC.


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