Coupling between tuned circuits

[temujin]

Hello

I have two resonant circuits (tuned to the same frequency) that are magnetically coupled to each other via two coils placed parallel 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
t.

 

[Astronuc]

I believe one is referring to Mutual inductance, which occurs in addition to self-inductance. The mutual inductance will affect the frequencies of the two circuits.

Here some basic information - http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indmut.html

http://farside.ph.utexas.edu/teaching/302l/lectures/node84.html

http://www.pact.cpes.sussex.ac.uk/~edmundjc/EMG/Lecture17/emg17.pdf (save target as and then view)

Course notes in Finnish only - Problems [in English and Finnish] - http://www.ct.tkk.fi/courses/ca1/opetusmoniste.html

 

[Averagesupernova]

I suspect that overcoupling refers to the selectivity of a tuned circuit. Two inductors that are both part of a bandpass filter for instance can be too closely coupled resulting in a bandpass that is too wide.

 

[pervect]

http://www.webref.org/electronics/o/overcoupling.htm

The degree of coupling beyond the critical point in resonant circuits which produces a dip at the resonant-frequency point on the response curve.

This definition may be a little misleading, though, because if the coils are very tightly coupled, they become a broad-band transformer.

The mathematical model for a pair of coupled coils is

...V1...
\/I1...|
_______
Coil1Coil2
_______
/\I2 ...|
...V2...

V1 = L11 I1 + L12 I2
V2 = L21 I1 + L22 I2

L12 = L21

the coefficient of coupling is L12 = k*sqrt(L11*L22)

The rest is analyzing the problems in terms of differential equations. The problem of calculating the mutal inductance from geometry is hard enough that it's generally not attempted - it's easier to adjust experimentally.