Martin,
?
When you have been experimenting with pairs of tuned loops at close spacing the degree of magnetic coupling K between them rouglhly? 0.75 or higher which means that
two resonant circuits form a common resonance frequency.
If we change the strength of magnetic coupling we can change the frequency of the common resonance frequency.
In adition to that common lower frequency f1 a second higher resonance frequency f2 is formed as well. This is clearly visible in simulation and also in the impedance measurement. At frequency f2 the currents in both loops flow in push-pull.
The lower frequency: f1= 1/2x pi x sqrt ((La+Lm) x C), where Lm=kxLa - mutual inductance?
Let's assume K=1, then Lm=L? and? f1= 1/2 pi sqrt 2Lx C?
For uncoupled loop: f0= 1/2 pi sqrt La x C, then? f1= f0/sqrt 2 showing how much the frequency can be lowered vs. uncoupled loop with resonant frequency f0.
Also a second effect comes into play - additional capacitive coupling ( mutual capacity ) between loops.
Thus, the common frequency: f1= 1/2x pi x sqrt ((La+Lm)x(C-Cm)), where Cm - mutual capacitance
If we bring two tuned loops closer together Lm and Cm increase equally. So, in practice f1 will change lesser than calculated 1/sqrt2.
The behaviour of two tuned loops corresponds largerly to behaviour of dual-circuit band filter.
To observe critical coupling in MLA, the two tuned loops would have to be several meters apart, starting to see two humps in the frequency characteristics.
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Raphael
