Would introducing a magnetic amplifier to a wireless power transmission system made of two lc circuits increase efficiency?
Would the diode system shown on the website also increase efficiency?
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There's a better explanation about magnetic amplifiers on Wikipedia.
These work by the principle that if you saturate the core of a transformer signal variations can be amplified.
For wireless power transmission you actually want optimum coupling between primary and secundary side of the transformer. Anything reducing that or making the power transfer less efficient should be avoided.
This includes saturating the core(s) because then the magnetic energy is lost.
So what is shown on the website in your link would actually decrease the efficiency of the power transfer.
The diodes are used as rectifiers, converting AC into DC and this always decreases efficiency.
The website in your link is more focused on signal amplification and as such no conclusions can be drawn from that in relation to wireless power transfer.