Three-frequency parametric amplification in magneto-inductive ring resonators

Parametric amplification of magneto-inductive (MI) waves propagating in magnetically coupled chains of nonlinear L–C resonators is studied. Analysis is first presented for a three-frequency travelling wave scheme in which the signal, idler and pump all propagate as MI waves. The effect of de-coupling the idlers is then considered and it is shown that this configuration relaxes the standard phase matching condition. Confirmation of the theory is provided using low-frequency PCB unit cells containing varactor diodes. The cells are characterised individually and then arranged as a 16-element ring resonator. Frequency matching and selective amplification of the primary resonance is demonstrated. The primary resonance can be excited using the field of a rotating magnetic dipole, and an application in magnetic resonance imaging is described.