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RF: active anti-resonance circuit

I am attempting to develop a circuit that would actively minimize the near-field coupling of a certain "black-box" load Z to an external antenna (outside our control) with an unknown and (slowly) time-varying frequency that varies between some given f(low) and f(high). Normally Z is powered through near-field coupling with this external antenna, but when we switch on the desired circuit, Z's power would become effectively minimized. We can assume Z has characteristic like 1.5k ohm resistance, 200 pF capacitance, and minimal inductance. Please assume physical shielding is not an option. The induced currents would be 20mA or less, but normally in the range of 0.5mA - 5mA. Also assume Z's operation will not be adversely affected by any overall change in impedance.

I've been imagining something like a parallel tunable LC circuit (ie, varicap) in series with the load acting as a tunable band-stop filter. The LC circuit's resonant frequency would need to be regularily and dynamically adjusted so as to match the external antenna's current frequency and minimize the current flow through the loop by showing very high impedance at that resonant frequency. But how would I go about varying the varicap accordingly to make current as close to zero as possible? A binary search to minimize rectified current? Or just try one capacitance step in both directions, take the directional step that reduces current, and continually repeat? What sort of implementation considerations are likely to arise? If anyone has any links or schematics to a similar project I'd be very grateful.

Or maybe someone has a wholly simpler way to do this. This is pre-implementation so I am open to any ideas.
 
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