Ok, there's no antenna matching or any refinement, just leaving a single LC filter to tune the receiver. Such selectivity there is comes from making this LC as high Q as possible: nice big air-core coil and air capacitor.
Now, in the interests of miniaturizing and "modernizing" the design, I found this, by Karl Nagy:
The component V replaces the air capacitor, so lowering the Q of the tuned circuit by introducing R2 to apply capacitance-reducing volts to V. And ah! yes, there is an extra switchable capacitor in parallel with V, so as to give enough capacitance range to tune the whole AM broadcast band. -Or one could just have a single 500pF air capacitor and thus better selectivity and ease of operation? Yes, the varactor could make it small, even allow for two together to give a larger capacitance range?
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