The description of the operation of this thing always seems incomplete. From the Wikipedia article:

The length of the antenna and the dimensions of the cavity were engineered in order to make the re-broadcast signal a higher harmonic of the illuminating frequency.

That wouldn't actually work by itself. There would have to be some sort of non-linear element to cause the harmonics. Chances are there was something like a varactor in there. The original technical description probably omitted critical details because spooks are like that...