Ferromagnetic materials have very high magnetic permeability, but
saturate at some point; in some cases, especially for extremely
ferromagnetic materials like the electrical steel used in
transformers, the transition is quite abrupt.

A major problem in the historical development of radio was the
"detector": some way of converting the high-frequency AC signal of the
detected radio wave into a DC or low-frequency signal that could be
used, for example, to activate a solenoid.  This was eventually solved
by the development of the vacuum-tube diode and later the
semiconductor junction diode, but before that, there were a number of
Rube Goldberg contraptions, some of which remained in use for a long
time in special circumstances: the "coherer", which sintered metal
particles together with the RF energy and then measured the DC
resistance of the result; the "cat's-whisker detector", a delicate
Schottky diode made with a point contact between a finely-pointed wire
and a crystal of a semiconductor such as galena, iron pyrite,
carborundum, or even the iron oxide on a razor blade of a "foxhole
radio"; Marconi's "magnetic detector", which used the nonlinear
hysteresis behavior of moving iron wire to convert an RF magnetic
field into a tiny DC voltage; and Fessenden's "electrolytic detector",
which used the electrolytic formation of a layer of bubbles on a fine
platinum wire electrode to preferentially impede current in one
direction.  Somewhat related is the "mercury-vapor rectifier", which
uses the enormous difference in work function between mercury and
graphite to conduct in only one direction.

It occurs to me that the saturation transition in low-hysteresis
electrical steel could be used to form a detector for frequencies up
to some limit, as follows.  You bias the primary winding of an
iron-core transformer almost to saturation with DC, then superimpose
the AC signal on it.  The part of the AC signal opposing the DC bias
will dip into the high-permeability region and will therefore see
strong inductive effects --- a high impedance, either inductive (in
the case of an open-circuit secondary winding) or resistive (in the
case of a dummy load connected across the secondary).  The part of the
AC signal in concert with the DC bias will experience much smaller
inductive effects, perhaps two orders of magnitude less.

This should give you an entirely-solid-state "detector" that works
without any semiconductors or vacuums.

I think this device is limited in frequency only by hysteresis and
eddy-current losses, which increase linearly with frequency.  In this
application, though, much larger losses are acceptable than in the
usual applications of transformers: a 1%-efficient detector is still
usable.  Wikipedia tells me that laminated-steel transformers with
especially thin laminations are still sometimes used at 10kHz, so I am
guessing that this detector should work usably with a steel core up to
some 100kHz, and with ferrite or powdered iron, up to 1GHz.

You should be able to substitute a permanent magnet for the DC bias,
eliminating the need for a power supply.
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