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The published literature on pre-solid-state electronic analog
multipliers is scant except for production equipment from
analog computer makers (which by now is difficult to locate).
One example of a useful technique is a four quadrant electron
beam multiplier described he

http://dspace.mit.edu/bitstream/1721...9-04734375.pdf

More exotic tubes with curved deflection geometries followed,
however obtaining such tubes is now difficult.

Has anyone at some point tried using sheet-beam deflection
tubes as were used in synchronous detectors and balanced
modulator designs for analog multiplication? I imagine
that using four tubes each driven by quadrant-limited
amplifiers and whose outputs would be biased and summed
with scaling may work within a few percent of input values
based on a quick look at the characteristic curves published
for these tubes. Another option would be to add a magnetic
deflection yoke over the tubes to provide a proportional
steering of the beam sheet in conjunction with the electro-
static deflection (one of the deflection circuits could be
placed in the negative feedback loop of an op-amp) to
reduce the number of tubes required to two (+/-x, y; +/-x, -y).

It wouldn't take long to breadboard a test circuit for
investigation, but knowing past efforts is always welcome.
Surely someone has evaluated using these tubes in this fashion,
even if just for kicks

Michael