Posted to two newsgroups known to be read by likely respondents ;)
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 here:
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