Does somebody know what the parts "D1" (top left) and "D2" (bottom left) are? I would expect them to be a special kind of diode, but I have never seen this symbol before in 10+ years of electronics.
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They look suspiciously like constant current diodes. These are devices usually made like JFETs but internally they have gate connected to source and produce a half-decent constant current. Here's the symbol: -
Picture from iconfinder. Sometimes this symbol is used: -
And Wikipedia has a nice article about them showing their relationship with a JFET: -

Andy aka
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Since there's no other path for current to flow, it seems obvious that these diodes are being used to linerize the charging rate of the two capacitors. Which, of course, would otherwise be non-linear.
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1That's unlikely. They regulate the Zener current. Why should the charging rate of the capacitor matter in the reference voltage section? – Marc Nov 07 '20 at 00:27