In a homework exercise I need to sketch the Vout-vs-Vin graph, having it first obtained analytically. I know that Ur and Vin are both nonnegative, and the circuit is shown here:
It seems like there is a lot of symmetry in the circuit, and that this apparenntly complicated circuit can be broken down into a few smaller ones. All four of the op-amp stages resemble the classical logarithmic amplifier, however I feel that we can somehow bypass invoking the \$\ln\$ function in this analysis.
UPDATE: Here is an Lt-spice dc sweep graph I did for R=0.5k, and Ur=5V. Seems, like Q3 was at first saturated, then went off.