Jim said:

I think it takes you into "Lambert W" land.

So I have another educational experience to look forward to.

Did you not note that the extra differential pair I added is pure

linear, because of the feedback from the emitters.

In Mathcad I'd sum TANH + linear with various weightings until I

achieved "optimum", whatever that might be, since it's really just

your choice.

I have little problem setting up a figure of merit for the fit I want,

so that Mathcad can search for the optimization I want, once I have an

expression or even an implicit description of the functions involved.

I have already done quite a few different optimizations for two tanh

functions (both in parallel and in series) and also in parallel with a

linear gain. I also looked into adding positive feedback around one

or both tanh functions. (That makes my curve fit considerably better,

if I could put up with the tolerance exaggerations. I had a Duh!

moment when I realized that if negative feedback improves linearity,

positive feedback enhances nonlinearity.) So I have a pretty good idea

what I can do with those cases.

Now I want to explore how adding emitter resistors to one or both

differential pairs alters the optimizations. (My hunch is that one

tanh function will be best with nonlinear enhancement [positive

feedback] and one will be best with some linear enhancement and input

range expansion [emitter degeneration]. But I am having difficulty

producing an expression for this transfer function.

I am pretty sure I once knew how to do this. But I am having a senior

moment about it, now.