Hello Danny
I think your maths is ok, but I will try to give you some brief explanations... Did you ever see the equivalent 'circuit diagram' of the OTA? It is not too complicated and shows the following basic stages:
Both inputs are the base-electrodes of a differential npn transistor pair. The sum of their emitter currents Ie1+Ie2 is fed by a common npn current mirror set by Iabc. With a current amplication of 1A/1A,
Ie1+1e2=Iabc!
-> Emitter-, collector- and base currents of the differential amp are all biased by Iabc.
The collector currents Ic1 and Ic2 are fed into two complementary current mirrors with a current amplication of 1A/1A. Their collectors are tied together and form the current driven output.
All in all, the OTA works similar to an ideal differential amp, where the output current equals the diffence of the collector currents of the input stage, which is an exponential function of the differential voltage between base1 - base2 of the input stage, multiplied by the sum Ie1 + Ie2 = Iabc. Without doing extended maths, it evident that
1) with Vbase1=Vbase2: Ic1=Ic2=Iabc/2 Iout=Ic2-Ic1=0 -> perfectly balanced
2) with Vbase1=Vbase2 +/- (>100mV) Ic1 = Iabc/0 Ic2 = 0/Iabc Iout= +/-Iabc -> 100% overdriven
As with any differential amp, rising the base1-base2 differential voltage beyond 100mV does not make any difference, as the whole Iabc is fed through one single input Transistor. Keep in mind that at that stage output CURRENT of the OTA is controlled in the linear region by an input VOLTAGE in the range of few 10 mVs.
On the other side, if you use the linearizing diodes parallell to the base-inputs, you shunt the inputs by the low impedance of a diode, which decreases linearly as diode bias current increases. Now the OTA is converted to an input current controlled current source!
Combined with the current limiting series resistors, it turns back to a voltage driven current source again.
Without linearization diodes, I recommend a differential voltage limitation done by to antiparallell 1n4148 or similar. This is a good practise that does not affect the transfer function anyway.
Using linearization diodes, there is no need for an input voltage limitation provided that the input is driven by some opa or similar with a restricted voltage drive capability: Match the current limiting input resistor to the diode biasing current and everything should run fine. So I agree to your first condition, the second one being adjusted by me.
Joe