Linearity and input differential range of amp?

[JackyH]

For a differntial amplifier, or just an op-amp as an example, the relations between some parameters are not very clear to me.

What is the relation between its linearity and input differential range?

When the linearity better, is the input differential range also definitely larger? further the distortion is less? the gain is less?

 

[saro_k_82]

Linearity requires that the gain be independent of the input voltage
Input differential range spec is taken from observing for how large an input, the input devices are maintained in saturation., Isn't it easy to see that if this range is large, the gain will be independent of input voltage?