Reading up on the various building blocks of bjt circuits (long tailed pair, current mirror, exponential converter) I always end up in places that discuss the principles and then throw up their hands going "but why even bother with discrete, the matching is too hard!" without actually discussing what these apparently horrible consequences of unmatched transistors are.
Now since I'm doing DIYish stuff I'm probably ok with more trimming and component picking than one would be in an industrial setting. The question is, what should I match and or trim for?
For most of the above mentioned we mainly care about Vbe matching which is maybe a bit of a misnomer anyway since Vbe isn't an inherent property of the transistor. Assuming the Ebers Moll model, my understanding is that by "matching Vbe" we are actually matching Ies which acts as a scale factor on the exponential relationship between Vbe and Ie.
So how does a Ies mismatch affect the aforementioned building blocks? From what I found so far:
- Current mirror: instead of Ia = Ib we get Ia = C*Ib where the constant C is a function of the mismatch. So as long as I don't care for the mirroring to be exact but merely proportional that may be ok.
Long tailed pair: The mismatch causes an input offset, which at high amplification (without feedback) may cause a significant output offset. If we are using feedback of some form such as when building a discrete opamp only the input offset is really an issue though.
Exponential converter: Instead of Iout = Iin*exp(Vbe/Vt) we get Iout = C*Iin*exp(Vbe/Vt) where C= Ies1/Ies2 so again just a scaler in front of the exponential law