Re: BGR
Hi,
By equating Vo1 and Vo2 you impress the difference in VBEs (which is a PTAT...Proportional to Absolute temperature) across that resistor which forces the currents to be PTAT,. which you need to generate a PTAT voltage to sum with CTAT voltage inorder to get BGR.
Without the resistor, you need to amplify the difference (Vo1-Vo2) (You can't have an amp to equate them) which is not going to be simple (Not advisable to load the circuit). The major thing to worry about will be the stability of such a loop.
The currents in the two arms won't be equal because of channel-length modulation and PSRR will be poor., but this is only a slight disadvantage.