Bandgap
Figure   3
Figure 4   The current mirror formed by the pnp transistor
with two collectors is equivalent to a current mirror formed using
two separate transistors. Note that bases and emitters are connected.
In silicon this can be acomplished with pnp transistors
by having one base and one emitter
with two separate collectors.
This current mirror assures I1=I2.
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3.   For the circuit shown in Figure 3;
Use the transistors described in the Widlar current mirror problem.
Answer
For temperature stability the derivative of Vbg with respect to T should be zero.
The current in R is 2I.
The bandgap voltage, Vbg, is the drop across R plus Vbe2.
The output voltage Vo is related to Vbg by the voltage divider rule.