Banba's Bandgap Voltage Reference

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Hello!

This is Banba's bandgap voltage reference problem from Razavi Design of Analog CMOS Integrated Circuits 2nd edition book page 538:

Suppose (W/L)3 = K(W/L)4 in Fig. 12.32(c). How should R2 and R3 be chosen?

I suppose that R2 = KR3 since the M3 has larger aspect ratio (K). This is to balance the currents and maintain the nodal voltages equal. Am I correct? Thanks in advance.
 

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X and Y are equal to Vbe and R3 and R4 are there to make sure the emitter currents of the two bipolar transistors are the same or scaled by their areas. Having this in mind, you can figure out what the resistors have to be if you scale the PMOS currents.
 

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I agree with sutapanaki. R3 should equal R4 and (W/L)3= (W/L)4. The value of R3 (R4) depends on the chosen current (VEB/R3).
 

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Well, let me give a different point of view. The current in R2 summed with the current in R1 form the temperature independent quantity that will be use to produce the bandgap voltage across R4. So, choosing the currents in R1 and R2 is the primary task. Then once the current through R2 is known, the current through R3 is easily chosen.
 

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