Consider the circuit in Fig. P7.17. a. A start-up circuit is needed for the bias circuit. What are the startup node voltages that will cause the circuit not to startup properly? b. Find an expression...

Consider the circuit in Fig. P7.17.

a. A start-up circuit is needed for the bias circuit. What are the startup node voltages that will cause the circuit not to startup properly?

b. Find an expression for in terms of the circuit parameters. Under what conditions is a bandgap reference? You may assume infinite for the MOSFETs in active mode and no mismatch.

c. Select values for , , and to make this circuit a bandgap reference, assuming of the large BJTs has a temperature coefficient of -2 mV/K.

d. If the threshold voltages of the two NMOS devices differ by , give an expression for in terms of .