Figure P1.52 shows an alternative realization of the VPTAT concept of Problem 1.51, and its advantage is that VPTAT is now referenced to ground instead of being the difference between two fl oating...

Figure P1.52 shows an alternative realization of the VPTAT concept of Problem 1.51, and its advantage is that VPTAT is now referenced to ground instead of being the difference between two fl oating node voltages. For the present circuit to function, we must have I1 . I2.

(a) Show that the circuit of yields VPTAT 5 KT, where K is a temperatureindependent proportionality constant, and obtain an expression for K in terms of the diodes’ saturation currents Is1 and Is2 and the bias currents I1 and I2. Assume n 5 1.

(b) Find the value of the proportionality constant K if I1 5 100 A, I2 5 20 A, and D1 and D2 are matched.

(c) Find the value of the proportionality constant K if I1 5 100 A, I2 5 50 A, and D2 has a junction area twice as large as that of D1.

(d) For the conditions of part (b), use an op amp to design a circuit that synthesizes the voltage VO(T) 5 (10 mV/8C)T.