(a) Using the relationship VD 5 VT ln(IDyIs ), show that the circuit of Fig. P1.51 yields VPTAT 5 KT, where K is a temperature-independent proportionality constant, and obtain an expression for K in...

(a) Using the relationship VD 5 VT ln(IDyIs ), show that the circuit of Fig. P1.51 yields VPTAT 5 KT, where K is a temperature-independent proportionality constant, and obtain an expression for K in terms of the diodes’ saturation currents Is1 and Is2 and bias currents I1 and I2. Assume n 5 1. The voltage VPTAT is proportional to absolute temperature (PTAT), and as such it is at the basis of digital thermometers and other temperature-related instrumentation. (b) Find the value of the proportionality constant K if I1 5 I2 5 100 A, and D2 has a junction area 10 times as large as that of D1 so that Is2 5 10Is1. (c) What happens if the bias currents of part (b) are inadvertently reduced to I1 5 I2 5 50 A? Will the value of VPTAT change? (d) Find the gain by which the voltage VPTAT of (b) needs to be amplifi ed if we want to synthesize the voltage V(T) 5 (10 mV/8C)T