If the current gain provided by a given BJT is not suffi cient for the application at hand, we can follow it by another BJT to further amplify the current already amplifi ed by the fi rst BJT. This is...

If the current gain provided by a given BJT is not suffi cient for the application at hand, we can follow it by another BJT to further amplify the current already amplifi ed by the fi rst BJT. This is similar to following the lens of a telescope by a second lens to increase the overall magnifying power. The resulting two-transistor team, known as the Darlington confi guration, fi nds application especially in power-handling circuits. Figure P2.9 illustrates the Darlington concept for the case of npn BJTs (the pnp case is shown in Fig. P2.10). The current iI enters Q1’s base and exits Q1’s emitter amplifi ed by (F1 1 1). This current is then fed to Q2’s base, and exits Q2’s emitter amplifi ed by (F2 1 1). The overall current gain is thus iOyiI 5 (F1 1 1) 3 (F2 1 1) > F1 3 F2, or F 2 when the BJTs have identical betas. Assume RL 5 8 V and VS 5 24 V, and let the BJTs have, respectively, Is1 5 10 fA and F1 5 100, Is2 5 1 pA and F2 5 50. Using vBE1 5 VT ln (iC1yIs1) for Q1, and vBE2 5 VT ln (iC2yIs2) for Q2, with iC > iE and iB 5 iEy(F 1 1) for both BJTs, fi nd the input current iI as well as the input voltage vI (accurate within 1 mV) needed to achieve: (a) vO 5 1 V, (b) vO 5 4 V, (c) vO 5 16 V. Hint: use the rules of thumb to speed up your calculations.