We wish to investigate the design of the inverter shown in

Chapter 13, Problem 13.24

(choose chapter or problem)

We wish to investigate the design of the inverter shown in Fig. 13.7(a). In particular, we wish to determine the value for R. Selection of a suitable value for R is determined by two considerations: propagation delay and power dissipation. (a) Show that if vI changes instantaneously from high to low and assuming that the switch opens instantaneously, the output voltage obtained across a load capacitance C will be where Hence show that the time required for vO(t) to reach the 50% point, is tPLH = 0.69CR (b) Following a steady state, if vI goes high and assuming that the switch closes immediately and has the equivalent circuit in Fig. 13.7(c), show that the output falls exponentially according towhere . Hence show that the time for vO(t) to reach the 50% point is tPHL = 0.69CRon (c) Use the results of (a) and (b) to obtain the inverter propagation delay, defined as the average of tPLH and tPHL as(d) Show that for an inverter that spends half the time in the 0-state and half the time in the 1-state, the average static power dissipation is(e) Now that the trade-offs in selecting R should be clear, show that, for VDD = 5 V and C = 10 pF, to obtain a propagation delay no greater than 10 ns and a power dissipation no greater than 10 mW, R should be in a specific range. Find that range and select an appropriate value for R. Then determine the resulting values of tP and P.