In this problem we investigate the effect of the selection of the ratio Wp/Wn on the

Chapter 14, Problem 14.55

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In this problem we investigate the effect of the selection of the ratio Wp/Wn on the propagation delay of an inverter driving an identical inverter, as in Fig. 14.32. Assume all transistors have the same L. (a) Noting that except for Cw each of the capacitances in Eqs. (14.58) and (14.59) is proportional to the width of the relevant transistor, show that C can be expressed as C = Cn 1+ Wp Wn +Cw where Cn is determined by the NMOS transistors. (b) Using the equivalent resistances RN and RP, show that for (W/L)n = 1, tPHL = 8.625103 C tPLH = 20.7103 Wp/Wn C (c) Use the results of (a) and (b) to determine tP in the case Wp = Wn, in terms of Cn and Cw. (d) Use the results of (a) and (b) to determine tP in the matched case: that is, when Wp/Wn is selected to yield tPHL = tPLH . (e) Compare the tP values in (c) and (d) for the two extreme cases: (i) Cw = 0 (ii) Cw Cn What do you conclude about the selection of Wp/Wn?