Transcript Slide 1
Final Exam Review 1 word0 is high if A2 A1 A0 = 000 logical effort of each input is (1+3.5)/3 per wordline output word7 is high if A2 A1 A0 = 111 2 Skewed gates HI-skew gu = 2.5/3 = 5/6 gd = 2.5/1.5 = 5/3 gavg = 5/4 p = 2.5/3 = 5/6 3 LO-skew gu = 2/1.5 = 4/3 (unskewed inverter with equal rise time pMOS size 1, nMOS size 0.5 gd = 2/3 (unskewed inverter with equal fall time pMOS size 2, nMOS size 1 4 HI- and LO-Skew • Def: Logical effort of a skewed gate for a particular transition is the ratio of the input capacitance of that gate to the input capacitance of an unskewed inverter delivering the same output current for the same transition. • Skewed gates reduce size of noncritical transistors – HI-skew gates favor rising output (small nMOS) – LO-skew gates favor falling output (small pMOS) • Logical effort is smaller for favored direction • But larger for the other direction 5 Asymmetric Gates • Asymmetric gates favor one input over another • Ex: suppose input A of a NAND gate is most critical – Use smaller transistor on A (less capacitance) A – Boost size of noncritical input reset – So total resistance is same • gA = 10/9 2 2 Y A 4/3 • gB = 2 4 reset • gtotal = gA + gB = 28/9 • Asymmetric gate approaches g = 1 on critical input • But total logical effort goes up Y 6 Input Order • Our parasitic delay model was too simple – Calculate parasitic delay for Y falling • If A arrives latest? 2t • If B arrives latest? 2.33t 2 2 A 2 B 2x Y 6C 2C 7 a unit CMOS inverter delivers current I in both rising and falling transitions Pseudo-nMOS inverter: pMOS delivers I/3; nMOS delivers 4I/3 (net pull down current is 4I/3 – I/3 = I logical effort gd = (4/3)/3 = 4/9 parasitic delay pd = (6/3)/3 = 6/9 logical effort gu = gd x 1/3 = 4/3 parasitic delay pu = pd x 3 = 18/9 ( only I/3) 8 9 10 4-input NAND unfooted + Hi INV g = 4/3; g = 5/6 G = 20/18=10/9 p = 5/3; 4-input NAND footed + Hi INV g = 5/3; g=5/6 G = (5/3)(5/6) = 25/18 p = 2.5/3 = 5/6 p = 6/3 p = 5/6 P = 6/3 + 5/6 = 17/6 11 8-input footed domino AND gate For H > 2.9 4-stage is better electrical effort 12 Chapter 1: Chapter 2: Chapter 3: Chapter 4: Chapter 6: Chapter 7: Chapter 11: Flash Memory 13