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Design and Implementation of VLSI Systems (EN01600) Lecture 19: Combinational Circuit Design (1/3) Prof. Sherief Reda Division of Engineering, Brown University Spring 2008 [sources: Weste/Addison Wesley – Rabaey/Pearson] S. Reda EN160 SP’08 Circuit Families 1. Static CMOS 2. Ratioed Circuits 3. Cascode Voltage Switch Logic 4. Dynamic Circuits 5. Pass-transistor Circuits S. Reda EN160 SP’08 1. Static CMOS • Start with network of AND / OR gates • Convert to NAND / NOR + inverters • Push bubbles around to simplify logic – Remember DeMorgan’s Law Y Y (a) (b) Y (c) D S. Reda EN160 SP’08 Y (d) Compound gates • Logical Effort of compound gates S. Reda EN160 SP’08 Input ordering delay effect – 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 If input arrival time is known –Connect latest input to inner terminal S. Reda EN160 SP’08 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) – Boost size of noncritical input – So total resistance is same • • • • • gA = 10/9 gB = 2 gavg = (gA + gB)/2 = 14/9 Asymmetric gate approaches g = 1 on critical input But total logical effort goes up S. Reda EN160 SP’08 Symmetric gates • Inputs can be made perfectly symmetric S. Reda EN160 SP’08 2 2 A 1 1 B 1 1 Y Skewed gates • Skewed gates favor one transition over another • Ex: suppose rising output of inverter is most critical – Downsize noncritical nMOS transistor • Calculate logical effort by comparing to unskewed inverter with same effective resistance on that edge. – gu = 2.5 / 3 = 5/6 – gd = 2.5 / 1.5 = 5/3 S. Reda EN160 SP’08 Hi- and Lo-Skew • Definition: Logical effort of a skewed gate for a particular transition is the ratio of the input capacitance of the skewed gate to the input capacitance of an unskewed inverter with equal drive 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 S. Reda EN160 SP’08 Catalog of skewed gates S. Reda EN160 SP’08 What is the P/N ratio that gives the least delay? • We have selected P/N ratio for unit rise and fall resistance (m = 2-3 for an inverter). • Alternative: choose ratio for least average delay • By sacrificing rise delay, pMOS transistors can be downsized to reduced input capacitance, average delay, and total area S. Reda EN160 SP’08 Beware of PMOS B 4 A 4 Y 1 1 • pMOS is the enemy! – High input and diffusion capacitance for a given current • Can we take the pMOS capacitance off the input? – Various circuit families try to do this… S. Reda EN160 SP’08