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# Lecture19

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• 1. Design and Implementation of VLSI Systems (EN01600) Lecture 19: Combinational Circuit Design (1/3)S. Reda EN160 SP’08
• 2. Circuit Families 1. Static CMOS 2. Ratioed Circuits 3. Cascode Voltage Switch Logic 4. Dynamic Circuits 5. Pass-transistor CircuitsS. Reda EN160 SP’08
• 3. 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 Y D (c) (d)S. Reda EN160 SP’08
• 4. Compound gates • Logical Effort of compound gatesS. Reda EN160 SP’08
• 5. Input ordering delay effect – Calculate parasitic delay for Y falling • If A arrives latest? 2τ • If B arrives latest? 2.33τ 2 2 Y A 2 6C B 2x 2C  If input arrival time is known –Connect latest input to inner terminalS. Reda EN160 SP’08
• 6. 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 upS. Reda EN160 SP’08
• 7. Symmetric gates • Inputs can be made perfectly symmetric 2 2 Y A 1 1 B 1 1S. Reda EN160 SP’08
• 8. 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 = 5/3S. Reda EN160 SP’08
• 9. 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 directionS. Reda EN160 SP’08
• 10. Catalog of skewed gatesS. Reda EN160 SP’08
• 11. What is the P/N ratio that gives the least delay? • We have selected P/N ratio for unit rise and fall resistance (µ = 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 areaS. Reda EN160 SP’08
• 12. 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