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Lecture 5 Static CMOS Gates Jack Ou, Ph.D.

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2-Input NOR Gate F can only be pulled up if A=B=0 V F can be pulled down by either A=1 or B=1. (Or Both)

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2-Input NAND Gate F can only be pulled down if both A=B=1. F will be pulled up if either A or B is 0 V.

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NAND Gates

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NOR Gates

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2-Input AND Gate NAND

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2-Input OR Gate NOR

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Alternative Implementation for High Fanin Gates

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Steps for Generating Non-Trivial Static CMOS Logic Circuits

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DeMorgans Theorem

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Dual The dual of any logic function can be obtained by exchanging the AND and OR operations. – ab a+b – (a+b)c ab+c

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A fictional AND Circuit The current flows only when both A and B are closed.

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Fictional OR Circuit The current flows when either A or B is closed.

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Implementation Use transistors in series to implement a logical AND function Use transistors in parallel to implement a logical OR function

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XOR/XNOR

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Mux

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Determine a Boolean Expression a Schematic

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2-Input XOR XNOR

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CMOS Gate Sizing

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Device Sizing Obtain the same delay as the inverter for the rise/fall cases. – R effN =12.5 Kohm/SQ, R effP =30 Kohm/SQ – R eff =R eff (L/W) – R effP /R effN =2.4 – To achieve the same delay, (assume L P =L N, W P =2.4W N, W P /W N is approximately 2.

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Size Devices for the Worst Case Series transistors: Increase W to reduce R eff. Parallel transistors: assume the worst case, i.e. only one of the parallel transistor is ON.

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Transistor Sizing Without Velocity Saturation Figure 5.2 Assumption: Equal rise delay and fall delay Consideration: Effective Resistance

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Inverter

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Inverter t PHL tPHL= pS

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NAND2 Test Circuit

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NAND2 t PHL tPHL=66.01 pS

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Effective Width Transistors in Series – W1||W2||W3 Transistors in Parallel – W+W2+W3

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Trade-Off Increase W to reduce the effective Resistance for the pull down network. The area is increased.

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FO4 Fanout ratio: total capacitance driven by a gate dividing by its input capacitance

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VTC of Gates

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Adjust V S Knob: – χ as defined in EQ – Increase W N L P /L N W P to decreased V S. – Decrease W N L P /L N W P to increased V S.

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Switching Voltage of a NAND Gate Both inputs tied together: effective W N =W, W P =4W, VS shifts to the right. Both input A=high, sweep VB: effective W N =2W, W P =2W, VS shifts to the left.

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Switching Voltage of a NOR Gate Both inputs tied together: effective W N =2W, W P =2W, VS shifts to the left. Both input A=ground, sweep VB: effective W N =W, W P =4W, VS shifts to the right.

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