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Design and Implementation of VLSI Systems
                  (EN0160)
 Lecture 17: Static Combinational Circuit Design (1/2)

                     Prof. Sherief Reda
         Division of Engineering, Brown University
                        Spring 2007




                [sources: Weste/Addison Wesley – Rabaey/Pearson]

S. Reda EN160
How to convert an AND/OR to a
  NAND/NOR network?
   Sketch a 2 by 1 multiplexer design using AND, OR, and
   NOT gates.

                   D0
                   S
                                       Y
                   D1
                   S




S. Reda EN160
Converting AND/OR networks to
  NAND/NOR networks
   • 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
Compound gates

    • Logical Effort of compound gates




S. Reda EN160
Delay calculation example

   • The multiplexer has a maximum input capacitance of
     16 units on each input. It must drive a load of 160
     units. Estimate the delay of the NAND and
     compound gate designs.

     D0                             D0
     S                              S
                           Y                          Y
     D1
                                    D1
     S                              S

                H = 160 / 16 = 10
                B=1
                N=2



S. Reda EN160
Solution: simple versus compound for the
  MUX case
      D0                        D0
      S
                                S
                         Y                              Y
      D1                        D1
      S                         S

   P = 2+2 = 4
                                     P = 4 +1 = 5
   G = (4 / 3)g / 3) = 16 / 9
               (4                    G = (6 / 3)g = 2
                                                 (1)
   F = GBH = 160 / 9                 F = GBH = 20
   ˆ
   f = N F = 4.2                     ˆ
                                     f = N F = 4.5
         ˆ
    D = Nf + P = 12.4τ                    ˆ
                                     D = Nf + P = 14τ

S. Reda EN160
Annotating design with transistor sizes

   • Annotate your designs with transistor sizes
     that achieve this delay.

           8    8
                8                            10        10
                8    25         25           10        10       24
                                      Y                              Y
                                25           6         6        12
           8    8               25           6         6
                8
                8
      16            160 * (4/3) / 4.2 = 50        16   160 * 1 / 4.5 = 36




S. Reda EN160
Parasitic modeling
   • Our parasitic delay model was too simple
       – 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 terminal

S. Reda EN160
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
  • gtotal = gA + gB = 28/9
  • Asymmetric gate approaches g = 1 on critical input
  • But total logical effort goes up


S. Reda EN160
Symmetric gates


    • Inputs can be made perfectly symmetric

                    2    2
                             Y
                A   1    1
                B   1    1




S. Reda EN160
Skewed gates
   • Skewed gates favor one edge 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
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



S. Reda EN160
Catalog of skewed gates




S. Reda EN160

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Lecture17

  • 1. Design and Implementation of VLSI Systems (EN0160) Lecture 17: Static Combinational Circuit Design (1/2) Prof. Sherief Reda Division of Engineering, Brown University Spring 2007 [sources: Weste/Addison Wesley – Rabaey/Pearson] S. Reda EN160
  • 2. How to convert an AND/OR to a NAND/NOR network? Sketch a 2 by 1 multiplexer design using AND, OR, and NOT gates. D0 S Y D1 S S. Reda EN160
  • 3. Converting AND/OR networks to NAND/NOR networks • 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
  • 4. Compound gates • Logical Effort of compound gates S. Reda EN160
  • 5. Delay calculation example • The multiplexer has a maximum input capacitance of 16 units on each input. It must drive a load of 160 units. Estimate the delay of the NAND and compound gate designs. D0 D0 S S Y Y D1 D1 S S H = 160 / 16 = 10 B=1 N=2 S. Reda EN160
  • 6. Solution: simple versus compound for the MUX case D0 D0 S S Y Y D1 D1 S S P = 2+2 = 4 P = 4 +1 = 5 G = (4 / 3)g / 3) = 16 / 9 (4 G = (6 / 3)g = 2 (1) F = GBH = 160 / 9 F = GBH = 20 ˆ f = N F = 4.2 ˆ f = N F = 4.5 ˆ D = Nf + P = 12.4τ ˆ D = Nf + P = 14τ S. Reda EN160
  • 7. Annotating design with transistor sizes • Annotate your designs with transistor sizes that achieve this delay. 8 8 8 10 10 8 25 25 10 10 24 Y Y 25 6 6 12 8 8 25 6 6 8 8 16 160 * (4/3) / 4.2 = 50 16 160 * 1 / 4.5 = 36 S. Reda EN160
  • 8. Parasitic modeling • Our parasitic delay model was too simple – 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 terminal S. Reda EN160
  • 9. 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 • gtotal = gA + gB = 28/9 • Asymmetric gate approaches g = 1 on critical input • But total logical effort goes up S. Reda EN160
  • 10. Symmetric gates • Inputs can be made perfectly symmetric 2 2 Y A 1 1 B 1 1 S. Reda EN160
  • 11. Skewed gates • Skewed gates favor one edge 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
  • 12. 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 S. Reda EN160
  • 13. Catalog of skewed gates S. Reda EN160