Integrated Circuits & Systems

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1 Federal University of Santa Catarina Center for Technology Computer Science & Electronics Engineering Integrated Circuits & Systems INE 5442 Lecture 16 CMOS Combinational Circuits - 2

2 Switch Delay Models for Complementary Gates NAND2 INV NOR2 A R p B R p A R p B R p A R n C L R n A C L A R p C int B R n C int R n A R n B C L Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.2

3 Complementary Logic Dynamic Behavior 4-input NAND R 5 R 6 R 7 A B C D R 8 A B C D R 4 A C L A B C 3 C L R 3 B C 3 C C 2 R 2 C 2 D C 1 C R 1 D C 1 Slide 16.3

4 Complementary Logic Dynamic Behavior 4-input NAND Intra-cell capacitances cannot be disregarded Distributed RC model ( Elmore Delay ) t phl = 0,69 (R 1 C 1 + (R 1 +R 2 ) C (R 1 +R 2 +R 3 ) C 3 + (R 1 +R 2 +R 3 +R 4 ) C L ) A R 5 B R 4 A R 3 B R 6 C R 7 C 3 D R 8 C L If R 1 =R 2 =R 3 =R 4 =R N then: t phl = 0.69 R N x (C 1 +2C 2 +3C 3 +4C L ) Intra-cell capacitances consist of: junction source and drain capacitances and gate-to-source and gate-to-drain capacitances. R 2 C R 1 D C 2 C 1 Slide 16.4

5 Problems with Static CMOS Style 1. N-input gates require 2N transistors 2. Propagation delay deteriorates rapidly as a function of the fan-in (i.e., number of inputs) Intrinsic capacitance increases linearly with the number of inputs. The series connection of transistors causes an additional slowdown Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.5

6 Propagation Delay as a Function of Fan-In Propagation delay of CMOS NAND gate approx. quadratic t p (ps) t phl t p t p t plh LH linear fanin Gates with more than 4 inputs should be avoided Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.6

7 Propagation Delay as a Function of Fan-Out t p (psec) t p NOR2 t p NAND2 t p INV All gates have the same drive current. Slope is a function of driving strength eff. fan-out Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.7

8 Propagation Delay as a Function of Fan-Out Fan-in: quadratic due to increasing resistance and capacitance Fan-out: each additional fan-out gate adds two gate capacitances to C L t p = a 1 FI + a 2 FI 2 + a 3 FO Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.8

9 Spice Simulations for 4-input NAND Modify file nand2-v0.cir ( -CMOS/ ) A B C D A C L B C D C 3 C 2 C 1 Slide 16.9

10 Spice Simulations for 4-input NAND Results t plh t phl A=B=C=B= B=C=D=1 A= A=C=D=1 B= A=B=D=1 C= A=B=C=1 D= Slide 16.10

11 Design Techniques for Static CMOS Gates Transistor Sizing 15,4µm 4,8µm 4,8µm Only effective when the load is dominated by the fanout (not by the intrinsec capacitance) x x x x 4,8µm 4,8µm Gnd Slide 16.11

12 Design Techniques for Static CMOS Gates Progressive Sizing In N MN C L t phl = 0,69 (R 1 C 1 + (R 1 +R 2 ) C (R 1 +R 2 +R 3 ) C 3 + (R 1 +R 2 +R 3 +R 4 ) C L ) In 3 In 2 M3 M2 C 3 C 2 Equalize efective resistances by: W M1 > W M2 > W M3 > > W MN In 1 M1 C 1 Up to 20% gate delay reduction can be achieved (according to Rabaey) Problem: difficult to be accomplished in layout, due to different Ws. Slide 16.12

13 Design Techniques for Static CMOS Gates Transistor Reordering Critical path Critical path In 3 1 In 2 1 In M3 M2 M1 C 2 C 1 C L charged charged charged 0 1 In 1 M3 In 2 1 M2 In 3 1 M1 C 2 C 1 C L charged charged charged Delay determined by the time to discharge C L, C 1 e C 2 Delay determined by the time to discharge C L Slide Source: Rabaey; Chandrakasan; Nikolic, 2003

14 Design Techniques for Static CMOS Gates Logic Decomposition/Restructuring F = ABCDEFGH High fanin (avoid) Two-level CMOS logic Fanin of 2, unitary fanout Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.14

15 Design Techniques for Static CMOS Gates Bufer Insertion Isolate an-in from fanout C L C L C L may represent the capacitance o a long wire (e.g., a bus line) Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.15

16 Ratioed Logic Resistive load R L S Depletion transist. V T <0 S PMOS transist S PDN PDN PDN Resistive Load (general idea) with depletion transistor Pseudo-NMOS Target: transistor reduction Problem: the nominal low output voltage (V OL ) is not 0 V. Slide 16.16

17 Ratioed Logic Resistive load PDN R L S N+1 transistors V OH = V OL = R PN /(R PN + R L ) Asymmetric response Static power consumption Tp L = 0,69 R L C L Slide 16.17

18 Ratioed Logic Active Load Depletion transist. V T <0 PMOS transist S S PDN PDN with depletion transistor Pseudo-NMOS Smaller Area & self load But static power dissipation and V OL > 0 (less robust to noise) Slide 16.18

19 Ratioed Logic Features (Noise Margins) To improve robustness V OL must be as small => k p << k n (=> W p << W n ) With W p << W n => tp LH increases Source: Rabaey; Chandrakasan; Nikolic, 2003 Slide 16.19

20 Ratioed Logic Features (VTC) Effect of sizing the PMOS transistor in a pseudo-nmos inverter 3.0 Ratios W/L p < 1 => L p > W p (> L min ) 2.5 size V OL Static power tp LH 2.0 W/L p = V 564µW 14ps V 298µW 56ps V o u t [V] W/L p = V 160µW 123ps V 80µW 268ps V 41µW 569ps 0.5 W/L p = 0.5 W/L p = W/L p = 1 Slide V in [V] Source: Rabaey; Chandrakasan; Nikolic, 2003

21 Application of Ratioed Logic to PLAs But, applying De Morgan s theorem A B AND Plane OR Plane C D imput buffers m n outputs A B inputs Slide C D

22 Application of Ratioed Logic to PLAs Pseudo-NMOS to realize a many-input NOR gate NOR Plane 1 NOR Plane 2 S n A B C D imput buffers m outputs inputs Slide 16.22

23 Improved Ratioed Logic Differential Cascode Voltage Switch Logic (DCVSL) When PDN1 conducts, PDN2 is off (and vice -versa) Each input must be provided in complementary format out M 1 M 2 PDN1 PDN2 The feedback mechanism turns off the load device that is not used out Slide 16.23

24 Improved Ratioed Logic - DCVSL Circuit is in steady state (no current flows) out on off M 1 M out PDN1 PDN2 no path to Gnd there is a path to Gnd Slide 16.24

25 Improved Ratioed Logic - DCVSL PDN1 must bring out below V DD - V Tp on off A new input vector is applied out M 1 M 2 PDN1 PDN2 0 out Becomes in high impedance (M2 and PDN2 are both off) there is a path to Gnd no path to Gnd Slide 16.25

26 Improved Ratioed Logic - DCVSL ( < V DD - V Tp ) out on turns on M 1 M 2 out A new input vector is applied PDN1 PDN2 there is a path to Gnd no path to Gnd Slide 16.26

27 Improved Ratioed Logic - DCVSL turns turns on M 1 off M 2 ( < V DD - V Tp ) ( > V DD - V Tp ) out out A new input vector is applied PDN1 PDN2 there is a path to Gnd no path to Gnd Slide 16.27

28 Improved Ratioed Logic - DCVSL out is completely discharged through this path (when no more current flows) out off on M 1 M 2 out out is completely charged through this path (when no more current flows) A new input vector is applied PDN1 PDN2 there is a path to Gnd no path to Gnd Slide 16.28

29 Improved Ratioed Logic - DCVSL Circuit reaches steady state No current out off on M 1 M out No current A new input vector is applied PDN1 PDN2 there is a path to Gnd no path to Gnd Slide 16.29

30 Improved Ratioed Logic - DCVSL M 1 M 2 out out PDN1 PDN2 Full rail-to-rail swing No static currents However: During transition, short circuit current (dynamic consumption) Device rationing is still important for functionality (not only for performance) Slide 16.30

31 V o l t a g e [V] CMOS Combinational Circuits Improved Ratioed Logic - DCVSL AND/NAND Gate Transient Response A,B A, B out=a.b out =A.B 1.5µm/ 0.25µm out M 1 M 2 M 3 M 4 1.0µm/ 0.25µm M 5 M 6 1.5µm/ 0.25µm 0.5µm/ 0.25µm out Time [ns] Source: Rabaey; Chandrakasan; Nikolic, 2003 tp(out)= 197ps tp(out )= 321ps Slide 16.31

32 Improved Ratioed Logic - DCVSL XOR-XNOR Gate Source: Rabaey; Chandrakasan; Nikolic, 2003 It is possible to share transistors among the two PDNs, thus reducing the overhead Slide 16.32

33 CMOS Combinational References Circuits 1. RABAEY, J; CHANDRAKASAN, A.; NIKOLIC, B. Digital Integrated Circuits: a design perspective. 2 nd Edition. Prentice Hall, ISBN: WESTE, Neil; HARRIS, David. CMOS VLSI Design: a circuits and systems perspective. Addison-Wesley, 4 th Edition, ISBN Slide 16.33

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