EEC 118 Lecture #6: CMOS Logic. Rajeevan Amirtharajah University of California, Davis Jeff Parkhurst Intel Corporation

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1 EEC 118 Lecture #6: CMOS Logic Rajeevan mirtharajah University of California, Davis Jeff Parkhurst Intel Corporation

2 nnouncements Quiz 1 today! Lab 2 reports due this week Lab 3 this week HW 3 due this Friday at 4 PM in box, Kemper 2131 mirtharajah/parkhurst, EEC 118 Spring

3 Outline Review: CMOS Inverter Transient Characteristics Review: Inverter Power Consumption Combinational MOS Logic Circuits: Rabaey (Kang & Leblebici, ) Combinational MOS Logic Transient Response C Characteristics, Switch Model mirtharajah/parkhurst, EEC 118 Spring

4 Review: Logic Circuit Delay For CMOS (or almost all logic circuit families), only one fundamental equation necessary to determine delay: I = C Consider the discretized version: Rewrite to solve for delay: dv Only three ways to make faster logic: C, ΔV, I dt Δt = I C = C ΔV I ΔV Δt mirtharajah/parkhurst, EEC 118 Spring

5 t t PHL PLH Review: Inverter Delays High-to-low and low-to-high transitions (exact): = C 2V T 0, n 4( VOH V ) L T 0, n + ln k ( ) + 1 n VOH VT 0, n VOH VT 0, n VOH VOL = C 2V T 0, p 4( VOH VOL V ) L T 0, p + ln k ( ) + 1 p VOH VOL VT 0, p VOH VOL VT 0, p VOH VOL Similar exact method to find rise and fall times Note: to balance rise and fall delays (assuming V OH = V DD, V OL = 0V, and V T0,n =V T0,p ) requires k k p n =1 W L W L 2.5 mirtharajah/parkhurst, EEC 118 Spring p n = μ μ n p

6 Review: Inverter Power Consumption Static power consumption (ideal) = 0 ctually DIL (Drain-Induced arrier Lowering), gate leakage, junction leakage are still present Dynamic power consumption P P avg avg / 1 T 2 dv T = out Vout Cload dt + DD out load T dt dt 0 T / 2 T / 2 2 T 1 V = out 1 2 Cload + VDDVoutCload CloadVout T T 2 2 Pavg = CloadVDD = CloadVDD f 1 T P avg = 1 T T 0 ()() t i t dv out ( V V ) C dt mirtharajah/parkhurst, EEC 118 Spring v dt / 2

7 Static CMOS Complementary pullup network (PUN) and pulldown network (PDN) Only one network is on at a time C PUN PUN: PMOS devices Why? PDN: NMOS devices C PDN F Why? PUN and PDN are dual networks mirtharajah/parkhurst, EEC 118 Spring

8 Dual Networks Dual networks: parallel connection in PDN = series connection in PUN, viceversa If CMOS gate implements logic function F: PUN implements function F Example: NND gate parallel F series PDN implements function G = F mirtharajah/parkhurst, EEC 118 Spring

9 NND function: F = NND Gate PUN function: F = = + Or function (+) parallel connection Inverted inputs, PMOS transistors PDN function: G = F = nd function ( ) series connection Non-inverted inputs NMOS transistors mirtharajah/parkhurst, EEC 118 Spring

10 NOR Gate NOR gate operation: F = + PUN: F = + = PDN: G = F = + mirtharajah/parkhurst, EEC 118 Spring

11 nalysis of CMOS Gates Represent on transistors as resistors 1 1 W R 1 W W R R Transistors in series resistances in series Effective resistance = 2R Effective length = 2L mirtharajah/parkhurst, EEC 118 Spring

12 nalysis of CMOS Gates (cont.) Represent on transistors as resistors W W R R W R Transistors in parallel resistances in parallel Effective resistance = ½ R Effective width = 2W mirtharajah/parkhurst, EEC 118 Spring

13 CMOS Gates: Equivalent Inverter Represent complex gate as inverter for delay estimation Typically use worst-case delays Example: NND gate Worst-case (slowest) pull-up: only 1 PMOS on Pull-down: both NMOS on W P W P W P W N ½W N W N mirtharajah/parkhurst, EEC 118 Spring

14 Example: Complex Gate Design CMOS gate for this truth table: C F F = (+C) mirtharajah/parkhurst, EEC 118 Spring

15 Example: Complex Gate Design CMOS gate for this logic function: F = (+C) = + C 1. Find NMOS pulldown network diagram: G = F = (+C) C Not a unique solution: can exchange order of series connection mirtharajah/parkhurst, EEC 118 Spring

16 Example: Complex Gate 2. Find PMOS pullup network diagram: F = +( C) C F Not a unique solution: can exchange order of series connection ( and C inputs) mirtharajah/parkhurst, EEC 118 Spring

17 Example: Complex Gate Completed gate: W P W P C W N W P F What is worse-case pullup delay? What is worse-case pulldown delay? Effective inverter for delay calculation: C W N ½W P W N ½W N mirtharajah/parkhurst, EEC 118 Spring

18 CMOS Gate Design Designing a CMOS gate: Find pulldown NMOS network from logic function or by inspection Find pullup PMOS network y inspection Using logic function Using dual network approach Size transistors using equivalent inverter Find worst-case pullup and pulldown paths Size to meet rise/fall or threshold requirements mirtharajah/parkhurst, EEC 118 Spring

19 nalysis of CMOS gates Represent on transistors as resistors 1 1 W R 1 W W R R Transistors in series resistances in series Effective resistance = 2R Effective width = ½ W (equivalent to 2L) Typically use minimum length devices (L = L min ) mirtharajah/parkhurst, EEC 118 Spring

20 nalysis of CMOS Gates (cont.) Represent on transistors as resistors W W R R W R Transistors in parallel resistances in parallel Effective resistance = ½ R Effective width = 2W Typically use minimum length devices (L = Lmin) mirtharajah/parkhurst, EEC 118 Spring

21 Equivalent Inverter CMOS gates: many paths to Vdd and Gnd Multiple values for V M, V IL, V IH, etc Different delays for each input combination Equivalent inverter Represent each gate as an inverter with appropriate device width Include only transistors which are on or switching Calculate V M, delays, etc using inverter equations mirtharajah/parkhurst, EEC 118 Spring

22 Static CMOS Logic Characteristics For V M, the V M of the equivalent inverter is used (assumes all inputs are tied together) For specific input patterns, V M will be different For V IL and V IH, only the worst case is interesting since circuits must be designed for worst-case noise margin For delays, both the maximum and minimum must be accounted for in race analysis mirtharajah/parkhurst, EEC 118 Spring

23 Equivalent Inverter: V M Example: NND gate threshold V M Three possibilities: & switch together switches alone switches alone What is equivalent inverter for each case? mirtharajah/parkhurst, EEC 118 Spring

24 Equivalent Inverter: Delay Represent complex gate as inverter for delay estimation Use worse-case delays Example: NND gate Worse-case (slowest) pull-up: only 1 PMOS on Pull-down: both NMOS on W P W P W P W N ½W N W N mirtharajah/parkhurst, EEC 118 Spring

25 Example: NOR gate Find threshold voltage V TH when both inputs switch simultaneously W P W P F Two methods: Transistor equations (complex) Equivalent inverter W N Should get same answer W N mirtharajah/parkhurst, EEC 118 Spring

26 Example: Complex Gate Completed gate: W P W P C W N W P F What is worse-case pullup delay? What is worse-case pulldown delay? Effective inverter for delay calculation: W N C W N ½W P ½W N mirtharajah/parkhurst, EEC 118 Spring

27 Transistor Sizing Sizing for switching threshold ll inputs switch together Sizing for delay Find worst-case input combination Find equivalent inverter, use inverter analysis to set device sizes mirtharajah/parkhurst, EEC 118 Spring

28 Common CMOS Gate Topologies nd-or-invert (OI) Sum of products boolean function Parallel branches of series connected NMOS Or-nd-Invert (OI) Product of sums boolean function Series connection of sets of parallel NMOS mirtharajah/parkhurst, EEC 118 Spring

29 Graph-ased Dual Network Use graph theory to help design gates Mostly implemented in CD tools Draw network for PUN or PDN Circuit nodes are vertices Transistors are edges F F gnd mirtharajah/parkhurst, EEC 118 Spring

30 Graph-ased Dual Network (2) To derive dual network: Create new node in each enclosed region of graph Draw new edge intersecting each original edge Edge is controlled by inverted input F n1 vdd F n1 F gnd Convert to layout using consistent Euler paths mirtharajah/parkhurst, EEC 118 Spring

31 Propagation Delay nalysis - The Switch Model = R ON V DD V V DD DD R R p R p R p p F F R n C L R n C L R n R n R n R p F C L (a) Inverter (b) 2-input NND (c) 2-input NOR t p = 0.69 R on C L (assuming that C L dominates!) mirtharajah/parkhurst, EEC 118 Spring

32 Switch Level Model Model transistors as switches with series resistance Resistance R on = average resistance for a transition Capacitance C L = average load capacitance for a transition (same as we analyzed for transient inverter delays) R N R P C L mirtharajah/parkhurst, EEC 118 Spring

33 What is the Value of R on? mirtharajah/parkhurst, EEC 118 Spring

34 Switch Level Model Delays R N C L I I t t 1 p Delay estimation using switch-level model (for general RC circuit): = = t = C V R 0 dv dt = RC t p = V 1 V 0 dt RC dv V = dt RC V V [ ] 1 ln( V = 1) ln( V0 ) RC ln V0 = C I dv dv mirtharajah/parkhurst, EEC 118 Spring

35 Switch Level Model RC Delays For fall delay t phl, V 0 =V DD, V 1 =V DD /2 t t t t p p phl plh = = = = V V RC ln 1 = RC ln 2 V V 0 RC ln(0.5) 0.69R C 0.69R n p C L L 1 DD DD Standard RC-delay equations from literature mirtharajah/parkhurst, EEC 118 Spring

36 Numerical Examples Example resistances for 1.2 μm CMOS mirtharajah/parkhurst, EEC 118 Spring

37 nalysis of Propagation Delay V DD R p R p F 1. ssume R n =R p = resistance of minimum sized NMOS inverter 2. Determine Worst Case Input transition (Delay depends on input values) R n R n C L 3. Example: t plh for 2input NND - Worst case when only ONE PMOS Pulls up the output node - For 2 PMOS devices in parallel, the resistance is lower t plh = 0.69R p C L 2-input NND 4. Example: t phl for 2input NND - Worst case : TWO NMOS in series t phl = 0.69(2R n )C L mirtharajah/parkhurst, EEC 118 Spring

38 Design for Worst Case V DD V DD F C L D 2 C D C 2 F NND Gate Complex Gate Here it is assumed that R p = R n mirtharajah/parkhurst, EEC 118 Spring

39 Fan-In and Fan-Out V DD C D Fan-Out Number of logic gates connected to output (2 FET gate capacitances per fan-out) C D Fan-In Number of logical inputs Quadratic delay term due to: 1.Resistance increasing 2.Capacitance increasing for t phl (series NMOS) t p proportional to a 1 FI + a 2 FI 2 + a 3 FO mirtharajah/parkhurst, EEC 118 Spring

40 Fast Complex Gates - Design Techniques Increase Transistor Sizing: Works as long as Fan-out capacitance dominates self capacitance (S/D cap increases with increased width) Progressive Sizing: In N MN Out C L M 1 > M 2 > M 3 > MN In 3 M3 C 3 In 2 In 1 M2 M1 C 2 C 1 Distributed RC-line Can Reduce Delay by more than 30%! mirtharajah/parkhurst, EEC 118 Spring

41 Fast Complex Gates - Design Techniques (2) Transistor Ordering Place last arriving input closest to output node critical path critical path In 3 M3 C L In 1 M1 C L In 2 M2 C 2 In 2 M2 C 2 In 1 M1 C 1 In 3 M3 C 3 (a) mirtharajah/parkhurst, EEC 118 Spring (b)

42 Fast Complex Gates - Design Techniques (3) Improved Logic Design Note Fan-Out capacitance is the same, but Fan-In resistance lower for input gates (fewer series FETs) mirtharajah/parkhurst, EEC 118 Spring

43 Fast Complex Gates - Design Techniques (4) uffering: Isolate Fan-in from Fan-out C L C L Keeps high fan-in resistance isolated from large capacitive load C L mirtharajah/parkhurst, EEC 118 Spring

44 4 Input NND Gate VDD V DD In 1 In 2 In 3 In 4 In 1 Out Out In 2 In 3 In 4 GND In1 In2 In3 In4 mirtharajah/parkhurst, EEC 118 Spring

45 Capacitances in a 4 input NND Gate VDD Cgs Cgs 5 Csb 6 Csb 5 6 Cgs 7 Csb Cgs In In 7 8 Csb In 3 In 4 Cgd Cgd 5 Cdb 6 Cdb 5 6 Cgd 7 Cdb Cgd 7 8 Cdb 8 In 1 In 2 In 3 In 4 Cgd 1 Cgs 1 Cgd 2 Cgs 2 Cgd 3 Cgs 3 Cgd 4 Cgs Cdb 1 Csb 1 Cdb 2 Csb 2 Cdb 3 Csb 3 Cdb 4 Csb 4 Vout Note that the value of Cload for calculating propagation delay depends on which capacitances need to be discharged or charged when the critical signal arrives. Example: In 1 = In 3 = In 4 = 1. In 2 = 0. In 2 switches from low to high. Hence, Nodes 3 and 4 are already discharged to ground. In order for Vout to go from high to low Vout node and node 2 must be discharged. CL = Cgd5+Cgd7+Cgd8+2Cgd6(Miller)+Cdb5+Cdb6+Cdb7+Cd b8 +Cgd1+ Cdb1+ Cgs1+ Csb1+ 2Cgd2+ Cdb2+ Cw mirtharajah/parkhurst, EEC 118 Spring

46 Next Topic: Sequential Logic asic sequential circuits in CMOS RS latches, transparent latches, flip-flops lternative sequential element topologies Pipelining mirtharajah/parkhurst, EEC 118 Spring

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