EE 330 Lecture 41. Digital Circuits. Propagation Delay With Multiple Levels of Logic Overdrive

Transcription

1 EE 330 Lecure 41 Digial ircuis Propagaion Delay Wih Muliple Levels of Logic Overdrive

2 Review from Las Time The Reference Inverer Reference Inverer V DD R =R PD PU = IN= 4OX WMIN LMIN V IN M 2 M 1 L VTn.2VDD MIN MIN R PD= μ n OX W MIN V DD -V Tn μ n OX W MIN 0.8V DD HL = LH = RPD L ssume μ n /μ p =3 = HL + LH = 2RPD W n =W MIN, W p =3W MIN L n =L p =L MIN In 0.5u proc =20ps, =4fF, R PD =R PU =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process)

3 Review from Las Time Quesion: Why is V Tp V Tn V DD /5 in many processes?

4 Review from Las Time ssume μ n /μ p =3 L n =L p =L MIN Device Sizing Equal Worse-ase Rise/Fall Device Sizing Sraegy -- (same as V TRIP =V DD /2 for wors case delay in ypical process considered in example) How many degrees of freedom were available? V DD V DD V DD k M 2k 1 2 k M 21 M 22 M 2k M 2 2 M 22 k M 1k V IN 1 M 21 M 1 2 M 2k M 11 1 M 12 2 M 1k k 1 M 1k INV W n =W MIN, W p =3W MIN = IN FI=1 k-inpu NOR W n =W MIN, W p =3kW MIN 3k+1 IN= 4 3k+1 FI= 4 k-inpu NND W n =kw MIN, W p =3W MIN 3+k IN= 4 3+k FI= 4

5 Review from Las Time Muliple Inpu Gaes: 2-inpu NOR VDD Device Sizing 2-inpu NND k-inpu NOR k-inpu NND VDD VDD VDD k M2k 1 2 k M21 M22 M2k VOUT B 2 1 M22 M21 k M1k B VOUT M11 M12 M1k 1 2 k 2 M2k 1 M1k Equal Wors ase Rise/Fall (and equal o ha of ref inverer when driving ) Wn=? Wp=? Fases response ( HL or LH ) =? Wors case response (, usually of mos ineres)? Inpu capaciance (FI) =? Minimum Sized (assume driving a load of ) Wn=Wmin Wp=Wmin Fases response ( HL or LH ) =? Slowes response ( HL or LH ) =? Wors case response (, usually of mos ineres)? Inpu capaciance (FI) =?

6 Review from Las Time Device Sizing V DD V DD V DD V DD k M 2k VDD 1 2 k M 21 M 22 M 2k M 2 V IN M 1 B 2 1 M 22 M 21 B k M 1k 2 M 2k M 11 1 M 12 2 M 1k k 1 M 1k Minimum Sized (assume driving a load of ) W n =W min W p =W min Inpu capaciance (FI) =? IN = OXWn L n+oxwp L p = OXWminL min + OXWminL min = 2ox WminL min= 2 1 FI = 2 Fases response ( HL or HL ) =? Slowes response ( HL or HL ) =? Wors case response (, usually of mos ineres)?

7 Review from Las Time Device Sizing minimum size driving V DD V DD V DD k M 2k 1 2 k M 21 M 22 M 2k M 2 V IN 2 M 22 k M 1k M 1 1 M 21 2 M 2k M 11 1 M 12 2 M 1k k 1 M 1k INV? 0.5 FI = R R R PU PD PD R k-inpu NOR? 0.5 PD R 3k 2 3k 1 2 FI = PD 2 R PU 3kR PD k-inpu NND? 3 k 2 2 FI = 3 k 2 2 R 3R R 3R PD PD PU PD

8 Review from Las Time Device Sizing Summary V DD V DD V DD k M 2k 1 2 k M 21 M 22 M 2k M 2 V IN 2 M 22 k M 1k M 1 1 M 21 2 M 2k M 11 1 M 12 2 M 1k k 1 M 1k INV k-inpu NOR k-inpu NND IN for N ND gaes is considerably smaller han for NOR gaes for equal wors-case rise and fall imes IN for minimuim-sized srucures is independen of number of inpus and much smaller han IN for he equal rise/fall ime case R PU ges very large for minimum-sized NOR gae

9 Digial ircui Design Hierarchical Design Basic Logic Gaes Properies of Logic Families haracerizaion of MOS Inverer Saic MOS Logic Gaes Raio Logic Propagaion Delay Simple analyical models Elmore Delay Sizing of Gaes Propagaion Delay wih Muliple Levels of Logic Opimal driving of Large apaciive Loads Power Dissipaion in Logic ircuis Oher Logic Syles rray Logic Ring Oscillaors

10 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading F ssume all gaes sized for equal wors-case rise/fall imes For n levels of logic beween and F n = ( k) k=1

11 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading nalysis sraegy : Express delays in erms of hose of reference inverer Reference Inverer V DD = IN= 4OX WMIN LMIN FI= 1 V IN M 2 R PD V.2 L Tn VDD MIN LMIN μ W V -V μ W 0.8V n OX MIN DD Tn n OX MIN DD M 1 = HL + LH =2R PD ssume μ n /μ p =3 L n =L p =L MIN W n =W MIN, W p =3W MIN In 0.5u proc =20ps, =4fF,R PD =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process)

12 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading F ssume: all gaes sized for equal wors-case rise/fall imes all gaes sized o have rise and fall imes equal o ha of ref inverer when driving Observe: Propagaion delay of hese gaes will be scaled by he raio of he oal load capaciance on each gae o Wha loading will a gae see? Inpu capaciance o oher gaes ny load capaciors Parasiic inerconnec capacinaces

13 V IN Propagaion Delay wih Sage Loading =2R PDref = 4OX WMIN LMIN FI of a capacior FI of a gae (inpu k) FI of an inerconnec Overall FI FI = INk FI G= FI = INI FI I= + + INGi INi INIi Gaes apaciances Inerconnecs FI can be expressed eiher in unis of capaciance or normalized o Mos commonly FI is normalized bu mus deermine from conex If gaes sized o have same drive as ref inverer = FI prop-k LOD-k

14 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading Example F ssume all gaes sized for equal wors-case rise/fall imes ssume all gae drives are he same as ha of reference inverer Neglec inerconnec capaciance, assume load of 10 on F oupu Deermine propagaion delay from o F

15 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading F 3k+1 FI NOR= k FI NND= 4 ssume all gaes sized for equal wors-case rise/fall imes ssume all gae drives are he same as ha of reference inverer Neglec inerconnec capaciance, assume load of 10 on F oupu Deermine propagaion delay from o F Wha loading will a gae see? Derivaion: 6 FI = 4 2 FI = 7 4 FI = FI LOD =FI "5" =10

16 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading Example F 10 ssume all gaes sized for equal wors-case rise/fall imes ssume all gae drives are he same as ha of reference inverer Neglec inerconnec capaciance, assume load of 10 on F oupu DERIVTIONS 6 FI = 4 6 1= 4 2 Deermine propagaion delay from o F 7 FI = 4 7 2= FI = = 4 4 4=10 3 FI 4= 5 n n = k= FI (k+1) = = k=1 k=

17 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading (assuming gae drives are all same as ha of reference inverer) G x2 G xx G 1 G 2 G 3 G n F F I2 F I3 F I4 F I(n+1) G x3 G x4 Idenify he gae pah from o F k = FI (k+1) Propagaion delay from o F: n = FI (k+1) k=1 This approach is analyically manageable, provides modes accuracy and is faihful

18 Digial ircui Design Hierarchical Design Basic Logic Gaes Properies of Logic Families haracerizaion of MOS Inverer Saic MOS Logic Gaes Raio Logic Propagaion Delay Simple analyical models Elmore Delay Sizing of Gaes Propagaion Delay wih Muliple Levels of Logic Opimal driving of Large apaciive Loads Power Dissipaion in Logic ircuis Oher Logic Syles rray Logic Ring Oscillaors done parial

19 Wha if he propagaion delay is oo long (or oo shor)? G x2 G xx G 1 G 2 G 3 G n F F I2 F I3 F I4 F I(n+1) G x3 G x4 Propagaion delay from o F: (k+1) k=1 n = FI k = FI (k+1)

20 Recall: Muliple Inpu Gaes: 2-inpu NOR VDD Device Sizing 2-inpu NND k-inpu NOR k-inpu NND VDD VDD VDD k M2k 1 2 k M21 M22 M2k VOUT B 2 1 M22 M21 k M1k B VOUT M11 M12 M1k 1 2 k 2 M2k 1 M1k Equal Wors ase Rise/Fall (and equal o ha of ref inverer when driving ) W n =? consider he fine prin! W p =? Fases response ( HL or LH ) =? Wors case response (, usually of mos ineres)? Inpu capaciance (FI) =? Minimum Sized (assume driving a load of ) W n =W min W p =W min Fases response ( HL or LH ) =? Slowes response ( HL or LH ) =? Wors case response (, usually of mos ineres)? Inpu capaciance (FI) =?

21 Recall: Device Sizing Muliple Inpu Gaes: 2-inpu NOR W n =? W p =? Equal Wors ase Rise/Fall (and equal o ha of ref inverer when driving ) (n-channel devices sized same, p-channel devices sized he same) ssume L n =L p =Lmin and driving a load of Inpu capaciance =? FI=? DERIVTIONS B V DD =? (wors case) One degree of freedom was used o saisfy he consrain indicaed W n =W MIN W p =6W MIN 7 7 IN = INB=OX WMIN L MIN+6OX WMINL MIN=7OX WMINL MIN= 4OXWMIN L MIN= FI= 7 or FI= 4 4 Oher degree of freedom was used o achieve equal rise and fall imes = (wors case)

22 Overdrive Facors Ref Inv F Example: Deermine prop in 0.5u process if =10pF In 0.5u proc =20ps, =4fF,R PD =2.5K 10 pf = FI = = ff =20ps 2500 = 50nsec Noe his is unaccepably long!

23 Overdrive Facors V DD M 2 V IN M 1 Scaling widhs of LL devices by consan (W scaled =WxOD) will change drive capabiliy relaive o ha of he reference inverer bu no change relaive value of HL and LH L 1 R PD= PDOD μ W V -V n OX 1 DD Tn R = L1 RPD μ OD W V -V OD n OX 1 DD Tn = L 2 R PU= μ p OX W 2 V DD +V Tp W L +W L IN OX L2 R PUOD= μ OD W V +V p OX 2 DD Tp RPU OD Scaling widhs of LL devices by consan will change FI by OD = O D W L + O D W L O D INOD OX IN

24 Overdrive Facors Ref Inv Inv wih OD =1000 F F =50nsec =? Example: Deermine prop in 0.5u process if =10pF and OD= pf 1 = FI = = 2.5 OD 4 ff 1000 Noe sizing he inverer wih he OD improved delay by a facor of 1000!

25 Overdrive Facors 1000 F By definiion, he facor by which he W/L of all devices are scaled above hose of he reference inverer is ermed he overdrive facor, OD Scaling widhs by overdrive facor DERESES resisance by same facor Scaling all widhs by a consan does no compromise he symmery beween he rise and fall imes (i.e. HL = LH ) Judicious use of overdrive can dramaically improve he speed of digial circuis Large overdrive facors are ofen used Scaling widhs by overdrive facor INRESES inpu capaciance by same facor - So is here any ne gain in speed?

26 Propagaion Delay wih Over-drive apabiliy Overdrive V IN OD L R = = OD PD HL LH L symmeric Overdrive RPDL = HL+ LH=2 OD OD Define he symmeric Overdrive Facors of he sage o be he facor by which PU and PD resisors are scaled relaive o hose of he reference inverer. RPD RPU R PDEFF = R PUEFF = OD OD R HL PD HL= L OD HL R F IL LH PD LH= L OD LH R PD RPD = + = R F ODHL ODLH ODHL ODLH 2 ODHL ODLH HL LH L L PD L IL

27 Propagaion Delay wih Over-drive apabiliy Overdrive V IN OD L F IL If inverer wih OD is sized for equal rise/fall, OD HL =OD LH =OD =RPDL RPDL ODHL ODLH OD = FIL OD OD may be larger or smaller han 1

28 Propagaion Delay wih Over-drive apabiliy Example ompare he propagaion delays. ssume he OD is 900 in he hird case and 30 in he fourh case. Don worry abou he exra inversion a his ime. V IN =900 L =900 V IN L =900 = V IN 900 L =900 = V IN 30 L =900 = Dramaic reducion in is possible (inpu is driving same in las 3 cases) Will laer deermine wha opimal number of sages and sizing is

29 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G 1 G 2 G 3 G n F OD 1: F I2 OD 2: F I3 OD 3: F I4 OD n: F I(n+1) F Ik denoes he oal loading on sage k which is he sum of he F I of all loading on sage k Summary: Propagaion delay from o F: = F n I(k+1) k=1 OD k

30 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading Will consider an example wih he five cases Equal rise/fall (no overdrive) Equal rise/fall wih overdrive symmeric Overdrive Minimum Sized ombinaion of equal rise/fall, minimum size and overdrive Will develop he analysis mehods as needed

31 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G x2 G xx G 1 G 2 G 3 G n F F I2 F I3 F I4 F I(n+1) Equal rise/fall (no overdrive) Equal rise/fall wih overdrive G x3 G x4 (k+1) k=1 n FI(k+1) k=1 OD k = n = FI symmeric overdrive =? Minimum Sized =? ombinaion of equal rise/fall, minimum size and overdrive =?

32 Driving Noaion Equal rise/fall (no overdrive) Equal rise/fall wih overdrive OD Minimum Sized M symmeric Overdrive OD HL OD LH Noaion will be used only if i is no clear from he conex wha sizing is being used

33 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading symmeric Overdrive V IN L Recall: Define he symmeric Overdrive Facors of he sage o be he facors by which PU and PD resisors are scaled relaive o hose of he reference inverer. R PDEFF R = OD PD HL R PUEFF R = OD PU LH

34 Propagaion Delay in Muliple-Levels of symmeric Overdrive Logic wih Sage Loading V IN V IN Gae L L Recall: If inverer is no equal rise/fall R 1 F = = OD 2 OD PD HL L HL PU LH L LH = HL+ LH= F IL + 2 ODHL OD IL HL R 1 F = = OD 2 OD IL LH = + = LH HL LH FIL OD

35 Propagaion Delay in Muliple-Levels of symmeric Overdrive Logic wih Sage Loading V IN V IN Gae L L = HL+ LH= F IL + 2 ODHL OD When propagaing hrough n sages: G 1 G 2 G 3 G n LH F OD HL1 OD LH1 F I2 OD HL2 OD LH2 F I3 OD HL3 OD LH3 F I4 F Ik denoes he oal loading on sage k which is he sum of he F I of all loading on sage k 1 1 n 1 FI(k+1) 2 OD OD k=1 HLk LHk OD HLn OD LHn F I(n+1)

36 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G x2 G xx G 1 G 2 G 3 G n F F I2 F I3 F I4 F I(n+1) Equal rise/fall (no overdrive) Equal rise/fall wih overdrive G x3 G x4 (k+1) k=1 n FI(k+1) k=1 OD k = n = FI symmeric overdrive 1 1 n 1 FI(k+1) 2 OD OD k=1 HLk LHk Minimum Sized =? ombinaion of equal rise/fall, minimum size and overdrive =?

37 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading and Overdrives Will now consider o F propagaion for his circui as an example wih differen overdrives F 50fF 20fF

38 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G x2 G xx G 1 G 2 G 3 G n F F I2 F I3 F I4 F I(n+1) Equal rise/fall (no overdrive) Equal rise/fall wih overdrive G x3 G x4 (k+1) k=1 n FI(k+1) k=1 OD k = n = FI symmeric overdrive 1 1 n 1 FI(k+1) 2 OD OD k=1 HLk LHk Minimum Sized =? ombinaion of equal rise/fall, minimum size and overdrive =?

39 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading Equal rise-fall gaes, no overdrive F 50fF 20fF =2HL In 0.5u proc =20ps, =4fF,R PD =2.5K n = F I k=1 k+1

40 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading Equal rise-fall gaes, no overdrive Equal Rise/Fall IN / Inverer NOR NND Overdrive Inverer HL LH NOR HL LH NND HL LH 1 3k k n F / 5 I(k+1) = FI k=1 k+1 k=1

41 Equal rise-fall gaes, no overdrive In 0.5u proc =20ps, =4fF,R PD =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process) 1 1 3k fF fF =5 4fF 3k k k 1 4 F I2 =10.25 F I3 =4.25 F I4 =4.25 F I5 =1.25 F I6 = k = 3 k fF =12.5 4fF 5 I k+1 k=1 = F F 50fF =32.5

42 End of Lecure 41