EE 330 Lecture 40. Digital Circuits. Propagation Delay With Multiple Levels of Logic Overdrive

Transcription

1 EE 330 Lecure 0 Digial ircuis Propagaion Delay Wih Muliple Levels of Logic Overdrive

2 Review from Las Time Propagaion Delay in Saic MOS Family F Propagaion hrough k levels of logic HL HLn LH(n-1) HL n-2 XY LH LHn HL(n-1) LH n-2 YX1 where x=h and Y=L if n odd and X=L and Y=h if n even n i1 i Will reurn o propagaion delay afer we discuss device sizing

3 Review from Las Time The Reference Inverer Reference Inverer V DD R =R PD PU = IN= OX 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 W n =W MIN, W p =3W MIN L n =L p =L MIN = HL + LH = 2RPD 8L 2 MIN = μ n V DD -V Tn In 0.5u proc =20ps, =ff, R PD =R PU =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process)

4 Review from Las Time Fan In The Fan In (FI) o an inpu of a gae device, circui or inerconnec ha is capaciive is he inpu capaciance Ofen his is normalized o some capaciance (ypically of ref inverer). FI = alernaely FI IN IN

5 Review from Las Time Device Sizing Equal Wors ase Rise/Fall (and equal o ha of ref inverer when driving ) Muliple Inpu Gaes: k-inpu NOR V DD W n =W MIN k M 2k W p =3kW MIN = W L +3k W L INx OX MIN MIN OX MIN MIN 3k+1 = 3k+1 W L = W L 3k+1 = OX MIN MIN OX MIN MIN 2 M 22 1 M 21 M 11 1 M 12 2 M 1k k 3k+1 FI= 3k+1 or FI= =

6 Review from Las Time Device Sizing Equal Wors ase Rise/Fall (and equal o ha of ref inverer when driving ) Muliple Inpu Gaes: k-inpu NND V DD 1 2 k M 21 M 22 M 2k W n =kw MIN W p =3W MIN k M 1k =k W L +3 W L INx OX MIN MIN OX MIN MIN 3+k = 3+k W L = W L 3+k = OX MIN MIN OX MIN MIN 2 1 M 2k M 1k 3+k FI= 3+k or FI= =

7 Review from Las Time Device Sizing The minimum-sized inverer pair V DD V DD ssume μ n /μ p =3 L n =L p =L MIN W n =W MIN, W p =W n M 2 M 2 = OX WMIN LMIN V IN V OUT L1= 0.5 =2 OXWMIN LMIN M 1 L1 M 1 L R PD LMIN W V V n OX MIN DD Tn 2 = + =R 0.5 3R 0.5 R HL LH PD PD PD = FI=0.5 or FI=0.5

8 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) =?

9 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 LH ) =? Slowes response ( HL or LH ) =? Wors case response (, usually of mos ineres)?

10 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? k-inpu NOR? 0.5 3k 2 3k 1 2 k-inpu NND? 3 k k 2 FI = 2 FI = FI = 2 2 R PU = 3R PD R PD = R PD R RPU 3kR PD RPD PD R PD = kr PD RPU 3R PD

11 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

12 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

13 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 i=1 = i

14 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= OX 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 10L μv n 2 MIN DD In 0.5u proc =20ps, =ff,r PD =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process)

15 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

16 V IN Propagaion Delay wih Sage Loading =2R PDref = OX 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-i LOD-i

17 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

18 Propagaion Delay in Muliple-Levels of Logic wih Sage Loading F 3k+1 FI NOR= 10 3+k FI NND= 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 = 2 FI = 7 FI = FI LOD =FI "5" =10

19 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 = 6 1= 2 Deermine propagaion delay from o F 7 FI = 7 2= FI = = =10 3 FI = 5 n n = i= FI (i+1) = = i=1 i=1

20 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading (assuming gae drives are all same as ha of reference inverer) 3k+1 FI NOR= G xx G x2 3+k FI NND= G 1 G 2 G 3 G n F k = #inpus FI 2 FI 3 FI FI (n+1) G x3 G x Idenify he gae pah from o F i = FI (i+1) Propagaion delay from o F: n = FI(i+1) i=1 This approach is analyically manageable, provides modes accuracy and is faihful

21 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

22 Wha if he propagaion delay is oo long (or oo shor)? 3k+1 FI NOR= G xx G x2 3+k FI NND= G 1 G 2 G 3 G n F FI 2 FI 3 FI FI (n+1) G x3 G x Propagaion delay from o F: n (i+1) i=1 = FI i = FI (i+1)

23 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) =?

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

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

26 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 Scaling widhs of LL devices by consan will change FI by OD RPU OD = O D W L + O D W L O D INOD OX IN

27 Overdrive Facors 1000 F The facor by which he devices are W/L 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 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

28 Propagaion Delay wih Over-drive apabiliy Overdrive V IN OD L F IL 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. R PDEFF R = OD PD If inverer sized for equal rise/fall, define OD by HL R PUEFF R = OD PU LH OD HL =OD LH =OD R = = OD PD HL LH L = LH+HL =R PD = FIL OD FIL OD = IN OD OD may be larger or smaller han 1

29 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 = Noe: Dramaic reducion in is possible Will laer deermine wha opimal number of sages and sizing is

30 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G 1 G 2 G 3 G n F OD 1: FI 2 OD 2: FI 3 OD 3: FI OD n: FI (n+1) FI i denoes he oal loading on sage i which is he sum of he FI of all loading on sage i 3k i+1 FI NORi=ODi Summary: Propagaion delay from o F: 3+ki FI NNDi=ODi = n (i+1) i=1 FI OD i

31 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 Minimum Sized symmeric Overdrive ombinaion of equal rise/fall, minimum size and overdrive Will develop he analysis mehods as needed

32 Propagaion Delay in Muliple- Levels of Logic wih Sage Loading G x2 G xx G 1 G 2 G 3 G n F OD 1: FI 2 OD 2: FI 3 OD 3: FI OD n: FI (n+1) Equal rise/fall (all overdrive =1) Equal rise/fall wih overdrive Minimum Sized symmeric overdrive ombinaion of equal rise/fall, minimum size and overdrive G x3 G x n (i+1) i=1 = FI = n (i+1) =? =? =? i=1 FI OD i

33 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

34 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

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

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

37 Propagaion Delay in Muliple-Levels of Overdrive Noaion Logic wih Sage Loading OD HL OD OD LH Equal Rise/Fall wih overdrive OD Rise/Fall may be differen wih overdrive OD HL and OD LH Examples 8 1 1/3 Equal Rise/Fall wih overdrive of 8 If W n =W MIN, minimum sized inverer

38 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading (assuming gae drives are all same as ha of reference inverer) 3k+1 FI NOR= 3+k FI NND= G xx G x2 G 1 G 2 G 3 G n F FI 2 FI 3 FI FI (n+1) G x3 G x Idenify he gae pah from o F Idenify each gae FI and delay: i = FI (i+1) Propagaion delay from o F: n (i+1) i=1 = FI

39 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading Each gae has is own overdrive relaive o ha of reference inverer G x2 G xx 3k i+1 FI NORi=ODi G 1 G 2 G 3 G n F 3+k FI i NNDi=ODi OD 1: FI 2 OD 2: FI 3 OD 3: FI OD n: FI (n+1) G x3 G x Idenify he gae pah from o F Idenify each gae s FI Idenify each gae s OD Propagaion delay from o F: = k = n (i+1) i=1 FI FI (i+1) OD i OD i

40 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading Each gae has possibly asymmeric overdrives G x2 3kiOD LHi+1 OD FI HLi NORi = G xx 3OD LHi+kiOD FI HLi NNDi = G 1 G 2 G 3 G n OD HL1 OD LH1 FI 2 Idenify he gae pah from o F OD HL2 OD LH2 FI 3 G x3 OD HL3 OD LH3 FI G x OD HLn OD LHn FI (n+1) F Idenify each gae s FI 1 1 Idenify each gae s OD HL and OD i = FI(i+1) LH 2 ODHLi OD LHi Propagaion delay from o F: n = FI 2 i1 (i+1) 1 1 ODHLi OD LHi

41 Propagaion Delay Through Muliple Sages of Logic wih Sage Loading Minimum size sraegy: 3kiOD LHi +1 OD FI HLi NORi = se 11 G xx G x2 OD LH =1/3k; OD HL =1 3OD se LHi +kiodhli 11 FI NNDi = OD LH =1/3; OD HL =1/k G 1 G 2 G 3 G n OD HL1 OD LH1 FI 2 Idenify he gae pah from o F OD HL2 OD LH2 FI 3 G x3 OD HL3 OD LH3 FI G x OD HLn OD LHn FI (n+1) F ll gae inpus have FI = 1/2, aps sill have FI=/ Plugin he above OD HL and OD LH = FI 1+3k or k+3 i 2 i1 Propagaion delay from o F: n = FIi 1 1+3k or k+3 2 i1

42 End of Lecure 0

43 Equal rise-fall gaes, no overdrive In 0.5u proc =20ps, =ff,r PD =2.5K (Noe: This OX is somewha larger han ha in he 0.5u ON process) 1 1 3k 1 20fF 13 20fF =5 ff 3k 1 7 3k k 1 FI 2 =10.25 FI 3 =.25 FI =.25 FI 5 =1.25 FI 6 = k 1 7 = 3 k 5 50fF =12.5 ff 5 k+1 k=1 = FI F 50fF =32.5

44 Equal rise-fall gaes, wih overdrive 8 In 0.5u proc =20ps, =ff,r PD =2.5K OD 5 (Noe: This OX is somewha larger han ha in he 0.5u ON process) 1 3k 1 13 OD 20fF 5 20fF =5 ff 3k 1 21 OD 2 6 3k 1 10 OD FI 2 =1.25 FI 3 =13 FI =.25 FI 5 =5 FI 6 =12.5 3k 1 10 OD 3 k 2 0 OD 3k 1 7 OD = n k+1 k=1 50fF =12.5 ff FI OD k F 50fF = =23.6