System Design Considerations When Using Cypress CMOS Circuits

Transcription

1 When Using Cypress CMOS Circuis This appicaion noe describes some facors o consider when eiher designing new sysems using Cypress high-performance CMOS inegraed circuis or when using Cypress producs o repace bipoar or NMOS circuis in exising sysems. The wo major areas of concern are device inpu sensiiviy and ransmission ine effecs due o impedance mismaching beween he source and oad. To achieve maximum performance when using Cypress CMOS ICs, pay aenion o he pacemen of he componens on he prined circui board (PCB); he rouing of he mea races ha inerconnec he componens; he ayou and decouping of he power disribuion sysem on he PCB; and perhaps mos imporan of a, he impedance maching of some races beween he source and he oads. The aer races mus, under cerain condiions, be anayzed as ransmission ines. The mos criica races are hose of cocks, wrie srobes on SRAMs and FIFOs, oupu enabes, and chip enabes. Repacing Bipoar or NMOS ICs Cypress CMOS ICs are designed o repace boh bipoar ICs and NMOS producs and o achieve equa or beer performance a one-hird (or ess) he power of he componens hey repace. When high-performance Cypress CMOS circuis repace eiher bipoar or NMOS circuis in exising sockes, be aware of condiions in he exising sysem ha coud cause he Cypress ICs o behave in unexpeced ways. These condiions fa ino wo genera caegories: device inpu sensiiviy and sensiiviy o refeced voages. Inpu Sensiiviy High-performance producs, by definiion, require ess energy a heir inpus o change sae han ow- or medium-performance producs. Unike a bipoar ransisor, which is a curren-sensing device, a MOS ransisor is a voage-sensing device. In fac, a MOS circui design parameer caed K is anaogous o he gm of a vacuum ube and is inversey proporiona o he gae oxide hickness. Thin gae oxides, which are required o achieve he desired performance, resu in highy sensiive inpus. These inpus require very ie energy a or above he device inpu-voage hreshod (approximaey.5v a 25 C) o be deeced. CMOS producs may deec high-frequency signas o which bipoar devices may no respond. MOS ransisors aso have exremey high inpu impedances (5 o 0 MΩ), which make he ransisors gae inpus anaogous o he inpu of a high-gain ampifier or an RF anenna. In conras, because bipoar ICs have inpu impedances of 000Ω or ess, hese devices require much more energy o change sae han do MOS ICs. In fac, a ypica Cypress IC requires ess han 0 picojoues of energy o change sae. Thus, when Cypress CMOS ICs repace bipoar or NMOS ICs in exising sysems, he CMOS ICs migh respond o puses of energy in he sysem ha are no deeced by he bipoar or NMOS producs. Refeced Voages Cypress CMOS ICs have very high inpu impedances and o achieve TTL compaibiiy and drive capaciive oads ow oupu impedances. The impedance mismach due o ow-impedance oupus driving high-impedance inpus migh cause unwaned voage refecions and ringing under cerain condiions. This behavior coud resu in ess-han-opimum sysem operaion. When he impedance mismach is very arge, a neary equa and opposie negaive puse refecs back from he oad o he source when he ine s eecrica engh (PCB race) is greaer han r = Eq. 2 pd where r is he rise ime of he signa a he source, and pd is he one-way propagaion deay of he ine per uni engh. The cassica way of saing he condiion for a voage refecion o occur is ha i wi occur if he signa rise ime is ess han or equa o he round-rip (wo-way) propagaion deay of he ine. Inpu camping diodes o ground were added o bipoar IC famiies (e.g., TTL, AS, LS, ALS, FAST) when he circui designers decided ha he fas rise and fa imes of he oupus coud cause voage refecions. The camping diodes o V CC are inheren in he juncion isoaion process. For a more deaied expanaion, see Inpu/Oupu Characerisics of Cypress Producs. Hisoricay, as circui performance improved, he oupu rise and fa imes of he bipoar circuis decreased o he poin where voage refecions began o occur (even for shor races) when an impedance mismach exised beween he ine and he oad. Mos users, however, were unaware of hese refecions because hey were suppressed by he diodes camping acion. Conveniona CMOS processing resus in PN juncion diodes, which adversey affec he ESD (eecrosaic discharge) proecion circuiry a each inpu pin and cause an increased suscepibiiy o ach-up. In addiion, when he inpu pin is negaive enough o forward bias he inpu camping diodes, eecrons are injeced ino he subsrae. When a sufficien number of eecrons are injeced, he resuing curren can disurb inerna nodes, causing sof errors a he sysem eve. Cypress Semiconducor Corporaion 390 Norh Firs Sree San Jose CA January 992 Revised March, 993

2 To eiminae he prospec of having his probem, a Cypress CMOS producs use a subsrae bias generaor. The subsrae is mainained a a negaive 3V poenia, so he subsrae diodes canno be forward biased uness he voage a he inpu pin becomes a diode drop more negaive han 3V. (See Figure 9 in Inpu/Oupu Characerisics of Cypress Producs for a schemaic of he inpu proecion circui used in a Cypress CMOS producs.) To he sysems designer, his ransaes o approximaey five imes (3.8V divided by 0.8V =4.75) he negaive undershoo safey margin for Cypress CMOS inegraed circuis versus hose ha do no use a bias generaor. Voage refecions shoud be eiminaed by using impedance maching echniques and passive componens ha dissipae excess energy before i can cause sof errors. Crossak shoud be reduced o accepabe eves by carefu PCB ayou and aenion o deais. Crossak The rise and fa imes of he waveforms generaed by Cypress CMOS circui oupus are 2 o 4 ns beween eves of 0.4 and 4V. The fas ransiion imes and he arge voage swings coud cause capaciive and inducive couping (crossak) beween signas if insufficien aenion is paid o PCB ayou. Crossak is reduced by avoiding running PCB races parae o each oher. If his is no possibe, run ground races beween signa races. In synchronous sysems, he wors ime for he crossak o occur is during he cock edge ha sampes he daa. In mos sysems i is sufficien o isoae he cock, chip seec, oupu enabe, and wrie and read conro ines from each oher and from daa and address ines so ha he signas do no cause couping o each oher or o he daa ines. I is sandard pracice o use ground or power panes beween signa ayers on muiayered PCBs o reduce crossak. The capaciance of hese isoaion panes increases he propagaion deay of he signas on he signa ayers, bu his drawback is more han compensaed for by he isoaion he panes provide. The Theory of Transmission Lines A connecion (race) on a PCB shoud be considered as a ransmission ine if he waveengh of he appied frequency is shor compared o he ine engh. If he waveengh of he appied frequency is ong compared o he engh of he ine, conveniona circui anaysis can be used. In pracice, ransmission ines on PCBs are designed o be as neary ossess as possibe. This simpifies he mahemaics required for heir anaysis, compared o a ossy (resisive) ine. Ideay, a signas beween ICs rave over consan-impedance ransmission ines ha are erminaed in heir characerisic impedances a he oad. In pracice, his idea siuaion is sedom achieved for a variey of reasons. Perhaps he mos basic reason is ha he characerisic impedances of a rea ransmission ines are no consans, bu presen differen impedances depending upon he frequency of he appied signa. For cassica ransmission ines driven by a singe frequency signa source, he characerisic impedance is more consan han when he ransmission ine is driven by a square wave or a puse. According o Fourier series expansion, a square wave consiss of an infinie se of discree frequency componens-he fundamena pus odd harmonics of decreasing ampiude. When he square wave propagaes down a ransmission ine, he higher frequencies are aenuaed more han he ower frequencies. Due o dispersion, he differen frequencies do no rave a he same speed. Dispersion indicaes he dependence of phase veociy upon he appied frequency (see Reference, page 92). The resu is ha he square wave or puse is disored when he frequency componens are added ogeher a he oad. A second reason why pracica ransmission ines are no idea is ha hey frequeny have muipe oads. The oads may be disribued aong he ine a reguar or irreguar inervas or umped ogeher, as cose as pracica, a he end of he ine. The signa-ine refecions and ringing caused by impedance mismaches, non-uniform ransmission ine impedances, inducive eads, and non-idea resisors coud compromise he dynamic sysem noise margins and cause inadveren swiching. One sysem design objecive is o anayze he criica signa pahs and design he inerconnecions such ha adequae sysem noise margins are mainained. There wi aways be signa overshoo and undershoo. The objecive is o accuraey predic hese effecs, deermine accepabe imis, and keep he undershoo and overshoo wihin he imis. The Idea Transmission Line An equivaen circui for a ransmission ine appears in Figure. The circui consiss of subsecions of series resisance (R) and inducance (L) and parae capaciance (C) and shun admiance (G) or parae resisance, R p. For cariy and consisency, hese parameers are defined per uni engh. Muipy he vaues of R, L, C, and R p by he engh of he subsecion,, o find he oa vaue. The ine is assumed o be infiniey ong. If he ine of Figure is assumed o be ossess (R = 0, R p = infiniy), Figure reduces o Figure 2. A sma series resisance has ie effec upon he ine s characerisic impedance. In pracice and by design, he series resisance is quie sma. For -ounce (0.005-inch-hick), -mi-wide (0.00-inch) copper races on G-0 gass epoxy PCBs, he race resisance is beween 0.5 and 0.3Ω per foo. 2-ounce copper has a resisance 50 percen ower han ha of -ounce copper. Inpu or Characerisic Impedance To cacuae he characerisic impedance (aso caed AC impedance or surge impedance) ooking ino erminas a-b of he circui in Figure 2, use he foowing procedure. Le Z be he inpu impedance ooking ino erminas a-b, wih Z 2 for erminas c-d, Z 3 for erminas e-f, ec. Z is he series impedance of he firs inducor (L) in series wih he parae combinaion of Z 2 and he impedance of he capacior (C). From AC heory: X L = jωc where X L is he inducive reacance. X C jωc Eq. 2 Eq. 3 2

3 R L R L V /R p = G C V 2 G C TO INFINITY Figure. Transmission Line Mode Z Z 2 Z 3 Z 4 L L L a c e g V C V 2 C V C TO 3 V 4 INFINITY b d f h Figure 2. Idea Transmission Line Mode where X C is he capaciive reacance. Then Z 2 X C Z = X L Eq. 4 Z 2 + X C If he ine is reasonaby ong, Z = Z 2 = Z 3. Subsiuing Z = Z 2 ino Equaion 4 yieds Z X C Z = X L Z + X C The AC inpu impedance of a purey reacive, uniform, ossess ine is a resisance. This is rue for AC or DC exciaion. Propagaion Veociy and Deay The propagaion veociy (or phase veociy) of a sinusoid raveing on an idea ine (see Reference ) is α = Eq. 8 LC The propagaion deay for a ossess ine is he reciproca of he propagaion veociy: or pd = LC = Z C Eq. 9 2 Z Z X L X C X L = 0 Subsiuing he expressions for X C and X L yieds Eq. 5 2 L Z jωl = --- Eq. 6 C Equaion 6 conains a compex componen ha is frequency dependen. The compex componen can be eiminaed by aowing o become very sma and by recognizing ha he raio L/C is consan and independen of or ω: where L and C are once again he inrinsic ine inducance and capaciance per uni engh. Adding addiiona subs or oads o he ine (see Reference 2 of his appicaion noe) increases he propagaion deay by he facor + C D C Eq. 0 where C D is he oad capaciance. Therefore, he propagaion deay of a oaded ine, T pdl, is Z = L C Eq. 7 pdl = pd + C D C Eq. 3

4 This appicaion noe shows aer ha a ransmission ine s unoaded or inrinsic propagaion deay is proporiona o he square roo of he dieecric consan of he medium surrounding or adjacen o he ine. Propagaion deay is no a funcion of he ine s geomery. The characerisic impedance of a capaciivey oaded ine decreases by he same facor ha he propagaion deay increases: Z ' Z = C D C Eq. 2 Noe ha he capaciance per uni engh mus be muipied by he ine engh,, o cacuae an equivaen umped capaciance. The Condiion for Voage Refecion I is reaivey sraighforward o obain a cosed-form souion for a ransmission ine s maximum aowabe engh, which, if exceeded, migh cause a voage refecion. If he ine is no erminaed in is characerisic impedance, a refecion is guaraneed o occur. The refecion s ampiude depends on he amoun of impedance mismach beween he ine and he oad and wheher he rise ime of he signa a he source equas or is greaer (sower) han wo imes he propagaion deay of he ine. The condiion for a voage refecion o occur is r L Eq. 3 2 pdl Soving for he oaded propagaion deay yieds r pdl = L However, he acua physica engh of he ine is Eq. 4 r = Eq. 5 pd The inrinsic capaciance of he ine from Equaion 9 is T pd C O = Eq. 6 I is sandard pracice o use C O o designae he inrinsic ine capaciance, L O he inrinsic ine sef inducance, and he inrinsic ine characerisic impedance. Subsiuing Equaions 4, 5, and 6 ino Equaion gives he reaionship for he ine engh a which voage refecions migh occur. Two condiions mus be presen for voage refecions o occur: he ine mus be ong and here mus be an impedance mismach beween he ine and he oad. r = 2L pd C D r pd pd Soving Equaion 7 for he ine engh, L, yieds Eq. 7 r L = pd C D r Eq. 8 Equaion 8 is very usefu o he sysem designer. I is generic and appies o a producs irrespecive of circui ype, ogic famiy, or voage eves. The equaion aows you o esimae when a ine requires erminaion, using variabes you can easiy deermine. When driving a disribued or non-umped oad, he signa s rise ime depends on he source no he oad, as you migh expec. The inrinsic, or unoaded, ine propagaion deay per uni engh is a funcion of he dieecric consan and can be easiy cacuaed. The inrinsic ine characerisic impedance is a funcion of he dieecric consan and he PCB s physica consrucion or geomery and can aso be cacuaed. Finay, you can esimae he equivaen (umped) oad capaciance by adding up he number of oads (device inpus) being driven and muipying by 0 pf. For I/O pins, use 5 pf per pin. Signa Transiion Times The sandard Cypress 0.8µ (L drawn) CMOS process yieds oupu buffers whose signas ransiion approximaey 4 2 ns, or, have a sew rae of 2V per nanosecond. The rise ime/fa ime is 2 ns. Producs fabricaed using he Cypress BiCMOS process have he same rise imes. The Cypress ECL process yieds producs wih 500-ps oupu signa rise imes and fa imes, or sew raes of V/0.5 ns = 2V per nanosecond. Inerna signa sew raes are 0V per nanosecond, bu ony for shor (usuay ess han 500 mv) voage excursions. Thus, high-frequency noise is generaed on chip, which you can eiminae by using 00- o 500-pF ceramic or mica fier capaciors beween V CC and ground. The vaues in Tabe come from using Equaion 8 o cacuae he ine engh a which voage refecions may occur. The cacuaions assume a 50Ω inrinsic ine characerisic impedance and ha he PCB is muiayer, using sripine consrucion on G-0 gass epoxy maeria (dieecric consan of 5). These condiions resu in an unoaded ine propagaion deay of 2.27 ns per foo. Tabe. Line Lengh a Which a Voage Refecion Occurs r (ns) C D (pf) L (inches)

5 Tabe reveas ha decreasing he source rise ime from 2 o 0.5 ns (a facor of 4) decreases he ine engh a which a voage refecion migh occur by a facor of 5 (4.73 divided by 0.93 = 5.09) for he same oad (0 pf) and inrinsic propagaion deay (2.27 ns/f.). A second observaion is ha for signas wih rise imes of 0.5 ns, a ines shoud be erminaed. Refecion Coefficiens Anoher aribue of he idea ransmission ine, refecion coefficiens, are no acuay ine characerisics. The ine is reaed as a circui componen, and refecion coefficiens are defined ha measure he impedance mismaches beween he ine and is source and he ine and is oad. The reason for defining and presening he refecion coefficiens becomes apparen aer when i is shown ha if he impedance mismach is sufficieny arge, eiher a negaive or posiive voage migh refec back from he oad o he source, and he voage migh eiher add o or subrac from he origina signa. A mismach beween he source and ine impedance may aso cause a voage refecion, which in urn refecs back o he oad. Therefore, wo refecion coefficiens are defined. For cassica ransmission ines driven by a singe frequency source, he impedance mismaches cause sanding waves. When puses are ransmied and he source s oupu impedance changes depending upon wheher a LOW-o-HIGH or a HIGH-o-LOW ransiion occurs, he anaysis is compicaed furher. You can use cassica ransmission ine anaysis-where puses are represened by compex variabes wih exponenias-o cacuae he voages a he source and he oad afer severa back and forh refecions. However, hese compex equaions end o obscure wha is physicay happening. Energy Consideraions Now consider he effecs of driving he idea ransmission ine wih digia puses and anayze he behavior of he ine under various driving and oading condiions. The firs ask is o define he oad and source refecion coefficiens. Figure 3 shows he circui o be anayzed. The idea ransmission ine of engh is driven by a digia source of inerna resisance R S and oaded wih a resisive oad R L. The characerisic impedance of he ine appears as a pure resisance, ( = L C) o any exciaion. R S + A X Eq. 9 Figure 3. Idea Transmission Line Loaded and Driven + + I A I B V S V A V B ( X) R L I A I B SOURCE LINE LOAD B The idea case is when R S = = R L. The maximum energy ransfer from source o oad occurs under his condiion, and no refecions occur. Haf he energy is dissipaed in he source resisance, R S, and he oher haf is dissipaed in he oad resisance, R L (he ine is ossess). If he oad resisor is arger han he ine s characerisic impedance, exra energy is avaiabe a he oad and is refeced back o he source. This is caed he underdamped condiion, because he oad under-uses he energy avaiabe. If he oad resisor is smaer han he ine impedance, he oad aemps o dissipae more energy han is avaiabe. Because his is no possibe, a refecion occurs ha signas he source o send more energy. This is caed he overdamped condiion. Boh he underdamped and overdamped cases cause negaive raveing waves, which cause sanding waves if he exciaion is sinusoida. The condiion = R L is caed criicay damped. The safes erminaion condiion, from a sysems design viewpoin, is he sighy overdamped condiion, because no energy is refeced back o he source. Line Voage for a Sep Funcion To deermine he ine voage for a sep funcion exciaion, you appy a sep funcion o he idea ine and anayze he behavior of he ine under various oading condiions. The sep funcion response is imporan because any puse can be represened by he superposiion of a posiive sep funcion and a negaive sep funcion, deayed in ime wih respec o each oher. By proper superposiion, you can predic he response of any ine and oad o any widh puse. The principe of superposiion appies o a inear sysems. According o heory, he rise ime of he signa driven by he source is no affeced by he characerisics of he ine. This has been subsaniaed in pracice by using a specia coaxiay consruced reed reay ha deivers a puse of 8A ino 50Ω wih a rise ime of ns (see Reference ). The equaion represening he voage waveform going down he ine (see Figure 3) as a funcion of disance and ime is V L ( X, ) = V A ()U ( X pd ) for < T O Eq. 20 V A () = V S () Eq. 2 + R S where V A = he voage a poin A X = he voage a a poin X on he ine = he oa ine engh pd = he propagaion deay of he ine in nanoseconds per foo T O = pd, or he one-way ine propagaion deay U() = a uni sep funcion occurring a x = 0 V S () = he source voage When he inciden voage reaches he end of he ine, a refeced voage, V, occurs if R L does no equa. The refecion coefficien a he oad, ρl, can be obained by appying Ohm s Law. The voage a he oad is V L + V L, which mus be equa o (I L + I L )R L. Bu 5

6 V L I L = Eq. 22 and V L ' I L ' = Eq. 23 (The minus sign is due o I L being negaive; i.e., I L is opposie o he curren due o V L.) Therefore, V L V L ' V B = V L + V L ' = RL Eq. 24 V O By definiion: refeced voage V L ' ρ L = = Eq. 25 inciden voage V L Soving for V L /V L in Equaion 24 and subsiuing in he equaion for ρ L yieds R L ρ L = Eq. 26 R L + The refecion coefficien a he source is R S ρ S = Eq. 27 R S + Re-arranging Equaion 24 yieds V B V L + V L ' V L = = ' VL = ( + ρ Eq. 28 V L L )V L Equaion 28 describes he voage a he oad (V B ) as he sum of an inciden voage (V L ) and a refeced voage (ρ L V) a ime = T O. When R L =, no voage is refeced. When R L <, he refecion coefficien a he oad is negaive; hus, he refeced voage subracs from he inciden voage, giving he oad voage. When R L >, he refecion coefficien is posiive; hus, he refeced voage adds o he inciden voage, again giving he oad voage. Noe ha he refeced voage a he oad has been defined as posiive when raveing oward he source. This means ha he corresponding curren is negaive, subracing from he curren driven by he source. This piecewise anaysis is cumbersome and can be edious. However, i does provide an insigh ino wha is physicay happening and demonsraes ha a compex probem can be soved by dividing i ino a series of simper probems. Aso, eiminaing he exponenias which provide phase informaion in he cassica ransmission ine equaions simpifies he mahemaics. To use he piecewise mehod, you mus do carefu bookkeeping o combine he refecions a he proper ime. This is quie sraighforward, because a puse raves wih a consan veociy aong an idea or ow-oss ine, and he ime deay beween refeced puses can be prediced. The rues o keep in mind are ha a any ocaion and ime he voage or he curren is he agebraic sum of he waves raveing in boh direcions. For exampe, wo voage waves of he same poariy and equa ampiudes, raveing in opposie direcions, a a given ocaion and ime add ogeher o yied a voage of wice he ampiude of one wave. The same reasoning appies o a poins of erminaion and disconinuiies on he ine. The oa voage or curren is he agebraic sum of a he inciden and refeced waves. Poariies mus be observed. A posiive voage refecion resus in a negaive curren refecion and vice versa. Sep Funcion Response of he Idea Line Before examining refecions a he source due o mismaches beween he source and ine impedances, consider he behavior of he idea ine wih various oads when driven by a sep funcion. The circui for anaysis appears in Figure 3. Figure 4 shows he voage and curren waveforms a poin A (ine inpu) and poin B (he oad) for various oads. (These vaues are drawn from Reference, pg ) Noe ha R S = and ha V A a = 0 equas V S /2. This means ha no impedance mismach exiss beween he source and he ine; hus, here is no refecion from he source a = 2 T O. T O is he one-way propagaion deay of he ine. The ime-domain response of he reacive oads are obained by appying a sep funcion o he LaPace ransform of he oad and hen aking he inverse ransform. Noe ha he refecion coefficien a he oad is no he oa refecion coefficien (a compex number) bu represens ony he rea par of he oad. The piecewise mehod eiminaes he compex (jω) erms by performing he bookkeeping invoving he phase reaionships, which he compex erms accoun for in cassica ransmission ine anaysis. Noe ha for he open-circui condiion in Figure 4b, Z L = infiniy, so ha ρ L = +. The voage is refeced from he oad o he source (a ampiude V O = V S /2). Thus, a ime = 2 T O, he refeced voage adds o he origina voage, V O = V S /2, o give a vaue of 2V O = V S. Whie he voage wave is raveing down o and back from he oad, a curren of V O V S I O = = Z Eq O exiss. This curren charges up he disribued ine capaciance o he vaue V S, hen he curren sops. The waveforms a he source and oad for he series RC erminaion shown in Figure 4g are of paricuar ineres because his nework dissipaes no DC power; you can use his nework o erminae a ransmission ine in is characerisic impedance a he inpu o a Cypress IC. Figure 4h represens he equivaen circui of a Cypress IC s inpu. Combining boh neworks modes a Cypress IC driven by a ransmission ine erminaed in he ine s characerisic impedance, when he vaues of R and C are propery chosen. Refecions Due o Disconinuiies Figure 5 iusraes hree ypes of common disconinuiies found on ransmission ines. Any change in he characerisic impedance of he ine due o consrucion, connecors, oads, ec., causes a disconinuiy, which causes a refecion ha direcs some energy back o he source. The amoun of energy refeced back is deermined by he disconinuiy s refecion coefficien. Because disconinuiies are usuay sma by design, mos of he energy is ransmied o he oad. In genera, a disconinuiy has series inducance, shun capaciance, and series resisance. An exampe is a via from a 6

7 Figure 4. Sep Funcion Response of Figure 3 for Various Terminaions signa pane hrough a ground pane o a second signa pane in a muiayer PCB or modue. IC sockes and oher connecors can aso cause disconinuiies. The Idea Transmission Line s Puse Response Consider nex he behavior of he idea ransmission ine when driven by a puse whose widh is shor compared o he 7

8 a) Series Inducance L 2V A V A ' 2T 0 - b) Shun Capaciance 2V A C V A c) Series Resisance R 2V A ' 2T 0 - V A ( R+ Z 2V 0 ) A R + 2Z 0 ' 2T 0 - Figure 5. Refecions from Disconinuiies wih an Appied Sep Funcion ine s eecrica engh-when he puse widh is ess han he ine s one-way propagaion deay ime, T O. Figure 6 shows anoher series of response waveforms for he circui in Figure 3, his ime for a puse insead of a sep (drawn from Reference, pg. 60 6). Noe ha R S = and ha V A a = 0 equas V S /2. This means ha here is no impedance mismach beween he source and he ine; hus, here is no refecion from he source a = 2 T O. Finie Rise Time Effecs Now consider he effecs of sep funcions wih finie rise imes driving he idea ransmission ine. During he rise ime of a puse, haf he energy in he saic eecric fied is convered ino a raveing magneic fied and haf remains as a saic eecric fied o charge he ine. If he rise ime is sufficieny shor, he voage a he oad changes in discree seps. The ampiude of he seps depends on he impedance mismach, and he widh of he seps depends on he ine s wo-way propagaion deay. As he rise ime and/or he ine ges shorer (smaer T O ), he resu converges o he famiiar RC ime consan, where C is he saic capaciance. A devices shoud be reaed as ransmission ines for ransien anaysis when an idea sep funcion is appied. However, as he rise ime becomes onger and/or he races shorer, he ransmission ine anaysis reduces o conveniona AC circui anaysis. Refecions from Sma Disconinuiies Figure 7 shows a puse wih a inear rise ime and rounded edges driving he ransmission ine of Figure 5a and Figure 5b. The expressions for V r are derived on pages 7 and 72 of Reference. The refecion caused by he sma series inducance is usefu for cacuaing he vaue of he inducor, L, bu ie ese. The refecion caused by he sma shun capacior is more ineresing. If his capacior is sufficieny arge, i can cause a device conneced o he ransmission ine o see a ogic 0 insead of a ogic. The Effec of Rise Time on Waveforms Nex, consider he idea ine erminaed in a resisance ess han is characerisic impedance and driven by a sep funcion wih a inear rise ime. The simuus, he circui, and he response appear in Figure 8a, Figure 8b, and Figure 8c, respecivey. Once again, noe ha because he source resisance equas he ine characerisic impedance, here are no refecions from he source. The resuing waveforms are simiar o hose of Figure 4c when modified as shown in Figure 8c. The fina vaue of he waveform mus be he same as before The resuan wave a he ine inpu ( ) is easiy obained by superposiion of he appied wave and he refeced wave a 8

9 Figure 6. Puse Response of Figure 3 for Various Terminaions 9

10 V A V S (a) Appied Puse from Generaor APPLIED STEP FUNCTION T R (a) simuus V A V S = (b) Refecions from Sma Series Inducor L V r = L' V A T r V S R L < (b) circui T R ' 2T O - T R V r = L' V A T r REFLECTED WAVE (c) Refecions from Sma Shun Capaciance C T pw = r +.5 'C T R 2T O R V S S R L + T R ' 2T O - Figure 7. Refecions from Sma Disconinuiies wih a Finie Rise Time Puse he proper ime. In Figure 8, because he sep funcion s rise ime is ess han he ine s wo-way propagaion deay, he inpu wave reaches is fina vaue, V S /2. A = 2 T O, he refeced wave arrives back a he source and subracs from he appied sep funcion (he oad refecion coefficien is negaive). Figure 9 iusraes waveforms for wo reaionships beween he sep funcion rise ime and he propagaion deay. Muipe Refecions Now consider he case of an idea ransmission ine wih muipe refecions caused by improper erminaions a boh ends of he ine. The circui and waveforms appear in Figure 0. The refecion coefficiens a he source and he oad are boh negaive-he source resisance and he oad resisance are boh ess han he ine characerisic impedance. (c) response Figure 8. Effec of Rise Time on Response of Mismached Line wih R L < When he swich is iniiay cosed, a sep funcion of ampiude V S V O = = Eq. 30 R S + appears on he ine and raves oward he oad. Afer a one-way propagaion deay ime, T O, he wave refecs back wih an ampiude of ρ L V O. This firs refeced wave hen raves back o he source, and a ime = 2 T O, he wave reaches he inpu end of he ine. A his ime, he firs refecion a he source occurs, and a wave of ampiude ρ S (ρ L V O ) refecs back o he oad. A ime = 3 T O, his wave again refecs from he oad back o he source wih ampiude 2 ρ L ρ S ( ρ L V O ) = ρ S ρ LVO Eq. 3 0

11 V S REFLECTED WAVE R S V L R L V S R L V S R L + (a) circui 2T O =T R 4T O V O EXPONENTIAL APPROXIMATION (a) T R = 2T O V S 2 R E R L V S R L + R S 2T O 4T O 6T O (b) T R R V L S R L + I in 2T O T R 4T I O 2T O 4T O 6T O R L R L + R S (b) T R > 2T O (c) inpu curren Figure 9. Effecs of Rise Time on Response for R L < This back and forh refecion process coninues uni he ampiudes of he refecions become so sma ha hey canno be observed. The circui is hen said o be in a quiescen sae. Effecive Time Consan Voage refecions in sma incremens and of shor duraions approximae an exponenia funcion, as indicaed by he dashed ine in Figure 0b. The smaer and narrower he seps become, he more cosey he waveform approaches an exponenia curve. The mahemaica derivaion is presened in Reference. The ime consan is 2T O K = Eq. 32 ρ S ρ L Thus, he resuan voage waveform a he oad can be approximaed by V () = V O e K --- Eq. 33 For Equaion 32 o be accurae, ρ L and ρ S mus be reasonaby arge (approaching ±) so ha he incremena seps are sma. Because he produc ρ S ρ L is a posiive number, ess V R V L S R L + R S (+r L )V O 2T O 4T O 6T O (d) oad voage Figure 0. Sep Funcion Appied o Line Mismached on Boh Ends; Shown for Negaive Vaues of ρ S and ρ L han one, he ime consan is a negaive number, which indicaes ha he exponenia decreases wih ime. This is usuay he case in ransien circuis. Boh refecion coefficiens mus aso have he same sign o yied a coninuay decreasing or increasing waveform. Opposie signs give osciaory behavior ha canno be represened by an exponenia funcion. From Transmission Line o Circui Anaysis When a ransmission ine is erminaed in is characerisic impedance, he ine behaves ike a resisor. I usuay does no

12 maer if you use ransmission ine or circui anaysis, provided ha you ake he propagaion deays ino accoun. Consider he case of a shor-circuied ransmission ine driven by a sep funcion wih a source impedance unequa o he characerisic ine impedance. The genera case is shown in 0a. For R L = 0 he refecion coefficiens are Z S ρ S = , ρ Z S + Z L = O The approximae ime consan is 2T O 2T O T O ( Z S + ) k = = = ρ S ρ L + ρ S Z S or T O k = T O Z S Reca ha T O = LC Eq. 34 Eq. 35 Eq. 36 Microsrip ines Srip ines Coaxia Cabe Coaxia cabe offers many advanages for disribuing high-frequency signas. The we-defined and uniform characerisic impedance permis easy maching. The cabe s ground shied reduces crossak, and he ow aenuaion a high frequencies make he cabe idea for ransmiing he fas rise-ime and fa-ime signas generaed by Cypress CMOS ICs. However, because of high cos, coaxia cabe is usuay resriced o appicaions ha permi no aernaives. These appicaions usuay invove cock disribuion sysems on PCBs or backpanes. Because coaxia cabe is no easiy handed by auomaed assemby echniques, is appicaion requires human assembers. This requiremen furher increases coss. Coaxia cabes have characerisic impedances of 50Ω, 75Ω, 93Ω, or 50Ω. These vaues are he mos common, ahough specia cabes can be made wih oher impedances. Coaxia cabe s propagaion deay is very ow. You can compue i using he formua (one-way deay) and pd =.07 e r ( ns/f) Eq. 4 = L C Eq. 37 where is he physica engh of he ine, and L and C are he per-uni-engh parameers. Subsiuing hese variabes ino Equaion 35 yieds k = T O = L Eq. 38 Z S I is necessary o have Z S smaer han. Thus, he refecion coefficiens have he same sign o give exponenia behavior. Opposie signs give osciaory behavior. If Z S <, he exponenia approximaion becomes more accurae. If Z S is very sma compared o, hen T O is negigibe compared o L/, so ha Equaion 35 reduces o k = L Eq. 39 Z S Bu L is he oa oop inducance, and Z S is he circui s oa series impedance. The ime consan is hen L' k = Eq. 40 R S This is he same ime consan you woud obain by a circui anaysis approach if you considered he ine a series combinaion of L and R S. By open-circuiing he ine and performing a simiar anaysis, i can be shown ha an RC ime consan resus. Types of Transmission Lines The ypes of ransmission ines incude Coaxia cabe Twised pair Wire over ground where e r is he reaive dieecric consan and depends upon he dieecric maeria used. For soid Tefon and poyehyene, he dieecric consan is 2.3. The propagaion deay is.54 ns per foo. For maximum propagaion veociy, you can use coaxia cabes wih dieecric Syrofoam or poysyrene beads in air. Many of hese cabes have high-characerisic impedances and are sowed consideraby when capaciivey oaded. Twised Pair You can make wised pairs from sandard wire (AWG 24 28), wised abou 30 urns per foo. The ypica characerisic impedance is 0Ω. Because he propagaion deay is direcy proporiona o he characerisic impedance (Equaion 9), he propagaion deay is approximaey wice ha of coaxia cabe. Twised pairs are used for backpane wiring, someimes for driving differenia receivers, and for breadboarding. Wire Over Ground Figure shows a wire over ground. This configuraion is used for breadboarding and backpane wiring. The characerisic impedance is approximaey 20Ω. This vaue can vary as much as ±40 percen, depending upon he disance from he groundpane, he proximiy of oher wires, and he configuraion of he ground. Microsrip Lines A microsrip ine (Figure 2) is a srip conducor (signa ine) on a PCB separaed from a ground pane by a dieecric. If he ine s hickness, widh, and disance from he ground pane are conroed, he ine s characerisic impedance can be prediced wih a oerance of ±5 percen. The formua given in Figure 2 has proven o be very accurae for widh-o-heigh raios beween 0.: and 3.0: and for dieecric consans beween and 5. The inducance per foo for microsrip ines is 2

13 Figure. Wire Over Ground Figure 2. Microsrip Line L = ( ) 2 C O Eq. 42 where is he characerisic impedance and C O is capaciance per foo. The propagaion deay of a microsrip ine is pd = e r ( ns/f) Eq. 43 Noe ha he propagaion deay depends ony upon he dieecric consan and is no a funcion of he ine widh or spacing. For G-0 fibergass epoxy PCBs (dieecric consan of 5), he propagaion deay is.74 ns per foo. Srip Lines A srip ine consiss of a copper srip cenered in a dieecric beween wo conducing panes (Figure 3). If he ine s hickness, widh, dieecric consan, and disance beween ground panes are a conroed, he oerance of he characerisic impedance is wihin ±5 percen. The equaion given in is accurae for W/(b ) < 0.35 and /b < The inducance per foo is given by he formua L = ( ) 2 C O Eq. 44 The propagaion deay of he ine is given by he formua pd =.07 e r ( ns/f) Eq. 45 Figure 3. Srip Line Consrucion For G-0 fibergass epoxy boards, he propagaion deay is 2.27 ns per foo. The propagaion deay is no a funcion of ine widh or spacing. Modern PCBs Mos PCBs empoy microsrip, sripine, or some combinaion of he wo. Microsrip consrucion on a doube-sided board wih power and ground nes can suffice for ow- o medium-performance, and ow-densiy PCBs. For high-performance, high-densiy PCBs, sripine consrucion is preferred. Power panes isoae signa ayers from each oher and provide higher-quaiy power and grounds han hose of a wo-ayer board. Manufacuring quaiy conro assures ha he meaizaion is of uniform hickness and ha he ayers are propery aminaed, hus ensuring uniform, predicabe eecrica characerisics. When o Terminae Transmission Lines Transmission ines shoud be erminaed when hey are ong. From he preceding anaysis, i shoud be apparen ha r Long Line > Eq pdl where pdl is he oaded propagaion deay of he ine per uni engh. For Cypress CMOS and BiCMOS producs, he rise ime, r, is ypicay 2 ns. For sripine consrucion (muiayer PCBs), he ine engh a which voage refecions migh occur has been shown o vary from 4.73 inches for a 0-pF oad o 3.05 inches for an 80-pF oad (see Equaion 8 and Tabe ). No a ines exceeding hese enghs need o be erminaed. Terminaions are usuay required on conro ines (such as cock inpus, wrie and read srobe ines on SRAMs and FIFOs) and chip seec or oupu-enabe ines on RAMs, PROMs, and PLDs. Address ines and daa ines on RAMs and PROMS usuay have ime o see because hey are normay no he highes-frequency ines in a sysem. However, if very heaviy oaded, address and daabus ines migh require erminaions. Line Terminaion Sraegies There are wo genera sraegies for ransmission ine erminaion:. Mach he oad impedance o he ine impedance 2. Mach he source impedance o he ine impedance 3

14 In oher words, if eiher he oad refecion coefficien or he source refecion coefficien can be made o equa zero, refecions are eiminaed. From a sysems design viewpoin, sraegy is preferred. Eiminaing he refecion a he oad (i.e., dissipaing he excess energy) before he energy raves back o he source causes ess noise, eecromagneic inerference (EMI), and radio frequency inerference (RFI). Muipe Loads, Buses, and Nodes In he case where muipe oads are conneced o a ransmission ine, ony one erminaion circui is required. The erminaion shoud be ocaed a he oad ha is eecricay he greaes disance from he source. This is usuay he oad ha is he greaes physica disance from he source. A poin-o-poin or daisy chain connecion of oads is preferred. Bidireciona buses shoud be erminaed a each end wih a circui whose impedance equas he inrinsic, characerisic ine impedance. The reason is ha each ransmiing device sees he characerisic impedance of he ine when he device is ransmiing. Consider nex a ine ha has hree bidireciona nodes: one on each end and one in he midde. The midde node, when driving he ine, sees an impedance equa o /2, because he node is ooking ino wo ines in parae wih each oher. The end nodes, however, see an impedance of. In his case, as in a backpane, each end of he ine shoud be erminaed in an impedance equa o /2. When heaviy oaded, Equaion 2 mus be used o cacuae he oaded characerisic impedance, and his mus be used insead of. Types of Terminaions There are hree basic ypes of erminaions: series damping, pu-up/pu-down, and parae AC erminaions. Each has is advanages and disadvanages. Excep for series damping, he erminaion nework shoud be aached o he inpu (oad) ha is eecricay he greaes disance from he source. Componen eads shoud be as shor as possibe o preven refecions due o ead inducance. Series Damping Series damping is accompished by insering a sma resisor (ypicay 0Ω o 75Ω) in series wih he ransmission ine, as cose o he source as possibe (Figure 4). Series damping is a specia case of damping in which he series resisor vaue pus he circui oupu impedance equas he ransmission ine impedance. The sraegy is o preven he wave refeced back from he oad from refecing back from he source. This is done by making he source refecion coefficien equa o zero. A B C R d Figure 4. Series Damping Terminaion The channe resisance (on resisance) of he pu-down device for Cypress ICs is 0Ω o 20Ω, depending upon he curren-sinking requiremens. Thus, subrac his vaue from he series-damping resisor, R d. = R S + R d Eq. 47 A disadvanage of he series-damping echnique, as iusraed in Figure 5, is ha during he wo-way propagaion deay ime of he signa edges, he voage a he inpu o he ine is hafway beween he ogic eves, due o he voage divider acion of R S. The haf voage propagaes down he ine o he oad and hen back from he oad o he source. This means ha no inpus can be aached aong he ine, because hey woud respond incorrecy during his ime. However, you can aach any number of devices o he oad end of he ine because a he refecions are absorbed a he source. If wo or more ransmission ines mus be driven in parae, he vaue of he series-damping resisor does no change. T O Figure 5. Series Damping Timing The advanages of series erminaion are: Requires ony one resisor per ine Consumes ie power Permis inciden wave swiching a he oad afer a T O propagaion deay 4

15 Provides curren imiing when driving highy capaciive oads; he curren imiing aso heps reduce groundbounce The disadvanages of series erminaion are: Degrades rise ime a he oad due o increased RC ime consan Shoud no be used wih disribued oads The ow inpu curren required by Cypress CMOS ICs resus in esseniay no DC power dissipaion. The ony AC power required is o charge and discharge he parasiic capaciances. Pu-Up/Pu-Down Terminaion The pu-up/pu-down resisor erminaion shown in Figure 6 is incuded for hisorica reasons and for he sake of compeeness. For TTL driving ong cabes, such as ribbon cabes, he vaues R = 220Ω and R 2 = 330Ω are recommended by severa bus inerface sandards. If he cabe is disconneced, he voage a poin B is 3V, which is we above he 2V minimum high TTL specificaion. Because mos conro signas are acive LOW, a disconneced cabe resus in he unassered sae. A Figure 6. Pu-Up/Pu-Down The maximum vaue of R is deermined by he maximum accepabe signa rise ime, which is a funcion of he charging RC ime consan. The minimum vaue of R is deermined by he amoun of curren he driver can sink. The vaue of R 2 is chosen such ha a ogic HIGH is mainained when he cabe is disconneced. The equivaen Thévenin resisance is R R 2 R T = Eq. 48 R + R 2 The vaue of R and R 2 in parae is sighy ess han he cabe s characerisic impedance. Ribbon cabes wih characerisic impedances of 50Ω are ypica. If boh resisors are used, DC power is dissipaed a he ime. If ony a pu-down resisor (R 2 ) is used, DC power is dissipaed when he inpu is in he ogic HIGH sae. Conversey, if ony a pu-up resisor (R ) is used, power is dissipaed when he inpu is in he LOW sae. Due o hese power dissipaions, his erminaion is no recommended. If an unerminaed conro signa on a PCB is suspeced of causing a probem, a resisor whose vaue is sighy ess han he characerisic impedance of he ine (e.g., 47Ω) can be conneced beween he inpu pin and ground. Be sure ha he driver can source sufficien curren o deveop a TTL high voage eve (2.0V) across he resisor. B V CC R R 2 In specia cases where inpus shoud be eiher pued up (HIGH) for ogic reasons or because of very sow rise and fa imes, you can use a pu-up resisor o V CC in conjuncion wih he erminaing nework shown in Figure 7. DC power is dissipaed when he source is LOW. A Figure 7. Parae AC Terminaion Parae AC Terminaion Figure 7 iusraes he recommended genera-purpose erminaion. I does no have he disadvanage of he haf-voage eves of series damping erminaions, and i causes no DC power dissipaion. You can aach oads anywhere aong he ine, and hey see a fu voage swing. The disadvanage is ha a parae AC erminaion requires wo componens, versus he one-componen series-damping erminaion. Commerciay Avaiabe RC Neworks A variey of combinaions of R and C vaues are avaiabe as series RC neworks in SIP packages from a eas wo sources. Bourns cas hese neworks he Series 70 and 702 RC Terminaion Neworks. You can obain daashees by caing he facory in Logan, Uah ( ) or a oca saes office. Thin Fim Technoogy aso refers o he neworks as RC Terminaion Neworks. You can obain daashees by caing he facory in Norh Mankao, Minnesoa a Dae Eecronics cas heir produc Resisor/Capacior Neworks. Ca for informaion. Caifornia Micro Devices cas heir produc R C Neworks. Ca for informaion. Low-Pass Fier Anaysis The parae AC erminaion has anoher advanage: i acs as a ow-pass fier for shor puses. You can verify his by anayzing he response of he circui iusraed in Figure 8 o a posiive and a negaive sep funcion. The posiive sep funcion is generaed by moving he swich from posiion 2 o posiion. The negaive sep funcion is generaed by moving he swich from posiion o posiion 2. The response of he circui o a puse is he superposiion of he wo separae responses. The inpu impedance of he Cypress circuis conneced o he erminaion nework are so arge ha hey can be ignored for his anaysis. Cassic circui anaysis usuay assumes an idea source (R = R 2 = 0). In rea-word digia circuis, he source oupu impedance is no ony non-zero, bu aso varies depending upon wheher he oupu is changing from LOW o HIGH or vice versa. B C R < 5

16 For Cypress ICs, 00Ω > R > 50Ω and 20Ω > R 2 > 0Ω, depending upon speed and oupu curren-sinking requiremens. Posiive Sep Funcion Response The iniia voage on he capacior is zero. A = 0, he swich is moved from posiion 2 o posiion. A = 0+, he capacior appears as a shor circui, and he voage V is appied hrough R o charge he oad (R 3 C). The voage across he capacior V C (), is ( R + R 3 )C V C () = V e Eq. 49 In heory, he voage across he capacior reaches V when equas infiniy. In pracice, he voage reaches 98 percen of V afer 3.9 RC ime consans. You can verify his by seing V C ()/V = 0.98 in Equaion 49 and soving for. Negaive Sep Funcion Response The capacior is charged o approximaey V. A = 0, he swich is moved from posiion o posiion 2, and he capacior is discharged. The voage across he capacior, V C () is ( R V C () Ve 2 + R 3 )C = Eq. 50 The voage decays o 2 percen of is origina vaue in 3.9 RC ime consans. You can verify his by seing V C ()/V =0.02 in Equaion 50 and soving for. The Idea Case Consider he idea case where R = R 2 = 0. Le R 3 = R in Equaions 49 and 50. If a posiive puse of widh T is appied o he modified circui of Figure 8, he puse disappears if 4RC > T. Because he discharging ime consan is he same as he charging ime consan for he idea case, a negaive-going puse of widh T aso disappears if 4RC > T. Tha is, if he appied signa is normay HIGH and goes LOW, as does he wrie srobe on an SRAM, he erminaion fiers ou a negaive giches ess han 4 RC ime consans in widh. The maximum frequency ha he circui passes is Fmax ( ) = T Eq. 5 Figure 8. Lumped Load; AC Terminaion This is rue because he charging and discharging ime consans are equa for he idea case. Capaciance for he Idea Case The vaue of he capacior, C, mus be chosen o saisfy wo conficing requiremens. Firs, he capacior shoud be arge enough o eiher absorb or suppy he energy conained or removed when posiive-going or negaive-going giches occur. Second, he capacior shoud be sma enough o avoid eiher deaying he signa beyond some design imi or sowing he signa rise and fa imes o more han 5 ns. A hird consideraion is he impedance caused by he capacior s capaciive reacance, X C. The digia waveforms appied o he AC erminaion can be expressed as a Fourier Series so ha hey can be manipuaed mahemaicay. However, because hese signas are no periodic in he cassica meaning of he word, i is no cear ha he AC seady-sae anaysis mode of X C appies here. In mos appicaions, he degradaion of he signa s rise and fa imes beyond 5 ns deermines he maximum vaue of he capacior. The procedure is o cacuae he rise ime beween he 0- and 90-percen ampiude eves, equae his rise ime o 5 ns, and sove for C in erms of R: RC V () = V e for yieds = RCn V () V V () For = 0., = 0.0 RC. V V R 2 R 2 SOURCE LOAD V() Eq. 52 Eq. 53 V () For = 0.9, = 2.3 RC. V The ime for he signa o ransiion from 0 o 90 percen of is fina vaue is hen T = 2.2 RC. Soving for C yieds T C = Eq R For T = 5 ns, Tabe 2 can be consruced. This abe indicaes ha 50Ω ransmission ines on PCBs ha are erminaed wih RC neworks shoud use a 47Ω resisor and a capacior of 48 pf max; 47 pf is a sandard vaue. This nework eiminaes giches of 9 ns or ess. The abe s second coumn appies o wirewrapping consrucion, which is no recommended for sysems operaing a frequencies over 0 MHz. An excepion is if he sysem consiss of ess han six MSI or SSI ICs.. Tabe 2. Terminaion Vaue for an Idea Case PCB Wirewrapped (Ω) R (Ω) 47 0 C R 3 6

17 Tabe 2. Terminaion Vaue for an Idea Case C (max., pf) RC (ns) RC (ns) The Rea Word To go from he idea o he rea word, cacuae he vaues of R and R 2 from he curves on he daashee of he device driving he ine. R is he sope of he oupu source curren vs. oupu voage beween 2 and 4V. R 2 is he sope of he oupu sink curren vs. oupu voage beween 0 and 0.8V. Add he vaue of R o 47Ω and cacuae C, using Equaion 54. Then check o see ha he RC charging ime consan does no vioae some minimum posiive puse-widh specificaion for he ine. If so, reduce C. Add he vaue of R 2 o 47Ω and cacuae C. Then check o see if he discharging RC ime consan vioaes some minimum puse-widh specificaion for he ine. If so, reduce C. If he ine is heaviy oaded, Equaion 2 mus be used o cacuae he oaded characerisic impedance, which deermines he maximum vaue of R. The Maximum vaue of C is hen cacuaed using Equaion 54. Schoky Diode Terminaion In some cases i can be expedien o use Schoky diodes or fas-swiching siicon diodes o erminae ines. The diode swiching ime mus be a eas four imes as fas as he signa rise ime. Where ine impedances are no we defined, as in breadboards and backpanes, he use of diode erminaions is convenien and can save ime. A ypica diode erminaion appears in Figure 9. The Schoky diode s ow forward voage, V f (ypicay 0.3 o 0.45V), camps he inpu signa o a V f beow ground (ower diode) and V CC + V f (upper diode). This significany reduces signa undershoo and overshoo. Some appicaions may no require boh diodes. The advanages of diode erminaions are: Impedance mached ines are no required The diodes repace erminaing resisors or RC erminaions V CC Ahough diodes cos more han resisors, he oa cos of ayou migh be ess because a precise, conroed ransmission-ine environmen is no required If ringing is discovered o be a probem during sysem debug, he diodes can be easiy added As wih resisor or RC erminaions, he eads shoud be as shor as possibe o avoid ringing due o ead inducance. A few of he ypes of Schoky diodes commerciay avaiabe are HSMS-2822 (Hewe-Packard) N57 MBD0, MBD02 (Mooroa) SN74S050/52/56 (TI, singe-diode arrays) SN74S05/53 (TI, doube-diode arrays) Unerminaed Line Exampe The foowing exampe iusraes he procedure for cacuaing he waveforms when a Cypress PLD generaes he wrie srobe for four Cypress FIFOs. The PLD is a PALC6L8 device and he FIFOs are CY7C429s. The equivaen circui appears in Figure 20 and he unmodified driving waveform in Figure 2. The rise and fa imes are 2 ns. The engh of he sripine race on he PCB is 8 inches and he inrinsic characerisic ine impedance is 50Ω. The voage waveforms a he source (poin A) and he oad (poin B) mus be cacuaed as funcions of ime. Sripine consrucion is used for his exampe because in mos modern high-performance digia sysems, he PCBs have muipe ayers. The equivaen ON channe resisance of he PLD pu-up device, 62Ω, is cacuaed using he oupu source curren versus voage graph, over he region of ineres (2 o 4V), from he PALC20 series daashee. The equivaen resisance of he pu-down device, Ω, is cacuaed in a simiar manner, using he oupu sink curren versus oupu voage graph, over he region of ineres (0.4 o 2V), aso on he daashee. V CC = 5V + V 62Ω A 2 + Ω V A = 8 V B B + 40 pf.25 MΩ Figure 9. Schoky Diode Terminaion Figure 20. Equivaen Circui for Cypress PAL Driving The diodes camping acion reduces overshoo and undershoo 7

18 V V A () 24 The inrinsic ine impedance is reduced by he same facor by which he propagaion deay is increased (.524; see Equaion 2): 50Ω ' = = 32.8Ω Eq Iniia Condiions A ime = 0, he circui shown in Figure 20 is in a quiescen sae. The voage a poins A and B mus be he same. By inspecion: 0 Figure 2. V A (), Unmodified The equivaen inpu circui for he FIFO is consruced by approximaing he inpu and sray capaciance wih a 0-pF capacior and he inpu resisance wih a 5-MΩ resisor. The inpu eakage curren for a Cypress producs is specified as a maximum of ±0 µa, which guaranees a minimum of 500 KΩ a = 5V. Typica eakage curren is 0 pa. Because he PLD is driving four FIFOs in parae, he equivaen umped capaciance is 4 x 0 pf = 40 pf, and he equivaen umped resisance is 5,000,000/4 =.25 MΩ. The nex sep is o cacuae he propagaion deay and he oaded characerisic impedance of he ine. The unoaded propagaion deay of he ine is cacuaed using Equaion 45 wih a dieecric consan of 5: pd = 2.27( ns/f) Eq. 55 To cacuae he oaded ine propagaion deay, he inrinsic capaciance mus firs be cacuaed using Equaion 9. pd = C O Eq. 56 where is he inrinsic characerisic impedance, and C O is he inrinsic capaciance. pd 2.27 ns/f C O = = = 45.4 pf/f. Eq Because he ine is oaded wih 40 pf, Equaion is used o compue he oaded propagaion deay of he ine. pdl = pd + C D C O pdl = 3.46 ns/f Eq. 58 Noe ha he capaciance per uni engh mus be muipied by he ine engh o arrive a an equivaen umped capaciance pf pdl = 2.27 ns/f in 45.4 pf/f in/f R L V A = V B = ( V CC Vf) R S + R L = ( 5 ) Eq = 4V + A = 0, he driving waveform changes from 4V o approximaey 0V wih a fa ime of 2 ns. This is shown in Figure 20 by he swich arm moving from posiion o posiion 2. The wave propagaes o he oad a he rae of 3.46 ns per foo and arrives here 8 in. T O = 3.46 ns/f = 2.3 ns Eq. 6 2 in./f aer, as iusraed in Figure 22b. Because he refecion coefficien a he oad is ρl =, an eary equa and opposie poariy waveform is propagaed back o he source from he oad. The refecion arrives a =2T O = 4.6 ns (Figure 22a). Noe ha he fa ime is preserved. The refecion coefficien a he source is R S ' 32.8 ρ S = = = Eq. 62 R S + ' To simpify he cacuaions ha foow, consider 0.5 o be he ow-eve source refecion coefficien. The magniude of he refeced voage a he source is hen V S = 4V ( 0.5) = 2V Eq. 63 This wave propagaes from he source o he oad and arrives a = 3 T O. The wave adds o he 0V signa. The rise ime is preserved, and hus he ime required for he signa o go from 0 o 2V is 2V 2 ns r = = ns Eq. 64 4V The signa a he oad hus reaches he 2V eve a ime = 3T O + ns = 7.9 ns Eq. 65 and remains a ha eve uni he nex refecion occurs a = 5T O Eq. 66 The wave ha arrives a he oad a 3 T O refecs back o he source and arrives a 8

19 V A T O 4T O 6T O 8T O 0T O 2T O Figure 22a. Unerminaed Line Exampe; V A () V B T O 3T O 5T O 7T O 9T O T O 3T 4.3 O Figure 22b. Unerminaed Line Exampe; V B () 9

20 = 4T O = 9.2 ns Eq. 67 The 2V eve adds o he 4V eve, for a oa of 2V. The rise ime is preserved, so ha his eve is reached a = 4T O + ns = 0.2 ns and mainained uni he nex refecion occurs a Eq. 68 = 6T O Eq. 69 The 2V wave ha arrives a he source a = 4T O refecs back o he oad and arrives a = 5T O. The porion ha is refeced back o he oad is V S2 = 2 ( 0.5) = V Eq. 70 This vaue subracs from he 2V eve o give 2 = V. Because he fa ime is preserved, he ime required for he signa o go from 2 o V is V 2 ns f = = 0.5 ns 4V The V eve is hus reached a ime = 5T O ns = 2 ns Eq. 7 Eq. 72 A = 6T O, he V wave arrives back a he source, where i subracs from he 2V eve o give V. The rise ime is r = 0.5 ns/v = 0.5 ns Eq. 73 The 0.25V signa arrives a he oad a = 0T O = 23 ns and subracs from he 0.5V signa o give 0.25V. This process coninues uni he voages a poins A and B decay o approximaey 0V. Observaions The posiive refecion coefficien a he oad and he negaive refecion coefficien a he source resu in an osciaory behavior ha evenuay decays o accepabe eves. The voage a poin A reaches V afer 6T O deays and he voage a poin B reaches 0.5V afer 7T O deays. The refecion a he oad ha causes he voage o equa he TTL minimum one eve (2V) a T = 3T O causes a probem. The acua inpu voage hreshod eve is.5v for TTL-compaibe devices ha do no exhibi hyseresis. The voage a he oad fas from 4V o 0 2 ns, beginning a = T O. Because T O = 2.3 ns, he voage reaches zero a 2.3 ns + 2 ns = 4.3 ns The.5V eve occurs a 2 ns 4.3 ns V = 3.55 ns 4V The rising edge begins a = 3T O = 6.9 ns The.5V eve occurs a Eq. 78 Eq. 79 Eq ns 6.9 ns = 7.65 ns Eq. 8 4V The ime difference ( = 4. ns) is ong enough for he FIFO o inerpre he signa as a LOW. Nex, consider he widh of he posiive puse ha begins a he oad a = 3T O. Because he rise ime is preserved, he signa akes ns o reach 2V, or 0.75 ns o reach.5v. The signa begins o fa a = 5T O, reaching.5v a The signa a he source reaches he V eve a = 5T O ns =.75 ns Eq. 82 = 6T O = 4.3 ns Eq. 74 The V wave ha arrives a he source a = 6T O is refeced back o he oad and arrives a = 7T O. The porion ha is refeced back is V S3 = ( 0.5) = 0.5V Eq. 75 This vaue subracs from he V eve o give 0.5V. The fa ime is 0.25 ns. The 0.5V eve remains uni he nex refecion reaches he oad a = 9T O Eq. 76 A = 8T O he 0.5V wave ha refecs from he oad a = 7T O arrives back a he source, where i subracs from he V eve o give 0.5V. The rise ime is 0.25 ns. The porion ha refecs back o he oad is V S4 = 0.5 ( 0.5) = 0.25V Eq. 77 The difference ( ) is 4. ns, which is wide enough for he FIFO o inerpre as a second cock. To eiminae his puse, he ine mus be erminaed. Srobe Shorening Consideraions In his exampe he widh of he negaive srobe is 22 o 24 ns. If a CY7C FIFO is used, he wrie (or read) srobe mus no be shorer han 20 ns. Even if he FIFO does no recognize he 4.5-ns negaive puse, he shorening of he wrie srobe by 5T O =.5 ns is sufficien o vioae he minimum negaive-puse-widh specificaion. This srobe-shorening phenomenon migh aso occur on oher acive-low conro ines such as oupu enabes and chip seecs. Cock ines mus aso be anayzed for his probem; in genera, hese ines shoud be erminaed. Now consider an anaysis of he wrie srobe s rising edge o assure ha he refecions associaed wih his edge do no cause muipe cocks or fase riggering of he FIFO. A = 22 ns, he rising edge of he wrie srobe begins, which is he equivaen of cosing he swich in Figure 20 in he posiion. For his anaysis, i is convenien o sar he imescae over a zero, as appears in Figure 22a and Figure 22b. If he forcing funcion were a sep funcion, he equaions of Figure 4h woud appy. The ime consan in he equaion is R 'C e T = R + ' Because Eq