A Review of Time Jitter and Digital Systems

Transcription

1 A Review f Time Jitter ad Digital Sytem Victr S. Reihardt Raythe Space ad Airbre Sytem El Segud, CA/USA Abtract Time jitter i a imprtat parameter fr determiig the perfrmace f digital ytem. Thi paper review hw time jitter impact the perfrmace f digital ytem. Fr the purpe f later dicui, digital ytem are brke dw it three majr categrie: ychru data trafer, aychru data trafer, ad digital amplig ytem. A tatitical framewrk i firt develped fr treatig time jitter. Thi framewrk eplicitly deal with iue f badwidth ad ie prcee with 1 / f pectra. It i hw that variu frm f the tadard variace f time jitter are cverget i the preece f 1/ f ie, if e eplicitly cider the prpertie f the ytem phae repe fucti fr each f thee categrie. It i al hw that tadard variace are preferred ver d differece variace i dealig with digital perfrmace iue uch a bit errr, becaue tadard variace ca be directly related t the ttal time errr (jitter plu kew). Detailed dicui f hw time jitter impact the eumerated categrie f digital ytem are the preeted. I ychru data trafer ytem, it i hw that time jitter caue hard bit errr, that ly the white ie cmpet f clck cillatr ad gate ie make appreciable ctributi t the time jitter, ad that aliaig f thi white ie i a majr iue. I aychru ytem, it i hw that time jitter ca al caue ft errr r bit errr rate degradati ad that there i a additial time jitter term due t relative mater clck-lcal clck cillatr jitter, whe value i determied by 1 / f cillatr ie a well a the white ie. Fially, fr digital amplig i aalg-t-digital ad digital-t-aalg cverter, it i hw that ie pwer r multiplicative decrrelati ie geerated by amplig clck jitter i a majr limitati the bit reluti (effective umber f bit) f thee device. I. ITRODUCTIO Time jitter i a imprtat parameter fr determiig the perfrmace f digital ytem. Thi paper review hw time jitter impact the perfrmace f digital ytem. Firt, a verview f time jitter ad digital ytem i preeted. I thi verview, three type f digital ytem ueful fr categrizig the variu impact f time jitter are decribed, ad defiiti f time errr are dicued. et, a tatitical framewrk fr later dicui i preeted. Fially, uig thi framewrk, a detailed dicui f the impact f time jitter ytem perfrmace fr each categry f digital ytem i give. Hitrically, the digital cmmuity ha dealt with time jitter uig tadard variace a the meaure f jitter [1-9]. Such treatmet ue the tl f tatiary tatitic ad fte d t eplicitly deal with iue f badwidth ad -tatiary ie; that i, ie prcee with 1 / f pectra [10-18]. w, with digital ytem achievig clck peed i the multigigahertz regi ad time jitter requiremet reachig the ubp level, it i imprtat t treat uch badwidth ad 1 / f pectra iue eplicitly. The precie time cmmuity, the ther had, ha hitrically dealt with bth thee iue by uig d differece variace t avid cvergece prblem aciated with the tadard variace i the preece f 1 / f ie [10-18]. Hwever, it will be hw that thee d differece meaure f jitter are t eaily cected t digital perfrmace parameter. Thu, tatitical treatmet f time jitter preeted here will attempt t meld bth apprache. It will ue the tadard variace a the meaure f time jitter, eplicitly treatig iue f badwidth ad 1 / f pectra, ad it will hw that the tadard variace cverge fr digital ytem becaue f the uique prpertie f thee ytem. II. A OVERVIEW OF TIME JITTER AD DIGITAL SYSTEMS Categrie f Digital Sytem. Figure 1 hw a (mewhat verlappig) categrizati f digital ytem ueful fr dicuig the variu impact f time jitter. Thee categrie are a fllw: Sychru Dig Clck Dig Aychru Digital amplig Dig Dig Aalg A/D Vltage Clck Clck PLL Clck Figure 1. Categrizati digital ytem ueful fr dicuig time jitter. (1) Sychru data trafer ytem ditribute a igle hard-lie clck betwee all ubytem alg with the data. Clck cmmality cacel mt direct effect frm the clck cillatr ad jitter cme frm the lgic gate themelve. Here time jitter ca geerate hard bit errr r direct bit errr withut ay ther factr beig ivlved. () Aychru data trafer ytem ditribute ly data betwee ubytem. Each ub-ytem ha it w lcal clck cillatr (LO) that i ychrized t the mater uit clck cillatr (MO) uig a phaed lcked lp (PLL). Digital cmmuicati ytem are i thi categry [19]. I aychru ytem, there i additial relative MO-LO time jitter alg with the ychru gate jitter. Thi additial jitter ca create ft bit errr r bit errr rate (BER) degradati, which i the term ued fr a icreae i the BER that ly ccur whe thermal ie i al preet [19]. (3) Digital amplig ytem iclude aalg-t-digital cverter (A/D), digital-t-aalg cverter (D/A), ad decii circuit i cmmuicati ytem [19]. I thi categry, amplig clck jitter degrade the itegrity f the ampled igal [0-3]. I A/D ad D/A, thi geerate ie pwer, which degrade the effective umber f bit /05/$ IEEE. 38

2 (EOB) f thee device [0-3]. I cmmuicati ytem, amplig clck jitter i ymbl (r bit) decii circuit--which are pecialized A/D cverter that cvert a aalg igal it a digital data tream--geerate ft bit errr [19]. Hard Errr Widw Clck Sft Errr & ie Pwer V δv t Clck Figure. Time jitter ad digital ytem degradati. Type f Degradati Caued by Time Jitter. Figure hw hw time jitter ca degrade the perfrmace f digital ytem. The left had figure hw hw hard bit errr are created. Fr data t be traferred prperly frm digital ubytem t ub-ytem at clck traiti epch, the clck epch mut fall withi a data-timig widw where data i ettled it the crrect tate. A hard errr thu ccur whe the time jitter caue the clck traiti epch t fall utide f thi widw. The right had figure hw hw bth ft errr ad ie pwer are geerated i digital amplig. I ymbl decii circuit, a aalg igal i tured it a tream f digital ymbl by cmparig the ampled igal t e r mre decii threhld at the amplig clck epch [19]. Samplig clck jitter caue variati i the ampled igal level. Thee variati create a greater ptetial fr bit errr i the preece f thermal ie. Thi prduce a higher BER fr a give iput SR tha there wuld be withut the variati [19]. I A/D ad D/A cverter, time jitter iduced radm variati i the ampled igal geerate multiplicative decrrelati ie frm the cheret igal that i called ie pwer [0-3]. Samplig errr caued by thi ie pwer add t that prduced by the quatizati errr f the device. The et effect f thi i t reduce the effective umber f bit (EOB) f the device t methig le tha i give by the umber f quatizati bit. Time jitter ca be determiitic, uch a that geerated by pur, r radm, uch a that geerated by true ie prcee. Radm ie ca be clred r -tatiary. I the fllwig ecti, we will maily dicu radm jitter. Hwever, the thery preeted al applie t determiitic jitter. Defiiti f Time Errr. Befre plugig it the tatitic f time jitter, it i imprtat clarify what i meat by time r timig errr i digital applicati ad hw time errr i pecified. A hw i Figure 3 i the left had figure, fr data trafer applicati, the time differece betwee the data ymbl ceter ad the clck edge i the time errr parameter. A hw i the right had figure, fr digital amplig applicati, the time differece betwee the clck drivig the aalg igal ad amplig clck epch i the time errr parameter. Trafer Skew Clck Jitter Errr V(t) Digital Samplig Jitter t Skew Errr Figure 3. Timig errr i eparated it kew ad jitter. A al hw i Figure 3, the ttal time errr i brke dw it kew ad jitter term fr bth type f errr. The kew r average errr, i geerally further partitied it fied, lwly varyig, ad evirmetal term. The mt fte ued meaure f kew i the arithmetic mea f the time errr ver me time-perid that may r may t be pecified. The jitter i cidered the high frequecy variati ad i pecified by the rt mea quare (RMS), peak, r peak-t-peak value. The RMS value, which will be ued here, i geerally iterpreted a a -ample ubiaed tadard deviati f the time errr, ad fte the ytem badwidth prpertie are t eplicitly defied [1-8]. It i imprtat t te that bit errr are tied t the ttal errr, t t either the jitter r kew ale. Thu, tadard variace are preferred a the jitter meaure i bit errr applicati becaue thee variace directly referece the kew ad allw the ttal errr t be epreed imply a the um f the jitter ad the kew. Smetime d differece variace baed Alla variace are ued t defie the time jitter [9, 17, 18], but thee variace have the weake f t directly referecig the kew. Mre will be aid abut thi i the et ecti. Fr digital amplig applicati, referece t the kew i imprtat fr ft errr. Fr ie pwer, the kew referece i t imprtat, but it i imprtat fr amplig accuracy ciderati. III. A STATISTICAL FRAMEWORK FOR DISCUSSIG TIME JITTER I the fllwig ecti, we will develp a tatitical framewrk fr later dicui f time jitter ad digital ytem, ad the framewrk develped will eplicitly treat iue f badwidth ad 1/ f ie. It will utilize variu frm f the tadard variace a the meaure f time jitter, rather tha d differece variace, becaue f their direct cecti t the ttal time errr. It will be hw that thee tadard variace cverge i the preece f 1/ f ie becaue f the prpertie f the ytem phae repe fucti. 39

3 Subject Clck Readig V(t) = A(t)F(ω ο t+ φ(t)) V ref (t) = A F(ω ο t) φ ref = 0 Ref Clck Readig t φ δt t t t Baic Clck f Freq Surce Phae Cuter Clck Readig i Phae Cut i 1/ω uit Figure 4. Time errr ad clck readig errr. Time Errr Variable. A hw i Figure 4, there are tw variable fr time errr that are i ue i the literature [1-18]: δt(t ) the time r zer crig errr, ad (t ) the clck readig r rmalized phae errr. T udertad the differece betwee thee tw variable, cider the fllwig. Let the vltage f a ubject clck be give by V(t) = A(t)F(ω t+ φ (t)) (1) where F() i a peridic fucti with a perid f π, A(t) i the amplitude, ω i the mial agular clck frequecy (f = ω /(π) i the mial clck frequecy), ad φ(t) i the phae errr. Thu, V(t) i a early peridic fucti whe pitive gig clck edge t are ued t defie a equece f clck epch. Thee edge t ca be cmpared with equivalet edge t f a referece clck t defie the time errr y (dφ / dt) / ω = d / dt = d( δt) / dt (5) wherea, the derivative f δt i the egative f y. Fr thi rea, (t) will be ued a the time errr variable fr the ret f thi paper. The Variace f Regularly Spaced Sample. Regularly paced ample f are aumed t be give by = dt (t)h (τ t) (6) where h (t) i a liear time-dmai phae repe fucti decribig the filterig prpertie f the ytem f iteret, ad τ i the uifrm amplig iterval. Thi eplicit ue f h (t) will becme very imprtat later fr demtratig the cvergece prpertie f the tadard variace f. A the baic time jitter meaure, we will che t ue the -pit ubiaed tadard variace f the ample (al kw a the ample variace i tatiary tatitic) give by σ d )) = 1 ( τ, ) =< ( ) ( M ( τ, > (7) becaue f it direct referece t the kew. I the abve, < > repreet a eemble average, ad M (τ,) i the kew give by the -pit arithmetic mea where δt(t ) = t t φ(t )/ω () t = π/ω ο = /f (3) M ( τ, ) = (8) = 1 Fr cmpari, the clet d differece variace i give by [10] ad where the apprimate eprei fr δt(t ) give by -φ(t )/ω ca be derived frm (1). A i al hw i Figure 4, a baic clck ca be defied a a frequecy urce with vltage V(t) ad a phae cuter whe readig i i uit f ω -1. Thi rmalized phae cuter readig i equivalet t the readig f a clck face drive by V(t). It ca be hw uig (1) that (t) the clck readig errr betwee the ubject ad referece clck face i give by (t) = φ(t)/ω (4) te that (t) i defied a a ctiuu variable thrugh φ(t). (t) i cidered the preferred variable becaue it derivative i jut the fractial frequecy errr y where ad σ a 0.5τ ( τ, ) =< = 0.5τ y (y M y ( τ, )) > = (9) 1 σ (, τ, τ) y = τ ( ) (10) M ( τ, ) = y (11) y a = 1 Oe ca hw that σ (, τ) ca al be writte a 40

4 σ a 1 1 ( τ, ) = < + > + 1 (1) 4( 1) = 1 Thi hw eplicitly that the direct referece t the kew M (τ,) i σ (, τ) ha bee elimiated. a Bth thee variace ca be related t S (f) the dubleidebad (DSB) pwer pectral deity (PSD) f by uig the pectral itegral repreetati f the variace [5] σ = S (f ) H (f ) K (f )df (13) 0 where: (a) f i the furier frequecy frm the carrier, (b) K (f) i a kerel decribig the prpertie f each type f variace (K (f) i a tad-i fr either K d (f) r K (f).), ad (c) H (f) i the DSB frequecy-dmai repe fucti crrepdig t time-dmai repe h (t). The rea a kerel i ued rather tha the quare f a frequecy repe fucti i that -pit kerel cat be writte a the quare f a igle repe fucti. Fr σ ( τ, ) ad σ (, τ ), e mut write d a (f ) = H (f ) K (14) where H (f) i the repe fucti fr the th reidual. d The kerel fr σ (, τ) i give by 1 i (πfτ) K d (f ) = 1 (15) i ( πfτ) a τ ad the kerel fr σ (, ) i give by i (πfτ) K a (f ) = i ( πfτ) 1 (16) i ( πfτ) Thee kerel are pltted i Figure 5. Fr >> 1ad πfτ << 1, the kerel ca be apprimated by K K d (f ) (1/ 3) ( πfτ) [ >> 1ad πfτ << 1] (17) 4 a (f ) (1/ 3) ( πfτ) [ >> 1ad πfτ << 1] (18) db Thu i geeral, fr f K d f 4 fτ = 1/ f K a (=100) Lg(fτ) Figure 5. Kerel K d(f) ad K a(f) v fτ. α S (f ) 1/ f (19) σd ( τ, ) diverge whe α >, but σ a (, τ) de t diverge util α > 4. Hwever, whe H (f) ha a lw-frequecy cut-ff, σ (, ) ca cverge fr α >. d τ Fr but fiite τ, (f ) ca be writte a K d K d (f ) 1 i c ( πfτ) [, fiite τ] (0) Frm (0), e ca ee that K d (f ) 1 whe τ al ge t ifiity, τ d td 0 Lim σ ( τ, ) σ = df H (f ) S (f ) (1) td where σ i a igle pit tadard variace give by σ td ) =< ( < > > () Thu, whe τ i large, e ca ue σ fr σ d ( τ, ) ule mathematical difficultie frce e t retai the ue f σ (, ) with fiite but large τ. d τ (f ) H i fte apprimated by a quare badpa filter. I thi cae, σ td becme a badpa variace σ td σ bpa = fh fl td S (f ) df (3) where f h i a high frequecy cut-ff ad f l i a lw frequecy cut-ff. w let u ue the tatitical thery etablihed i the previu ecti a a framewrk fr dicuig the prpertie f time jitter fr the variu categrie f digital ytem hw i Figure 1. 41

5 IV. TIME JITTER AD SYCHROOUS DATA TRASFER The firt categry i Figure 1 i ychru data trafer. A metied previuly, thi categry ha a cmm clck that i ditributed t all digital ubytem alg with the data. The et effect f thi i t cacel clck cillatr ctributi t the time jitter at lw frequecie. There i me reidual cillatr ie at the very highet Furier frequecie due t time mialigmet betwee the gate clck i variu part f the ytem. Thi mialigmet ca be repreeted by a highpa repe fucti give by m H (f ) = 4i ( πfτ ) (4) where τ m i the time mialigmet. Fr implicity, let u fld i thi highpa filtered cillatr ie it the lgic gate white ie. The PSD f lgic gate ca be repreeted by S (f ) = g (1 f / f ) (5) + Here, we are aumig that the lgic gate PSD ha the ame pectral frm a the PSD f the amplifier ad traitr that lgic gate are cmped f [4]. g i the white- ie deity cefficiet ad f k i a parametric 1/f kee that i give by the frequecy at which the 1/f ie deity equal the white ie deity. Fr thi categry, H (f) ca be apprimated with a quare lwpa filter. Thu, f l i equal t zer becaue there i phyical rea t itrduce a lw frequecy cut-ff, ad f h i equal t f g, where f g i the aalg ie badwidth f the cmpet ued i the gate. te that f h i t f the clck frequecy, which i geeral i much maller tha f g. Sice a digital ytem tep uifrmly i time frm tate t tate at the clck frequecy f, it i equivalet t a uifrmly ampled ytem. Thu the aalg S (f) ie i badwidth f g i aliaed by thi amplig it a maller ampled badwidth f [5]. A hw i Figure 6, thi multiplie the effect f the white ie i S (f) by a factr f f g /f fr time jitter ciderati. S (f) Sampled S Multiplied by (f g /f ) Aalg S (f) f f 3f.... f g Freq frm carrier k Aalg ie Sampled ie ha ame σ i BW f T T 3T... T 0 Clck Cycle Figure 6. Aliaig f white ie i digital ytem. Sice we have icluded a 1/f term i (5), we eed t cider it impact σ d. Uig (17) i (13), e ca hw that d σ f g l( πf τ) + f g (6) k Thu, the 1/f term i (6) equal the white term whe g g T k fg / fk e = τ = (7) πf Oe ca hw, fr all the type f lgic familie that eit, that T k i much greater tha the life f the uivere. Thu, we ca igre the flicker term i (5) ad (6) fr all practical value f τ ad write d td g σ ( τ,) σ f g (8) I ther wrd, fr ychru ytem, we ly eed ue white ie term fr jitter calculati. V. TIME JITTER AD ASYCHROOUS DATA TRASFER I aychru ytem, ly data i et frm the mater uit r tramitter t remte uit r receiver, ad lcal clck cillatr (LO) i the remte uit are ychrized t the mater clck cillatr (MO) uig phae lcked lp (PLL). Becaue f thi, relative MO-LO clck cillatr time jitter i geerated at the receiver i additi t ychru jitter. The PLL i each receiver ca be decribed by a baebad repe fucti pair h p (t) ad H p (f) [6]. H p (f) ha a lwpa repe with a badwidth B p. Fr furier frequecie le tha B P, the LO track the MO ad uppree the MO-LO jitter, the MO-LO ctributi t the time jitter variace ca be writte a [19] σ td = (f ) 1 Hp(f ) Hh (f ) df 0 g f h Bp S S (f ) df (9) where: (a) S (f) i the um f the PSD f all the cillatr i the T-R lik (MO ad LO plu ther LO i the T-R lik), ad (b) H h (f) i the DSB cmple evelpe repe f the tramit-receiver lik [19]. Fr cmmuicati ytem, H h (f) ca be apprimated by a quare lwpa filter where f h i equal t ½ the ymbl rate R [19]. Fr ther aychru data trafer ytem uch a RS-4, e ha t aalyze the ytem i detail t btai f h (f g ca be ued a a wrt cae value). VI. TIME JITTER AD DIGITAL SAMPLIG RMS Jitter Req fr 0.1 db BER Deg Symbl Rate - dbhz Jitter - lg(ec) Figure 7. RMS Jitter that will prduce 0.1 db BER degradati i QPSK ytem [19]. 4

6 Time jitter i digital amplig caue tw effect: (1) BER degradati i digital cmmuicati ytem ymbl (r bit) decii circuit, ad () ie pwer i A/D ad D/A. Symbl decii circuit i cmmuicati receiver tur the received aalg igal it a tream f digital ymbl by cmparig the igal t e r mre decii threhld at amplig clck epch [19]. Jitter i thee epch create multiplicative vltage ie, which i geerated frm the cheret iput igal by lpe mdulati a hw i Figure. I ymbl decii circuit, thi multiplicative ie iteract with thermal ie that i preet alg with the igal t icreae the BER fr a give iput SR, ad i called BER degradati [19]. The apprpriate time jitter variace fr cmputig thi effect i the um f the ychru ad aychru MO-LO variace. Figure 7 hw the RMS Jitter that will prduce 0.1 db f BER degradati i QPSK ytem a a fucti f ymbl rate [19]. te that, fr ytem i the GHz ymbl rate rage, the time jitter requiremet apprache 1 p. A φ ie Pwer δv Time Jitter Phae Jitter Figure 8. ie pwer geerati i A/D ad D/A cverter []. I A/D ad D/A, the multiplicative ie i called ie pwer [0-3]. T determie the ize f thi ie pwer a a fucti f the amplig clck jitter, cider Figure 8. The fllwig imple derivati f the ie pwer i A/D due t amplig clck jitter i baed that i referece []. The derivati ca al apply t D/A with me redefiiti i termilgy. Let u aume the iput igal i a iewave give by V(t) = A i( ωt + φ) (30) where φ i the phae errr due t amplig clck jitter, ω = πf i the iewave agular frequecy, ad A i the iewave amplitude. If we aume that the amplig pit i ear the middle f the iewave, e ca ee frm Figure 8 that φ = ω = δv / A [ear zer] (31) Takig the variace f bth ide f (31), we btai ear zer V V φ td σ / A = σ / P = σ = ω σ [ear zer] (3) where P the average pwer i the iewave i P = A / (33) Equati (3) i peimitic fr the average ie t igal rati (SR) becaue the amplig pit i t alway ear the ceter f the iewave. Uig σ φ withut the factr f a a better apprimati fr σ V / P, the ie t igal rati (SR) ad igal t ie rati (SR) ca be writte a SR jitter SR jitter φ td = = σ = ω σ (34) te that the SR jitter limit i (34) i idepedet f the umber f digitized bit. Thu, time jitter requiremet becme mre retrictive a the umber f digitized bit i A/D ad D/A icreae. Fr white time jitter, the ampled vltage PSD i the digitized igal i give by the vltage variace divided by the clck frequecy f [7] V td S (f ) f P ω σ [fr white -jitter] (35) The effective umber f bit (EOB) ca be derived frm (34), if we make me further aumpti abut the peratig cditi. Thee aumpti are t uique. The e che here lead t mre cervative EOB frmula tha the i ther referece [], but are mre realitic i term f actual peratig cditi. T geerate the EOB frm (34), e firt ha t defie the relatihip betwee variu ctributi t the SR. Fr ur defiiti f EOB, let u aume that the SR jitter equal SR quat the SR due t quatizati errr ad that there are ther SR ctributr (uch a A/D iaccuracie abve the quatizati level). Thu, we will aume the ttal SR i give by SR = (36) tt SR jitter Secd, e ha t defie the iput igal pwer relative t A/D full cale. Let u aume the iput igal pwer i backedff (BO) by a factr η frm the value fr a full-cale culatig iewave (A = ½ f full cale). Fr the purpe f geeratig the EOB chart t be decribed belw, we will aume the BO η i -10 db becaue thi value apprimately ptimize the SR fr a Gauia igal iput [0, ]. Thi differ frm the BO ued i [], which ue the value f η = 0 db, a urealitic value fr cmple igal iput. Fr a BO f η, SR quat i give by [0, 7] SR qaut = ( / 3) L / η (37) where L i the umber f A/D quatizati bit. Uig (34), (36), ad (37), we ca thu write SR tt a EOB td / tt SR tt = ω σ = ( /3) η (38) 43

7 where we have et SR tt equal t a SR quat value that wuld be btaied if it were the ly ctributr t the SR. Rewritig (38), we btai EOB tt 1/ = lg [(3η) ω σ ] (39) td The graph i Figure 9 hw the time jitter requiremet a a fucti f the ttal SR ad EOB vere the iewave frequecy, ad the table i the figure give typical umerical value. te, fr a 16-bit EOB tt, that 1 p f jitter i required fr digitizig a 4 MHz igal, ad 0.1 p f jitter i required at 44 MHz. Crrepdigly, fr a 10 bit EOB tt, the 1 p ad 0.1 p threhld are cred fr 300 MHz ad 3 GHz igal. Thu, time jitter requiremet fr high peed A/D ad D/A are etremely triget. Thi i a majr perfrmace limitig iue fr high-peed A/D ad D/A. SR tt-db -db Lg 10 (SW Freq Hz) p p 1 p p p p Time Time Jitter Jitter EOB tt fr 10 db BO Jitter 1 p 0.1 p EOB tt SW Freq MHz SW Freq MHz Figure 9. SR tt ad EOB tt a a fucti f time jitter ad iewave frequecy fr η db = -10 db. td Hw t calculate σ r σ d fr digital amplig ytem i the preece f 1 / f ie i a matter f applicati. Fr ytem i which there i a cmm aalg igal ad amplig clck, e wuld ue the frmula fr ychru data trafer. Similarly, whe the amplig clck i lcked t the aalg igal clck thrugh a PLL r me equivalet, e wuld add the MO-LO time jitter frmula fr aychru data trafer t the ychru jitter. Fr ttally uychrized clck, the tadard variace diverge i the preece f 1/f 3 ad higher pwer ie. Hwever, the equivalet f a PLL i fte buried i hidde calibrati applied t mially uychrized ytem. VII. SUMMARY & COCLUSIOS w let u ummarize me f the majr cclui frm the paper. Firt, it ha bee hw that if e eplicitly iclude the prpertie f the ytem repe fucti h (t) fr variu type f digital ytem, e ca ue the tadard variace σ d ( τ, ) ad σ td t defie time jitter whe 1 / f ie i preet. Secd, i ychru data trafer, time jitter caue hard bit errr, e eed ly cider the white ie cmpet, ad e mut cider the effect f aliaig thi ie cmpet. Third, i aychru ytem, time jitter ca al caue ft errr r bit errr rate degradati, ad there i additial jitter due t relative MO-LO clck cillatr jitter. Furthermre, 1 / f clck cillatr ie ctribute t thi MO-LO jitter, ad the jitter i buded becaue f the highpa prpertie PLL i the ytem. Fially, fr digital amplig, ie pwer i A/D ad D/A geerated by amplig clck jitter i a majr limitati the effective umber f bit i high-peed device. [1] IEEE Stadard fr Digitizig Wavefrm Recrder, IEEE Std , IEEE, [] ASI/IEEE Std 80.3a,b,c,e-1988, (Supplemet t ASVIEEE Std ), A America atial Stadard IEEE Stadard fr Lcal Area etwrk: Supplemet t Carrier See Multiple Acce with Cllii Detecti (CSMA/CD) Acce Methd ad Phyical Layer Specificati, IEEE [3] IEEE Std 80.11, Ifrmati techlgy Telecmmuicati ad ifrmati echage betwee ytem Lcal ad metrplita area etwrk Specific requiremet Part 11: Wirele LA Medium Acce Ctrl (MAC) ad Phyical Layer (PHY) pecificati, IEEE [4] IEEE Std , IEEE Stadard Traiti, Pule, ad Related Wavefrm, IEEE 003. [5] Jea-Marie Jaik, Daiel Blyet, ad Beît Guyt, Meauremet f Time Jitter Ctributi i a Dyamic Tet Setup fr A/D Cverter, IEEE Tra. I&M, VOL. 50, O. 3, JUE 001, p786. [6] Agilet ( authr lited), Meaurig Jitter i Digital Sytem, Applicati te , Jue 1, 003. [7] Bria Fetz, Jitter Meauremet i Digital Circuit, Digital-Circuit-Fetz_794-OTES.pdf, Jauary 4th, 003. [8] S. Saad, The effect f accumulated time jitter me ie-wave meauremet, IEEE Tra. Itrum. Mea., 44, pp , [9] ITU-T Recmmedati G.810 (08/96), Defiiti ad Termilgy fr Sychrizati etwrk. ITU, [10] Jame A. Bare, et. al., Characterizati f Frequecy Stability, IEEE Tra. I&M, v IM-0,, May, 1971, p105. [11] B. E. Blair, Ed, Time ad Frequecy Fudametal, BS Mgraph 140, U. S. Gvt. Pritig ffice, CODE:BSMA6, 1974 p166. [1] L. S. Cutler ad C. L. Searle, Sme Apect f the Thery ad Meauremet f Frequecy Fluctuati i Frequecy Stadard, Prc. IEEE v 54,, February, p 136. [13] Patrick Leage ad Claude Audi, Characterizati f Frequecy Stability: Ucertaity due t the Fiite umber f Meauremet, IEEE Tra. I&M, v IM-,, Jue, 1973, p [14] J. Rutma ad F. L. Wall, Characterizati f Frequecy Stability i Precii Frequecy Surce, Prc. IEEE, v 79, 7, July, 1991, p95. [15] D. B. Sulliva, D. W. Alla, D. W. Hwe, F. L. Wall, Characterizati f Clck ad Ocillatr, IST Techicla te 1337, CODE:TOEF, U. S. Gvermet Pritig Office, Jauary, [16] W.F. Wall ad F.L. Wall, Cmputati f Time-dmai Frequecy Stability ad Jitter frm PM ie Meauremet, Prc. 001 IEEE It. Freq. Ct. Symp., [17] D. A. Hwe ad T.. Taet, Clck Jitter Etimati baed PM ie Meauremet, Prceedig f the 003 IEEE Iteratial Frequecy Ctrl Sympium Jitly with the 17th Eurpea Frequecy ad Time Frum, Augut, 003, Mtreal. [18] IEEE : Stadard Defiiti f Phyical Quatitie fr Fudametal Frequecy ad Time Metrlgy Radm Itabilitie, IEEE, [19] Victr S. Reihardt, The Calculati f Frequecy Surce Requiremet fr Digital Cmmuicati Sytem, Prceedig f the IEEE Iteratial Frequecy Ctrl Sympium 50th Aiverary Jit Cferece, 4-7 Augut, 004, Mtréal, Caada. See al [0] Gle A. Grey ad Gee W. Zeli, Quatizati ad aturati ie due t aalg-t-digital cveri, IEEE Tra. Aerpace ad Electric Sytem, Ja. 1971, pp

8 [1] T. Michael Suder, Dald R. Flach, Charle Hagwd, Grace L. Yag, The Effect f Time Jitter i Samplig Sytem, IEEE Tra. I&M, VOL. 39, O. 1, FEBRUARY, 1990, p80. [] Aalg Device ( authr lited), Mied-Sigal ad DSP Deig Techique, Secti, Sampled Sytem, iteret publihed, ee gal_sect.pdf, p [3] IEEE Stadard fr Termilgy ad Tet Methd fr Aalg-t-Digital Cverter, IEEE Std , IEEE 000. [4] F.L. Wall, E.S. Ferre-Pikal, ad S.R. Jeffert, The Origi f 1/f PM ad AM ie i Biplar Jucti Traitr Amplifier, IEEE Tra. Ultraic, Ferrelectric, ad Frequecy Ctrl, 44, pp , March 1, [5] Jh G. Praki, Digital Cmmuicati, McGraw-Hill, [6] William F. Ega, Frequecy Sythei by Pahe Lck, Wiley- Iterciece, [7] Lawrece R. Rabier ad Berard Gld, Thery ad Applicati f Digital Sigal Prceig, Pretice-Hall