A Dual-Mode Synchronous/Asynchronous CORDIC Processor
|
|
- Annis Lambert
- 5 years ago
- Views:
Transcription
1 A Dual-Mode Synchronous/Asynchronous CORDIC Processor Eckhard Grass, Bodhsatya Sarker and Koushk Maharatna IHP Im Technologepark Frankfurt (Oder), Germany grass@hp-mcroelectroncscom Abstract For applcaton n a software defned rado a CORDIC processor has been developed that can operate both n synchronous and asynchronous mode Each mode of operaton has advantages and drawbacks Dependng on the actual applcaton, an optmal trade-off can be acheved by selectng the mode of operaton that fts best wth system demands We beleve that for a system developer ths addtonal degree of freedom sgnfcantly ncreases the applcaton space The desgn has been mplemented on a 05 µm SGe:C BCMOS process Smulaton results usng post-layout extracted parameters ndcate that the desgn s compettve both wth purely synchronous and purely asynchronous mplementatons 1 Introducton Fourth generaton (4G) wreless and moble systems are currently the focus of research and development They wll allow new types of servces to be unversally avalable to consumers and for ndustral applcatons Broadband wreless networks wll enable packet based hgh datarate communcaton sutable for vdeo transmsson and moble Internet applcatons Ths paper s based on a project whch ams to develop a sngle-chp wreless broadband communcaton system n the 5 GHz band, complant wth the Hperlan/ [1] and IEEE 8011a [] standards Both standards specfy broadband communcaton systems usng Orthogonal Frequency Dvson Multplexng (OFDM) wth data rates rangng from 6-54 Mbt/s The duraton of one OFDM symbol, whch can carry 4 to 16 bts of nformaton s 4 µs For such a system a large porton of the dgtal baseband processor has to operate on complex sgnals whch are sampled at a rate of 0 MS/s The most dffcult to mplement functonal blocks of the baseband processor are FFT/IFFT processor, Vterb Decoder, and Numerc Controlled Oscllator (NCO) The NCO s used to perform a frequency correcton on the ncomng sgnals A Coordnate Rotaton Dgtal Computer (CORDIC) offers an elegant way of mplementng an NCO To open a broad market for consumer products, low cost of the requred hardware s essental One way to realse low-cost systems s to reduce system complexty and mplement all functons of a wreless modem n a sngle chp Potentally, a sngle-chp soluton s also advantageous n terms of performance and power dsspaton when compared wth mult-chp mplementatons Fewer sgnals have to be routed va slow and power-hungry pad drvers In addton, short nterconnectons allow faster operaton of the system Our n-house 05 µm SGe:C BCMOS technology enables the ntegraton of complex dgtal baseband functonalty together wth the analog RF front-end (AFE) Ths process technology forms the bass for the sngle-chp mplementaton of a complete wreless modem Ths sngle-chp wreless modem wll hence comprse analog crcutry, processor cores as well as dedcated hardware For the sngle-chp modem, a number of crtcal desgn problems have to be solved One major ssue s the reducton of crosstalk from the dgtal part to the analog crcutry The hgh energy whch s delvered by clock drvers can nfluence the AFE and deterorate ts sgnal to nose (S/N) rato The most predomnant crosstalk mechansms are substrate nose, supply voltage varatons as well as electro-magnetc effects (EMR) [3] Secondly, system power dsspaton s a crtcal ssue Snce many functonal blocks are actve for a lmted perod only, there s potental to reduce power dsspaton drastcally A token-flow approach [4] s adopted by addng sgnals whch ndcate the valdty of data at nputs and outputs of functonal blocks Dstrbutng the control of data flow, ths token-flow approach allows easy mplementaton of clock gatng and lends tself to asynchronous mplementatons of blocks Currently a number of extensons to the standards for 5 GHz broadband communcaton systems are beng dscussed by the standardsaton commttee Therefore, t
2 w ou ld b e b e n e fc a l fo r c u s to m e rs a n d s upp le rs o f tho s e s y s te m s f h a rd w a re w ou ld b e a b le to acc o m m od a te fu tu re c o mm un ca to n s ta nd a rd s A s o ftw a re d e fn e d ra d o, n p rn c p a l, o ff e rs th s n ee d e d fle x b lty H e re w e e x te nd th e d ea o f s o ftw a re d e fn e d ra d o s u c h th a t th e s o ftw a re d e v e lop e r ca n c ho s e ce rta n h a rd w a re acce le ra to rs to op e ra te e th e r s yn c h ro n ou s ly o r a s yn c h ro n ou s ly T h s a dd ton a l d e g ree o f fr e e do m n c rea s e s th e a pp lca ton s p ace o f th e c o m p le te s y s te m F u rth e rm o re, a ls o w th a g v e n s ta nd a rd, d ff e re n t a pp lca ton s ce n a ro s re q u re d ffe re n t p ro p e rte s o f th e h a rd w a re W e a re c onv n c e d th a t h a v ng th e fr ee d o m fo r ce rta n k e y b lo c k s o f c h o o s ng b e tw ee n s yn c h ro nou s a n d a s yn c h ro n ou s o p e ra ton a llo w s fn d ng a s u ta b le tra d e -o ff b e tw ee n po w e r d ss p a ton, c ro ss ta lk, d a ta th rou g hpu t, la te n c y a nd (s e lf-) te s ta b lty A s a n e x a m p le, t m a y b e d e s ra b le w th v e ry s m a ll s gn a l a m p ltud e s on th e rece v e r to re d u ce th e m p ac t o f th e C L K s gn a l by op e ra tng th e C O R D IC n a s yn c h ro nou s ( w h s p e r ) m od e O n th e o th e r h a nd, f th e rece v e s g n a l s v e ry s trong a nd fo r c on tnu o u s rece p to n o f d a ta, th e m o re p o w e r e ff c e n t s y n c h ro n ou s op e ra to n n c o n jun c to n w th c lo c k -g a tn g ca n b e u s e d T h e p a p e r d s c u ss e s a du a l m od e m p le m e n ta ton o f a C O R D IC p ro ce ss o r a nd c o m p a re s th e m a n p a ra m e te rs o f th s d e s gn w th a pu re ly s yn c h ro n ou s a s w e ll a s a pu re ly a s yn c h ro n ou s m p le m e n ta ton It s d e m on s tra te d th a t a s yn c h ro n ou s c rc u ts ca n b e m p le m e n te d n VHD L u s ng s yn c h ro n ou s too ls VHD L s yn th e s s a nd la y ou t a re s uppo rte d by a nu m b e r o f a ttrbu te s a n d c on s tra n ts w h c h a re s p ec fc to th e to o ls u s e d T h e h a rd w a re ov e rh ea d o f th e du a l m o d e C O R D IC p ro ce ss o r c o m p a re d to th e s yn c h ro n ou s v e rs o n s a bou t 1 % It s ho w s a s m la r p e rf o rm a n ce w h e n c o m p a re d to ts s yn c h ro n ou s c oun te rp a rt T h e re m a n n g p a p e r s s tru c tu re d a s fo llo w s : In S ec ton th e a rc h tec tu re o f th e C O R D IC p ro ce ss o r s d e rv e d fro m th e a lgo rth m c s p ec fca ton S ec ton 3 d s c u ss e s s tra te g e s fo r m p le m e n tn g th e d e s gn In S ec ton 4, a n u m b e r o f ss u e s re la te d to th e d e s gn flo w fo r a s yn c h ro n ou s m p le m e n ta ton s a nd th e u s e d too ls a re h gh lgh te d F n a lly n S ec ton 5 th e re s u lts o f o u r m p le m e n ta ton a re re p o rte d a n d c on c lu s on s a re d ra w n n S ec ton 6 C O RD I C P r o c e ss o r A rc h te c tu re T h e v e rs a tlt y o f C O R D IC s upp le m e n te d w th ts m u ltp le rle ss fea tu re h a s p ro p e lle d d g ta l d e s gn e rs to n c o rp o ra te t n s e v e ra l a rth m e tc p ro ce ss o rs a s w e ll a s to fo rm u la te a n d m p le m e n t m a n y m od e rn D SP a lgo rth m s [5-9 ] th a t re qu re c o m p le x n u m b e r m u ltp lca ton, e le m e n ta ry p la n e ro ta ton o r la ttce op e ra ton s In e ss e n ce, th e C O R D IC acce p ts th ree npu t v a ra b le s x0, y 0, a n d z 0 a nd g e n e ra te s th e o u tpu t x 1, y 1 a n d z 1 It ca n b e o p e ra te d n tw o d ff e re n t m o d e s v z, th e ro ta to n a nd th e v ec to rn g m od e w h e re, v a ra b le s z a n d y a re fo rc e d to ze ro re s p ec tv e ly E ac h o f th e s e m o d e s ca n b e u tls e d n c rc u la r, ln ea r a nd h yp e rbo lc c o o rd n a te s y s te m s T h s llu s tra te s th e v e rs a tlt y o f th e C O R D IC a nd e xp la n s w hy t s re g a rd e d a s on e o f th e m a jo r too ls n d g ta l c o m p u te r a rth m e tc H o w e v e r, fo r o u r p u rp o s e t s s u ff c e n t to u s e th e ro ta ton a n d v ec to rng o p e ra ton s n th e c rc u la r c oo rd n a te s y s te m on ly H e n ce w e c o n ce n tra te on th e rea lza ton o f a c rc u la r C O R D IC p ro ce ss o r It s op e ra ton re le s on th e p rn c p le o f v ec to r ro ta ton T h e b a s c op e ra ton s d e s c rb e d b e lo w : T h e ro ta ton o f a v ec to r [ x0 y 0 ] T n th e C a rte s a n c o - o rd n a te s y s te m ca n b e d e s c rb e d a s, Ø x1 ø Œ œ º y 1 ß Ø cos q Œ º - sn q sn q ø Ø x 0 ø cos q œ Œ œ ß º y 0 ß w h e re, [x 1 y 1 ] T s th e fn a l v ec to r a n d q s th e a ng le o f ro ta ton ( q ) In th e a bov e e qu a to n t w a s a ss u m e d th a t th e ro ta to n ta k e s p lace n c lo c k w s e d rec ton N o w, th e ta rg e t a n g le q ca n b e e xp re ss e d a s th e s u mm a ton o f a nu m b e r o f e le m e n ta ry a ng le s a s o th a t b - 1 q s a ( ) 0 w h e re, b s th e b t p rec s on o f th e m a c h n e n w h c h th e op e ra to n s to b e m p le m e n te d a n d s { 1, - 1 }, s kno w n a s th e d rec ton o f ro ta ton In th e c o nv e n to n a l c rc u la r C O R D IC op e ra ton a s e xp re ss e d a s, a tan ( ) (3 ) S ub s ttu tng ( ) n (1 ) a nd u b - Ø x 1 1 ø Œ œ º y 1 ß a nd z 0 cos Ø 1 Œ Œº - s s ng (3 ) o n e m a y w rte - s 1 - ø Ø x œ Œ œß º y ø œ ß (1 ) a (4 ) - 1 s (5 ) Sgn [ a - a r r z + s (6 ) T h e p h y s ca l m ea n ng o f th e s e e qu a to n s s th a t th e ta rg e t a ng le g v e n a s th e z v a ra b le s d rv e n to ze ro by to -a nd -fr o m o ton o f th e v ec to r A t ea c h te ra ton s te p th e s gn o f th e re s du a l a ng le (s ) s ca lc u la te d a n d acc o rd ng ly th e v ec to r s ro ta te d n c lo c k w s e o r c o u n te r c lo c k w s e d rec ton F ro m th e h a rd w a re m p le m e n ta ton p o n t o f v e w, th s op e ra ton c a n b e c a rr e d ou t u s ng on ly s h fta nd -a d d ton o p e ra ton s s n ce m u ltp lca ton o f a n y - qu a n tty b y s a s h ft o f th e b n a ry re p re s e n ta ton o f th e qu a n tty b y -b t to th e rgh t H o w e v e r, th e c onv e n ton a l C O R D IC a lgo rth m s u ff e rs fr o m tw o p rn c p a l d ra w b ac k s, v z, th e re qu re m e n t o f a s ca le fac to r a nd th e s lo w ra te o f c onv e rg e n ce In o rd e r to ov e rc o m e th e s e d ff c u lte s w e d e v e lo p e d a m od fe d C O R D IC a lgo rth m w h c h s d e s c rb e d b e lo w ]
3 In o u r s c h e m e, th e ta rg e t a n g le s ac h e v e d b y ro ta tng th e v ec to r on ly n on e d rec ton (e th e r c lo c k w s e o r c oun te rc lo c k w s e ) th ro u gh s u ff c e n tly s m a ll e le m e n ta ry a ng le s a T h e y c a n b e e xp re ss e d b y th e fo llo w ng e q u a ton s n a - (7 ) T h s a ss u m p ton m po s e s a lo w e r lm t o n th e v a lu e o f te ra ton nd e x T h e lo w e r lm t o f ca n b e ca lc u la te d fr o m th e fac t th a t th e la rg e s t v a lu e n e g lec te d n th e e xp a n s on o f th e s n e s e re s s ( 3 + log 6 ) - ( 3 + / T hu s, th e c o nd ton fo r p re s e rv n g th e acc u rac y d u rn g s u c h a pp rox m a ton b ec o m e s b o r Ø (b ) / 3 ø p (13 ) (s n ce ca n a d o p t on ly n te g e r v a lu e s ) T h e u p p e r lm t o f s b - 1 s n ce a rgh t s h ft o f a ny b -b t nu m b e r b y b -b t w ll re s u lt n m ac h n e ze ro U n d e r th e a bov e c rc u m s ta n ce s, th e v a lu e s o f s n a a n d c o s a ca n b e e xp re ss e d a s, s n a - (14 ) c o s a ( + 1 ) (15 ) C on s d e rng th e a p p ro x m a ton, s + 1 (s n ce th e s gn o f th e re s du a l a ng le s a lw a y s th e s a m e fo r a ll te ra ton s ) a nd c lo c k w s e ro ta to n o f th e v ec to r, e qu a to n (1 ) m a y b e re w rtte n a s b - 1 Ø x 1 ø Œ œ º y 1 ß p Ø1 - Œ - º - - ( + 1 ) 1 - ) - - ( + 1 ) ø Ø x œ Œ ß º y ø œ ß (16 ) E qu a ton (16 ) ca n b e rea lze d n p rac tce u s ng on ly s h ft-a nd -a d d op e ra ton s F u rth e rm o re, c on tra ry to e qu a ton (4 ), n o s ca lng te rm a p p ea rs n e qu a to n (1 6 ), w h c h m p le s a s ca lng fr ee C O R D IC op e ra ton T h e e lm n a ton o f th e s ca lng te rm s a s gn fca n t s te p, s n ce t a vo d s th e re q u re m e n t o f e x tra po s t-p ro ce ss ng c rc u try a nd s a v e s p ro ce ss ng tm e T h e d a ta p a th c o m pon e n ts fo r m p le m e n tng th e op e ra to n o f e qu a to n (1 6 ) a re s h o w n n F gu re 1 T h s ca n b e v e w e d a s a n e le m e n ta ry ro ta to n a l s ta g e re nd e rn g a ro ta to n o f a to ts npu t v ec to r T h s re qu re s fo u r s h fte rs, tw o s ub trac to rs a n d tw o a dd e r / s ub trac to rs a s d a ta p a th c o m po n e n ts T hu s, c o m p a re d to th e d a ta p a th o f th e e le m e n ta ry ro ta to n a l s ta g e o f a n un s ca le d C O R D IC, t re qu re s tw o s h fte rs a nd tw o s ub trac to rs m o re H o w e v e r, fo r th e e le m e n ta ry ro ta ton a l s ta g e s c o rr e s po n d ng to b /, th e s e e x tra s h fte rs a nd s ub trac to rs ca n b e o m tte d a s th e rg h t s h ft o f th e n p u t qu a n tty b y ( + 1 ) b e c o m e s m ac h n e z e ro a n d thu s d o e s no t a ff ec t th e ac c u rac y a ny m o re H o w e v e r, e q u a ton (7 ) m p le s th a t th e c onv e rg e n ce ra ng e o f th e C O R D IC w ll b e s m a ll T h e c onv e rg e n ce ra ng e ca n b e e x te nd e d ov e r th e e n tre c o o rd n a te s p ace by re p ea tng ce rta n te ra to n s te p s a nd by e x p lo tng th e s y mm e try o f th e c o o rd n a te a x e s In p rn c p le, w e fo u nd th a t to c ov e r th e w ho le c oo rd n a te s p ace, t s s u ff c e n t to c o m pu te th e a ng le s n th e n te rv a l [0, 5 ] T h e re s u lts o f C O R D IC ro ta ton s fo r a n y a ng le b e tw ee n 5 a n d ca n b e e x tra po la te d fro m th e re s u lt o f a ro ta ton c o rr e s po n d ng to [0, 5 ] x (- 1 ) y (- 1 ) x (- 1 ) y (- 1 ) b t s h fte r + + x () -b t s h fte r -b t s h fte r + 1 -b t s h fte r y () F gu r e 1 B lo c k d a g r a m o f a n e le m e n ta r y d a ta p a th c o m pon e n t ( r o to r s ta g e ) T h e c o m p le te C O R D IC p ro ce ss o r ca p a b le to op e ra te n th e ro ta ton a nd v ec to rng m od e ov e r th e e n tre c oo rd n a te s p ace h a s th ree p a rts, v z, s gn a nd d o m a n d e tec to n c rc u try, b a s c C O R D IC s ec ton w th c onv e rg e n ce ra ng e 5 a n d th e o u tpu t c rc u try T h s s s ho w n n F gu re T h e s gn a n d do m a n d e tec ton c rc u try (d e s gn a te d a s s gn_d e tec t) d e tec ts th e s gn o f th e npu t a n g le, q u a d ra n t a nd th e d o m a n (po s ton o f th e v ec to r n a qu a d ra n t) o f th e npu t v ec to r A cc o rd ng ly, th e n p u t v a ra b le s a re p ro ce ss e d a nd th e y m a y b e re g a rd e d a s th e m o d fe d n pu t to th e b a s c C O R D IC p ro ce ss o r T h e d e tec ton o f s gn a n d do m a n, p re -p ro ce ss ng a n d a p p ro p ra te npu t o p e ra ton s re qu re tw o c lo c k c y c le s T h e b a s c C O R D IC p ro ce ss o r (d e s gn a te d a s c o rd_p p e ) s a b t p a ra lle l p p e ln e d m p le m e n ta ton w th n te rn a l w o rd le n g th o f 1 6 b ts F ro m e qu a ton (13 ), th e v a lu e o f p fo r a 16 -b t m p le m e n ta to n s a pp rox m a te ly 4 T h e p p e ln e s 1 7 s ta g e s long w h e re th e e le m e n ta ry ro ta ton a l s ta g e c o rre s po n d ng to - 4 s re p ea te d 6 tm e s O u r a m s to a p p rox m a te z a nd y fo r th e ro ta ton a n d th e v ec to rng m od e re s p ec tv e ly w th n a n acc u rac y o f O ( - 16 ) In th e c on s tru c to n o f th e e le m e n ta ry ro ta ton a l s ec ton s, th e c o nv e n to n a l tw o s c o m p le m e n t a dd ton s u s e d T h e n fo rm a ton a bou t th e qu a d ra n t a nd do m a n o f th e n ta l v ec to r d e tec te d a t th e s gn_d e tec t m odu le s tra n s fe rr e d b e tw ee n tw o c on s ec u tv e s ec ton s o f
4 th e p p e ln e a lo n g w th th e d a ta n a lo ca l re g s te r tra n s fe r m a nn e r T h s m ea n s th a t th e d a ta n d ff e re n t s ec ton s o f th e p p e ln e h a s a to k e n a ttrbu te d to t th a t e ss e n ta lly ca rr e s th e n fo rm a ton a b ou t ts n ta l qu a d ra n t a nd do m a n A s ng le b t s gn a l, s gn a nd tw o -b t s gn a ls do m a n a nd qu a d a re u s e d to tra n s fe r th s n fo rm a ton b e tw ee n s u cce ss v e ro ta ton a l s ta g e s x 0 y 0 z 0 m o d e d a ta _v a ld x_ n y _ n z _ n x_ o u t y _ou t z _ o u t s gn_d e te c t ( p p e ln e s ta g e s ) q u a d d o m a n m o d e _ n c o rd_p p e (17 p p e ln e s ta g e s ) q u a d d o m a n d a ta _ v a ld _ n m o d e _ ou t d a ta _ v a ld _ o u t ou tpu t c rc u try (1 p p e ln e s ta g e ) s ta g e ) x 1 y 1 z 1 d a ta _v a ld _ o u t F gu r e S tru c tu re o f t h e s y n c h r onou C O RD IC p r o c ess o r s p p e ln e d T h e ou tp u t c rc u try c on s s ts o f a fx e d s ca lng un t o f 1 / a n d a c o up le o f a dd e r/s ub trac to r un ts T h s c rc u t po s t-p ro ce ss e s th e ou tp u t v ec to r e m e rg n g fro m th e c o rd _ p p e s ec ton n ac c o rd a n ce w th th e n fo rm a to n on th e n ta l v ec to r d e rv e d b y th e s g n_d e tec t c rc u try a n d g e n e ra te s th e fn a l ou tpu t A ll th e op e ra to n s a t th e ou tpu t a re c o m p le te d n on e c lo c k c y c le A m od e s gn a l s a ls o p ro v d e d w th th e p ro ce ss o r T h e log c H IGH s ta te o f th e m od e s gn a l m a k e s th e p ro ce ss o r to op e ra te n ro ta ton m od e w h e rea s ; ts log c L O W s ta te m ea n s th e v ec to rn g m o d e o f op e ra ton s ca rr e d ou t A p a rt fr o m th e m o d e s gn a l, th e (s yn c h ron o u s ) p ro ce ss o r s a ls o e qu pp e d w th a n n pu t d a ta _v a ld a nd a n ou tp u t d a ta _v a ld s g n a l th a t nd ca te s th e v a ld ty o f n pu t a n d ou tpu t d a ta re s p ec tv e ly 3 I m p le m e n ta to n S tr a te g e s m p le m e n te d u s n g a d a ta p a th a rc h tec tu re T h e m o s t c o m p le x b lo c k s n th s d a ta p a th a re C O R D IC -P ro ce ss o r, FF T p ro ce ss o r a nd V te rb D ec o d e r It s ou r go a l to m a k e th e d e s gn o f th e c o m p le te b a s e b a n d p ro ce ss o r a s m u c h a s po ss b le tec hno lo g y nd e p e nd e n t T h e re fo re t h a s b ee n d ec d e d to u s e VHD L fo r d e s g n e n try th ro ug h ou t In o rd e r to d e -ce n tra ls e c on tro l, a to k e n -f lo w a p p ro ac h s u s e d T h e v a ld ty o f d a ta to k e n s s nd ca te d u s n g a dd ton a l s gn a ls a t th e n p u t a nd ou tp u t o f f un c to n a l b lo c k s T o a llo w p e rfo rm a n c e c o m p a rs on, th ree d ff e re n t c rc u ts w e re d e s gn e d : C rc u t M IX -C O R D IC ca n op e ra te b o th s yn c h ro n ou s ly a s w e ll a s a s yn c h ro nou s ly, c rc u t A S Y -C O R D IC op e ra te s a s yn c h ro n ou s ly a n d c rc u t S YN -C O R D IC s a no rm a l s yn c h ron o u s d e s gn w th e x tra s gn a ls to nd ca te d a ta v a ld ty a t npu ts a n d ou tpu ts Dual-mode crcut (MIX-CORDIC): A 4 -ph a s e h a nd s h a k e p ro to c o l s d e p loy e d s n ce t a llo w s th e u s e o f s ng le e dg e trgg e re d flp -f lop s T h e h a nd s h a k e c rc u t o f th e M IX -C O R D IC d e s gn s m p le m e n te d u s n g tw o C -e le m e n ts a s s ho w n n F gu re 3 In o rd e r to a vo d c on fu s on b e tw ee n th e typ e o f th e s gn a l ( npu t o r ou tp u t ) a nd th e po rt o f th e h a nd s h a k e c rc u t, n th s p a p e r w e d e fn e th e npu t p o rt o f th e h a n d s h a k e c rc u t a s po rt a a nd th e ou tpu t p o rt s la b e lle d p o rt b P o r t a re q _a C Element C Element re q _b a c k _ b F gu r e 3 H a nd s h a ke c r c u t f o r c r c u t M IX - C O RD IC P o r t b U n fo rtun a te ly o u r ce ll lb ra ry do e s n o t c on ta n a ny C - e le m e n ts R S flp -f lop s a re a ls o no t a v a la b le C on s e qu e n tly th e C -e le m e n ts h a d to b e c on s tru c te d fr o m g a te s W e m od e lle d th e b e h a v o u r o f th e C -e le m e n ts n VHD L a nd s yn th e s ze d th e m T h e y w e re th e n u s e d a s c o m pon e n ts n th e VHD L d e s gn It w a s fo u nd th a t th e S ynop s y s s yn th e s s e r do e s m e rg e th e fun c ton a lty o f a nu m b e r o f C -e le m e n ts n to a s ng le c rc u t d u rng op tm za ton s ta g e S n ce n th s p ro ce ss tm ng c on s tra n ts a re v o la te d, th e C -e le m e n t c o m p on e n ts h a d to b e p ro tec te d fr o m o p tm s a ton u s ng do n t tou c h a ttrbu te s T h e nd v du a l C -e le m e n ts w e re e x te n s v e ly s m u la te d u n d e r a v a re ty o f c ond to n s a nd w e re fo u nd to b e fun c ton n g c o rr ec tly th rou g hou t B e fo re a p p lca ton n th e C O R D IC p ro ce ss o r, o u r h a nd s h a k e c rc u t w a s a ls o e x te n s v e ly te s te d u s ng a n a s yn c h ro n ou s F IF O T h e m a n c o m p o n e n ts o f th e O F D M b a s e b a nd p ro ce ss o r f o r H p e rla n / a nd IEEE a ca n ea s ly b e
5 n p u t o u tp u t C lo c k _g lo b a l s y n c r e q _ a _ t o p F gu r e 4 S ng le s ta g e o f a n a s y mm e le m e n t e tr c d e lay F o r c o m p le to n d e tec ton a bo u nd e d d e la y m e th od w a s u s e d d e p lo y ng a s p ec a l a s y mm e trc d e la y e le m e n t w th s ho rt rec ov e ry tm e A s ng le s ta g e o f th s d e la y e le m e n t s s ho w n n F gu re 4 A lte rn a tv e ly a ca s ca d e o f tw o -npu t AND g a te s ca n b e u s e d w h e re b y th e npu t s gn a l s c onn ec te d n p a ra lle l to a ll AND g a te s H o w e v e r th e n p u t ca p ac ta n ce o f th s s tru c tu re s ca le s w th th e le ng th o f th e ca s ca d e w h c h c rea te s a h g h ca p ac tv e lo a d on th e npu t s gn a l m a k ng th e d e la y h gh ly un p re d c ta b le A ca s ca d e o f te n s ta g e s o f th e s tru c tu re s ho w n n F gu re 4 d e lv e rs n ou r c rc u t a d e la y o f 13 4 n s a nd 4 8 n s fo r a rs ng a nd a fa llng tra n s ton re s p ec tv e ly (m ea s u re d a fte r b ac k a nno ta to n fro m la y o u t) T h e rec ov e ry tm e fo r th e fa lln g tra n s ton o f s u c h a ca s ca d e s e qu v a le n t to th e d e la y o f fou r nv e rte rs o f a s ng le s ta g e e a pp rox m a te ly 0 8 n s n ou r ca s e T h s rec ov e ry tm e s d m e n s on e d s u c h th a t t s w e ll b e lo w a ny p o ss b le re s pon s e tm e o f th e h a n d s h a k e c rc u try T h e ac h e v e d ra to b e tw ee n rs e tm e a n d fa ll tm e o f n ea rly 3 :1 y e ld s a s ub s ta n ta l s p ee dup o f th e h a nd sh a k e c rc u t w h e n c o m p a re d to u s ng a n o rm a l n v e rte r c h a n T h e c rc u t do e s no t s u ff e r f ro m h gh n pu t ca p ac ta n ce w h c h a ls o k ee p s ts po w e r d ss p a ton lo w T o a llo w s w tc h ng b e tw ee n s yn c h ro nou s a n d a s yn c h ro n ou s m o d e, fo r th e du a l-m od e c rc u t a dd ton a l log c s n trodu c e d to e th e r e n a b le th e a s yn c h ron o u s h a nd s h a k e c rc u t o r th e s yn c h ro n ou s c lo c k to d rv e th e p p e ln e s ta g e s a s s ho w n n F gu re 5 If th e s yn c s gn a l s n log c h g h s ta te, th e c lo c k s gn a l C lo c k_g lo b a l s e n a b le d v a th e NAND g a te a t th e n p u t T h e s tru c tu re s c on fg u re d to w o rk n s yn c h ro n ou s m od e A t th e s a m e tm e r e q_ a _ top s d s a b le d v a th e NO R g a te d rv n g r e q_ a T h e c o m p le te h a nd s h a k e c rc u t s d s a b le d by fo rc ng r e q _ a to log c lo w O n th e c on tra ry f s yn c s n lo g c lo w s ta te, th e g lo b a l c lo c k C lo c k_g lob a l s d s a b le d a nd th e c rc u t s c on fg u re d fo r a s yn c h ro nou s o p e ra ton by e n a b lng r e q_ a _ top to d rv e s gn a l r e q _ a C u rre n tly th e re s no dyn a m c s w tc h ng o f m o d e c o n s d e re d e s gn a l s yn c s a llo w e d to c h a n g e s ta te on ly w h e n C lo c k _ g lob a l s lo w a nd th e p p e ln e s c o m p le te ly s e ttle d T h s p re v e n ts po te n ta l h aza rd s d u rn g m o d e -c h a n g e o p e ra ton s w h c h c ou ld re s u lt n und e fn e d s ta te s o f th e s y s te m x 0 y0 z P p e l n e s ta g e 1 P p e l n e s ta g e P p e l n e s ta g e x 1 y1 z 1 r e q _ a r e q r e q r e q H a n d s h a k e 1 a c k H a n d s h a k e a c k a c k H a n d s h a k e 0 r e q _ b F gu r e 5 S c h e m a tc d a g r a m o f du a l-m od e C O RD IC a c k _ b A s y n c h r o n o u s c r c u t u s n g la tc h e s (A S Y -C O R D I C ): A s ec ond v e rs o n u s e s la tc h e s n s tea d o f f lp -f lop s fo r bu ff e rng th e d a ta S n ce la tc h e s a re s m a lle r a n d c on s u m e le ss po w e r, th s ca n po te n ta lly re du ce s lc on a rea a nd po w e r d ss p a ton F o r ou r a pp lca ton, th e s e m -d ec o up le d la tc h c on tro lle r do e s re p re s e n t a rea s on a b le c o m p ro m s e b e tw ee n h a rd w a re c o m p le x ty a n d p e rfo rm a n c e [1 1 ] T h e a s y mm e trc C -e le m e n ts u s e d n th s c on tro lle r w h e re d e s gn e d n th e s a m e w a y a s d e s c rb e d a bov e T h e re s u ltng h a nd s h a k e c rc u try w a s a g a n te s te d n a n a s yn c h ro n ou s F IF O P e rf o rm a n ce m ea s u re m e n ts b a s e d o n s m u la ton s u s ng po s t-la y o u t e x trac te d p a ra m e te rs a re g v e n n T a b le 1 S y n c h r o n o u s c r c u t (S Y N -C O R D I C ): T h e s yn c h ron o u s m p le m e n ta ton w a s d on e u s n g e x ac tly th e s a m e p p e ln e a rc h tec tu re a s fo r th e o th e r tw o d e s gn s In o rd e r to s up p o rt th e to k e n -f lo w a p p ro ac h d a ta v a ld s gn a ls w h e re n trodu ce d a t n p u t a nd ou tpu t po rts o f th e p p e ln e A p e rf o rm a n ce c o m p a rs on o f th e th ree d ff e re n t m p le m e n ta ton s s g v e n n T a b le 1 In te rf ac n g o f th e a s yn c h ronou s ou tp u ts w th th e s yn c h ro n ou s e n v ron m e n t s don e u s ng a n a dd ton a l (s yn c h ro nou s ) D -typ e flp -f lo p fo r th e re q u e s t s gn a l a t th e ou tpu t ( r e q _b n F gu re 5 ) U s ng a typ ca l c lo c k
6 fr e qu e n c y o f 0 M H z fo r th e s yn c h ro n ou s c rc u t w ll -55 re s u lt n a v e ry lo w p rob a b lty o f m e ta s ta b lty o f P 10 o r a n M T B F o f 3x y ea rs [1 ] F o r ty p ca l a pp lca ton s th s w ll no t re qu re a n y a d d ton a l m ea s u re s to re du ce m e ta s ta b lty p rob a b lty fu rth e r 4 D e s g n -F lo w Iss u e s A ll v e rs on s o f th e C O R D IC p ro ce ss o r w e re m od e le d n VHD L a nd a re fu lly s yn th e s ze d F o r s m u la ton a n d fun c ton a l v e rfca ton w e u s e d M od e ls m fro m M e n to r G ra ph c s S yn th e s s w a s ca rr e d ou t w th S y n op s y s D e s gn A n a ly ze r a n d th e la yo u t w a s g e n e ra te d u s ng S lc on E n s e m b le fr o m C a d e n ce T h e d e s gn w a s m a p p e d to ou r n -h o u s e 0 5 m m S G e :C B C M O S tec hno logy u s ng th e IH P d g ta l d e s g n k t T h e no m n a l s u pp ly vo lta g e fo r c o re ce lls s 5 V F ou r m e ta l la y e rs a re a v a la b le fo r n te rc o n n ec t T h e C O R D IC p ro ce ss o r u tlze s on ly th e C M O S p a rt o f o u r B C M O S tec hno logy B o th, fo r s yn th e s s a nd la you t s o m e a ttrbu te s a nd c on s tra n ts w e re a dd e d to s up p o rt th e a s yn c h ro nou s m p le m e n ta ton A fte r s y n th e s s th e g a te le v e l V e rlog n e tls t g e n e ra te d by th e D e s gn A n a ly ze r w a s re -s m u la te d n c lud ng th e S ta nd a rd D e la y F o rm a t (S D F ) f le T h e c o rr ec t tm ng b e h a v o r o f th e p ro ce ss o r n b o th th e ro ta ton a n d v ec to rng m od e w a s ob s e rv e d F o r d rv n g th e lo ca l c lo c k s gn a ls o f th e nd v d u a l s ta g e s w e ftte d th e c lo c k s gn a l o f e v e ry p p e ln e s ta g e w th a n a pp rop ra te c lo c k b u ff e r T h s bu ffe r w a s s yn th e s ze d s e p a ra te ly a nd p ro tec te d w th th e h e lp o f don t tou c h a ttrbu te s T h e a rea o f a tra n s p a re n t la tc h u s e d n th e A S Y - C O R D IC d e s gn s 118 m m a nd th e a rea o f th e D -ty p e flp - flop s u s e d n M IX -C O R D IC a nd S YN -C O R D IC s 180 m m (acc o rd n g to IH P ce ll lb ra ry ) T h e la tc h b a s e d v e rs on ca n th e re fo re po te n ta lly re s u lt n s m a lle r s lc on a rea T h e d e s g n flo w fo r d e s g n A S Y -C O R D IC s d e s c rb e d n d e ta l b e lo w In p rn c p a l, th e s a m e a p p ro ac h w a s u s e d fo r th e M IX -C O R D IC c rc u t T h e no rm a l s yn c h ro n ou s m p le m e n ta ton d o e s no t re q u re a n y e x tra m ea s u re s a nd s th e re fo re g e n e ra te d u s n g th e s ta nd a rd s yn th e s s flo w w th c lo c k -tree g e n e ra ton du rn g la y o u t ph a s e T h e la tc h e s w th n eac h p p e ln e s ta g e a re c o n tro lle d w th a s gn a l lt w h c h ca u s e s th e la tc h to b e tra n s p a re n t w h e n lo w a n d n h o ld s ta te w h e n h gh S n ce th e d a ta p a th s n to ta l 50 b t w d e, th e lt s gn a l m u s t h a v e a rea s on a b le d rv e s tre ng th T h e re fo re a bu ff e r s u s e d fo r eac h p p e ln e s ta g e to d rv e s gn a l lt T o k ee p th e s lc on a rea a s s m a ll a s po ss b le, w e u s e d la tc h e s w th a n a s yn c h ro n ou s re s e t s gn a l T h s s ac h e v e d by n s e rtn g th e S yn th e s ze r s p ec fc a ttrbu te a s yn c _ s e t_ re s e t n th e VHD L s ou rce c od e A fte r s e p a ra te ly s yn th e s z ng ea c h o f th e 0 p p e ln e s ta g e s, th e y w e re c onn ec te d w th th e r re s p ec tv e h a nd s h a k e c rc u t E a c h h a n d s h a k e c rc u t h a d a d e la y e le m e n t (tu n e d to th e c rtca l p a th o f th e c o m b n a ton a l lo g c ) n s e rte d n to th e n pu t re qu e s t s gn a l A tm ng m a rg n o f 30 % w a s a dd e d to gu a ra n tee re la b le op e ra ton a fte r la y o u t T h e n th e to p le v e l d e s gn w a s s yn th e s ze d s e p a ra te ly a nd th e n e tls ts o f th e nd v du a l p p e ln e s ta g e s w h e re n te g ra te d n to th e top -le v e l n e tls t T h e la you t w a s ca rr e d ou t u s ng th e s ta nd a rd ce ll a pp ro a c h o f S lc on E n s e m b le w th 8 0 % ro w u tlza ton P o s t la you t p a ra s tc p a ra m e te rs w e re e x trac te d a n d a V e rlog n e tls t tog e th e r w th th e po s t la you t S D F fle w e re e xpo rte d T h s V e rlog n e tls t w a s a g a n s m u la te d u s ng th e s a m e VHD L te s t b e n c h th a t w a s u s e d fo r th e b e h a v o ra l m od e l T h s s m u la ton c o n frm e d th e c o rr ec t op e ra ton a nd fo rm s th e b a s s fo r th e la te n c y a nd th rou g hpu t m ea s u re m e n ts re p o rte d n th e fo llo w n g S ec ton 5 R e s u lts a nd C o m p a r s o n F o r m ea s u rng th e p e rfo rm a n ce o f th e a s yn c h ro n ou s c rc u ts th e v a rou s h a nd s h a k e s gn a ls a re g e n e ra te d fr o m th e te s t b e n c h u s ng a n d ea l d a ta s o u rce a n d a n d ea l d a ta s nk T h e n p u t d a ta s s upp le d n th e te s t b e n c h fr o m a fle F o r th e a s yn c h ro n ou s m o d e o f op e ra to n, d a ta s b e ng s upp le d to th e e n tty w th th e rs ng e dg e o f n p u t re q u e s t s gn a l r e q_ a _ top s h o w n n F g u re 5 W th th e d e la y n th e h a nd s h a k e c rc u t b e n g n s e rte d n th e p a th o f s gn a l r e q_ a _ top, th e ac k no w le dg e s gn a l ac k_ a _ top go e s h g h a fte r th e c o m b n a ton a l lo g c b lo c k fn s h e s t s c o m pu ta ton T h e lo ca l c lo c k s gn a l n ea c h o f th e c o m pon e n ts s c onn ec te d to s gn a l ac k _ a o f eac h re s p ec tv e h a nd s h a k e c rc u t H e n ce, w th th e rs ng tra n s ton o f a c k_ a, th e c o m p u te d d a ta s la tc h e d to th e d a ta re g s te rs T h e la te n c y fo r a s y n c h ronou s op e ra to n s m ea s u re d a s th e tm e n te rv a l fro m th e rs ng e dg e o f n p u t s gn a l r e q_ a _ top to th e rs ng e dg e o f o u tpu t s gn a l r e q_ b _ to p T h s m ea s u re m e n t s ca rr e d o u t w th a n e m p ty p p e ln e a s a n n ta l s ta te a nd h e n ce a ss u m e s op e ra ton n th e d a ta lm te d re g o n a s d e fn e d n [1 3 ] T h e m a x m u m th ro ug h pu t s m ea s u re d a s th e nu m b e r o f d a ta s a m p le s e m e rg ng a t th e ou tp u t w h e n th e npu t s d rv e n by a n d ea l s ou rce a nd th e ou tp u t s c onn ec te d to a n d ea l d a ta s nk F o r th e s yn c h ro n ou s d e s gn, th e la te n c y s d e p e nd e n t on th e c lo c k fr e qu e n c y T h e c o re a rea fo r a ll th ree d e s gn s s m ea s u re d fr o m th e la y o u t a n d re p o rte d n T a b le 1 tog e th e r w th p o w e r d ss p a ton, la te n c y a nd th ro u gh p u t
7 T a b le 1 P e r fo r m a n c e c o m p a r s on o C O RD IC m p le m e n ta ton s C o re a rea (n mm ) P o w e r (n m W ) L a te n c y (n n s ) T h ro u gh - pu t (M S /s ) f t h r ee A S Y - M IX -C O R D IC S YN - C O R D IC S yn c h m od e A s yn c h m od e C O R D IC (16 ) (9 4 ) (7 ) (9 8 ) It s s ho w n n T a b le 1 th a t th e M IX -C O R D IC d e s gn re qu re s on ly 13 % m o re s lc on a rea th a n th e S YN - C O R D IC A s ub s ta n ta l a dv a n ta g e s th e re du c e d la te n c y In p a rtc u la r fo r tra n s m ttng ac k no w le dg e m e n t fr a m e s w h c h h a v e to b e g e n e ra te d a t a fx e d tm e n te rv a l o f 1 6 m s a fte r r ece p to n o f a fr a m e, a ny re du c to n n la te n c y n th e d a ta p a th s w e lc o m e T h e d a ta th rou g hpu t o f M IX - C O R D IC a nd S YN -C O R D IC a re s m la r T h e d ff e re n ce o f 45 M S /s v e rs u s 40 M s /s s p rob a b ly du e to th e p a rtc u la r la you t F u rth e rm o re, th e le v e l o f m a n u a l n te rac ton fo r th e M IX -C O R D IC d e s gn w a s h gh e r, w th b u ff e rs b e ng e xp lc tly n s e rte d n to e v e ry p p e ln e s ta g e C rc u t A S Y -C O R D IC h a s s gn fca n tly s m a lle r s lc on a rea e % le ss th a n S YN -C O R D IC T h s s p a rtly du e to th e s m a lle r s ze o f tra n s p a re n t la tc h e s c o m p a re d to e d g e trgg e re d flp -f lo p s F u rth e rm o re, n c on tra s t to S YN - C O R D IC a nd M IX -C O R D IC, th e A S Y -C O R D IC d e s gn do e s no t re qu re a ny c lo c k tree T h e u s e o f lo ca l n te rc onn ec t on ly, re s u lts n c on s d e ra b le s a v n g s n s lc on a rea T h e h gh e r la te n c y o f c rc u t A S Y -C O R D IC s du e to th e m o re c o m p le x h a nd s h a k e c rc u t fo r th s d e s gn T h e tra n s p a re n t p h a s e o f th e la tc h e s re qu re s c o u p lng o f c on s ec u tv e s ta g e s th a t s re flec te d by a dd ton a l d e la y s T h e po w e r d ss p a ton fgu re s g v e n n T a b le 1 w e re d e rv e d fro m th e s yn th e s s too l F ro m p re v ou s e xp e re n ce th e s e fgu re s a re v e ry u n re la b le T h e d s tn c tly h gh e r po w e r d ss p a ton o f A S Y -C O R D IC m a y re s u lt fr o m th e S ynop s y s s o ftw a re fa ls e ly e s tm a tng h g h g ltc h n g ac tv ty n th e do w n s trea m c rc u ts du rng th e tra n s p a re n t ph a s e o f th e la tc h e s C u rre n tly w o rk s u n d e rw a y to g e n e ra te m o re acc u ra te fgu re s u s n g th e p o w e r s m u la to r P o w e r M ll T h e la you t o f th e M IX -C O R D IC p ro ce ss o r, ftte d w th a n a log te s t c rc u ts fo r c ro ss ta lk nv e s tg a ton, s s ho w n n F gu re 6 In o rd e r to p re v e n t d rec t c oup ln g fro m n p u t s gn a ls n to th e a n a log te s t c rc u ts a C -s h a p e d p lace m e n t o f th e d g ta l p a d s w a s und e rta k e n F o u r d e n tca l o s c lla to rs a re p lace d a t th e ea s t s d e o f th s la you t, eac h ftte d w th a d ff e re n t s tru c tu re fo r p ro tec ton fr o m s ub s tra te no s e F ro m to p to bo tto m th e d e p loy e d p ro tec ton s tru c tu re s a re : 1 ) GND rn g a n d n -w e ll rn g, ) bu re d la y e r s h e ld, 3 ) n o p ro tec ton, a nd 4 ) G ND rng on ly A d d ton a lly th re e s ub s tra te c on tac ts fo r d rec t m ea s u re m e n t o f s ub s tra te no s e a re p lac e d a t top e nd, m dd le a nd bo tto m e nd o f th e rgh t e d g e re s p ec tv e ly W e hop e th a t th s d e s g n w ll d e lv e r v a lu a b le n fo rm a ton on th e e ff c e n c y o f d ffe re n t m ea s u re s fo r p ro tec to n fr o m s ub s tra te no s e, bo th fo r s y n c h ro nou s a n d a s yn c h ro n ou s op e ra ton o f th e C O R D IC p ro ce ss o r C O R D I C c o r e s u b s t r a te c o n ta c ts a n a lo g o s c ll a to r s F gu r e 6 L ay ou t o f c r c u t M IX -C O RD IC w th a n a log tes t c r c u ts a t r gh t s d e 6 C o n c lu s o n s a nd F u tu re Wo r k A p p e ln e d C O R D IC p ro ce ss o r w h c h ca n o p e ra te b o th s yn c h ro n ou s ly a s w e ll a s a s yn c h ro nou s ly h a s b ee n d e s gn e d n VHD L a n d m p le m e n te d u s ng a 0 5 m m S G e :C B C M O S p ro ce ss W th n a s o ftw a re d e fn e d ra d o fra m e w o rk, th e op p o rtun ty to op e ra te k e y h a rd w a re c o m pon e n ts e th e r n s yn c h ro n ou s o r a s yn c h ro n ou s m od e ca n o ff e r a dd to n a l fr ee d o m fo r th e s y s te m d e v e lop e r U s ng th s fea tu re, a m o re o p tm a l c o m p ro m s e b e tw ee n po w e r- d ss p a ton, c ro ss ta lk, th ro u gh p u t, la te n c y a nd (s e lf-) te s ta b lty ca n b e fo und A s a n e x a m p le, to re du ce c ro ss ta lk, th e c rc u t ca n b e s w tc h e d n to a s yn c h ro n ou s m od e w h e n th e rece v e s gn a l le v e l s v e ry lo w F o r rea s on a b le s gn a l s tre ng th a nd c on tn u ou s op e ra ton th e m o re p o w e r e ff c e n t s y n c h ro n ou s m od e ca n b e c h o s e n A n a dd ton a l a pp lca to n o f ou r M IX -C O R D IC c rc u t s to s e rv e a s a n v e h c le fo r d e ta le d nv e s tg a tng o f th e n te rf e re n ce c a u s e d by s y n c h ro n o u s a nd a s yn c h ro nou s d g ta l c rc u ts on S G e :C b po la r a nd C M O S a n a log c rc u ts F u rth e r w o rk w ll fo c u s o n e x te n d ng ou r ce ll lb ra ry a nd d e s gn k t by a nu m b e r o f ce lls c ru c a l fo r a s yn c h ro n ou s d e s gn S u c h ce lls a re, fo r n s ta n ce, v a rou s C -e le m e n ts, c o m p le te h a nd s h a k e c rc u ts a nd lo w -po w e r
8 tun a b le d e la y e le m e n ts T h e ce lls w ll b e d e s gn e d on tra n s s to r le v e l, n c lud e d n to th e ce ll lb ra ry a n d m a d e a v a la b le a s c o m p o n e n ts n VHD L a nd V e rlo g T h e M IX -C O R D IC d e s gn re po rte d h e re, n c lu d ng th e a n a log te s t c rc u ts, h a s b ee n ta p e d o u t fo r fa b rca to n o n ou r n -hou s e 0 5 m m S G e :C B C M O S p ro ce ss n D ece m b e r 0 01 F rs t re s u lts, n c lud n g m ea s u re m e n ts on n te rf e re n ce o f th e a n a log c rc u ts fo r s yn c h ro nou s a n d a s yn c h ro n ou s o p e ra ton o f th e M IX -C O R D IC d e s gn w ll b e a v a la b le b y th e m d d le o f M a rc h 00 A c kn o w le d g e m e n ts W e w ou ld lk e to ac k n o w le dg e th e s upp o rt fro m U lrc h J a gdho ld fo r g e n e ra tn g th e d g ta l la y ou t F u rth e rm o re, w e a re g ra te fu l o f th e s u p po rt fr o m W o lfg a ng W nk le r fo r d e s g n a nd la you t o f th e a n a logu e te s t c rc u ts fo r th e du a l-m od e C O R D IC m p le m e n ta ton R e fe re n c e s [1 ] S ta nd a rd ET S I D T S /BR AN , B ro a d b a n d R a d o A cce ss N e tw o rk s (BR AN ); H IP E R L AN T yp e F un c ton a l S p ec fca to n s P a rt 1 P hy s ca l (P HY ) la y e r ; J un e [ ] S ta nd a rd IEEE P a /D 7 0, P a rt 1 1 : W re le ss L AN M e d u m A cce ss C on tro l (M A C ) a nd P h y s ca l L a y e r (P HY ) s p ec fca ton s : H gh S p ee d P h y s ca l L a y e r n th e 5 GH z B a nd ; J u ly [3 ] J M C a s a lta, X A ro g on e s a n d A R ub o, S ub s tra te C ou p ln g e v a lu a to n n B C M O S T e c h n o lo gy, IEEE J ou rn a l o f S o ld S ta te C rc u ts, vo l 3, n o 4, p p , A p rl [5 ] D S C o c h ra n, A lgo rth m s a n d acc u rac y n th e H P 35, H e w le tt P ac k a rd J, pp , J u n e [6 ] A M D e s p a n, V e ry fa s t F ou re r tra n s fo rm a lg o rth m s fo r m p le m e n ta to n, IE E E T ra n s C o m p u t, v o l C 8, no 5, p p , M a y [7 ] D T L ee a n d M M o rf, G e n e ra lze d C O R D IC fo r d g ta l s gn a l p ro ce ss ng, P ro c IC A SSP, v o l 3, p p , M a y [8 ] M C M a nd a l, A S D h a r a n d S B a n e rjee, M u ltp le rle ss a rr a y a rc h tec tu re fo r c o m pu tn g d s c re te c o s n e tra n s fo rm, C o m p u te rs E lec E ng, v o l 1, n o 1, p p , [9 ] A S D h a r a nd S B a n e rjee, A n a rr a y a rc h tec tu re fo r fa s t c o m pu ta to n o f d s c re te H a rtle y tra n s fo rm, IEE E T ra n s C rc u ts a n d S y s t, vo l 3 8, n o 9, p p , [10 ] I S u th e rla n d, M c ro p p e ln e s, C o mm u n c a to n s o f th e A C M, 3 (6 ), pp , Jun e [11 ] P D a y, J V W o o d s, In v e s tg a to n n to M c rop p e ln e L a tc h D e s gn S ty le s, IE E E T r a n s O n V L S I S y s te m s, 3 ( ), pp 64-7, [1 ] J N S e z o v c, P p e ln e S yn c h ro n s a ton, P ro c In te rn a to n a l S y m po s u m o n A d v a n ce d R e s ea rc h n A s yn c h ro n o u s C rc u ts a n d S y s te m s, pp , N o v e m b e r [13 ] T E W lla m s, P e rf o rm a n ce o f I te ra tv e C o m p u ta to n n S e lf- T m e d R n g s J ou rn a l o f V L S I S g n a l P ro ce ss ng, (7 ), pp , [4 ] J B u c k a n d E A L ee, T h e to k e n flo w m o d e l, D a ta F lo w W o rk sh o p, H a m lto n Is la n d, A u s tra la, p p , M a y 1 9 9
A L A BA M A L A W R E V IE W
A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N
More informationc. What is the average rate of change of f on the interval [, ]? Answer: d. What is a local minimum value of f? Answer: 5 e. On what interval(s) is f
Essential Skills Chapter f ( x + h) f ( x ). Simplifying the difference quotient Section. h f ( x + h) f ( x ) Example: For f ( x) = 4x 4 x, find and simplify completely. h Answer: 4 8x 4 h. Finding the
More informationLU N C H IN C LU D E D
Week 1 M o n d a y J a n u a ry 7 - C o lo u rs o f th e R a in b o w W e w ill b e k ic k in g o ff th e h o lid a y s w ith a d a y fu ll o f c o lo u r! J o in u s fo r a ra n g e o f a rt, s p o rt
More informationT h e C S E T I P r o j e c t
T h e P r o j e c t T H E P R O J E C T T A B L E O F C O N T E N T S A r t i c l e P a g e C o m p r e h e n s i v e A s s es s m e n t o f t h e U F O / E T I P h e n o m e n o n M a y 1 9 9 1 1 E T
More informationheliozoan Zoo flagellated holotrichs peritrichs hypotrichs Euplots, Aspidisca Amoeba Thecamoeba Pleuromonas Bodo, Monosiga
Figures 7 to 16 : brief phenetic classification of microfauna in activated sludge The considered taxonomic hierarchy is : Kingdom: animal Sub kingdom Branch Class Sub class Order Family Genus Sub kingdom
More informationGrain Reserves, Volatility and the WTO
Grain Reserves, Volatility and the WTO Sophia Murphy Institute for Agriculture and Trade Policy www.iatp.org Is v o la tility a b a d th in g? De pe n d s o n w h e re yo u s it (pro d uc e r, tra d e
More information600 Billy Smith Road, Athens, VT
600 Billy Smith Road, Athens, VT Curtis Trousdale, Owner, Broker, Realtor Cell: 802-233-5589 curtis@preferredpropertiesvt.com 2004 Williston Road, South Burlington VT 05403 www.preferredpropertiesvt.com
More informationMOLINA HEALTHCARE, INC. (Exact name of registrant as specified in its charter)
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 FORM 8-K Current Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event
More informationTTM TECHNOLOGIES, INC. (Exact Name of Registrant as Specified in Charter)
Table of Contents UNITED STATES SECURITIES AND EXCHANGE COMMISSION WASHINGTON, DC 20549 FORM 8-K CURRENT REPORT Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 November 15, 2006
More information176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s
A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps
More informationClass Diagrams. CSC 440/540: Software Engineering Slide #1
Class Diagrams CSC 440/540: Software Engineering Slide # Topics. Design class diagrams (DCDs) 2. DCD development process 3. Associations and Attributes 4. Dependencies 5. Composition and Constraints 6.
More informationBeechwood Music Department Staff
Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d
More informationPR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n
R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th
More information4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd
n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,
More informationH NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f
More informationP a g e 5 1 of R e p o r t P B 4 / 0 9
P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e
More informationH STO RY OF TH E SA NT
O RY OF E N G L R R VER ritten for the entennial of th e Foundin g of t lair oun t y on ay 8 82 Y EEL N E JEN K RP O N! R ENJ F ] jun E 3 1 92! Ph in t ed b y h e t l a i r R ep u b l i c a n O 4 1922
More information4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th
n r t d n 20 2 :24 T P bl D n, l d t z d http:.h th tr t. r pd l 4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n
More informationExecutive Committee and Officers ( )
Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r
More information,. *â â > V>V. â ND * 828.
BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,
More informationn r t d n :4 T P bl D n, l d t z d th tr t. r pd l
n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R
More informationTECHNICAL MANUAL OPTIMA PT/ST/VS
TECHNICAL MANUAL OPTIMA PT/ST/VS Page 2 NT1789 Rév.A0 TABLE OF CHANGES The information contained in this document only concerns : OPTIMA PT/ST/VS type, MCM 440 PT/OT type, MCM550 ST type. Technical Manual
More informationTh n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v
Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v ll f x, h v nd d pr v n t fr tf l t th f nt r n r
More informationForm and content. Iowa Research Online. University of Iowa. Ann A Rahim Khan University of Iowa. Theses and Dissertations
University of Iowa Iowa Research Online Theses and Dissertations 1979 Form and content Ann A Rahim Khan University of Iowa Posted with permission of the author. This thesis is available at Iowa Research
More informationANNUAL MONITORING REPORT 2000
ANNUAL MONITORING REPORT 2000 NUCLEAR MANAGEMENT COMPANY, LLC POINT BEACH NUCLEAR PLANT January 1, 2000, through December 31, 2000 April 2001 TABLE OF CONTENTS Executive Summary 1 Part A: Effluent Monitoring
More informationl f t n nd bj t nd x f r t l n nd rr n n th b nd p phl t f l br r. D, lv l, 8. h r t,., 8 6. http://hdl.handle.net/2027/miun.aey7382.0001.001 P bl D n http://www.hathitrust.org/access_use#pd Th r n th
More informationUNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C Form 8-K/A (Amendment No. 2)
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 Form 8-K/A (Amendment No. 2) Current Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report
More informationD t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d
More information0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r
n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.
More informationUNITED STATES SECURITIES AND EXCHANGE COMMISSION FORM 8-K. Farmer Bros. Co.
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 FORM 8-K CURRENT REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 Date of Report (Date of earliest event
More information828.^ 2 F r, Br n, nd t h. n, v n lth h th n l nd h d n r d t n v l l n th f v r x t p th l ft. n ll n n n f lt ll th t p n nt r f d pp nt nt nd, th t
2Â F b. Th h ph rd l nd r. l X. TH H PH RD L ND R. L X. F r, Br n, nd t h. B th ttr h ph rd. n th l f p t r l l nd, t t d t, n n t n, nt r rl r th n th n r l t f th f th th r l, nd d r b t t f nn r r pr
More informationC o r p o r a t e l i f e i n A n c i e n t I n d i a e x p r e s s e d i t s e l f
C H A P T E R I G E N E S I S A N D GROWTH OF G U IL D S C o r p o r a t e l i f e i n A n c i e n t I n d i a e x p r e s s e d i t s e l f i n a v a r i e t y o f f o r m s - s o c i a l, r e l i g i
More information46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th
n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l
More informationOH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9
OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at
More informationSTEEL PIPE NIPPLE BLACK AND GALVANIZED
Price Sheet Effective August 09, 2018 Supersedes CWN-218 A Member of The Phoenix Forge Group CapProducts LTD. Phone: 519-482-5000 Fax: 519-482-7728 Toll Free: 800-265-5586 www.capproducts.com www.capitolcamco.com
More informationI n t e r n a t i o n a l E l e c t r o n i c J o u r n a l o f E l e m e n t a r y E.7 d u, c ai ts is ou n e, 1 V3 1o-2 l6, I n t h i s a r t
I n t e r n a t i o n a l E l e c t r o n i c J o ue rlne am l e not fa r y E d u c a t i o n, 2 0 1 4, 1 37-2 ( 16 ). H o w R e a d i n g V o l u m e A f f e c t s b o t h R e a d i n g F l u e n c y
More informationAGRICULTURE SYLLABUS
Agriculture Forms 1-4.qxp_Layout 1 26/10/2016 12:29 PM Page 1 ZIMBABWE MInISTRY OF PRIMARY AnD SECOnDARY EDUCATIOn AGRICULTURE SYLLABUS FORM 1-4 2015-2022 Curriculum Development and Technical Services,
More informationM a n a g e m e n t o f H y d ra u lic F ra c tu rin g D a ta
M a n a g e m e n t o f H y d ra u lic F ra c tu rin g D a ta M a rc h 2 0 1 5, A n n a F ilip p o v a a n d J e re m y E a d e 1 W h a t is H y d ra u lic F ra c tu rin g? Im a g e : h ttp ://w w w.h
More informationUNITED STATES SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C FORM 8-K
Table of Contents UNITED STATES SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C. 20549 FORM 8-K CURRENT REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934 DATE OF REPORT (DATE
More informationTHE BANK OF NEW YORK MELLON CORPORATION (Exact name of registrant as specified in its charter)
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 FORM 8-K CURRENT REPORT Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event
More informationK E L LY T H O M P S O N
K E L LY T H O M P S O N S E A O LO G Y C R E ATO R, F O U N D E R, A N D PA R T N E R K e l l y T h o m p s o n i s t h e c r e a t o r, f o u n d e r, a n d p a r t n e r o f S e a o l o g y, a n e x
More informationColby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1871 Colby College Catalogue 1871-1872 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
More informationST 602 ST 606 ST 7100
R e s to n Preserve Ct P r e s e rve Seneca Rd S h e r m a n ST 193 B2 Georgetown Pike B6 B8 Aiden Run Ct B9 Autumn Mist Ln B12 B11 B16 B15 B13 B17 Shain Ct B19 B21 B26 B24 B23 N o r th fa lls B28 B27
More informationUNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C FORM 8-K
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 FORM 8-K CURRENT REPORT Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event
More informationNORWEGIAN MARITIME DIRECTORATE
PAME Snap shot Analysis NORWEGIAN MARITIME DIRECTORATE PAME Snap Shot Analysis of Maritime Activities in the Arctic Revision No. 01 REPORT NO. 2000-3220 Page 1 PAME Snap shot Analysis Table of Contents
More informationRanking accounting, banking and finance journals: A note
MPRA Munich Personal RePEc Archive Ranking accounting, banking and finance ournals: A note George Halkos and Nickolaos Tzeremes University of Thessaly, Department of Economics January 2012 Online at https://mpra.ub.uni-muenchen.de/36166/
More informationColby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1870 Colby College Catalogue 1870-1871 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
More informationn
p l p bl t n t t f Fl r d, D p rt nt f N t r l R r, D v n f nt r r R r, B r f l. n.24 80 T ll h, Fl. : Fl r d D p rt nt f N t r l R r, B r f l, 86. http://hdl.handle.net/2027/mdp.39015007497111 r t v n
More informationB ooks Expans ion on S ciencedirect: 2007:
B ooks Expans ion on S ciencedirect: 2007: 1 INFORUM, 22-24 May, Prague Piotr Golkiewicz Account Manager Elsevier B.V. Email: p.golkiewicz@elsevier.com Mobile: +48 695 30 60 17 2 Pres entation Overview
More informationColby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1866 Colby College Catalogue 1866-1867 Colby College Follow this and additional works at: http://digitalcommons.colby.edu/catalogs
More informationColby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1872 Colby College Catalogue 1872-1873 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
More informationHumanistic, and Particularly Classical, Studies as a Preparation for the Law
University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1907 Humanistic, and Particularly Classical, Studies as a Preparation for the Law
More information22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f
n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r
More informationUNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, DC FORM 8-K. Current Report
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, DC 20549 FORM 8-K Current Report Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event
More informationMcCormick & Company, Incorporated (Exact name of registrant as specified in its charter)
UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 FORM 8-K CURRENT REPORT Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934 Date of Report (Date of earliest event
More informationNe a l Mc lo ug hlin - Alb e rta Ag / Fo r Mike Fla nnig a n Uo fa Elle n Ma c d o na ld Uo fa
Using histo ric la nd sc a p e ve g e ta tio n struc ture fo r e c o lo g ic a l re sto ra tio n: e ffe c ts o n b urn p ro b a b ility in the Bo b Cre e k Wild la nd, Alb e rta, Ca na d a. Chris Sto c
More informationLesson Ten. What role does energy play in chemical reactions? Grade 8. Science. 90 minutes ENGLISH LANGUAGE ARTS
Lesson Ten What role does energy play in chemical reactions? Science Asking Questions, Developing Models, Investigating, Analyzing Data and Obtaining, Evaluating, and Communicating Information ENGLISH
More informationA new ThermicSol product
A new ThermicSol product Double-Faced Thermo-Electric Solar-Panel TD/PV & Solar Tracker & Rotation Device An EU-patent protected product TP4-referens.pdf D o y o u w a n t to c o n v e rt it i n to G re
More informationFunctional pottery [slide]
Functional pottery [slide] by Frank Bevis Fabens A thesis submitted in partial fulfillment of the requirements for the degree of Master of Fine Arts Montana State University Copyright by Frank Bevis Fabens
More informationgender mains treaming in Polis h practice
gender mains treaming in Polis h practice B E R L IN, 1 9-2 1 T H A P R IL, 2 O O 7 Gender mains treaming at national level Parliament 25 % of women in S ejm (Lower Chamber) 16 % of women in S enat (Upper
More informationExhibit 2-9/30/15 Invoice Filing Page 1841 of Page 3660 Docket No
xhibit 2-9/3/15 Invie Filing Pge 1841 f Pge 366 Dket. 44498 F u v 7? u ' 1 L ffi s xs L. s 91 S'.e q ; t w W yn S. s t = p '1 F? 5! 4 ` p V -', {} f6 3 j v > ; gl. li -. " F LL tfi = g us J 3 y 4 @" V)
More information35H MPa Hydraulic Cylinder 3.5 MPa Hydraulic Cylinder 35H-3
- - - - ff ff - - - - - - B B BB f f f f f f f 6 96 f f f f f f f 6 f LF LZ f 6 MM f 9 P D RR DD M6 M6 M6 M. M. M. M. M. SL. E 6 6 9 ZB Z EE RC/ RC/ RC/ RC/ RC/ ZM 6 F FP 6 K KK M. M. M. M. M M M M f f
More informationWinsome Winsome W Wins e ins e WUin ser some s Guide
Winsome Winsome Wins e Wins e U ser s Guide Winsome font faq HOW TO INSTALL YOUR FONT You will receive your files as a zipped folder. For instructions on how to unzip your folder, visit LauraWorthingtonType.com/faqs/.
More information". :'=: "t',.4 :; :::-':7'- --,r. "c:"" --; : I :. \ 1 :;,'I ~,:-._._'.:.:1... ~~ \..,i ... ~.. ~--~ ( L ;...3L-. ' f.':... I. -.1;':'.
= 47 \ \ L 3L f \ / \ L \ \ j \ \ 6! \ j \ / w j / \ \ 4 / N L5 Dm94 O6zq 9 qmn j!!! j 3DLLE N f 3LLE Of ADL!N RALROAD ORAL OR AL AOAON N 5 5 D D 9 94 4 E ROL 2LL RLLAY RL AY 3 ER OLLL 832 876 8 76 L A
More informationCertificate Sound reduction of building elements
Certificate Sound reduction of building elements Test report 040311.Z01b * ) Applicant GLAVERBEL GROUP Chaussée de la Hulpe 166 B- 1170 Brussels Specimen Monolithic glazing Foundation EN 20140-3 : 1995-01
More informationInstruction Sheet COOL SERIES DUCT COOL LISTED H NK O. PR D C FE - Re ove r fro e c sed rea. I Page 1 Rev A
Instruction Sheet COOL SERIES DUCT COOL C UL R US LISTED H NK O you or urc s g t e D C t oroug y e ore s g / as e OL P ea e rea g product PR D C FE RES - Re ove r fro e c sed rea t m a o se e x o duct
More informationF48T10VHO, F60T10VHO, F72T10VHO, F96T12HO (1 LAMP ONLY) ELECTRICAL DATA (120V APPLICATION)
LOW TEMPERATURE ELECTRONIC F72T8HO (1 ONLY) (1 ONLY) ELECTRICAL DATA (120V APPLICATION) /(N) /(L) INPUT VOLT: 120V ± 10%, 50/60Hz WATTS/TYPE F48T8HO F60T8HO F72T8HO F48T12HO F60T12HO F72T12HO F96T12HO
More informationTrade Patterns, Production networks, and Trade and employment in the Asia-US region
Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985
More informationUniversity Microfilms
University Microfilms International * i---------------------------------------------------------- ----------------------- MICROCOPY RESOLUTION TEST CHART N ATIO NAL HI IH l A l l o t ST AN PAR P S II A
More informationDangote Flour Mills Plc
SUMMARY OF OFFER Opening Date 6 th September 27 Closing Date 27 th September 27 Shares on Offer 1.25bn Ord. Shares of 5k each Offer Price Offer Size Market Cap (Post Offer) Minimum Offer N15. per share
More informationHandout on. Crystal Symmetries and Energy Bands
dou o Csl s d g Bds I hs lu ou wll l: Th loshp bw ss d g bds h bs of sp-ob ouplg Th loshp bw ss d g bds h ps of sp-ob ouplg C 7 pg 9 Fh Coll Uvs d g Bds gll hs oh Th sl pol ss ddo o h l slo s: Fo pl h
More information9.9 L1N1F_JL 19bo. G)&) art9lej11 b&bo 51JY1511JEJ11141N0fM1NW15tIr1
thunyitmn tn1 zni f1117n.nllfmztri Lrs v wu 4 t t701 f 171/ ti 141 o&oiv,3 if 042 9.9 L1N1F_JL 19bo vitioluutul fly11.1.g)onoo b5 et Nn`15fiwnwiymri1 nrikl5fini1nvi Ltol : Aeniln,flvnu 6m,wiutrmntn15Y
More informationTh pr nt n f r n th f ft nth nt r b R b rt Pr t r. Pr t r, R b rt, b. 868. xf rd : Pr nt d f r th B bl r ph l t t th xf rd n v r t Pr, 00. http://hdl.handle.net/2027/nyp.33433006349173 P bl D n n th n
More informationLSU Historical Dissertations and Theses
Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1976 Infestation of Root Nodules of Soybean by Larvae of the Bean Leaf Beetle, Cerotoma Trifurcata
More informationEKOLOGIE EN SYSTEMATIEK. T h is p a p e r n o t to be c i t e d w ith o u t p r i o r r e f e r e n c e to th e a u th o r. PRIMARY PRODUCTIVITY.
EKOLOGIE EN SYSTEMATIEK Ç.I.P.S. MATHEMATICAL MODEL OF THE POLLUTION IN NORT H SEA. TECHNICAL REPORT 1971/O : B i o l. I T h is p a p e r n o t to be c i t e d w ith o u t p r i o r r e f e r e n c e to
More informationAPPLICATION INSTRUC TIONS FOR THE
APPLICATION INSTRUC TIONS FOR THE DAISY HOPSCOTCH Pro duc t Numb e r: 12-2W-03 SIZE: a p p ro xima te ly 14 fe e t hig h x 4 fe e t wid e. ESTIMATED PAINT TIME: a p p ro xima te ly 1 2 p e o p le fo r
More informationR e p u b lic o f th e P h ilip p in e s. R e g io n V II, C e n tra l V isa y a s. C ity o f T a g b ila ran
R e p u b l f th e P h lp p e D e p rt e t f E d u t R e V, e tr l V y D V N F B H L ty f T b l r Ju ly, D V N M E M R A N D U M N. 0,. L T F E N R H G H H L F F E R N G F R 6 M P L E M E N T A T N T :,
More informationAPPLICATION INSTRUC TIONS FOR THE
APPLICATION INSTRUC TIONS FOR THE CHESS/ CHECKERBOARD Using the Che ss, Che c ke rs a nd Bo rd e rs: (SMALL), Pro duc t Numb e r: 11-1W-009 SIZE: a p p ro xima te ly 10 fe e t e a c h sid e ESTIMATED PAINT
More informationAPPLICATION INSTRUCTIONS FOR THE
APPLICATION INSTRUCTIONS FOR THE USA MA P WITH C A PITA LS & O C EA NS (LA RG E) Pro duc t Numbe r: 16-13W-051 SIZE: a ppro xima te ly 24 fe e t wide x 15 fe e t lo ng (ma inla nd o nly) ESTIMA TED PA
More informationN V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r
n r t d n 20 2 04 2 :0 T http: hdl.h ndl.n t 202 dp. 0 02 000 N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp. 2 24. NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r
More informationTHE LOWELL LEDGER. INDEPENDENT-NOT NEUTRAL.
: / LOLL LDGR NDNDNNO NRL VOL X NO 26 LOLL GN RDY DR 902 FV N ONDRFL GRO D x N Y NK LL & O OLD RDN GON ROR NR R «ROY ND R LON N V» Rx Rj K» O ««(» F R G GRLND x ( ) R OF FRND ;«QK L L RNG X R D 02 Q F
More informationP a g e 3 6 of R e p o r t P B 4 / 0 9
P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J
More informationfur \ \,,^N/ D7,,)d.s) 7. The champion and Runner up of the previous year shall be allowed to play directly in final Zone.
OUL O GR SODRY DUTO, ODS,RT,SMTUR,USWR.l ntuctin f cnuct f Kbi ( y/gil)tunent f 2L-Lg t. 2.. 4.. 6. Mtche hll be lye e K ule f ene f tie t tie Dutin f ech tch hll be - +0 (Rece)+ = M The ticint f ech Te
More informationDANISH METEOROLOGICAL INSTITUTE
DANISH METEOROLOGICAL INSTITUTE TECHNICAL REPORT 00-09 Evaluation of the HIRLAM Surface Analysis Scheme for 2 metre Temperature and Relative Humidity by Comparison with AMIS Gridded Observations March
More informationJoh n L a w r e n c e, w ho is on sta ff at S ain t H ill, w r ite s :
Minor Issue 168 S C I E N T O L O G Y A N D C H I L D R E N T h e r e a r e at p r e s e n t no b o o k s a v a ila b le on th e su b je c t of te a c h in g S c ie n to lo g y to c h ild r e n. A s th
More informationAPPLICATION INSTRUCTIONS FOR THE
APPLICATION INSTRUCTIONS FOR THE SNA KES A ND LA DDERS A DD O N FO R USE WITH THE C HESS, C HEC KERS & BO RDERS LARG E AND NUMBER SET Pro duc t Numb e r: 17-2W-062 SIZE: a ppro xima te ly 19 fe e t e a
More informationWelcome to the Public Meeting Red Bluff Road from Kirby Boulevard to State Highway 146 Harris County, Texas CSJ No.: December 15, 2016
Welcome to the Public Meeting Red Bluff Road from Kirby Boulevard to State Highway 146 Harris County, Texas CSJ No.: 0912-72-340 December 15, 2016 No formal presentation will be made. Seabrook Intermediate
More informationOperation Manual for Automatic Leveling Systems
Operation Manual for Automatic Leveling Systems 11/12 Power Gear #82-L0379 Rev. 0E Operation Manual for Automatic Leveling Systems with Touch Pad # 140-1226 and Control Box # 140-1229 Contents Before You
More informationTransaction Cost Economics of Port Performance: A Composite Frontier Analysis
IFSPA 2010 Chengdu, China Transaction Cost Economics of Port Performance: A Composite Frontier Analysis Presentation by: John Liu Director, C.Y. Tung International Centre for Maritime Studies Department
More informationAPPENDIX F WATER USE SUMMARY
APPENDX F WATER USE SUMMARY From Past Projects Town of Norman Wells Water Storage Facltes Exstng Storage Requrements and Tank Volume Requred Fre Flow 492.5 m 3 See Feb 27/9 letter MACA to Norman Wells
More informationCompany Case Study: The Market Hall. Prof.dr.ir. Mick Eekhout
30 years of Dutch Glass Developments and Innovations Company Case Study: The Market Hall Prof.dr.ir. Po r t fo l i o : 3 0 y e a rs o f s p a c e st r u c t u re s, 25 y e a rs o f g l a s s structure
More informationTHIS PAGE DECLASSIFIED IAW EO IRIS u blic Record. Key I fo mation. Ma n: AIR MATERIEL COMM ND. Adm ni trative Mar ings.
T H S PA G E D E CLA SSFED AW E O 2958 RS u blc Recod Key fo maon Ma n AR MATEREL COMM ND D cumen Type Call N u b e 03 V 7 Rcvd Rel 98 / 0 ndexe D 38 Eneed Dae RS l umbe 0 0 4 2 3 5 6 C D QC d Dac A cesson
More informationWireless & Hybrid Fire Solutions
ic b 8 c b u i N5 b 4o 25 ii p f i b p r p ri u o iv p i o c v p c i b A i r v Hri F N R L L T L RK N R L L rr F F r P o F i c b T F c c A vri r of op oc F r P, u icoc b ric, i fxib r i i ribi c c A K
More informationO. B. S H I M E, Q. C.
I N T H E MATT E R O F A N AR B I T RAT I O N B ETWE E N : O NTA R I O P RO P E RTY AS S ES S M E N T C O R PO RAT I O N AN D : O N TA R I O P U B L I C S E RV I C E E M P LOY E E S ' U N I O N A N D I
More informationSoftware Process Models there are many process model s in th e li t e ra t u re, s om e a r e prescriptions and some are descriptions you need to mode
Unit 2 : Software Process O b j ec t i ve This unit introduces software systems engineering through a discussion of software processes and their principal characteristics. In order to achieve the desireable
More informationREFUGEE AND FORCED MIGRATION STUDIES
THE OXFORD HANDBOOK OF REFUGEE AND FORCED MIGRATION STUDIES Edited by ELENA FIDDIAN-QASMIYEH GIL LOESCHER KATY LONG NANDO SIGONA OXFORD UNIVERSITY PRESS C o n t e n t s List o f Abbreviations List o f
More informationLabor and Capital Before the Law
University of Michigan Law School University of Michigan Law School Scholarship Repository Articles Faculty Scholarship 1884 Labor and Capital Before the Law Thomas M. Cooley University of Michigan Law
More informationSPECIFICATION SHEET : WHSG4-UNV-T8-HB
SPECIFICATION SHEET : WHSG4UNVT8HB ELECTRICAL DATA (120V APPLICATION) INPUT VO LT : 120V ± 10%, 50/60H z LAM P W ATTS/T YPE F17T8 F25T8 F30T8 F 32T8 F32T 8( 25W ) F32T8(28W ) F32T8(30W ) FB31T 8 FB32T8
More informationTECH DATA CORPORATION (Exact name of registrant as specified in its charter)
UNITED STATES SECURITIES AND EXCHANGE COMMISSION WASHINGTON, D.C. 20549 FORM 8-K CURRENT REPORT PURSUANT TO SECTION 13 OR 15 (d) OF THE SECURITIES EXCHANGE ACT OF 1934 Date of Report (Date of earliest
More informationt t t ér t rs r t ét q s
rés té t rs té s é té r t q r r ss r t t t ér t rs r t ét q s s t t t r2 sé t Pr ss r rs té P r s 2 t Pr ss r rs té r t r r ss s Pr ss r rs té P r q r Pr ss r t r t r r t r r Prés t r2 r t 2s Pr ss r rs
More information