The most significant MOSFET parameters impact in CMOS inverter switching characteristics

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1 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 The mos sigifica MOSFET arameers imac i CMOS iverer swichig characerisics Miaim Zabei, Nebi Caka, Myzafere Limai, Qami Kabashi * Absrac - The objecive of his aer is o research he imac of eecrica ad hysica arameers ha characerize he comemeary MOSFETs (NMOS ad PMOS rasisors) i he dyamic behaviour (ime-domai) of he CMOS iverer. I addiio o his, he aer aso aims a exorig he direcives ha are o be foowed durig he desig hase of he CMOS iverers ha eabe desigers o desig he CMOS iverers wih he bes ossibe dyamic erformace, deedig o oeraio codiios. The CMOS iverer desiged wih he bes ossibe dyamic feaures aso eabes he desigig of he CMOS ogic circuis wih he bes ossibe dyamic erformace, accordig o he oeraio codiios ad desigers requiremes. Keywords - CMOS-iverer, oad caaciace, NMOS rasisor, PMOS rasisor, roagaio deay ime, ower suy curre, hreshod voage, rascoducace arameer. I. INTRODUCTION The CMOS iverer rereses fudamea bock of he CMOS digia iegraed circuis based o CMOS iverer [1]. The swichig characerisic (ime-domai behaviour) of he CMOS iverer, esseiay deermie he overa oeraig seed of CMOS digia circuis. The dyamic (ime-domai) erformace requiremes of CMOS digia sysems are usuay amog he mos imora secificaios ha mus be ake io cosideraio durig he desig hase by circuis desiger [], [3]. Therefore he dyamic (rasie) behaviour of he circui mus be esimaed ad oimized by desiger durig he desig hase. The CMOS iverer srucure cosiss of a air of comemeary MOSFETs (of a ehaceme ye NMOS rasisor ad a ehaceme ye PMOS rasisor, because his ye of MOSFET have beer erformace comared o deeio ye of MOSFETs), which oerae i comemeary mode. The CMOS iverer circui is show i Fig. 1 [4]-[6]. Boh comemeary MOS rasisors (MOSFETs) are characerized by eecrica ad hysica arameers, which deermie he behaviour of he CMOS iverer i dyamic (swichig) ad saic codiio of oeraio. Severa of he mai eecrica arameers which characerize he comemeary MOSFET rasisors are: he rocess rascoducace arameer (k ), he zero-bias hreshod voage (V 0 ), he body-effec arameer (γ), he surface iversio oeia ( ø F ) ad he chae-egh arameer (λ). Whereas some of hysica arameers of he comemeary MOSFET rasisors are: he surface mobiiy (µ), he hi oxide hickess ( 0x ) ad subsrae doig (N b ). The vaues of a hese arameers deed o he fabricaio rocess echoogy. The MOSFET rasisors aso characerize a cosiderabe umber of oher arameers, which shoud be ake io cosideraio for secific cases of device oeraio, bu heir imac i overa erformace of he MOSFETs wi be ess meaigfu. If durig fabricaio rocess of MOSFET rasisors he heir eecrica ad hysica arameers are seeced by desired vaues dicaed by echoogy rocess, he MOSFET device behaviour ca be coroed accordig desiger s eeds, deedig o heir aicaio i digia circuis [7]. By coroig he comemeary MOSFET rasisor behaviour wi be abe coroed he CMOS iverer. The mauscri objecive is o ivesigae he some yica MOSFET rasisors arameers ha have he mos sigificace imac i dyamic (ime-domai) behavior of he CMOS iverer, ahough he swichig characerisics of he CMOS digia circuis ad i aricuar of CMOS iverer circuis, esseiay deermie he overa oeraig seed of digia sysems i commo. Therefore, he swichig characerisics of CMOS iverer mus be esimaed ad oimized very eary i he desig hase. Usig aayica ad umerica mehods suored wih he circui simuaor (SPICE) usuay rovides a very accurae esimae of he CMOS ime-domai behavior. Fig. 1 The srucure of he CMOS iverer which coais wo comemeary MOS ehaceme-ye rasisors. * Corresodig Auhor: Qami Kabashi, e-mai: qami.kabashi@ui-r.edu ISSN:

2 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 II. THE ROLE OF THE COMPLEMENTARY MOSFET (NMOS AND PMOS) TRANSISTORS PARAMETERS IN DELAY TIME OF THE CMOS INVERTERS For rasie resose of he CMOS iverer have o deermie he aure ad he amou of arasiic caaciaces associaed wih he comemeary MOSFET rasisors, where heir vaues are deermied by ayou geomeries ad he maufacurig rocesses. The mos of hese arasiic caaciaces are disribued, ad for simificaio he robem, we firs combie io a equivae umed iear caaciace. The seed of he CMOS iverer oeraio is deermied by roagaio deay ime of he CMOS iverer. To aayse he swichig oeraio of he CMOS iverer o deermie is deay ime (or roagaio deay ime), here wi be used CMOS iverer wih a equivae umed iear caaciace, coeced bewee he ouu ode ad groud, as i Fig. [8], [9]. - umber of ideica sages (he CMOS iverers) coeced a he ouu. I oad caaciace exressio are o icuded some of arasiic caaciaces show i Fig. 3, because have o effec o he dyamic behavior of he CMOS iverer. The facor arises before arasiic caaciaces C gd, ad C gd, as resu of he Mier effec, which wi have imac i CMOS iverer dyamic erformace, or i ime deays. This effec ca miimized if durig desig hase of he CMOS iverer, he arasiic caaciaces C db of he comemeary MOSFETs are miimized. Fig. 3 The CMOS iverer associaed wih is arasiic caaciaces, he umed iercoec caaciace ad oad caaciace for aayzig he roagaio deay. Fig. The CMOS iverer wih a equivae umed caaciace (equivae umed iear caaciace) a he ouu ode The vaue of he equivae umed caaciace is cacuaed by usig arasiic caaciaces of he NMOS ad PMOS rasisors, he umed iercoec caaciace ad iu caaciace of oad device (oe or more ideica CMOS iverer, fa-ou arameer) coeced a he ouu of he CMOS iverer, as i Fig. 3. The equivae umed caaciace a he ouu ode wi be caed he oad caaciace C, ad i ca be esimae by exressio [4], [9], [10]: I Fig. 4 is show he CMOS iverer circuis wih he equivae oad caaciace for aayzig he roagaio deay ime, whe he robem of aayzig ime-domai behavior is simified. Now, he CMOS iverer swichig characerisics are reduced o fidig he charge-u ad charge-dow imes of he oad caaciace hrough oe MOSFET rasisor [4]. C + C (1) = Cgd, + Cgd, + Cdb, + Cdb, + Ci g C gd, - he gae-drai caaciace of he NMOS C gd, - he gae-drai caaciace of he PMOS C db, - he drai-body caaciace of he NMOS C db, - he drai-body caaciace of he PMOS C i - he umed iercoec caaciace C g - he iu arasiic caaciace of oad (he oxide-reaed caaciaces) Fig. 4 CMOS iverer wih a equivae umed (combied) oad caaciace ISSN:

3 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 The roagaio deay imes ca be foud by usig he sae equaio of he ouu ode i he ime domai wih acceabe accuracy, as: dv C d o = i C = i D, i D, For cacuaig he roagaio deay ime PHL (roagaio deay ime of he ouu voage durig high-oow rasiio), whe he iu voage swiches from ow-ohigh, he NMOS rasisor is ured o ad i sars o discharge he equivae oad caaciace, whereas he PMOS rasisor is cu off. Afer cacuaio deedig o mode oeraio of he NMOS rasisor (he NMOS rasisor wi oeraes i he sauraio regio whe he V o >V OH - V, whereas for V o V OH - V he NMOS oeraes i he iear regio) of he CMOS iverer, ad by combiig hese wo searaed iervas ca be achieved he exressio of he roagaio deay [4]: = C V 4( V ) + ( ) + 1 (3) PHL k 0, 0, VOL For cacuaig he roagaio deay ime PLH (roagaio deay ime of he ouu voage durig ow-ohigh rasiio) whe he iu voage swiches from high-oow, he PMOS rasisor is ured o ad i sars o charge u he equivae oad caaciace, whereas he NMOS rasisor is cu off. Afer cacuaio deedig o mode oeraio of he PMOS rasisor (foowig a simiar derivaio rocedure, as for cacuaig he roagaio deay ime PHL ) of he CMOS iverer ca be achieved he exressio [4], [8]: PLH = C V 4( V ) + k ( ) 1 0, 0, From he exressio of he roagaio deay ime PHL, i is idicaed ha he imac o is vaue wi have equivae oad caaciace (C ), he vaue of he ower-suy voage (V DD ), he vaue of rascoducace arameer of he NMOS rasisor (k ) ad he vaue of he NMOS hreshod voage (V ). Whereas from he exressio of he roagaio deay ime PLH, i is idicaed ha he imac o is vaues wi have equivae oad caaciace (C ), he vaue of he ower-suy voage (V DD ), he vaue of rascoducace arameer of he PMOS rasisor (k ) ad he vaue of he PMOS hreshod voage (V ). Therefore, he deermiig arameers of he roagaio deay ime PHL are he eecrica ad hysica arameers ha characerize oy he NMOS rasisor, whereas he deermiig arameers of he roagaio deay ime PLH are he eecrica ad hysica arameers ha characerize oy he PMOS rasisor. For he usua case is assumed ha V = V = 0.V DD, he exressios reduce as i: 1.6 C () (4) PHL = (5) k 1.6 C PLH = (6) k The iverer roagaio deay ime ( P ) is defied as he average of roagaio deay imes: 1 P = ( PHL + PLH ) (7) The dyamic ower dissiaio has wo comoes, he firs comoe is due of curre which fows hrough he series of coecio of NMOS ad PMOS rasisors, ad curre eaks is a he swichig hreshod voage of CMOS iverer (for a symmeric case he hreshod voage of he CMOS iverer is V h = V DD /). However, he secod comoe of dyamic ower dissiaio is more sigifica comoe, resus from he curre ha fows i NMOS ad PMOS rasisors whe he CMOS iverer is oaded by oad caaciace. Now if he CMOS iverer is swichig by eriodic iu voage uses wih egigibe rise ad fa imes, he average dyamic ower dissiaio i CMOS iverer wi be: P = fc V (8) D DD Now, i is cear ha he average dyamic ower dissiaio of he CMOS iverer is roorioa o he swichig frequecy (f). Hece, he ow-ower advaage of CMOS circuis a he higher swichig frequecy becomes romie. Aso, he maxima oeraio frequecy of he CMOS iverer is reaed o he roagaio deay. The average swichig ower dissiaio esimae by exressio (8) wi hod for he CMOS iverer, whe he eakage ower is egeced. Uder he reaisic codiios, whe he iu voage uses (deviaes from idea se uses) have ozero rise ad fa imes, boh MOSFET (NMOS ad PMOS) rasisors wi simuaeousy coduc (or boh rasisors emorariy form a coducig ah bewee V DD ad he groud, whe iu voage is ear he hreshod voage of he CMOS iverer) a cerai amou of curre (he shor-circui curre), which gives rise o dyamic ower dissiaio i he CMOS iverer. For his reaso he dyamic ower exressio (8) i has o add he addiioa dyamic ower dissiaio, which is due o he shor-circuis curre. Bu, whe he oad caaciace has higher vaues, he dyamic ower dissiaio erm which is due o he shor-circui curre become egigibe i comariso he dyamic ower dissiaio erm which is due he oaded a oad caaciace [11], [1]. The iverer roagaio deay ime ca be used o esimae a fudamea arameer for measurig he quaiy ad he erformace of he CMOS rocess. This fudamea arameer is caed he deay-ower roduc (DP), ad i ca wrie as: DP = P D (9) The ower he of DP roduc he more effecive is he echoogy, which is used for fabricaio device. ISSN:

4 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 III. RESULTS AND DISCUSSION The deedece of he CMOS roagaio deay ime PLH o he NMOS rasisor rascoducace arameer (k ) for wo differe (arameric) vaues of he NMOS rasisor hreshod voage (V ) ad oher vaues remais cosa. This is show i Fig. 5. The resus reseed hrough curves i Fig. 5 idicae he foowig: for higher vaues of he NMOS rascoducace arameer (k ) i CMOS iverer, he roagaio deay ime PHL (he roagaio deay ime durig ouu voage rasiio from high-o-ow eve) wi be ower. Aso, he smaer vaue of he NMOS hreshod voage (V ) wi resu i ower vaues of he roagaio deay ime PHL, wih a more sigifica imac for he ower vaues of he NMOS rascoducace arameer (k ). Fig. 5 The deedece of roagaio deay ime PHL i he CMOS iverer o he NMOS rascoducace arameer (k ) for wo differe vaues of NMOS hreshod voage (V ), whe C = 0.1 F ad V DD =.5 V. The deedece of he CMOS roagaio deay ime PLH (he roagaio deay ime durig ouu voage rasiio from ow-o-high eve) o he rascoducace arameer of he PMOS rasisor (k ), for wo arameric vaues of he PMOS hreshod voage (by absoue vaue of he PMOS hreshod voage V ), ad oher vaues remais cosa ad i is same as he deedece of roagaio deay ime PLH i Fig. 5. For he same dimesios of NMOS ad PMOS rasisors (comemeary MOS rasisors) roagaio deay ime i he CMOS iverer are asymmerica PLH > PHL (because k >k ). Whie, for symmerica (machig) codiios (k = k ), he roagaio deay imes i he CMOS iverer are equa ( PHL = PLH ). I usua cases he maxima oeraio frequecy i CMOS iverer circuis is deermied by maxima vaue of roagaio deay imes. The ime resose waveforms of he ouu voage durig ow-o-high rasiio ad high-o-ow rasiio for hree differe cases of he comemeary MOS rasisors rascoducace arameers raio (k /k ), whe he CMOS iverer is drive by he idea use (wih zero rise ad fa imes) ad wih equivae oad caaciace C =1F, is show i Fig 6. Fig. 6 The waveforms of ouu voage for here differe cases of he comemeary MOS rascoducace arameers raio (k /k ), whe he CMOS iverer drives by he idea use ad equivae oad caaciace C = 1F, as we he NMOS rascoducace arameer (k ) hods same. From he ime waveforms reseed i Fig. 6, i is idicaed ha for symmeric cases (k = k ), he roagaio deay imes durig ow-o-high ad high-o-high rasiio of he ouu voage i CMOS iverer are equa ( PLH = PHL ), whereas i oher cases of he rascoducace arameers raio (k /k ) he roagaio deay imes are asymmerica. Whe k > k he roagaio deay ime PHL is ower ha roagaio deay ime PLH ( PHL < PLH ), ad for k < k he roagaio deay ime PHL is higher ha he roagaio deay ime PLH ( PHL > PLH ). Sigifica imac o roagaio deay imes has he oad caaciace coeced a he ouu of he CMOS iverer (whe oad caaciace (fa-ou effec) coeced a he ouu of he CMOS iverer is domia erm i he equivae oad caaciace, or exrisic erms are domia). The roe of he ouu oad caaciace (fa-ou) i deay imes is show i Fig. 7 by he waveforms of he ime resose of he ouu voage a he ouu of he symmeric CMOS iverer for hree differe vaues of equivae oad caaciace, whe he CMOS iverer is drive idea use. Form he waveforms of he ime resose i Fig. 7, i is idicaed ha he higher vaues of he equivae oad caaciace wi resu i higher vaues of he roagaio deays durig he rasiio of he ouu voage i he CMOS iverer. Sice he seed of he oeraio of he CMOS iverer deeds of is roagaio deay ime, he he higher vaues of he roagaio deay ime wi resu i ow seed of he CMOS iverer oeraio. Whe he combied ouu oad caaciace is maiy domiaed by is exrisic comoes (which are o very sesiive o he NMOS ad PMOS device dimesios), he direcive o icrease he oeraio seed (decrease he roagaio deay ime) of he CMOS iverer is by desigig he NMOS ad PMOS rasisors wih higher vaues of he rascoducace arameers. Bu, he irisic comoes of he combied oad caaciace are icreasig fucios of he NMOS ad PMOS rasisor dimesios, W (he chae widh of NMOS rasisor) ad W (he chae widh of PMOS rasisor) [1], [13]. ISSN:

5 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 C = f ( W + C db,, W ( W ) = C ) + C gd, db, ( W ( W ) + C ) + C gd, i + C ( W g ) (10) The chae eghs of he NMOS ad PMOS rasisors i he CMOS iverers are usuay equa ad fixed o each oher, deermied by fabricaio rocess, ad he he chae widh of MOS rasisor is more sigifica deermiig arameer of he MOS rasisor rascoducace arameer [14], [15]. The, ay effor o icrease he chae widh of NMOS ad PMOS rasisors i order o reduce roagaio deay ime i he CMOS iverer wi ieviaby icrease he irisic comoes of combied oad caaciace a he ouu of he CMOS iverer. The icreasig chae widh of he comemeary MOS rasisors o reduce roagaio deay ime, where he irisic caaciace erms wi have sigifica imac i equivae oad caaciace, he ifuece o he roagaio deay ime wi dimiish ad wi asymoicay aroach a imi vaue for arger vaues of he chae widh of comemeary MOS rasisor (he roagaio deay ime cao be reduced beyod he imi vaue). I hese codiios he roagaio deay imes are ideede of he exrisic caaciace comoes, C i ad C g. Whe he irisic caaciace comoes are domia o combied oad caaciace i he CMOS iverer (arasiic caaciace comoes of NMOS ad PMOS rasisors), he combied oad caaciace wi reduce by reducig he chae widh of NMOS ad PMOS rasisors, ad roagaio deay ime imi is reached for smaer vaues of he NMOS ad PMOS rasisor chae widh. The ifuece of comemeary MOSFET rasisors dimesios uo he roagaio deay of CMOS iverer are iherey imied by arasiic caaciaces, ad overa occuied area by CMOS iverer shoud aso be cosidered. I fac, he occuied area of CMOS device is roorioa o W ad W, sice he oher MOSFET dimesios are simy ke cosa. The sigifica facor which used as racica measure for quaifyig desig quaiy is he (area x roagaio deay ime) ha akes io accou for deay ime reducio [6], [15]. Fig. 7 The waveforms of ime resose of he symmeric CMOS iverer ouu voage durig swichig coducios, whe he equivae oad caaciace (C ) has hree differe vaues. A of he roagaio deay imes are derived uder simified assumio ha he iu drive siga is a idea use, bu i reaisic cases he waveform of he drive iu siga is o a idea use. The rea drive use a he iu of he CMOS iverer has fiie rise ime ( r ) ad fa ime ( f ). The exac cacuaio of he ouu voage roagaio deay ime is more comicaed, because uder hese codiios boh he NMOS rasisor ad PMOS rasisor coduc durig he charge-u ad charge-dow eves. The esimaio of he roagaio deays of he CMOS iverer, whe he drive iu siga has fiie rise ad fa ime, ca uiize he roagaio deay ime cacuaed by idea use (se-iu) assumio ad usig he rise ad fa ime of he drive iu siga, by usig he emirica exressios [4]: r ( ) = ( ) + PHL reae PHL idea use (11) f ( ) ( ) PLH reae = PLH idea use + (1) Fig. 8 The waveforms of he CMOS ouu voage durig swichig codiios for idea driver iu siga ad rea driver iu siga a he iu of he CMOS iverer, whe he equivae oad caaciace has fixed vaue C = F. The imac of he rise ad fa ime of he drive iu siga o he waveform ad roagaio deay imes of he ouu voage durig he swichig codiios i he symmeric CMOS iverer, whe he drive iu siga is a idea use ad whe he drive iu siga has a fiie rise ad fa ime, as we he equivae oad caaciace has a fixed vaue is show i Fig. 8. Durig swichig codiios i CMOS iverer, here wi be creaed he coduc ah bewee he ower source ad he groud uder reaisic codiios (he iu drive siga deviaes from he idea se use), hrough NMOS ad PMOS rasisor whe he iu voage is arger ha V,0 ad smaer ha (V DD - V,0 ). Uder hese codiios he NMOS ad he PMOS rasisors wi simuaeousy coduc a ozero curre (drai curre) durig ow-o-high ad high-o-ow rasiios, ad he curre reaches is eak vaue whe he iu voage is equa o he CMOS hreshod voage V i = V h. Oherwise, he shor-circui curre of CMOS iveror is caed he ower suy curre. Boh he NMOS ad PMOS ISSN:

6 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 rasisors oerae i he sauraio mode of oeraio whe he curre reaches is maximum (eak vaue) [8], [15]. I I DD DD k V = ( Vi 0, ), ( DD 0, Vi ) (13) k = ( Vi 0, ), ( Vi 0, ) (14) The CMOS iverer does o draw ay sigifica curre from he ower source, whe he iu voage is smaer ha V or arger ha (V DD - V ), exce some sma eakage ad subhreshod curres. From he exressio above, i is cocuded ha he rascoducace arameers of he NMOS ad PMOS rasisors ad he hreshod voage of he NMOS ad PMOS rasisors have imac i he curre eak vaue. The deedece of he drai curre eak vaue from he rascoducace arameers of he NMOS ad PMOS rasisors i he symmeric CMOS iverers is show i Fig. 9. The achieved resus idicae ha whe he rascoducace arameers of he boh NMOS ad PMOS rasisor icrease he shor-circui curre eak vaue of he symmeric CMOS iverer durig ouu voage rasiio wi icrease. Thus, he higher vaues of he rascoducace arameers wi resu o he higher vaue of shor-circui curre ad he higher vaue of dyamic ower dissiaio erm. Fig. 10 The waveforms of he ower suy curre (shorcircui curre) i he symmeric CMOS iverer, for some differe vaues of he hreshod voages of he NMOS ad PMOS rasisor durig rasiio oeraio, whe he rascoducace arameers are fixed. The imac of he chae- egh moduaio effec (λ) i he ower suy curre (shor- circui curre) of he CMOS iverer durig rasiio oeraio is show i Fig. 11. By waveforms reseed, he arger vaues of he chae egh moduaio cosa (λ) wi resu i arger eak vaues of he ower suy curre of CMOS iverer, bu does o have ay sigifica imac comared o he rascoducace arameers ad hreshod voages of comemeary MOS rasisors. The ower suy curre of he CMOS iverer durig rasiio oeraio wi coribue i he overa ower dissiaio of he CMOS iverer uder o idea codiios, wih sigifica roe whe ouu oad caaciace has a ower vaue. The waveforms of shor-circui curre (ower suy curre) ad is eak vaue o same differe vaues of equivae oad caaciace are show i Fig. 1. Fig. 9 The shor-circui curre i he symmeric CMOS iverer durig swichig oeraio whe he rascoducace arameers of he NMOS ad PMOS rasisors icrease roorioay. The imac of he hreshod voages of he NMOS ad PMOS rasisors o shor-circui curre eak of he symmeric CMOS iverer, whe he rascoducace arameers of boh MOS rasisors are fixed, is show i Fig. 10. The achieved resus idicae ha whe he vaue of he hreshod voage of he NMOS rasisor ad he absoue vaue of he hreshod voage of he PMOS rasisor are smaer, he shor-circui curre (drai curre or ower suy curre) eak vaue of he CMOS iverer wi be arger by vaues durig he rasiio oeraio. Fig. 11 The waveforms of he ower suy curre of he CMOS iverer for wo arameric vaues of he chae egh moduaio cosa (λ) durig rasiio oeraio, whe he rascoducace arameers of he NMOS ad PMOS rasisors ad heir hreshod voages are fixed. ISSN:

7 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 Fig. 1 The deedece of he ower suy curre eak vaue i he CMOS iverer o equivae oad caaciace (combied oad caaciace). I geera, he arger suy voage V DD resus i ower a ower vaue of roagaio ime deay. Bu, he dyamic ower dissiaio of CMOS iverer wi rise by exressio (8), he shor-circui curre wi be higher, hus he overa dyamic ower dissiaio wi rise. However, he suy voage V DD is deermied by rocess echoogy ad hus i is o uder he coro of he desiger. Moreover, moder rocess echoogies i which device size are reduced coiuay require ower vaue of V DD. A imora issue is he fac ha roagaio deay ime for sub-micro MOSFETs cao esimae by exressios (3) ad (4), bu have o modify. I sub-micro rasisors (or a sma-geomery rasisor) he curre drivig caabiiy reduced as ea resu of chae veociy sauraio. By usig he sauraio curre of a dee-sub-micro MOSFETs, ad he average curre mehod for esimae he roagaio deay imes, he exressio of he roagaio deay ime is [16], [17]: PHL C ( / ) = (15) κ W ( W V ) DD The roagaio deay ime for sub-micro rasisors has a weak deedece o he ower suy voage comared o he roagaio deay imes esimae by exressios (3) ad (4). The obaied resus by his exressio have a accurae abou 90%, bu o achieve he beer resus mus use he aoher MOSFET mode for sub-micro rasisors. The obaied resus for swichig characerisics of he CMOS iverer o secific arameers discussed ui ow, aso ca ay o a geera CMOS circuis. The CMOS circui cosiss of wo bocks of MOSFETs, a bock of he NMOS rasisors ad a bock of he PMOS rasisors, which ca be simified o oe equivae CMOS iverer wih equivae arameers [6]. IV. CONCLUSION If durig he desig hase of he CMOS iverer, he rascoducace arameers of he comemeary MOS rasisors, i.e. he rascoducace arameer of he NMOS rasisor (k ) ad he rascoducace arameer of he PMOS rasisor (k ), ad he hreshod voage vaues of comemeary MOS rasisors, i.e he hreshod voage of he NMOS rasisor (V ) ad he hreshod voage of he PMOS rasisor (V ), are coroed, or mached, he CMOS iverer ca be desiged wih high erformace i he dyamic codiios of oeraios, deedig o he desiger requiremes ad oeraig codiios. For he higher vaues of comemeary MOS rasisors rascoducace arameers (k ad k ), he roagaio deay imes durig ow-o-high ( PLH ) ad high-o-ow ( PHL ) rasiio of he CMOS iverer ouu voage wi have ower vaues, whe i equivae umed oad caaciace domiae he exrisic comoes. Bu icreasig he rascoducace arameers beyod cerai vaues, he ifuece o roagaio deay ime wi dimiish, ad he roagaio deay ime wi asymoicay aroach he imi vaues. Whe i he equivae umed caaciace domiae he irisic comoes, he imi vaues of he roagaio deay ime are reached for smaer vaues of he comemeary MOS rasisors rascoducace arameers. The icreasig of he rascoducace arameers of comemeary MOS rasisors i CMOS iverer are reached by icreasig he chae widh of he comemeary MOS rasisors. Bu he icreasig of he chae widhs wi ieviaby icrease he irisic comoes of he equivae umed oad caaciace. If rascoducace arameers of comemeary MOS rasisors are equa or machig (k = k ), he roagaio deay imes are equa (symmeric), ad for oher cases he roagaio deay imes wi be asymmeric. The MOSFETs rascoducace arameers raio is deermied arameer of he roagaio deay imes raio i he CMOS iverer. For he ower vaue of he NMOS rasisor hreshod voage (V ) ad higher vaue (or ower absoue vaue) of he PMOS rasisor hreshod voage (V 0. ), he roagaio deay imes durig ouu voage rasiios i CMOS iverer wi decrease ad vice versa. The ozero rise ad fa ime of he driver siga a he iu of CMOS iverer wi have sigifica ifuece o he roagaio deay ime durig ouu voage rasiio, ad he higher vaue of rise ad fa ime of drive iu siga (iu use) a he iu of CMOS iverer wi ead i icreasig he roagaio deay imes. The ozero rise ad fa ime of iu driver siga (iu use) ad he comemeary MOS rasisors rascoducace arameers i CMOS iverer wi have ifuece i shor- circui curre (ower suy curre) durig ouu voage rasiio, ad he higher vaues of rise ad fa ime of he iu driver siga, as we he higher vaues of comemeary MOS rasisor rascoducace arameer, wi resu i higher vaues of he shor- circui curre, as we i higher vaue of he overa dyamic ower dissiaio of he CMOS iverer. Aoher arameer caed he chae egh moduaio coefficie (rocess-echoogy arameer), ha has o be ake io accou eseciay whe MOSFET is defied as a shor-chae device, he for higher vaue of he chae egh moduaio coefficie (λ) wi have a sma icrease i ISSN:

8 INTERNATIONAL JOURNAL OF CIRCUITS, SYSTEMS AND SIGNAL PROCESSING Voume 1, 018 he vaue of he shor- circui curre eak durig he ouu voage rasiio of he CMOS iverer. REFERENCES [1] Muhammad H. Rashid, Microeecroics Circuis Aaysis ad Desig, 3rd, CL Egieerig, 016. [] David A. Hodges, Horace G. Jacko, Resve A. Saeh, Aaysis ad Desig of Digia Iegraed Circuis, Mc Graw Hi, 003. [3] J. M. Rabaey, A. Chadrakasa, ad B. Nikoic, Digia Iegraed Circuis: A Desig Persecive, Uer Sadde River, NJ: Pearso Educaio, 016. [4] S. Kag, Y. Lebebici, Chuwoo Kim, CMOS Digia Iegraed Circuis, 4rd ediio, McGraw-Hi, 014. [5] A. K. Maii, Digia eecroics: Pricies, Devices ad Aicaios, Jo Wiey, 007. [6] R Jacob Baker, CMOS Circui Desig, Layou, ad Simuaio, 3rd, IEEE Press, 010. [7] M. Zabei, N. Caka, M. Limai, Imac of MOSFET s srucure arameers o is overa erformace deedig o he mode oeraio, Ieraioa Joura of Circuis, Sysems ad Siga Processig, vo. 10, 016, [8] A. Sedra ad K. C. Smih, Microeecroic Circuis, 7h ediio, Oxford Uiversiy Press, 015. [9] J. E. Ayers, Digia Iegraed Circuis Aaysis ad Desig, d, CRC Press LLC, 009. [10] Joh F. Wakery, Digia Desig: Pricies ad Pracices, 5h, Pearso, UK, 017. [11] Sakurai, T. ad Newo, A. R., Deay aaysis of series-coeced MOSFET circuis, IEEE Joura of Soid-Sae Circuis, vo. 6, o., , February [1] N. Caka, M. Zabei, M. Limai, Q. Kabashi, Imac of MOSFET arameers o is arasiic caaciaces ad heir imac i digia circuis, WSEAS rasacios o Circuis ad Sysems, March 007, Issue 3, vo 6, [13] Yua, J. ad Svesso, C., High-seed CMOS circui echique, IEEE Trasacios o Circuis ad Sysems, vo. 38, o. 7, , Juy [14] James D. Pummer, Michea D. Dea, Peer B. Griffi, Siico VLSI Techoogy:, Fudameas, Pracice ad Modeig, Preice Ha, 000. [15] Nei H. E. Wese, David Moey Harris, CMOS VLSI Desig: A Circuis ad Sysem Persecive, Addiso-Wesey, 011. [16] Zhagcai Huag, Asushi Kurokawa, Masaori Hashimoo, Takashi Sao, Migu Jiag Yasuaki Ioue, Modeig he Overshooig Effec for CMOS Iverer Deay Aaysis i Naomeer Techoogies, IEEE Trasacios O Comuer-Aided Desig Of Iegraed Circuis Ad Sysems, vo. 9, o.,.50-60, February 010. [17] Jagaah Samaa, Bishu Prasad De, Deay aaysis of UDSM CMOS VLSI circuis, Procedia Egieerig, vo. 30, , 01. Miaim Zabei received he Di.Ig. (1994), Mr.sc. (006) ad Ph.D (01) degrees i Eecrica Egieerig from he Uiversiy of Prishia, Facuy of Eecrica ad Comuer Egieerig. He currey hods he osiio of Associae Professor a he Facuy of Mechaica ad Comuer Egieerig, Uiversiy of Mirovica. His research ieress are i he Digia Eecroics, focused o VLSI desig Nebi Caka received his Di. Ig. degree i Eecrica Egieerig from Uiversiy of Sarajevo, Bosia ad Herzegovia, i 1971 ad his Mr. sc. degree i Eecrica Egieerig from Uiversiy of Zagreb, Croaia i He received his Ph.D. degree i Eecrica ad Comuer Egieerig from he Uiversiy of Prishia, Kosovo i 001. He aso received he M. sc. (1979) ad Mr.sc (1986) degrees i Abaia Phioogy from he Uiversiy of Prishia, Facuy of Phioogy. He is currey ivoved i he Academy of Ars ad Scieces of Kosovo as exera exer for Comuer aguage rocessig. His research ieress are i Microeecroics, Ooeecroics ad Image aser rocessig, ad i Comuer iguisics. Myzafere Limai received her Di.Ig. degree i Eecrica Egieerig from Uiversiy of Prishia, Kosova, i 1978 ad her Mr.sc. degree i Eecrica Egieerig from Uiversiy of Begrade, Serbia i She received her Ph.D. degree i Eecrica ad Comuer Egieerig from he Uiversiy of Prishia i 000. She is currey a Fu Professor i he dearme of Eecroics a he Uiversiy of Prishia, Facuy of Eecrica ad Comuer Egieerig ad a Corresode Member of he Academy of Ars ad Scieces of Kosovo. Her curre research ieress icude eecroics ad audio siga rocessig. Qami Kabashi received he Di.Ig. (1996), Mr.sc. (007) ad Ph.D (01) degrees i Eecrica Egieerig from he Uiversiy of Prishia, Facuy of Eecrica ad Comuer Egieerig. He currey hods he osiio of Associae Professor a he Facuy of Mechaica ad Comuer Egieerig, Uiversiy of Mirovica. His research ieress are i he Power Eecroics, focused o harmoic effecs by PWM Ivereers.. ISSN: