A method for linking process-level variability to system performances
Descrição do Produto
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³JdlkhiJd rvlJe]qyhÒ`m9vhuf {`dxymdwl]m9h-d&ð sddxhu]d)jf ðr|jqJj¬`m9vhuf {`d9}Uhu]d sXf gu{9de]q]jkewiq]e]e]|r|dwhu]d sm9lJwhuf9l`h/sq]gigudlQhE}6f lJx´m`lJs&dhiJdrvl]eJqyh9m`hf {`d(dðysddEx]wrhE} hu]dm9qyhue]qyh/s&qJgigudlQh/xydsgidEf9widw¡kymJ}\hu]d sJf gu{9d(e]q]jke¹s&q]gi gudlQh/rtw/f e]eJgimMðyr|jkf hidEx_åÈfe]r|dsdërtwd|r|l]df9gnq]lJs1hurvm`l#l ¡ u)w nm`ghu]dÎ÷ú nBcd} zJl]rvhid[higf lXwrvhir|m9l¹hurvjkdEwnm`gkm9qyhue]qyhkgirtwdÎf lJx nÀf9v#f9gidjkmyxyd|dx\¡ xpdnm9gudp{`m9r|l]{)r|lQhim hi]ddðyf9jkrvlJf hir|m9l(m nJ]r|dgf gs]rtsf9`whufUhur|w hur|sf #f lXf |wirtwpërvhiv )" ¹}Jëà d zJguwh s&m`al zJguj÷hi]d/f`ssq]guf`s&m9n hu]d[Jrvdguf9gus]rtsf9Òe%dginm9gujf lJsdf lJf9vywir|w(qJwirvlJ{_hiJd[ãdgir|vm`{ u jkmx]dTü ¡ nJm9g(hi]rtwe]q]gueXmQwd`}-f_]r|dgf gs]rtsf ÷ 0m9lQhid0oÃf guvm f9lJf |ywrtwBërhukhi]d)ãdgurv|m9{9 uÄjkmyxydJr|wps&m9jkeJf9gidExërvhi[faïXfUh
Charge Pump
LPF
Lock up time by Verilog-A Simulation [µsec]
PDF
VCO
N Div.
M¡
C"DE$F ç ÜýÜþZþÿ$XP5W¤Y D U E NU
Correlation Coefficient 1.8
0.888
1.6 1.4 1.2 1.0 0.8 0.6 0.7
0.8
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Lock up time by SPICE Simulation [µsec]
1.7
¡
C"DE$F Jß5WU`-`-MNdæ$XPS`LÿM`2OgMM ] ß æ D WM¿U ] Y iMN D XP E ã Q\ D $X U` D P ]
Oscillation Frequency [MHz]
60 SPICE
55
1% Line
50 45
Verilog-A
40 35 30 25 20 15 10
0
0.5
1.0
1.5 2.0 Time [µsec]
2.5
3.0
52 Oscillation Frequency [MHz]
0m`lQhidÈoÃf gu|m´f9lJf |ywrtwkåJf9widxbm`l³]ú-ioÃz wr|jqJ|f hir|m9l#¡É
´d wid|ds&hÃ|mysq]ehurvjkd,f9wÃfwywhidj sJf gf9s&hidgurtwhur|sm9n6hu]dasm9j eJf9girtwim9l#¡í]de]gumys&dExyq]gudm9nphu]d]r|dgf gs]rtsf y 0m`lQhidoÃf guvm f9lJf |ywrtwÃërhu[hu]d,ãdgur|vm`{ u8jkmyxyd|wrtw f9wÃnm`v|mUë w¡ `µ ¡ _m9lQhidaoÃf9gi|m/f lXf |widw-m n#s&r|gusq]rvhÒå]|msywpf gudeXdgnm`gijkdx ërvhi°e]rts&d`¡/zÒf9s0eXf gf jkd&hudg)jkdl`hurvm`l]dxÈf å%mU9d(r|w d&ð huguf`s1hudxnm9gdf`sÎwid&hm9n4gf lJx]m9j Uf gurtf å]|dw¡ ~]¡íJd-vmys q]ehir|jkd-m nhiJd-ë]m9|d-wiwhidj8rtw#f9lJf |çdxaërvhi hu]dÃãdgurv|m9{9 u?jmyxyd|w!nm`g4dEf9swid&hBm nXguf9lJxym9j Uf gurtf å]|dw qXwr|l]{hi]d,dðhigf9s1hudx[eJf gf jkdhidgwÃrvl°`¡ u ï%fU h 0m`lQhid(oÃf gu|m f lJf9vywir|wrtw)xym`l]d,ërvhiÈeJr|sd/qJwirvl]{khu]d wuf jkdÎguf9lJxym9jìUf gurtf å]|dwkf9whiJdÎJrvdguf9gus]rtsf9¨ _m9lQhid_oÃf guvm f9lJf |ywrtwërhuhi]d(ãdgurv|m9{9 uµjkmyxydtw¡c q]d,hum]r|{9_s&m`jke]qy hfUhir|m9lXf !sm`whuwnm`g fkï%fUhaf9lJf |ywrtwërvhiÈ]ú-ioÃz }]hi]dwif9jeJvd wirvçdm n4hi]Ä d _m9lQhid(oÃf9gi|mf9lJf |ywrtwrtw,`]¡n4hi]d/å%dXfMQr|m9gf jkmyxyd|r|l]{Èërvhibãdgur|vm`{ u e]gudwidgu9dEw/dwuwidlQhirtf sJf gf9s&hidgirtw hur|swm n6hu]d,s&r|gusq]rvhm`eXdguf hir|m9l#}Qhu]dgidEwq]vhm n#hu]d,]r|dgf gs]rtsf f9lJf |ywrtwërvhibhu]d0ãdgurv|m9{9 u jkmyxydtwkgidEwqJhw(r|l³fÌ|mysQTq]e hurvjkd/s&|m`widhimkhuJfUh m9n!hu]d,ïXf h)f lJf9vywir|wërvhi_yúÒioÃz ¡]
lm`g xydgÃhims]dskhu]rtw}JfwusfUhihidge]vm9hm n6hu]d]r|dgf gs]r|sf >f lJf9vQ wir|wpërvhi[hi]daãdgurv|m9{9 uýjkmx]d>9dguwiqJwÒhi]daïXf hf9lJf |ywrtw-ërvhi eJr|sdrtw wi]mUël0r|} l n4rv{Xi¡ X¡)zð]s&deyh nm`gafkndë sf`wdEw}%gidEf9wim9ly f9å]vdÎf {`giddjkdlQhrtw(f`s]r|d9dEx\¡°í]dÎsm9gugid|f hir|m9l¹s&md srvdlQhuw å%d&hëÃddlhu]dj r|w ) Ñ `9J¡ í]dwm`q]gusd(m9npxyrtwisgideJf lXs&r|dwar|wdðye]|f9rvlJdxÌf`w nm9|vmUë w¡Äu xydr|f hidx?wif9jeJvd[r|wkwid|ds1hudx¹ëJr|sr|w(jf gu9dxGåQ¹fÈs&r|gusvd r|Ç l n4rv{X÷¡ X¡ n4rv{`q]gud´¹wi]mUë whu]d´vmysQTr|l³å%dJfMr|m9g m9n,hi]rtw wuf jke]|dåQ(åXm9hikhu]d]r|dgf gs]r|sf yf lXf |wirtwBërhukhi]dãdgir|vm`{ uþjmyxyd|w(f lJx¹hi]dïXfUh(f9lJf |ywrtw/ërvhibyú-ioÃz) ¡ {awus&r|vtfUhurvm`l ngudöQq]dlJs&(r|weJvm9hhidExf9w-fanqJlJs1hurvm`lm n%hir|jd nm9g-dEf9ssf`wd`¡6h sf låXdÃwif9r|x huJfUh#hu]dÒ|mysQTr|låXdJfMrvm`g\r|w6ëpdv`jmyxydvdExrvlhu]d ]r|dgf gs]rtsf9!f lXf |wirtw¡,h,rtw gud`df9vdExhiJf hhi]dxyrtwisgideJf lXs& sm9jkdwÃngum9jþhi]dx]d zJl]rvhir|m9lm9n!hu]d/|msq]ehir|jkd9¡
´d/xy d zJl]d hu]dÌ|mysq]e¾hir|jd´f9w[f°hir|jkdÈgudöQq]r|gidExhimwid&hihi|dÌërvhi]r|l m9nÒhiJd(hf gu{9dh)ngudöQq]dlXs&9¡(
l_hu]r|wdð]f jke]|d9}#f9wwiddlÌr|l´f jf {`l]Ar zJdxe]vm9hrv° l n4rv{X¡9y}MhiJd wdEs&m9lXx/e%df ngudöQq]dlJs&åQhu]d ]r|dgf gs]rtsf9Òf lJf9vywir|w/r|w)qJwhkfÌvrvhhuvdÎf å%mU9dhu]r|whiJgidEw]m`|x ë]dgidEf9wÒhiJf håQkhu]daïXfUh f9lJf |ywrtwÒrtw!qJwh)f|rhihi|dåXdvmUë³hu]d hu]gidEwJm9tx\}#ë]rts°gidEwq]vhuwr|l¹f[nÀf r|g/f jkm9q]lQh,m nxyrtwisgideJf lXs& r|lÌhu]d|msÌq]eÌhurvjkdEw¡h,rtw,f twm0s&m`al zJgujkdx0huJfUh,hu]d|msQ r|l³åXdJfMrvm`guw m n/wm`jkd0m hiJdg[wuf jke]|dw åQhiJdÌ]r|dgf gs]rtsf f9lJf |ywrtw!f9gidÃs&m`lJwrtwhidlQhBërhuhu]m`widÃåQhu]dÃïXfUhf lXf |wirtw6ërvhi yúÒioÃz J¡
´ds&m`lJs&|qJxydkhuJfUhhi]d Jrvdguf9gus]rtsf9f lJf9vywir|wërvhi hu]d ãdgur|vm`{ u jmyxyd|wsf lGwir|jq]tfUhudkhi]d |mysQTq]e°å%dJfMr|m9g ërvhigudf9wim9lXf å]|d f`ss&qJguf`s&9¡ ê)fMrvlJ{sm9al zXgijkdx(hu]d f9ss&q]gf9s,m n%hi]d Jrvdguf9gus]rtsf9yf lJf9 ywir|w}ëpd)hi]dl[å]qJrvt½ x )" _wfUhphi]d,s&r|gs&q]rvhÃ|d`d>f lJx hi]d,wiyw
2.0
51.5
Lock up time by Verilog-A
51 50.5 50
Lock up time by SPICE
49.5 49
SPICE
48.5 48
Verilog-A
47.5 47 1.0
¡
C"DE$F U ] USX b5\ D \
1.2
1.4
1.6 1.8 2.0 Time [µsec]
2.2
2.4
UKM RP^NÕPSRa`VT[MyXP5W¤P ] æ[NVP WM\-\ D] `VT[M¿ÞsP ] `-M÷Ý_USN-XP
hudj |d`dywqXs/hiXfUhBhi]deJQywir|sf QeJf gf jkdhidgw4fUhBhi]de]gumys&dEwiw |d`dsf9l?å%d[|rvlJ9dx?himÈhiJdwiq]åy
s&r|gs&q]rvhe%dginm9gujf lJsdwf lJx hu]dlhimÈhi]dwiwhidj eXdgnm`gijf9lJs&d`o ¡ n]m9ghu]r|we]qJgie%m`wid9}hu]d nm`v|mUërvlJ{(e]gumys&dEwiwidwf gud,xym9lJd9¡ n!r|gwhE¿ } )a _wm n)wiq]åy
s&r|gs&q]rvhsJf9guf`s1hudgur|whirtsw/f9gidå]q]r|hfUh hu]d[srvgs&q]rvh|d`dT¡_í]dwi½ d )a Ìw(f9gi° d zJgwhm9gxydgeXm`vl]m`jrv f9|w f9lJxs&m`al zJgujdEx[hiJf h hi]d[Xf9xÎdl]m`q]{90f`ss&qJguf`s& å hu]d f9lJf |ywrtwm9n)Uf gur|f9lJs&d°û u { dã uaüÎè Eé¶ ¡ u wf ld&ð]f jke]|d9}hu]d )" m9n øùrtw wi]mUëlr|v l n4rv{X¡J]¡ d&ðhE} f l )a m9n,f°|mys?q]ebhurvjkd9}ëJr|s³rtw f¹wiwhidj |d`deXdgnm`gijf9lJs&d`}Ur|w4å]q]r|vhBå,hu]dwif9jkdpëfM,f9wBs&r|gusq]rvh4|d`d sJf9guf`s1hudgur|whirtsw¡
l°hu]r|wsf`wd`}6hu]½ d )" r|wd&ðye]gudwuwdEx°f9w/f nq]lXs1hir|m9lm9n>wiq]åy
s&r|gs&q]rvhÒsJf gf9s&hidgirtwhur|swö} ¢ýf lX x 8m9n%hu]d|mUë eJf`wi¿w zJvhidgEy¡ u zJgwhÒm9gxydgÒeXm`vl]m`jrtf %f9s]r|d`dw-fgidEf9wim9lJf9å]|d f`ss&qJguf`s&9}4ë]rts?rtw`dgu7r zXdx°å¹f_jqJhurve]|ds&m9gugudtfUhir|m9lGsm d srvdlQs h ¢¡,
l_hu]rtw dðyeXdgir|jkdlQh_} ¢ ©) Ñ `9J}%f9lJx0rvh,wi]mUë w huJfUhhu] d )a f eJe]gimMðyr|jfUhidEw#hu]d wiwhidje%dginm9gujf lJsdpërvhi dl]m9q]{`_f9ss&q]gf9s9 ¡ n4r|{J¡ kwi]mUë w hu] d a ùm9n-vmysq]e0hurvjkd f`w hu]dnq]lJs1hurvm`lÈm9¨n ø ù m nÒhi]dkã o { f9lJ} x ¢ m9n-hi]dk|mUë eJf`wiw zJvhidg¡ n!r|lJf9v|9}ùwiq]åJwhirvhiqyhurvlJ{ srvgs&q]rvh|d9d )" _w r|lQhim hu]d
-2
1 2 0 1 -1 0 2 Ld (NMOS) -2 3 -3 Ld (PMOS) -1
3
¡dß[ÞÙPSRPSR"`-T$M
Lock up time [µsec]
dÝHIvKMNV\ [\"!#%$'&dÞ Iyß)(_U ] * Y !# C"DE$F $ýÜÞ Iyß+("$ý)USNVUM`-MNV\HUSNVM ] P^N USX D-, MYÿb `VT$M D N MU ] \HU ] Ys\`U ] Y$USNVY Y$M K D U` D P ] \(
-2
-1
0
1 Gain of VCO kv
2
-2
-1
0
1
2
3 -3 R of Low Pass Filter
¡
Lock up time [µ sec]
wiywhudjT|d`dZ )a ¹}Ehu]dp|mys,q]e/hurvjkdrtw!dðye]gidEwiwidx,f`wBfnq]lJs& hurvm`l(m9n%e]gumys&dEwiwT|d`dQUf gur|f hir|m9lJw¡LnJm9gBd&ð]f jke]|d9}>n4rv{X¡ awi]mUë w hu]dp d w%dEs1hBm nJñÒò2û ª{]ü!f lJ x ¢Äm9nyhi]dÃ|mUë¹eJf9wu_w zXhudg!him hu]d |mys(q]ehir|jkd sJf9guf`s1hidgirtwhirts ¡6
lhi]rtwpd&ðyeXdgir|jkdlQh}Qhu]d wirvj(qy tfUhurvm`l we%ddExm n>hiJd wiwhidj¬|d`d%f lJf9vywir|wërvhiãdgurv|m9{9 u³rtw f9åXm`qyh)` hir|jdEw-nÀf`whudghuJf l hi]dï%fUhpf9lJf |ywrtwërvhi[yúÒioÃz ¡
ÈdwJmUë hi]guddf e]eJvrtsf hir|m9lJwm n hu]d[Jrvdguf9gus]rtsf9ÒwhufUhur|w hur|sf pf9lJf |ywrtwv ¡ { l]d f9e]e]|r|sfUhurvm`l¹r| w 0m9lQhid[oÃf9gi|m_f lXf |wirtw} f9l]m hu]dgrtwpëÃm9gwh
sf9wid f9lJf |ywrtwÃf lJxhi]dm9hi]dgÃrtwwidlJwirhurvrvh f9lJf |ywrtw¡ 0m9lQhid_oÃf gu|mÌf lJf9vywidwm nhiJr|wkwiwhidjìeXdgnm`gijf lXs&d[f9gid xym`l]dbërhuhu]d )a vr|l]rvlJ{µjkdhi]myx\¡ í]d³wif9jdbgf ly xym`jUf gurtf å]|dw0f9gid¹f twimbqXwdExµf`w0r|l8hu]dGe]gudr|m9qJv w _m9lQhid oÃf9gi|m´f9lJf |ywdEwkërhuýe]rts&d_f9lJxbãdgurv|m9{9 u¡-í]d0gidEwqJh m9n hu]Q d 0m9lQhudÈoÃf guvm¹f lXf |wirtw(ërvhiÄhu]d0e]gum9e%m`widxjkd&hiJmxÄrtw sm9jkeJf gudxGërhu?m9lJdwërhuÄye]r|sdÎf9lJxGãdgir||m9{ u/¡4hr|wkf`w wiq]jkdxhuJfU÷h ¢8f lJ3 x 8m9n%hu]d |mUëÄeJf9wuw zJvhidgÒf gud whfUhur|whirtsf9v| r|lJxydeXdlJxydlQhf9lJx?f9gidÎl]m9gujf |vGx]r|whigurvåJqyhidEx\¡bíJdwusf hhudg 1.3 1.2 1.1
-3
-2
-1
0
Ld (NMOS)
1
2
3 1 2 -1 0 -2 3 -3 R of Low Pass Filter
C"DE$F4 dß[ÞÙPSR"XP5W NVU ]$E MyPSR"ýÜþZþ$ý)USNUM `-MNV\LUSNVM ] P^N USX D-, MY ÿb `VT[M D NMU ] \HU ] Ys\`U ] YUSNVYY$M K D U` D P ] \5(
1.8
Correlation Coefficient 0.880
1.6 1.4 1.2 1.0 0.8 0.6 0.6
0.8 1.0 1.2 1.4 1.6 1.8 Lock up time by Verilog-A Simulation [µsec]
2.0
¡
3
C"DE$F. dß[ÞÙPSRa`VT$MyXP W/ $æ¤` D MPSR"`-T$MyýÜþ>þ0$AýiUSNVUM `VMNV\HUSN-M Y \-`VU ] YUSN-YsY$M K D U` D P ] \( ] P^N USX D-, MY ÿ b `-T$M D N1MU ] \HU ]
2.0
C"DE$F6 Jß5WU`-`-MNdæ$XPS`LÿM`2OgMM ] iMN D XP E ã }U ] Y¤`VT[Myæ$NVP^æP^\VMY*M `-T$P Y
2.2 1.8 1.4 1.0 0.6 0.2 -3
¡
Lock up time by the proposed method [µsec]
-3
Lock up time by the proposed method [ µsec]
Gain of VCO kv [MHz/V]
75 70 65 60 55 50 45 40
1.8 1.6
Correlation Coefficient 0.858
1.4 1.2 1.0 0.8 0.6 0.7
0.8
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Lock up time by SPICE Simulation [µsec]
1.7
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