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K0 @ 9(     `gg1 ?p  T Click to edit Master title style! !@  Z gg1 ?Q  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     Sx  <Ԕ?#" `` 0r  <E9A(m1?"wf  c 0A CSeal"iV   HT 1?"3 @*    Hd CC"(-  3NSF ERC for Wireless Integrated MicroSystems (WIMS)4 24    fB   0DԔ?"ppB  s *޽h ? a(y___PPT10e.+D=' = @B +___PPT9:p::  Blank. K0 !P(    Z gg1 ? `     W#Click to edit Master subtitle style$ $~  B?#" ``` 0B  s *޽h ? a(___PPT10u..ȳn+D=' = @B + 0 ZR`( w @  ZGii1 ? F;  RClick to edit Master text styles Second level Third level Fourth level Fifth level!     Sp  01 ?69  B  s *i ? a(80___PPT10.@(g  p 0(   B  s *i ? a(80___PPT10.0YixK0 (    Zgg1?"^   61?P m  TAA ? ` eLecturer Michael S. McCorquodale Authors Michael S. McCorquodale, Mei Kim Ding, and Richard B. Brown6fn C f . @Ld  C <A$OfficialSealSmallP \  NpPpP ?P y;Top-Down and Bottom-Up Approaches to Stable Clock Synthesis<<$@  N ?   0Solid State Electronics Laboratory Center for Wireless Integrated Microsystems (WIMS) Department of Electrical Engineering and Computer Science University of Michigan Ann Arbor, MI USA 48109-2122.   K  N?p0 S International Conference on Electronic Circuits and Systems, Sharjah, U.A.E., 2003(ST.>   H  0޽h ? a(y___PPT10Y+D=' = @B +cI K0 }uP  (  x  c $$op     S ? <$ 0    Ho8c?"`` <Overview     HHt8c?"` @ Freq. Trans.     Hhx8c?"`  = Synthesis     H|8c?"`  ? Application     H8c?"`  c Design & Sim.    H̅8c?"`   ;Results   H\8c?"`   ? Conclusions   H  0޽h ? a(vAnA___PPT10NA+|LD@' = @B D@' = @BA?%,( < +O%,( < +D\' =%(%(DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-o6Bdissolve*<3<*TD ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Tu%(D' =-o6Bdissolve*<3<*TuD ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*u%(D' =-o6Bdissolve*<3<*uD ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D ' =%(DL' =%(D' =4@BBBB%(D' =1:B#ffffff [0]*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*DD' =%(D' =4@BBBB%(D' =1:B#ffcc00*a3>Bfillcolor<*D' =1:B solid*a3>Bfill.type<*D' =1:B true*]3>Bfill.on<*D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+ +U/  K0 { (  ~  s * p     c $ )<$ 0     B 8c?"`` <Overview     HԸ 8c?"` @ Freq. Trans.     H 8c?"`  = Synthesis     H 8c?"`  ? Application     Hh 8c?"`  c Design & Sim.     H 8c?"`   ;Results    H 8c?"`   ? Conclusions   H  0޽h ? a(b'Z'___PPT10:'+ _D&' = @B D&' = @BA?%,( < +O%,( < +DM' =%(%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*LD' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD7 ' =%(D ' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*LD' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(Dd' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*QD' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =-o6Bdissolve*<3<*QD' =%(D(' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =-o6Bdissolve*<3<*QD@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*+8+0+  +( K0 ?!7!`5qP (  ~  s *p   7 l   \ ,$D 0h  c $A ??$ l O n  s *A" ?? 3 H #  6  @  =Phase Noise: Power relative to fundamental at some offset fm F>:  q@`  NG|)?"`p ` fB H 6D8ch0 hfB I 6D8ch0 hT 0 @ p  J# H0 < K  BCpDE4F8c pX\H0Xp `0 @    "`0 @ P < LB  BCpDE4F8c pX\H0Xp `0 @    "`P @ p fB M 6D8ch  N H8c"` 5T  Gf*  O H8c"` bfo*  P H8c"`p D  GP*  T B1?P` z  Ffm( fB UB 6D1? } l `  [` ,$D 0  2 BA ? ?     0  GPeriod Jitter: s of the position of the next edge relative to the ideal2H7 q@`ZB  s *D1` `` fB  6D8c?M  /fB  6D8c? ]fB ( 6D1?fB * 6D8c?/fB + 6D1?M/fB , 6D1?}/fB - 6D1?m/fB . 6D1?=/fB / 6D1? /fB 0 6D1?-/fB 1 6D8c?]//fB 3 6D1?]/fB 4 6D1? ]/rB 5 BD1?p]p 6 N1?  x EIdeal Period  7 N1? ? Period Jitter `B < 0D8c?}0M 0`B = 0D8c?}0`B > 0D8c?M`B ? 0D1?]] R N1?c0 `tk(  S N#1? 0 Htk+1(  V HG|)?"`0  p Y2 C xggA @?1 ?  @  k B`(8c?"`` <Overview    l H,8c?"` @ Freq. Trans.    m HH08c?"`  = Synthesis    n H.8c?"`  ? Application    o H88c?"`  c Design & Sim.   p H0<8c?"`   ;Results  q H?8c?"`   ? Conclusions   H  0޽h ? a(@8___PPT10+ꮕD' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =-o6Bdissolve*<3<*[D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-o6Bdissolve*<3<*\+m'  K0 VN1d(  d~ d s *p   =l  (d,$D 0 d2 C x0e0eA M?5% ? 0  M  d 0:  5Phase and frequency are related by a linear operator:68n6l N0  )dN0 ,$D 0 d2 C x0e0eA T?5% ?0  T   d2 C x0e0eA R?5% ? /  R # d 0R N 7Frequency mult./div. results in phase noise mult./div.:88n8,  "d HG|)?"` t -l  r *d r,$D 0 d 0]    r"Using narrowband FM approximation:#8n# #d2 C x0e0eA W?5% ?} P  W  %d 0f r CLinear freq. translation results in quadratic change in noise powerD8nDB &d 0D1? l,$D  0B 'd 0D1? l ,$D  0 +d Hp8c?"`` <Overview    ,d Bi8c?"` @ Freq. Trans.    -d Hy8c?"`  = Synthesis    .d H|8c?"`  ? Application    /d H88c?"`  c Design & Sim.   0d Hԃ8c?"`   ;Results  1d H臥8c?"`   ? Conclusions   H d 0޽h ? a(___PPT10+pYD+' = @B D' = @BA?%,( < +O%,( < +D ' =%(%(D' =%(D' =A@BB"BB0B@ A%()))D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<*,d%()?)?)?D' }=/u8AC*Q3> Br<*,d%(D' }=/u8C*Q3> Br<*,d%(}D' }=/u8C*Q3> Br<*,d%(D' }=/u8AC*Q3> Br<*,d%(wD' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*(d%(D' =-o6Bdissolve*<3<*(dDz' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&d%(D' =-s6Bwipe(left)*<3<*&dD' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*)d%(D' =-o6Bdissolve*<3<*)dDz' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'d%(D' =-s6Bwipe(left)*<3<*'dD' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<**d%(D' =-o6Bdissolve*<3<**d+8+0+,d +c+  K0  T (  ~  s *|p   `  c $A  ??[  d      c $A  ?? 3  8  $@ 0 6 B̗1?"` J,$D  0 Typically p fo2c called corner or line width: select fm above the corner and below fo Lorentzian implies absence of flicker noise (slope must be 20dB/dec)   &  F,T ;gG7l @  L@ ,$D 0 72 3 r0e0eA ?5% ?_0      0Х @ DThe SSB phase noise PSD can be represented by a Lorentzian function:ED 0  y@` 5 <1?@  *  12 c 0e0eA ?8c ??"`F0  rB , BD8c?? rB - BD8c?? C lB . <D8c??@  / Tػ8c??"`@`  Ffm(   lB 3 <D8c??P0PlB 4 <D8c??P* @ Nd1? :20dB/dec  l 0  M0 ,$D 0 >2 C x0e0eA ?5% ?)    92 C x0e0eA ?5% ?b0    E 0<ͥ  pWhich can be approximated for: y@` F 0ϥ  0 ,$ 0 bUsing the above: y@`B K 0D1? ` ,$D  0 N H٥8c?"`` <Overview    O Bݥ8c?"` @ Freq. Trans.    P Hѥ8c?"`  = Synthesis    Q H,8c?"`  ? Application    R H8c?"`  c Design & Sim.   S H8c?"`   ;Results  T H8c?"`   ? Conclusions   H  0޽h ? a(___PPT10+GD-' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-o6Bdissolve*<3<*LD' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D' =-o6Bdissolve*<3<*MD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*K%(D' =-s6Bwipe(left)*<3<*KD' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*F%(D' =-o6Bdissolve*<3<*FD_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*6D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*6+p+0+6 ++0+F +z  K0 (A(  ~  s *p   B   0D1? l,$D  0B   0D1? l ,$D  0l X X,$D 0  0   :Using phase noise conversion expression, determine jitter:;8n;t  0A ? ? X t  0A ? ? X `B  0D1?p p XQl     1 ,$D 0  0 R 'Considering fractional, or ppm, jitter:(8n(  2 C x0e0eA r?5% ?    r {l ( r !( r,$D 0 2 C x0e0eA n?5% ?( `  n  2 C x0e0eA! t?5% ? @ x  t    0! r 7Frequency translation also enhances and degrades jitter88n8`B  0D1?p H p  " H#8c?"`` <Overview    # Bh&8c?"` @ Freq. Trans.    $ H*8c?"`  = Synthesis    % H/8c?"`  ? Application    & H038c?"`  c Design & Sim.   ' HT88c?"`   ;Results  ( H68c?"`   ? Conclusions   H  0޽h ? a(YQ___PPT101+xD' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*Dz' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* Dz' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =-o6Bdissolve*<3<*!+  K0 | t  T (  T~ T s *8Gp    T 0g 3,$ 0 Leeson model: Q-factor quadratically related to phase noise Q-factor is one of the most significant metrics indicating stability Typical quartz XTAL Q on the order of 10,000 Frequency translation also quadratically related to phase noise Consider effective Q-factor modification due to freq. translation If NdivNmult > Qmult/Qdiv then divided signal more stable Assumption: oscillator power and noise factor are the same Nmult for XTAL+ PLL up to 4096: high-Q, but large degradation 0n.Xk1      ;  l  ]  \:l Pm  TPm,$D 0 T 6A C?jJ?"`P0 m C T 0^  ` Leeson Phase Noise Model0Z   T HW8c?"`` <Overview     T B8Z8c?"` @ Freq. Trans.     T HP|8c?"`  = Synthesis    T H8c?"`  ? Application    T H8c?"`  c Design & Sim.   T HP8c?"`   ;Results  T H8c?"`   ? Conclusions   H T 0޽h ? a(___PPT10+uDZ' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* T%(D' =-o6Bdissolve*<3<* TDA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*T%(+8+0+T +#  K0 ""0P"(  ~  s *0p    0 C x0e0eA 3?5% ? X   3  0 # l0e0eA )?5% ?  )     #"&  * H<1?e  B @] ) H01?8  e B @] ( Hص1?  8  |Jppm,  @]  ' HO1?  Relative Period Jitter (ppm)n @] & Hd1?e3   B @] % H1?8 3 e  B @] $ Hh1? 3 8   OJ @] # H1?3   ^Period Jitter (s)n @] " H1?ew3  B @] ! H1?8 we3  B @]   H1? w8 3  B @]   H1?w 3  SSB Phase Noise PSD (dBc/Hz)n @]  Hp1?ew fref /ND  @]  H1?8 ew Nfref6  @]  H((1? 8 w |fref,  @]  Hp11? w bOutput Frequency (Hz)n @]  BP31?e dFrequency Division n @]  B<1?8 e jFrequency Multiplication n @]  B ,1? 8  fReference Oscillator n @]  BU1?  aVariable/Metric n @]`B + 0o ?ZB , s *1 ?ZB - s *1 ?wwZB . s *1 ?3 3 ZB / s *1 ?  `B 0 0o ?`B 1 0o ?ZB 2 s *1 ?  ZB 3 s *1 ?8 8 ZB 4 s *1 ?ee`B 5 0o ? 0 C x0e0eA 0?5% ?p (  0  0 C x0e0eA .?5% ?`  .  0 C x0e0eA 6?5% ?   6 l  0A :? ? p :l  0A <? ? up <  H[8c?"`` <Overview     Bl`8c?"` @ Freq. Trans.     Hd8c?"`  = Synthesis     Hh8c?"`  ? Application     Hl8c?"`  c Design & Sim.    H\q8c?"`   ;Results   Hu8c?"`   ? Conclusions   H  0޽h ? a(y___PPT10Y+D=' = @B +6 K0 P)*Z(  x  c $)p   >l 0P0  *P00 ,$D 0  <*8c"`@  0  DN&0 `B   0D8cP `B  B 0D8c   ZB  B s *D8c0 @ `B  0D8c0 ZB  s *D8c00 l   ) ,$D  0`B   0D8cpPPN a    z2  <8c?"`a    C BCPDE(F8c 0T`0  8PP @   "`0 P   0  kNfref00  l ` 0p (0` p,$D  0`B  0D8cPP  <쐹8c"`` 0p ELPF&0   0 ;`G kvctrl00  l  5 % 5,$D  0`B   0D8cP   0 o jfref00  N a    5z2  <8c?"`a    C BCPDE(F8c 0T`0  8PP @   "`0 P l @0` p '0@` p,$D  0  <8c"`@0 p DCP&0 `B  0D8c P` Pl  0@p &0 @p,$D  0  <8c"` 0p EPFD&0 `B  0D8c@`B  0D8c@  <1? X&Quartz XTAL reference oscillator + PLL''?  <1? &,$   0 mThe signal that actually drives the processor is a frequency multiplied (and degraded) image of the referencenn  HD8c?"`` <Overview     HP8c?"` @ Freq. Trans.      B컹8c?"`  = Synthesis    ! H8c?"`  ? Application    " Hù8c?"`  c Design & Sim.   # HTǹ8c?"`   ;Results  $ H˹8c?"`   ? Conclusions   H  0޽h ? a(KC___PPT10#.̨@+_ZD' = @B DB' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BB"BB0B@ A%()))D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<* %()?)?)?D' }=/u8AC*Q3> Br<* %(D' }=/u8C*Q3> Br<* %(}D' }=/u8C*Q3> Br<* %(D' }=/u8AC*Q3> Br<* %(wD' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =-s6Bwipe(left)*<3<*%D' =%(xD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =-s6Bwipe(left)*<3<*&D' =%(lD7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =-s6Bwipe(left)*<3<*'D' =%(` D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(T D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-s6Bwipe(left)*<3<*)D' =%(H D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-u6Bwipe(right)*<3<**D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*+p+0+ ++0+  +N K0 7/ (  ~  s * ܹp   l 0C`  0C` ,$D  0fB  6D8c6 2  B8c?"`  C BCPDE(F8c 0T`0  8PP @   "`_.k  B޹8c"`6 0 `  DN&0 fB  6D8c o   6Xy  jfref00     6$0Cp |fref N@0  ZB   s *D   <1? @ s+A harmonic LC (and monolithic) RF reference,, <   <1?* 0 ,$  0 jThe signal that actually drives the processor is a frequency divided (and enhanced) image of the referencekk1  <01?Z `,$  0 SLC reference also provides good accuracy as compared to ring or relaxation approach"TR  H8c?"`` <Overview     H8c?"` @ Freq. Trans.     B8c?"`  = Synthesis     H 8c?"`  ? Application     H8c?"`  c Design & Sim.    H88c?"`   ;Results   HP8c?"`   ? Conclusions   H  0޽h ? a(  ___PPT10 .ͨ`5+ڜWD ' = @B D ' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*+p+0+  ++0+ + K0  %(  ~  s *"p   r  S "0!  XB  0D1?000  <x$1?BK  v*All transistor design with TSMC 0.18 MM/RF0+   H*8c?"`` <Overview     HD/8c?"` @ Freq. Trans.      B28c?"`  = Synthesis      B 18c?"`  ? Application      H:8c?"`  c Design & Sim.     Hx>8c?"`   ;Results    HA8c?"`   ? Conclusions   H  0޽h ? a(___PPT10.ͨ09(+Dd' = @B D' = @BA?%,( < +O%,( < +DV' =%(%(D' =%(D' =A@BB"BB0B@ A%(D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<* %()?)?)?D' }=/u8AC*Q3> Br<* %(D' }=/u8C*Q3> Br<* %(}D' }=/u8C*Q3> Br<* %(D' }=/u8AC*Q3> Br<* %(w+8+0+  +dI K0 ==qs<(  x  c $HTp   L pP p # C # xB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB   <D8c?6 6 lB   <D8c?P P lB   <D8c?P P plB   <D8c?p 6  L @ p  #  # ! ZN ` @   ` @ z2  <8c"`` @ z2 B <8c"` @ ZN ` @   ` @  z2  <8c"`` @ z2 B <8c"` @ ZN ` @   `@  z2  <8c"`` @ z2 B <8c"` @ ZN ` @   `@ z2  <8c"`` @ z2 B <8c"` @ ZN ` @   ` pz2  <8c"`` @ z2 B <8c"` @ ZN ` @   ` pz2  <8c"`` @ z2 B <8c"` @ ZN ` @    ` pz2 ! <8c"`` @ z2 "B <8c"` @ fB #B 6D8c ` fB $ 6D8c  L pp0 %# C # 0 lB & <D8c? lB ' <D8c?  xB ( HD8c? lB ) <D8c?lB * <D8c?plB + <D8c?0lB , <D8c?pPPF @   -  # ` ZB . s *D8c@  ZB / s *D8c@   0 B`8c"`PK  p >30 1   1 Bdd8c"`;   >50 1   2 Be8c"` f  >389m   3 6k8c"` (  ?4.79f  RB 4 s *D8c@e @RB 5 s *D8cs  6  d0e0e    BpC DE(F0 @  8c 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E P p  p@c"$`  0 RB 7 s *D8c  RB 8 s *D8c #  L @   9#   ZB : s *D8c@  ZB ; s *D8c@  L @   <#  # ZB = s *D8c@  ZB > s *D8c@   ?  d0e0e    BpC DE(F0 @  8c 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E P p  p@c"$`` RB @@ s *D8c@s @RB A@ s *D8cs XB B 0D8c # RB C@ s *D8cXB D 0D8c@RB E s *D8cRB F@ s *D8ccXB G 0D8ccc RB H s *D8c S RB I@ s *D8c c# RB J s *D8c cc RB K s *D8c# XB L 0D8c RB M s *D8c  RB N s *D8c  RB O s *D8c cc RB P s *D8c  dB Q <D8c? 3 dB R <D8c? F dB S <D8c?YmdB T <D8c? cc dB U <D8c? S dB V <D8c? f dB W <D8c?ydB X <D8c?  dB Y <D8c?P S P dB Z <D8c?p  @ p dB [ <D8c?  - dB \ <D8c?# # P  ] B}8c"` C G  I900*    ^ BL8c"``   =30p   _ B8c"``   =30p  F @   `  ! ZB a s *D8c@  ZB b s *D8c@   c BT8c"``   <7p  XB d@ 0D8c c XB e 0D8c #   f Bt8c"` B ` J500k*    g <81? I3.125MHz XTAL reference h <L1?@` d2Requires off-chip XTAL + 2 capacitors + 1 resistor33Kl  `  s ` ,$D  0 i B1?"`` ` lB j <D1?`  k NХ1?  MXTAL lumped parameter model l H8c?"`` <Overview    m H8c?"` @ Freq. Trans.    n B8c?"`  = Synthesis    o B8c?"`  ? Application    p B8c?"`  c Design & Sim.   q H8c?"`   ;Results  r Hp8c?"`   ? Conclusions   H  0޽h ?     !" a(  ___PPT10 .ͨaC+!D ' = @B D> ' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BB"BB0B@ A%()))D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<*p%()?)?)?D' }=/u8AC*Q3> Br<*p%(D' }=/u8C*Q3> Br<*p%(}D' }=/u8C*Q3> Br<*p%(D' }=/u8AC*Q3> Br<*p%(wD' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*s%(D' =-s6Bwipe(left)*<3<*s+8+0+p +lZ K0 kYcY" X(  ~  s * p   Q8 q   @@P N p  e  N  0  f p  g B@8c"` 0  @4 0.18  ZB h s *D8cbP P fB i 6D8c?pN p  j p T pP p k# pp xB l HD8c?n P lB m <D8c?n n rB n BD8c?n P lB o <D8c?6 6 lB p <D8c?P P lB q <D8c?P P plB r <D8c?p 6 &N  P s 00 lB t <D8c?`P`lB u <D8c?=lB v <D8c?*lB w <D8c?  `T pP p xC# pp xB y HD8c?n P lB z <D8c?n n rB { BD8c?n P lB | <D8c?6 6 lB } <D8c?P P lB ~ <D8c?P P plB  <D8c?p 6 `B  0D8c`B  0D8cppT pp0 C#  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB  <D8c?plB  <D8c?0lB  <D8c?pPPT pp0 #  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB  <D8c?plB  <D8c?0lB  <D8c?pPPfB  6D8c?qP P `B  0D8cP z2  <8c?"``z2  <8c?"`r`0N  0   pp    B8c"` 0  @2 0.18  ZB  s *D8cbP P N p     N  0   p   BX8c"` 0  @4 0.18  ZB  s *D8cbP P fB  6D8c?pN p   p T pP p # pp xB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB  <D8c?6 6 lB  <D8c?P P lB  <D8c?P P plB  <D8c?p 6 &N  P  00 lB  <D8c?`P`lB  <D8c?=lB  <D8c?*lB  <D8c?  `T pP p C# pp xB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB  <D8c?6 6 lB  <D8c?P P lB  <D8c?P P plB  <D8c?p 6 `B  0D8c`B  0D8cppT pp0 C#  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB  <D8c?plB  <D8c?0lB  <D8c?pPPT pp0 #  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB  <D8c?plB  <D8c?0lB  <D8c?pPPfB  6D8c?qP P `B  0D8cP z2  <8c?"``z2  <8c?"`r`0N  0   pp    B8c"` 0  @2 0.18  ZB  s *D8cbP P ZB  s *D8c@@`B  0D8c@ZB  s *D8c@@`B  0D8cp ZB  s *D8cp p `ZB  s *D8cZB  s *D8cp ` `ZB  s *D8c ` ZB  s *D8c@ N p   0 N  0   p   B8c"` 0  @4 0.18  ZB  s *D8cbP P fB  6D8c?pN p   p T pP p # pp xB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB  <D8c?6 6 lB  <D8c?P P lB  <D8c?P P plB  <D8c?p 6 &N  P  00 lB  <D8c?`P`lB  <D8c?=lB  <D8c?*lB  <D8c?  `T pP p C# pp xB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB  <D8c?6 6 lB  <D8c?P P lB  <D8c?P P plB  <D8c?p 6 `B  0D8c`B  0D8cppT pp0 C#  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB  <D8c?plB  <D8c?0lB  <D8c?pPPT pp0 #  pP lB  <D8c? lB  <D8c?  xB  HD8c? lB  <D8c?lB   <D8c?plB   <D8c?0lB   <D8c?pPPfB   6D8c?qP P `B   0D8cP z2   <8c?"``z2   <8c?"`r`0N  0    pp     B 8c"` 0  @2 0.18  ZB   s *D8cbP P `B   0D8c pZB   s *D8cpp`B   0D8c ZB   s *D8c`ZB   s *D8c``ZB   s *D8c`ZB   s *D8cp0ZB   s *D8c ZB   s *D8c ZB   s *D8cp   B8c"` @bias 0  ZB   s *D8c  ZB   s *D8c     Bd8c"`q   Kfrom last stage 0     B8c"`Q  Kfrom last stage 0     <1? Z(20-stage 200MHz current-starved ring VCO))   H!8c?"`` <Overview      Hp 8c?"` @ Freq. Trans.      B *8c?"`  = Synthesis      B-8c?"`  ? Application      B|,8c?"`  c Design & Sim.   !  H058c?"`   ;Results  "  Hl98c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.ͨaC+D=' = @B + K0 "#(  ~  s *@t p   XB  0D8cPP  <@8c"`0` p ELPF&0   <0D8c"`0 p EPFD&0   <G8c"` @ 0  DN&0 XB  0D8c@XB  0D8cP XB  @ 0D8c   XB   0D8cPpPXB   0D8cP RB  @ s *D8c 0@ XB   0D8c0 RB  s *D8c00 F a    z2  <8c?"`a    C BCPDE(F8c 0T`0  8PP @   "`0 P   0N o jfref00    0S  kNfref00    00X`;G kvctrl00  F a    5z2  <8c?"`a    C BCPDE(F8c 0T`0  8PP @   "`0 P   <]8c"`0@ p DCP&0 XB  0D8cP ` PXB  0D8c@  <lb1? {'Remainder of PLL modeled with Verilog-A((  Hf8c?"`` <Overview     Hk8c?"` @ Freq. Trans.     Bo8c?"`  = Synthesis      Bs8c?"`  ? Application    ! Br8c?"`  c Design & Sim.   " H0{8c?"`   ;Results  # Hy8c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.̨@+D=' = @B +8 K0 77psx6(  x  c $p   3/8 0@ jPt`T pp0 C# @ @lB  <D8c? lB  <D8c?  xB  HD8c? lB   <D8c?lB   <D8c?plB   <D8c?0lB   <D8c?pPPT pP p  #   pxB  HD8c?n P lB  <D8c?n n rB  BD8c?n P lB  <D8c?6 6 lB  <D8c?P P lB  <D8c?P P plB  <D8c?p 6  T @ p #  8  ZN ` @   ` @ z2  <8c"`` @ z2 B <8c"` @ ZN ` @   ` @  z2  <8c"`` @ z2 B <8c"` @ ZN ` @   `@  z2  <8c"`` @ z2 B <8c"` @ ZN ` @   `@ z2   <8c"`` @ z2 !B <8c"` @ ZN ` @  " ` pz2 # <8c"`` @ z2 $B <8c"` @ ZN ` @  % ` pz2 & <8c"`` @ z2 'B <8c"` @ ZN ` @  ( ` pz2 ) <8c"`` @ z2 *B <8c"` @ fB +B 6D8c ` fB , 6D8c  T pp0 -#  @lB . <D8c? lB / <D8c?  xB 0 HD8c? lB 1 <D8c?lB 2 <D8c?plB 3 <D8c?0lB 4 <D8c?pPPT pP p 5C# @ pxB 6 HD8c?n P lB 7 <D8c?n n rB 8 BD8c?n P lB 9 <D8c?6 6 lB : <D8c?P P lB ; <D8c?P P plB < <D8c?p 6 `B = 0D8c ZB > s *D8c  ` ZB ? s *D8c@@0 ZB @ s *D8c@@ @ZB A s *D8c@ ZB B s *D8c `B C 0D8c ZB D s *D8c `B EB 0D8c@ `B F 0D8c @ @`B GB 0D8c@@ @ZB H s *D8c  @ZB I s *D8c  @`B JB 0D8c@ `B K 0D8c F F `B LB 0D8c@F ` F T pP p M# ! 0 xB N HD8c?n P lB O <D8c?n n rB P BD8c?n P lB Q <D8c?6 6 lB R <D8c?P P lB S <D8c?P P plB T <D8c?p 6 ZB U s *D8ca 0 0`B V 0D8c @ ZB W s *D8c! P!  X BX8c"`   A40 0.18   Y B,8c"` B100 0.18     Z B8c"` o i  A40 0.18   [ B,8c"` B100 0.18     \ Bh8c"`   A36 0.18   ] BĪ8c"`  0  =2nH   ^ B8c"`,  Nbias.    ZB _ s *D8c@  ZB ` s *D8c(  ZB a s *D8c  ZB b s *D8c(  ZB c s *D8c  `B d 0D8c 0 `B e 0LD8c ZB f s *D8c@ F F ZB gB s *D8c F F  h 68c"` @  ?950fF  `B i 0LD8c@ @  k <$1? t,3.2GHz monolithic RF LC reference oscillator,- m H 8c?"`` <Overview    n H8c?"` @ Freq. Trans.    o B8c?"`  = Synthesis    p BL8c?"`  ? Application    q B8c?"`  c Design & Sim.   r H8c?"`   ;Results  s H8c?"`   ? Conclusions   H  0޽h ? ! # $ & ' )* a(___PPT10i.ͨ09(+D=' = @B +8 K0 43l ~3(   ~   s *p    h  <1?0P \*Entire system designed at the device level++ %  <1?   b0Each feedback flip-flop divides frequency by two11 &  H8c?"`` <Overview    '  H8c?"` @ Freq. Trans.    (  B 8c?"`  = Synthesis    )  B8c?"`  ? Application    *  Bx8c?"`  c Design & Sim.   +  Hd8c?"`   ;Results  ,  H8c?"`   ? Conclusions   u+l f   f ,$D  0BB /  3 ]]T :  2 # : P 0  3 "`: \ 1  S ]"`:  3  <h  ODFF0GBB 4  3 ] D BB 5  3 ] ] T 6 :  8 # 6 : P 6  3 "`6 : \ 7  S ]"`6 :  9  <&h  ODFF0Gb :  c $]"`:  ;  <h  ODFF0GHB <  C D]RhHB = B C D]h  >  <`G MQ0G ?  < u%  MQ0G @  <BV MD0GBB A B 3 ]}~BB B  3 ]f}BB C  3 ]fgHB D  C D]]\^ E  C BCrDEFD]r @`"`l  F  <#|w  OAMP0GBB G  3 ]$%BB H  3 ]BB I  3 ]Ie f BB J  3 ]n  BB K  3 ]  BB L  3 ] e BB M  3 ]Ie f BB N  3 ]n  BB O  3 ]  BB P  3 ] e  Q  <*k M+0G R  </I~  M-0GBB S  3 ]: ; T   V #  B2 T  3  H2 U  C ] T R?  Y # R?  W  B C9 DE(F 4hv:~ n9   @   R?  X  BBC/DE(F] $LGk+/*B @   R? T   \ #  V2 Z  C "` \2 [  S ]"` @T R?  _ # R?  ]   B C9 DE(F 4hv:~ n9   @   "`R?  ^  # BBC/DE(F] $LGk+/*B @   "`R?  `  <6 L3.2GHz*G BB a  3 ]f}BB b B 3 ]}~BB c  3 ]U fV }BB d  3 ]U f gBB e  3 ]  BB f  3 ] f }HB g  C D]6 R HB h B C D]6   i  <<=` MQ0G j  <XAk %  MQ0G k  <p?T B  MD0GBB l B 3 ] }6 ~BB m  3 ] f }BB n  3 ] fLgHB o  C D]+]^BB p  3 ]LfM}BB q B 3 ] }K~HB r  C D]RbHB s B C D]b  t  <K`@ MQ0G u  <O  o%  MQ0G v  <lTBP MD0GBB w B 3 ]}~BB x  3 ]f}BB y  3 ]fgHB z  C D]]V^BB {  3 ]f}BB | B 3 ]}~BB }  3 ]  BB ~  3 ]  BB   3 ]  BB   3 ]W BB   3 ]]^ T  :d   #  :d P   3 "` :d \   S ]"` :d    <<\ h~   ODFF0G   <` `  MQ0G   <e B  MD0GBB  B 3 ]U } ~HB   C D] ] ^BB  B 3 ]j } ~   <j / %  MQ0GHB   C D] R" HB  B C D] "    <y   L200MHz*G H   0޽h ? a(ia___PPT10A.ͨ09(+r7D' = @B D' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +  K0    o(  ~  s *dvp   3 h Zwgg1 ?0 Bottom-up Approach Phase noise for reference OSC and VCO simulated at device level Device-level results modeled with Verilog-A Entire PLL modeled with phase domain approach using Verilog-A Top-down Approach Entire system simulated at the device level^nnn,n,,u7B i HD8c?"`` <Overview    j H@8c?"` @ Freq. Trans.    k B8c?"`  = Synthesis    l B8c?"`  ? Application    m Bԓ8c?"`  c Design & Sim.   n Ht8c?"`   ;Results  o H 8c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.ͨ09(+D=' = @B +  K0 yq  (  x  c $4p      3 r0e0eA5% ?p    H8c?"`` <Overview      H|8c?"` @ Freq. Trans.      B8c?"`  = Synthesis     BT8c?"`  ? Application     B8c?"`  c Design & Sim.    B8c?"`   ;Results   HD8c?"`   ? Conclusions   H  0޽h ? a( ___PPT10.ͨQ+D' = @B DO' = @BA?%,( < +O%,( < +D' =%(%(D' =%(D' =A@BB"BB0B@ A%()))D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<*%()?)?)?D' }=/u8AC*Q3> Br<*%(D' }=/u8C*Q3> Br<*%(}D' }=/u8C*Q3> Br<*%(D' }=/u8AC*Q3> Br<*%(w+8+0+ + K0   -(  x  c $8p       0e0eA1 ?p    H8c?"`` <Overview      H8c?"` @ Freq. Trans.      B8c?"`  = Synthesis      B8c?"`  ? Application     B8c?"`  c Design & Sim.    B8c?"`   ;Results   H8c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.Ϩ04s,+D=' = @B +z K0 yq  (  x  c $p     3 r0e0eA5% ?P   H8c?"`` <Overview      Hh8c?"` @ Freq. Trans.      B8c?"`  = Synthesis      BH8c?"`  ? Application      Bh8c?"`  c Design & Sim.     B8c?"`   ;Results   H`8c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.ͨσ+D=' = @B +z@ K0 y?q?G ?(  ~  s * p   8 `  #"J>p`  }  `1 ?` P0.23  @] {  `1 ?  O8.0  @] y  `8#1 ?  4Relative Period Jitter Accumulation/Reduction Factor5n5  @] v  `d1 ? ` O4.2  @] t  `41 ?  P0.12  @] r  `$>1 ?  w+Period Jitter Accumulation/Reduction Factor,n,  @] o  `F1 ? `  Q-23.8  @] m  `81 ?   P36.2  @] k  `X1 ?  7Phase Noise Density Accumulation/Reduction Factor, (dB)8n8  @] h  `b1 ? `  Q4.6  @] f  `j1 ?   Q5.9  @] d  `w1 ?  7Calculated Relative Period Jitter at Output J ppm (ppm)R8n,      ,. @] a  `Xo1 ? `  P23  @] _  `p1 ?    P29  @] ]  `܋1 ?  bHCalculated Period Jitter at Output from (No/Po)fm @ 10kHz offset, J (fs)In)               ,, @] B  `ܕ1 ? `  \-106.8 @ 10kHz  @] @  `1 ?   b-104.6dBc/Hz @ 10kHz  @] >  `1 ?   ::Synthesizer Output Phase Noise Density, (No/Po)fm (dBc/Hz);n)             ,, @] ;  `h1 ?0 `  N18  @] 9  `1 ? 0   P0.73  @] 7  `1 ?0  ;Calculated Relative Period Jitter at Reference, J ppm (ppm)L<n0      ,2 @] 4  `D1 ?@`0  O5.5  @] 2  `T1 ? @0  O233  @] 0  `1 ?@ 0  [KCalculated Period Jitter at Reference from (No/Po)fm @ 10kHz offset, J (fs)Ln,               ,/ @] -  `|1 ?P`@ ]-83dBc/Hz @ 10kHz  @] +  `1 ? P@ `-140.8dBc/Hz @ 10kHz  @] )  `81 ?P @ 4<Reference Oscillator Phase Noise Density, (No/Po)fm (dBc/Hz)=n+             ,. @]   `31 ?``P N10  @]   `;1 ? `P R10,000  @]$    `,E1 ?` P &Reference Oscillator Quality Factor, Q4'n%    @]    `N1 ?p`` N16  @]    `\V1 ? p` N64  @]    `pa1 ?p ` !Multiplication/Division Factor, N4"n     @]   `j1 ?`p Q3,200  @]   `r1 ? p Q3.125  @]X   `8u1 ? p *Reference Oscillator Frequency, fref (MHz)B+n        @]   `(1 ?` O200  @]   `1 ?  O200  @]K   `1 ?  Application Frequency, fo (MHz)@ n      @]  Z1 ?` dTop-Down Synthesis n  @]  ZP1 ?  eBottom-Up Synthesis n  @]  Z41 ?  dPerformance Metric n  @]B  To ?`~B  N1 ?`~B  N1 ?`~B  N1 ?p`p~B  N1 ?```B  To ?`B   To ?~B ! N1 ?  ~B " N1 ?B $ To ?``xB * H1 ?P`PxB 1 H1 ?@`@xB 8 H1 ?0 `0 xB ? H1 ? ` ZB ^ s *1 ? ` ZB e s *1 ? ` ZB l s *1 ? ` ZB s s *1 ? ` ZB z s *1 ?`  H 8c?"`` <Overview     H@8c?"` @ Freq. Trans.     B8c?"`  = Synthesis     B8c?"`  ? Application     B8c?"`  c Design & Sim.    B<8c?"`   ;Results   Ht8c?"`   ? Conclusions   H  0޽h ? a(___PPT10i.ͨσ+D=' = @B +, K0 _WP (  x  c $p     S 4 <$ 0    HDF8c?"`` <Overview     H8c?"` @ Freq. Trans.     B@c8c?"`  = Synthesis     B,8c?"`  ? Application     B8c?"`  c Design & Sim.     B8c?"`   ;Results    Bx8c?"`   ? Conclusions   H  0޽h ? a(6$.$___PPT10$.Ϩ`X]+~&Dr#' = @B D-#' = @BA?%,( < +O%,( < +Dc ' =%(%(D' =%(D' =A@BB"BB0B@ A%()))D}' =.7 BBBBB3M 0.0 0.0 L 0.0 -0.07213*3>*B ppt_xB ppt_y=B0B<* %()?)?)?D' }=/u8AC*Q3> Br<* %(D' }=/u8C*Q3> Br<* %(}D' }=/u8C*Q3> Br<* %(D' }=/u8AC*Q3> Br<* %(wD' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*fD' =1:Bvisible*o3>+B#style.visibility<*f%(D' =-o6Bdissolve*<3<*fD-' =%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*fD' =1:Bvisible*o3>+B#style.visibility<*f%(D' =-o6Bdissolve*<3<*fD-' =%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*;D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =-o6Bdissolve*<3<*;D-' =%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<*;D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =-o6Bdissolve*<3<*;D-' =%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<* D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bdissolve*<3<* D-' =%(D' =%(D}' =A@BB BB0B%(E5' =1B B`BPB,54*3>B ppt_c='`B@BPB<* cD' =1:Bvisible*o3>+B#style.visibility<* c%(D' =-o6Bdissolve*<3<* cD' =%(D' =%(D@' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*c%(D' =-o6Bdissolve*<3<*c+p+0+ ++0+  +v 0 6. (  d c $69   " 3 rOnini F:   hTHappy to report on low power integrated circuits activity since our last site visit.H  0i ? a(> 0 @(  d c $69    3 r|nini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. We also have Bruce Wooley From Stanford as an outreach faculty member, and we have hired a new faculty member in EECS to work on software issues in the ERC.2AH  0i ? a(> 0 p(  d  c $69     3 rnini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. We also have Bruce Wooley From Stanford as an outreach faculty member, and we have hired a new faculty member in EECS to work on software issues in the ERC.2AH  0i ? a(> 0 (  d  c $69     3 rnini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. We also have Bruce Wooley From Stanford as an outreach faculty member, and we have hired a new faculty member in EECS to work on software issues in the ERC.2AH  0i ? a(> 0 (  d  c $69     3 r nini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. We also have Bruce Wooley From Stanford as an outreach faculty member, and we have hired a new faculty member in EECS to work on software issues in the ERC.2AH  0i ? a(> 0 (  d  c $69     3 rpnini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. We also have Bruce Wooley From Stanford as an outreach faculty member, and we have hired a new faculty member in EECS to work on software issues in the ERC.2AH  0i ? a(> 0 X(  Xd X c $69    X 3 rnini F:   0As you see, Ken, Khalil and I are the UM faculty presently involved. 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