ECEN689: Special Topics in Optical Interconnects Circuits and Systems Spring 2016

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1 EEN689: Special Topic i Optical Itercoect ircuit ad Sytem Sprig 06 Lecture 6: Limitig mplifier (L) Sam Palermo alog & Mixed-Sigal eter Texa &M Uiverity

2 oucemet & geda Multi-tage limitig amplifier Badwidth exteio techique Offet compeatio

Limitig mplifier Limitig amplifier amplifie

of -.X data rate Wat group delay variatio <0%

3 Limitig mplifier Limitig amplifier amplifie the TI output to a reliable level to achieve a give BER with a certai deciio elemet (comparator) Typically deiged with a badwidth of -.X data rate Wat group delay variatio <0% over badwidth of iteret to limit DDJ TI Output L Output 3

4 How to chieve a mpilfier GBW > f T? ume for a 0Gb/ ytem that we eed to build a amplifer with v 30dB ad f 3dB 0GHz. GBW 3.60GHz 36GHz However, the peak f T of our techology i oly 00GHz, ad geerally we ca with v Max Sigle -Stage GBW 30dB oly achieve a igle - tage amplifier GBW of f 3dB 66.7GHz 3.6 ft 3 00GHz GHz.GHz, well below our 0GHz pec. Itead of uig a igle - tage, let' break the amplifier ito multiple tage with lower gai, but higher badwidth. optimal choice, from a maximum GBW perpective, i 7 tage, with v ad f 3dB 3GHz, or GBW 50.8GHz fter multi - tage badwidth compreio, thi will yield a al GBW 36GHz with our target gai of 3.6 ad with a igle - tage GBW 50.8GHz that our techology ca upport. 4

5 Multi-Stage mplifier GBW If every tage i a igle - pole amplifier v 3dB The al multi - tage amplifier trafer fuctio will be v v out i v 3 db 3 The gai ha icreaed igificatly, but the badwidth doe compre relative to a igle tage. v db 5

6 Multi-Stage mplifier Badwidth ompreio The al amplifier 3- db badwidth, 3dB, i where v v out i j 3dB 3dB v 3 3 db db v 3 3 db db 3dB 3dB The al multi - tage badwidth doe compre, although at a much lower rate tha the icreae i gai. Thu, a igificat icreae i GBW ca be achieved with a multi - tage amplifier approach. 6

7 Optimum Number of Gai Stage umig that there i a maximum per - tage GBW that the techology ca upport GBW v 3dB 3dB GBW v (Note, here GBW i i rad/) If we eed to achieve a high badwidth, we have to reduce the per - tage gai ad icreae the umber of tage. However, the badwidth will compre with cacaded tage. Thu, there mut be a optimum umber of tage for a maximum potetail gai badwidth. Recall that the al badwidth i 3dB 3dB GBW v ad we will achieve a al gai G with tage v G 3dB GBW G 7

8 Optimum Number of Gai Stage For a give al gai, we would like to maximize the badwidth. followig approximatio I order to do thi, let' make the 3dB GBW G GBW G l lo, itead of maximizig thi expreio, let' miimize it reciprocal w.r.t the umber of tage 3dB GBW G l d d 3 db GBW G l 0 Moreover, to make thi eaier, let' miimize the atural log of d d the deomiator, a thi hould yield the ame optimum. d d l 3 db d d l GBW G l d d l lg lgbw l 0 8

9 Optimum Number of Gai Stage d d l 3 db d d l GBW G l Thu, the optimum umber of ad the optimum tage gai i l l lg G l lg opt G v, opt d d l G l G v, opt 0 G l lg lgbw l tage i 0 v, opt e.65 9

10 Optimum Number of Gai Stage For example, a multi - tage amplifier with G opt l G l hould have umig 9 tage reult i v which i cloe to e.65 Relative to the per - tage badwidth, the al amplifier badwidth will compre to 3dB 3dB Note, while thi i the optimum umber of tage from a maximum GBW perpective, the badwidth doe t falloff too dramatically with lower Thu, from a power ad oie perpective, it may make ee to ue a lower umber of L tage Typically high-gai L ue betwee 3-7 tage 3dB 0

11 Badwidth Exteio Techique I order to icreae the badwidth of our multitage amplifier, we eed to icreae the badwidth of the idividual tage Paive badwidth exteio techique Shut Peakig Serie Peakig T-coil Peakig excellet referece

12 Shut Peakig ddig a iductor i erie with the load reitor itroduce a zero i the impedace trafer fuctio Thi zero icreae the impedace with frequecy, compeatig the decreae caued by the capacitor, ad extedig the badwidth

13 Shut Peakig While the iductor ca icreae the badwidth igificatly, frequecy peakig ca occur if the iductor i too big For a flat frequecy repoe, ~70% badwidth icreae ca be achieved maximum 85% badwidth icreae i poible with.5db of peakig Ratio of R time cotat L R 3

14 Bridged-Shut Peakig Max BW L, No B L B No L, B ddig a bridge capacitor i parallel with the iductor allow for compeatio of the frequecy peakig with the poible maximum hut peakig badwidth icreae real iductor will alway have ome paraitic B, ad thu k B will be >0 i practice eve without a extra cap 4

15 Serie Peakig Itroducig a erie peakig iductor i ueful to plit the load capacitace betwee the amplifier drai capacitace ad the ext tage gate capacitace Without L, the traitor ha to charge the al capacitace at the ame time With L, iitially oly i charged, reducig the rietime at the drai ad icreaig badwidth 5

16 Serie Peakig No L =0 the capacitace i more ditributed with a higher k value, a higher BWER i achieved Up to.5x badwidth icreae i achieved with o peakig Higher BWER i poible with ome frequecy peakig 6

17 Bridged-Shut-Serie Peakig ombiig both hut ad erie peakig ca yield eve higher badwidth exteio 7

18 Bridged-Shut-Serie Peakig Proper choice of compoet value ca yield cloe to 4x icreae i badwidth with o peakig However, thi require tight cotrol of thee compoet, which ca be difficult with PVT variatio 8

19 T-oil Peakig If the iput traitor drai capacitace ( ) i relatively mall, the the badwidth exteio through hut-erie peakig i limited T-coil peakig, which utilize the magetic couplig of a traformer, provide better badwidth exteio i thi cae L perform capacitive plittig, uch that the iitial curret charge oly curret begi to flow through L, magetically coupled curret alo flow through L, providig icreaed curret to charge which improve badwidth ad traitio time 9

20 T-oil Peakig 0

21 T-oil Peakig badwidth exteio of 4x i poible without ay frequecy peakig If peakig i acceptable, the a BWER ear 5 ca be achieved, depedig o the ize of

22 ctive Badwidth Exteio Techique While paive techique offer excellet badwidth exteio at ear zero power cot, there are ome diadvatage Geerally large area Proce upport/characterizatio of iductor/traformer ctive circuit techique ca alo be employed to exted amplifier badwidth Some active badwidth exteio techique Negative Miller apacitace TI Load ctive Negative Feedback

23 Negative Miller apacitace I moder techologie, gd i a igificat (50% to ear 00%) fractio of g mplifier effective iput capacitace ca icreae igificatly due to the Miller multiplicatio of gd Without additioal : i g gd gd gd i egative, ad ofte i the differetial gai of the amplifier, thi ca reult i igificat icreae i the effective iput capacitace 3

24 Negative Miller apacitace I order to mitigate thi gd multiplicatio, additioal cro-coupled capacitor ca be added from the amplifier iput to the output Effectively, the charge o thi additioal capacitor charge a (large) portio of the gd capacitor i g gd gd gd If i et equal to gd i g gd Thu, a log a the amplifier gai i, a reductio i the effective iput capacitace i achieved 4

25 TI Load 5 L D p D m gd g i D m v R R g R g F D m gd g i L D F L F F L F F L F F F o o o F F F T T m v R g R BW R BW R Q R BW Q R Z Z g for the ame gai. ca how that Butterworth repoe, with a 3dB

26 herry Hooper mplifier 6

27 ctive Negative Feedback Itead of uig imple firt-order amplifier cell, a ecod-order cell with active egative feedback ca provide badwidth ehacemet Ivertig 7

28 ctive Negative Feedback Thi ecod-order amplifier cell ca be optimized for differet objective, but G mf ca be et to yield a Butterworth repoe with a maximally-flat frequecy repoe 8

29 ctive Negative Feedback The G ratio vo m i proportioal to the techology 3dB G m G umig m T 3dB T G m T T T 3dB T The ecod-order cell gai-badwidth ca potetially achieve a value greater tha the techology f T 9

30 Limitig mplifier Example [Galal JSS 003] Reitive Load Oly ctive Negative Feedback Shut Iductive Peakig Negative Miller apacitace 30

31 Limitig mplifier Example T-coil i L tage allow for a combiatio of erie ad hut peakig ad cloe to 3x badwidth exteio [Proeel ISS 0] 3

32 Offet ompeatio The receiver eitivity i degraded if the limitig amplifier ha a iput-referred offet Thi i ofte quatified i term of a Power Pealty, PP It i importat to miimize the offet of thee multi-tage limitig amplifier! 3

33 Offet ompeatio The D offet, V o, of the limitig amplifier i compeated by a low-frequecy egative feedback loop Ideally, thi reduce the offet to Vo Vo However, if the error amplifier ha a offet, V o, the offet become Vo V o with ucorrelated offet voltage 33

34 Offet ompeatio The low-pa filterig i the feedback loop caue a low-frequecy cutoff f LF R / Note, the / factor aume a 50 driver ource Thu, the feedback loop badwidth hould be made much lower tha the lowet frequecy cotet of the iput data Thi may lead to large-area paive i the offet correctio feedback Some deig leverage Miller capacitive multiplicatio with the error amplifier to reduce thi filter area 34

35 Next Time High-Speed Tramitter 35

Tutorial 5: PLL, solutions

Tutorial 5: PLL, solutions TSE03 Itegrated Radio Frequecy Circuit 08 /6 Problem (9. Coure book) Tutorial 5: PLL, olutio Determie the cloed-loo trafer fuctio, the damig factor ζ, ad the atural frequecy ω for the frequecy-multilyig