Application of negative group delay active circuits to reduce the 50% propagation Delay of RC-line model

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Appliation of negative group delay ative iruits to redue the 50% propagation Delay of RC-line model Blaise Ravelo André Pérenne Mar Le Roy To ite this version: Blaise

th IEEE Workshop on Signal Propagation on Interonnets (SPI 08) May 008 Avignon Frane. pp.-4 008 <0.09/SPI.008.4558347>. <hal-004684> HAL Id: hal-004684 http://hal.

fr/hal-004684 Submitted on 30 Mar 00 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments whether they are published

1 Appliation of negative group delay ative iruits to redue the 50% propagation Delay of RC-line model Blaise Ravelo André Pérenne Mar Le Roy To ite this version: Blaise Ravelo André Pérenne Mar Le Roy. Appliation of negative group delay ative iruits to redue the 50% propagation Delay of RC-line model. th IEEE Workshop on Signal Propagation on Interonnets (SPI 08) May 008 Avignon Frane. pp <0.09/SPI >. <hal > HAL Id: hal Submitted on 30 Mar 00 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments whether they are published or not. The douments may ome from teahing and researh institutions in Frane or abroad or from publi or private researh enters. L arhive ouverte pluridisiplinaire HAL est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe publiés ou non émanant des établissements d enseignement et de reherhe français ou étrangers des laboratoires publis ou privés.

2 Appliation of negative group delay ative iruits to redue the 50% propagation Delay of RC-line model Blaise Ravelo André Pérenne and Mar Le Roy LAB-STICC FRE CNRS 367 Université de Bretagne Oidentale CS F Avenue Le Gorgeu Brest edex 3 Frane blaise.ravelo@univ-brest.fr Abstrat This paper presents a new method developed to redue the propagation delay by using a negative group delay (NGD) ative iruit. Analytial expressions are proposed to demonstrate the validity of our approah in the ase of an RCtransmission line model. The synthesis method of NGD iruits versus the line length is detailed. For a 0.5 Gbit/s digital signal and a -m-long RC-line model time-domain simulations arried out with a high-frequeny iruit simulator showed that the 50% propagation delay was redued by 94%. Finally potential appliations of this method to ompensate for time delays in different interonnet onfigurations (VLSI pakage on-hip long-line ) are disussed. I Introdution In high-speed appliations time delay has beome a major bottlenek in the design proess []-[3]. This general trend applies to bak plane and pakage interonnets on-hip and on-board transmission lines serial or parallel buses and also to VLSI interonnets. For these different domains various advaned models and robust frequeny- and time-domains simulator have been investigated but the ommon basi model is the Elmore RC-line one [4]. Starting from this simple model the effets of interonnets are limited to time delay magnitude distortion and degraded signal transitions. To enhane the signal integrity the priniple of redution of these phenomena was put forward in [5] by using a negative group delay (NGD) iruit. Experimental evidenes of the negative group delay for both mirowave modulated signals and baseband ones were provided in frequeny in [6] and in frequeny and time-domains in [7]. The topology of NGD ell under study is depited in fig. : it simply onsists of a series resistane R and an indutane L in feedbak with a field effet transistor (FET). In a first approximation this latter is modeled by the transondutane g m in asade with the drain-soure resistor R ds as shown in fig.. With this topology and for a transmittane G(jω) from the expression of the group delay (ω) given in () we established in [5] that the group delay an be negative in a low-pass bandwidth (when ω tends to 0) under the ondition set in (3): G( jω) ω ( ) ω () ( + gmrds) L ngd ( R + R )( g R ) () ds m gmr < 0 R >. (3) g R L FET m R L R DS Fig. : NGD ell with its simplified equivalent model. The priniple of redution of interonnet line effets (fig. ) onsists in asading at the output of the line one or several NGD ells. Gate Interonnet Line NGD Fig. : Blok diagram of the ompensation tehnique of interonnet line effets with NGD iruit. It is worth realling that the synthesis equations detailed in [5] are about a single ell. But in pratie in the ase of highspeed digital signals several ells must be used to get an NGD value high enough for the desired frequeny bandwidth. Fig. 3: RC-interonnet line model driven by a gate (output resistane: R s ) and asaded with n NGD ells. Let us onsider the system presented in fig. 3. The design approah requires to at first extrat the transfer funtion and the propagation delay of the interonnet line as a funtion of its length d. Then both of them have to be found in the ase

3 where the line is asaded with a single NGD ell. Let us now extend the study to the ase where n is the optimum number of NGD ells to be asaded at the output of the interonnet model to ompensate for its spurious effets. In Setion IV a synthesis method is proposed to get n versus d. This theoretial approah was ompleted by time-domain simulations. They showed a 94% redution of the 50% propagation time delay of a -m-long RC line for a 0.5 Gbit/s rate. At last and before onluding possible appliation of this tehnique to various interonnet onfigurations are disussed on onsidering its advantages and drawbraks. II Theoretial study of the RC-line model This setion deals with the analytial study of an RCinteronnet line model suh as the one in fig. 3. It onsists of a gate with an output resistane R s whih drives an interonnet RC-line model of length d with unit-length resistane R and apaitane C. Hene the harateristi impedane and the propagation onstant γ are defined in the Laplae domain by: R Cs (4) γ RCs. (5) Let V in (s) and V out (s) be the Laplae transform of the inputand output- voltages of the iruit with no NGD ells. Then the quantity G(s) V out (s)/v in (s) is the transfer funtion and is expressed as: G r ( s). (6) osh( γ d) + sinh( γd) Let us onsider the Elmore approah [4] to express the propagation delay. Therefore for the system under study by using the first-order Malaurin expansion of the denominator of (6) and from (4) the approximated transfer funtion is: Gr ( s). (7) Rd + ( + ) Cds Thus it an be assumed as an RC-iruit with an equivalent resistane R e R s + R d/ and a apaitane C e C d. As mentioned in [5] and [9] at low frequeny ( ω 0 ) the group delay ( ω) G ( jω) / ω is also the Elmore propagation delay. It ensues that the Elmore propagation delay is: Rd r ( + ) Cd. (8) III Synthesis method of the NGD ell ompensating for the RC-line effets Let us now fous on the RC-line model of setion II asaded by a single NGD ell (i.e. n in fig. 3 with R and L in feedbak). Its transfer funtion is expressed as: 4 Rds[ gm( R+ Ls )] Gs () (9) As ( ).( R + R+ Ls) + Bs ( ).( g R + ) ds m ds where: A( s) (3 + 5 )sinh( γ d) + (5 + 3 )osh( γd) (0) B( s) (5 + 3 )sinh( γ d) + (3 + 5 )osh( γd). () To simplify the analytial study as done above the firstorder term of the equation-(9) denominator expansion is kept; at low frequeny it leads to the magnitude and group delay expressions: Rds ( gmr ) G(0) R + Rds + Re ( + gmrds ) () ( R + Rds )[( + gmre ) ngd + r ] 0. R + R + R ( g R + ) (3) ds e m Under ondition (3) i.e. ngd < 0 it is lear that this propagation delay is lower than the RC-interonnet line one r alone (8). A full ompensation of interonnet effets means keeping the output waveform lose to the input one i.e. the transfer funtion lose to unity (G(s) ). Thus the NGD ell transfer funtion needs to be the reverse of the line one. From this priniple the synthesis relations of the NGD iruit are established as a funtion of the line length under the assumptions that G ( 0) and (0) 0 : Rds + ( gmrds + ) Re R gmrds (4) ( gmr )( R+ Rds) r L g R R + g ( R + R ) + (5) m ds e m ds e For a realisti line length d (5) gives a high indutane value L whih means that it is better to use n ells of NGD iruit (as shown in fig. 3). Unfortunately the extration of synthesis equations for n ells is analytially diffiult. So the next setion will be devoted to the development of a pragmati approah aimed at getting the optimal number of ells to be asaded at the end of the RC-line of length d.

4 IV Optimization of the NGD ell number and simulation results To evaluate n let us alulate the expression of the RCinteronnet line losses as a funtion of d from the insertion loss formula: d RCω L ( d ω ) 0.log( e ). (6) db The input trapezoidal signal V in shown in fig. 4 is defined by its period T with a rise/fall time t r 0.05T. Suh a signal an be haraterized by using the signifiant frequeny f s whih depends on the ramp time. In [0] f s was found to be suffiient to represent the signal high-frequeny behavior. In fat 85% of the frequeny omponents of the pulse are within the frequeny range set by f s. Then in [0]- [] the signifiant frequeny was finally expressed as a funtion of the lok rate: Fig. 4: Optimization of the n NGD ells aording to d for R 76 Ω /m and C.6 pf/m (FET: EC-6 g m 98 ms and R ds 7 Ω ). f 0.35/ t 7 / T. (7) s r Consequently in the frequeny band from DC up to f s the average of the interonnet line losses are: ( ) 7.5 RC LmoydB d d. (8) T To ompensate for these losses let us onsider the average in the frequeny band defined by f s of the S -parameter provided by the FET-manufaturer. As argued previously if the length d is very long a single NGD ell may be unable to ahieve the ompensation. This is why we suggested the use of n ells so that: Fig. 5: Shemati of the simulated RC-line (R s 90 Ω) ompensated by a two-stage NGD iruit (R 9 Ω L 40 nh R 0 Ω L 0 nh) L ( ) moydb d n int (9) S moydb where int(x) gives the lowest integer equal or higher than x. Fig. 4 is an example of hart for a given RC-model and a speifi FET. Fig. 5 shows the shemati of a -m-long line ompensated by an NGD iruit with two asaded ells for values as in fig. 4. For simulations the output voltages were omputed in the time-domain with the Advaned Design System (ADS) mirowave iruit simulator from Agilent TM. Final optimization of the NGD feedbak omponent values led to the results presented in fig. 6. Fig. 6: Input (V in ) and output voltages for the RC-line model alone (V r ) and for the overall asaded system (V ngd ). It shows that for a trapezoidal input signal at a rate of 0.5 Gbit/s and 00 ps in rise/fall-time the redution of the 50% propagation delay for V ngd is about 94% ompared to V r.

5 V Disussion on the approah potential and its domain of appliation First one should note that even with a two-stage iruit the indutane values remain signifiant. Moreover the bias networks generally inlude indutanes. The main drawbak is thus the on-hip implementation of suh indutanes during a lassial VLSI proess. So this approah as it is ould be applied diretly to redue propagation delay in on-board transmission line or in buses as well as in inter-hip interonnets. But for the ompensation of on-hip interonnet delay a substitution of indutanes (in RL feedbak and in bias networks) by an ative network as proposed in [] is worth being onsidered beause of the simpliity of our topology. Other investigations are foused on the searh for a new topology with no indutane but still exhibiting gain and NGD. VI Conlusion Here we analytially demonstrated that the use of an NGD ative iruit permits a redution of interonnet time delay and desribed the onditions to be fulfilled. For simpliity reasons the theoretial developments proposed in this study were about the well-known RC Elmore line model. We also developed synthesis equations suited to the ase of an NGD ell asaded at the end of the line model; in the event that a higher number of NGD ells is needed we also detailed an approah developed to determine the optimum number of ells to be used. Moreover this approah redues the indutane to realisti loalized omponent values. In the ase of a -m-long RC-line and a high-speed digital input signal time-domain simulations highlighted the derease of the spurious effets by using a two-stage NGD iruit. The method limitations and its appliation to various interonnet onfigurations were also disussed as well as future prospets. Referenes IEEE Mirowave and Wireless Components Letters Vol. 7 Issue De. 007 pp [7] B. Ravelo A. Perenne and M. Le Roy Synthesis of Broadband Negative Group Delay Ative Ciruits IEEE MTT-S Symp. Dig. -9 June 007 Honolulu (Hawaii) pp [8] B. Ravelo A. Perenne and M. Le Roy Negative Group Delay Ative Topologies Respetively Dediated to Mirowave Frequenies and Baseband Signals Aepted for Publiation in EuMA proeedings. [9] J. Vlah J. A. Barby A. Vannelli T. Talkhan and C. J. Shi. Neves Group Delay as an Estimate of Delay in Logi IEEE Tran. Computed-Aided Design vol. 0 no. 7 Jul. 99 pp [0]C. Chen J. Lillis S. Lin and N. Chang Interonnet Analysis and Synthesis New York: Wiley 000. []Y. Quéré Contribution à l identifiation et à la modélisation sur une large bande de fréquenes des phénomènes életromagnétiques induits par le réseau d interonnexions de iruits numériques avanés (in Frenh) Ph. D. thesis LEST (Laboratoire d Eletronique et des systèmes de Téléommuniations) UBO Brest Frane 006. []M. A. Y. Abdalla K. Phang and G. V.Eleftheriades : A 0.3-µm CMOS Phase Shifter Using Tunable Positive/Negative Refrative Index Transmission Lines IEEE Mirow. Wirel. Compon. Lett. 006 vol. 6 issue pp [] ITRS 006 Edition. [] J. L. Wyatt Signal Delay in RC Mesh Networks IEEE Transations on Ciruits and Systems CAS-3(5) pp May 985. [3] J. Rubinstein P. Penfield and M. A. Horowitz Signal Delay in RC Tree Networks IEEE Transations on Computer-Aided Design CAD-(3) July 983 pp. 0. [4] W. C. Elmore The Transient Response of Damped Linear Networks J. Appl. Phys. Vol. 9 Jan. 948 pp [5] B. Ravelo A. Pérenne M. Le Roy Equalization of Interonnet Propagation Delay with Negative Group Delay Ative Ciruits th IEEE Workshop on Signal Propagation On Interonnets Genova Italy May 007 pp [6] B. Ravelo A. Perenne M. Le Roy and Y. Bouher Ative Mirowave Ciruit with Negative Group Delay

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