Passive Compensation For High Performance Inter-Chip Communication

Transcription

1 Passive Comenion For High Performance Inter-Chi Communication Chun-Chen Liu, Haikun Zhu and Chung-Kuan Cheng Deartment of Comuter Science and Engineering University of California, San Diego Abstract This aer develos a novel high-seed inter-chi serial signaling scheme with leakage shunt resistors and termination resistors between the signal trace and the ground. For given abstract toology transmission line based on the data for IBM high-end AS/400 system[1] [2], we ut termination resistors at the end of receiver and adjust the shunt and termination resistors value to get the otimal distortion-less transmission line. Analytical formulas are derived to redict the worst case jitter and eye-oening based on bitonic ste Resonse Assumtion[3]. Our schemes and the other two comarison cases are discussed. 1 Introduction Ever-decreasing dimension LSI technology has resulted in higher current density and ower dissiation in global interconnects [4]. At ackaging level, serial link erformance is greatly restricted by signal distortion resulted from various factors such as frequency deendency of the interconnect arameters. In order to make a high seed, low ower, low latency transmission line, some classic methods have been roosed to deal with on-chi serial link signaling, such as clocked discharging [5],, non-linear transmission line [6] [7], and etc. Active comenion such as re-emhasis [8] and equalization [8] has been a oular technique for high erformance communication. However, delay and ower consumtion are two rimary concerns. For assive comenion, M. Hashimoto et al.[9] and M. Flynn et al. [9] fine-tuned the termination resistance at receiver end to maximize the window of the eye diagram for on-chi and off-chi interconnect. Chen et al. [2] adoted distributed shunt resistors to enforce the Heaviside s distortionless condition. This aer is artially suorted by UC MICRO grant. Address comments to [email protected]. Our new schemes is insired by the basic definition in theory of distortional transmission line which states if R/G=L/C, there will be no distortion at the receiver end and the signal roagates at the seed of light. The rimary reason for signal distortion over a serial channel is the frequency deendency of attenuation and hase velocity. We reduce both latency and energy for transmission line by shunt and termination resistor insertion. Comared with other methods, the roosed serial link scheme enjoys several advantages. First, there is no direct feedback ath from the transmission line network to the source. The transmission lines are linear network and thus the design and otimization involve no active comonents. The rest of aer is organized as below: section 2 resents a brief review of transmission line theory and our theoretical analysis to redict eye-oening and jitter values. We resent the overall exeriment results in Section 3 and conclude the aer in Section 4. 2 Eye-Oening rediction 2.1 Transmission-Line Theory Transmission-lines are a secial class of the more general electromagnetic waveguide. The voltage and current on the transmission line aear in the form of wave roagation which is a function of both roagation distance z and time t. Assuming the er-unit-length series resistance, series inductance, shunt conductance and shunt caacitance are R, L, G and C, resectively, the voltage and current on the transmission line are dictated by the telegraher s equations: (z,t) z I(z,t) z = RI(z,t) L I(z,t) t (z,t) = G (z,t) C t The general solution to the above telegraher s equations can be exressed as: (1) (2) /07/$ IEEE 547

2 Table 1 resents all definitions and terms used in this aer. Figure 1. Scheme with shunt and terminator resistor. (z) = + (z)+ (z) = + 0 (z)eγz + 0 (z)eγz (3) where + (z) and (z) are the waves traveling in z+and z- directions, resectively, with roagation constant γ: γ = α + jβ = (R + jωl)(g + jωc) (4) where α and β corresond to attenuation and hase velocity, and are functions of frequency in general. The characteristic imedance is defined as the ratio of voltage to current of at any oint of the line: Z 0 = + (z) I + (z) = R + jωl G + jωc Deending on the RLGC values and frequency, the transmission line can oerate in the RC region, LC region or skin effect region. When an ideal digital ulse train is transmitted over the channel, this frequency deendency of attenuation and hase velocity will result in distortion of the waveform, causing inter-symbol interference(isi). Assuming RLGC themselves are constant. Suose that we follow Heaviside s condition [10]. R G = L C. (6) We can obtain frequency-indeendentattenuation and hase velocity across the whole sectrum. Equation (4) and (6) are reduced to (5) γ = (R + jωl)(g + jωc)= R Z 0 + jω LC (7) L Z 0 = (8) C For inter-chi alication, R, L, G, C are frequency deendent because of the skin effect and roximity effect. However, we demonstrate that by inserting shunt and termination resistors we can imrove the eye-diagram. ariable R L G G max atten 1 H(s) Z 0 I rs, rt r l f f i γ α β Connotation Serial resistance er unit length, in Ω er meter Serial self loo inductance er unit length, in H er meter Shunt conductance er unit length, in S er meter Shunt caacitance er unit length, in F er meter Inut voltage value Maximum voltage of the ste resonse Final uration voltage of the ste resonse oltage after attenuation oltage value in eriod time T Transfer function Characteristic imedance Inut current value Shunt and terminator resistors Transmission line imedance value Frequency Inut frequency Proagation constant Attenuation constant Phase constant Table 1. Index table for definitions and terms. 2.2 Bitonic Ste Resonse Assumtion We use bitonic function to model the ste inut resonse. Due to the wave nature of transmission line, signals undergo multile reflections if erfect termination is not rovided. As a result, the outut ste resonse will fluctuate before it settles down to the uration voltage. However, for lossy transmission lines such as on-chi and MCM interconnect, the reflected wave will diminish to a negligible amount after two round tris. Thus, the outut ste resonse usually aears to be bitonic[3]. Definition 2.1 A ste resonse is defined to be bitonic if it monotonically increases to its eak voltage and then monotonically decreases to its uration voltage. For a generic bitonic ste resonse, we characterize the generic bitonic ste resonse s(t) with five ivotal oints: 1 = (T ) max = (T 0 )=maximum voltage of the ste resonse = final uration voltage of the ste resonse (9) Lemma 2.2 Both worst case eye-diagram and jitter values can be redicted by, 1, and max [3]:. The worst-case eye-oening is then bounded by eye = to min max bottom = 2(max 1 ) (10) The worst-case jitter is bounded by: t =max{t i 2 } max{ti 1 } (11) 548

3 atten(f) = in e α(f)l (15) 1 = atten(f = 1 2T ) 2Z t Z 0 + Z t (16) 2Z t max = atten(f 0) Z 0 + Z t (17) = out in DC ath (18) Figure 2. A generic bitonic ste resonse. where Z t is the termination imedance at the receiver. We discuss the three cases (1) Z t is real and bounded, G =, (2)Z t =, G is bounded, and (3), Z t and G are real and bounded. T-line with resistive termination We set a resistor as the terminator Z t = R t. α 1 2 (R(f) C L ) (19) Put equation (16) to (18) into equation (10) and (13), We can derive the worst-case jitter and eye: Figure 3. A qualitative view of the eye diagram. To determine the jitter, we will first extract the fastest rising edge, which will cross the threshold voltage /2 earliest at t 1. The slowest rising edge will cross the threshold voltage latest at t 2. And the worst-case jitter is bounded by t = t 2 t 1. Since the eye-diagram is symmetric with regard to its falling edge and rising edge, considering only rising edge is sufficient. From Figure 3, the worst-case jitter is bounded by: and can be solved: t = max{t i 2 } max{ti 1 } (12) P =(max eye )/2 (13) Jitter = PT Eye 2.3 Passive Comenion (14) We derive analytical formulation of three rimary comonents, out and max for our schemes and the other two comarison cases. We use the following function for the analysis [10]: R t = atten(f =0) (20) R w + R t where R w is the total line resistance at DC. T-line with shunt resistors: From equation (20), (21) and Z t =, wehave: α 1 ( ) R(f)/Z0 + GZ 0 (21) 2 From Telegraher s equation (1) (3) with DC ath,we derive : 2 = s [ (e RGl + e RGl ) ] (22) T-line with shunt and terminator resistors: Since Z l = R t,wehave α 1 ( ) R(f)/Z0 + GZ 0 (23) 2 From Telegraher s equation (1) to (3) with DC ath, we derive : 2R t = s [ ] R (R t G )e RGl R +(R t + G )e RGl (24) 549

4 R-t (Ω) Jitter (s) eye(v) max Jitter E (s) eye E (v) max P v Jitter (s) Eye (v) Table 2. Jitter and eye-oening with R- terminator only. 3 Exerimental Results We use an MCM striline as shown in Figure 8. The geometry is based on the data of IBM high-end AS/400 system [1]. However, we relace the substrate with liquid crystal olymer to reduce the loss tangent. The frequency deendent R, L, G, C tabular values are extracted by IBM EIP (electrical interconnect and ackage) CZ2D rogram. The roosed scheme have been transiently simulated in HSPICE. The inut is 1000 bit ieces of a 10Gbs seudo random bit sequence(prbs). The rising/falling edges are set to be 10% of the cycle time. We reort exeriment results using a Linux workstation with 3.4GHz P4-CPU and 2GB memory. We comare all our exeriment results with Surfliner [2] and T-line with termination resistor. 3.1 Transmission Line with Resistive Terminator Table 2 deicts the eye diagram of the transmission line with resistive terminator. The first row lists the termination resistance ranging from 70 to 140Ω. The next three section of rows describe the simulation results on the eye diagram, the ste inut resonse, and the eye diagram derived from the ste inut resonse,jitter E, eye E. The last two grous dislay the redicted ste inut resonse and the redicted eye diagram, Jitter, eye. The eye diagram estimated by the ste inut resonse matches the simulated results. The estimated eye height eye E is almost the same as the simulated result. The estimated jitter follows the trend of the simulation results by a factor of For the analytical formula, the urate voltage matches the simulation result. The maximum voltage max deviates from the simulation result by only 7%. The rise voltage 1 P looks different from the simulation result. However, after multilying by a factor 1.3, the revised rising voltage 1v fits the simulation result with an error smaller than 3%. Thus, we use the revised rising voltage 1v to redicted eye height eye and jitter Jitter. 3.2 Transmission Line with Shunt Resistors Table 3.4 lists the result of transmission line with shunt resistors. The to two rows describes the shunt resistance er centimeter. The eye height eye E derived from ste inut resonse deviates from the simulation result by u to 15%. The jitter Jitter E derived from ste inut resonse differs from the simulation result by a factor ranging from 1.9 to 3. For the analytical formula, the urate voltage matches the simulation result. The maximum voltage max deviates from the simulation result by only 1.8%. After multilying by a factor 1.3, the revised rising voltage 1v fits the simulation result with an error smaller than 5%. 3.3 Transmission Line with Terminator and Shunt Resistors Table 4 and 5 list the result of transmission line with terminator and shunt resistors. The to two rows describes the termination resistance and the shunt resistance er centimeter. In table 4, we fix the termination resistance at 100Ω and use shunt resistance from 1200Ω to 1800Ω. Intable5,we fix the shunt resistance at 1400Ω and use termination resistance from 80Ω to 140Ω. The eye height eye E derived from ste inut resonse deviates from the simulation result by u to 3.6%. The jitter Jitter E derived from ste inut resonse differs from the simulation result by a factor ranging from 2.1 to 3.4. For the analytical formula, the urate voltage matches the simulation result. The maximum voltage max deviates from the simulation result by 10%. After multilying by a factor 1.3, the revised rising voltage 1v simulation result with an error smaller than 5%. fits the 3.4 Comarison of Four Cases of Transmission Lines Table 6 reorts the comarison of four cases of transmission lines. We add a naked wire without termination and shunt resistance. We choose the best result of each case in terms of the eye/jitter. The line with terminator and shunt resistors has the best eye/jitter =0.54/4.2 = The naked line requires ower 4.2mW which is minimal in all four cases. However, after we normalize with the eye height, the naked line has P/eye 2 =86.7 which is the worst among all. We resent the naked T-line eye-diagram in figure 5. Notice that the jitter value is 66.5s. Figures 5-8 resent the eye diagrams of the four cases in table I. For the naked 550

5 R-s (Ω) Jitter (s) eye(v) max Jitter E (s) E eye (v) max P v Jitter (s) Eye (v) case naked T-line with T-line Rt-only Rs-only Rs+Rt Jitter (s) E h (v) Power (mw) E h /Jitter (v/s) P/Eh 2 (mw/v 2 ) Table 6. Otimal solution,ower consumtion and energy er bit comarison Table 3. Jitter and eye-oening with R-shunt only. R-t (Ω) R-s (Ω) Jitter (s) eye(v) max Jitter E (s) E eye (v) max P v Jitter (s) Eye (v) Table 4. Eye-oening and jitter by gradually adjust R-shunt and R-terminator. Figure 4. Cross section of the 10 cm MCM striline trace. Figure 5. Eye diagram and jitter in a naked transmission line. R-t (Ω) R-s (Ω) Jitter (s) eye(v) max Jitter E (s) E eye (v) max P v Jitter (s) Eye (v) Table 5. Otimal solution aroach by gradually adjust R-shunt and R-terminator. transmission line (Fig. 5), no terminators are used. The jitter 66.5s is more than half the clock cycle 100s. For the case of the terminator or shunt only, we use termination resistor R t = 70Ω and shunt resistor R s = 1000Ω, resectively. The jitters are 7.4s and 18.1s (Figs. 6,7). The comosite effect of both shunt resistor (R s = 1450Ω) and terminator (R t = 80Ω) reduces the jitter down to 4.2s with clear trace of the eye diagram (Fig. 8). 4 Conclusion In this aer, we have develoed a transmission line scheme faster yet lower ower comare with most existing work. We evenly insert shunt resistor and ut termination resistor in the receiver end. The exerimental results show that our scheme can tolerate higher frequency and is u to 551

6 Potentially, the roosed technique has alications in designing low-skew clock trees, and our future work includes incororating transmitter/receiver design and rototye chi fabrication. Acknowledgments Figure 6. Eye diagram and jitter in transmission line with terminator resistor. Figure 7. Eye diagram and jitter in transmission line with evenly shunt resistors. Figure 8. Eye diagram and jitter in transmission line with shunt and terminator resistors. 1.76x and 4.3x faster comared with the existing naked T- line and T-line with R-terminator, and u to 5.6x than only using shunt resistor insertions. Theoretical analysis are also derived to redict the worst case jitter and eye-oening for our schemes and the other two comarison cases based on bitonic ste resonse assumtion[3]. We would like to acknowledge UC-MICRO fund and IBM Faculty Award. The comments of the anonymous reviewers are areciated. The authors thank Prof. Wenjian Yu for useful discussion. References [1] E.D.Perfecto, A.P.Giri, R.R.Shields, H.P.Longworth, J.R.Pennachia, and M.P.Jeannerte, Thin-film multichi module ackages for high-end ibm servers, in IBM J.RES.DEELOP, [2] H.Chen, R.Shi, C. Cheng, and D. Harries, Surfliner: A distortionless electrical signaling scheme for seed of light on-chi communications, in Proc. Asia South Pacific Design Automation Conf., [3] H.k.Zhu and C.K.Cheng, High-erformance lowower vlsi design, in PHD thesis, [4] K. Banergee, A. H. Ajami, and M. Pedram, Analysis and otimization of thermal issues in higherformance vlsi, in ISPD, Ar. 2001, [5] O.Heaviside, Integrated transversal equalizers in high-seed fiber-otics systems, in XL. The Electrician XIX, 1887, [6] H. Wu, J. Tierno, P. Peeljugoski, J. S. S. G. J. Kash, and A. Hajimiri, Electromagetic induction and its roagation, in IEEE Journal of Solid-State Circuits, 2003, [7] E.Afshari and A. Hajimiri, Non-linear transmission lines for ulse shaing in silicon, in Proc. IEEE Custom Integrated Circuits Conf., [8] W. Dally, M.-J.E.Lillis, S.Lin, and N.Chang, Higherformance electrical signaling, in IEEE Int. Conf. on Massively Parallel Processing Using Otical Interconnections, [9] A. T. M.Hashmoto and H. Onodera, Design guideline for resistive termination of on-chi high seed interconnects, in Proc. IEEE Custom Integrated Circuits Conf., [10] H.W.Johnson, High seed signal roagation:advanced black magic, in Prentice Hall PTR,