Crosstalk Cancellation Method Based on Unitary Transformation of Coupled Transmission Lines-Channel Transmission Matrix

Transcription

1 Progress I Electromagetics Research Letters, Vol 5, 45 50, 05 Crosstalk Cacellatio Method Based o Uitary Trasformatio of Coupled Trasmissio Lies-Chael Trasmissio Matrix Yafei Wag * ad Xuehua Li Abstract Crosstalk is oe of the bottleecks for high-speed circuits to icrease its rate ad desity I order to make tradeoff betwee complexity ad effect of the crosstalk cacellatio circuit, a crosstalk cacellatio method based o uitary trasformatio is proposed I the method, two uitary matrixes are obtaied by Sigular Value Decompositio (SVD) of coupled trasmissio lies-chael trasmissio matrix (CTL-CTM), ad the accordig to the form of the uitary matrixes, the crosstalk cacelig circuits are built at both eds of the trasmissio lie, which could trasform the CTMes ito uit oes ad crosstalk would be cacelled out Circuit simulatio results show that at the sigalig rate of 5 Gbit/s, jitter performace of eye diagram improves 85% ad vertical performace improves 775%, which meas the method achieves better crosstalk cacelig effect with lower circuit cost INTRODUCTION I high-speed circuits, electromagetic wave couplig betwee closely spaced sigal lies limits itercoect performace, which has become a bottleeck to improve the rate of circuits [, ]; thus, miimizig the crosstalk amog itegrated sigal trasmissio lies, such as micro strip lies, has become a importat goal i desig of high-speed circuits Crosstalk, which is the trasfer of a uwated sigal from oe trace or circuit to its adjacet oes, is oe of the major challeges i today s sigal itegrity for high-speed, high-desity circuits I practice, the crosstalk distorts commuicatio sigals ad deteriorates the quality of digital ad aalog sigals It is foud that crosstalk exists everywhere iside a itegrated circuit, such as iside chips, prited circuit boards (PCB), itercoect packages, or ay o-shielded high desity itegrated circuits [3, 4] Cosequetly, ivestigatio for crosstalk miimizatio is a importat task i desig of high-speed, high desity circuits Crosstalk takes place maily due to the mutual couplig, eg, mutual capacitace ad mutual iductace, for ay arbitrary two adjacet trasmissio lies Curretly, crosstalk is suppressed maily from the physical structure of circuit board ad trasmissio lie [5 ], but the effect of these methods is limited I mobile commuicatio systems, MIMO (multi-iput ad multi-output), which employs multiple ateas at the trasmitter to trasmit sigals idepedetly ad receives the sigal with multiple ateas to recover it, is used to describe a abstract mathematical model of multi-atea wireless commuicatio system Based o MIMO cocept, T Oh [, 3] proposed a method with crosstalk cacellatio (XTC) equalizer to cacel crosstalk, which is similar to the space divisio multiplexig that separates idepedet data by elimiatig the iterferece from other ateas However, the circuit desig is relatively complicated From aother poit of view, the chael trasmissio matrix (CTM) of coupled trasmissio lies (CTL) ca be obtaied Sice CTM shows the relatioship betwee output ad iput sigals o the CTL, CTM was trasferred ito uit matrix through sigal processig, ad the output sigals are Received 6 Jauary 05, Accepted 6 March 05, Scheduled 4 March 05 * Correspodig author: Yafei Wag (wagyafei@bistueduc) The authors are with the School of Iformatio ad Commuicatio Egieerig, Beijig Iformatio Sciece ad Techology Uiversity, Beijig, Chia

2 46 Wag ad Li equal to iput oes, which made crosstalk completely elimiated The costructio of CTL-CTM is ivestigated ad usig sigular value decompositio (SVD) method, crosstalk cacellatio is proposed based o the uitary trasformatio of CTL-CTM The mathematics aalysis of CTL-CTM shows the SVD method helps the formatio of uit matrix As a result, the realizatio process of crosstalk cacellatio is to first costruct CTL-CTM, which experieces SVD to obtai the uitary matrixes, ad the accordig to the form of the uitary matrixes, the crosstalk cacelig circuits are built at both eds of the trasmissio lie The circuit simulatio results show that at the sigalig rate of 5 Gbit/s, jitter performace of eye diagram improves sigificatly ad the method is simple ad easy to apply i actual circuit MATHEMATICS ANALYSIS I high-speed, high-desity circuits, the crosstalk is ievitable due to the electromagetic couplig The crosstalk betwee two adjacet trasmissio lies is show i Figure A sigal is ijected ito oe ed of the lie, ad the the voltage oise is measured o the two eds of the adjacet lie The ed earest the sigal source is labeled as the ear ed crosstalk, while the ed far from the sigal source is labeled as the far ed crosstalk, which is i the forward directio to the sigal trasmissio directio The ear ed is i the backward directio to the sigal trasmissio directio From poit of sigal trasmissio, the CTLs i Figure (a), because of the existece of far crosstalk, the relatioship betwee the output sigal ad the iput sigal ca be represeted with vectors ad matrixes as ˆV = HV () where ˆV is the vector of output sigal, ˆV = (ˆv, ˆv,,ˆv ), V the vector of iput sigal, V = (,v,,v ), ad H a matrix The H is defied as CTL-CTM ad expressed as Formula () h h h h H = h h () h h h source sigal ear ed crosstalk far ed crosstalk Figure Near crosstalk ad far crosstalk v v (a) v v v v h h h h h (b) h h h h v v Figure Relatioship betwee iput ad output of CTL sigals (a) Model of CTL (b) Model of sigals with the elemets i matrix H

3 Progress I Electromagetics Research Letters, Vol 5, Accordig to Formula (), the elemets i matrix H idicate the relatioship betwee output ad iput of CTL sigals As to the CTL i Figure (b), the relatioship betwee output sigal o trasmissio lie i ad iput sigal o other trasmissio lie is writte as follow ˆv i = h i h i v h i v (3) where ˆv i ( i ) is the output sigal o trasmissio lie i, v i ( i ) the iput sigal o trasmissio lie i, adh ij ( i, j ) the elemets i matrix H Similarly, if the ports of CTL are amed accordig to Figure, where ports,,, are defied as iput oes ad,,, are output oes, accordig to the defiitio of the S-parameter, the relatioship betwee output sigal of trasmissio lie i ad iput sigal of other trasmissio lie expressed by S-parameters would be give i the port matchig case as below ˆv i = S i S i v S i v (4) where ˆv i ( i ) is the output sigal o trasmissio lie i, v i ( i ) the iput sigal o trasmissio lie i, ads ij ( i, j ) the elemets i matrix S From (3) ad (4), also i the port matchig case, the relatioship betwee the elemets i matrix H ad S-parameters is described as follow: h ji = S ij ( i, j ) (5) Because crosstalk betwee CTLs is mutual, H would be a symmetric matrix if trasmissio lie parameters are all same 3 PROPOSED METHOD Crosstalk cacellatio method based o uitary trasformatio of CTL-CTM i two trasmissio lies case is give here Figure 3 shows two parallel microstrip trasmissio lies with cosistet parameters Here, H is expressed with S-parameter as Formula (6) H = h h = h h S3 S 4 S 3 S 4 I weak couplig case, where secodary crosstalk is igored Accordig to [4], elemets i H are S 3 = S 4 = (7) S 4 = S 3 = jδkl (8) where Δk ω Z 0 (L C Z0 ), l is the legth of trasmissio lie Substitutig (7) ad (8) to (6), we have [ ] jδkl H = (9) jδkl Accordig to the SVD method of matrix, solvig the eigevalues ad eigevector of HH H ad H H H, the SVD form of H would be obtaied as Formula (0) H = UAV H (0) (6) v 3 4 v v H U H V - A v v Figure 3 Two parallel microstrip lies with cosistet parameters Figure 4 Crosstalk cacellatio model based o uitary trasformatio

4 48 Wag ad Li where A is a diagoal matrix; U ad V are uitary matrixes, ad jδkl 0 A = () 0 jδkl V = U = () Accordig to the character of uitary matrix, U = U H ad (V H ) =(V ) = V, ad observig the form of Formula (0), it is foud that if left multiplyig matrix U H ad right multiplyig matrix V by matrix H respectively, the chael trasmissio matrix would become a diagoal oe U H HV = U H UAV H V = A (3) Namely jδkl 0 U H HV = (4) 0 jδkl From Formula (3), if uitary trasformatios such as matrix U H ad V are take at iput ad output part of CTL separately, matrix H ca be chaged ito diagoal oe After makig appropriate sigal processig for each trasmissio lie respectively, H will be varied ito uit matrix That meas output sigals are equal to iput oes ad crosstalk is caceled out Therefore, the method usig uitary trasformatio for crosstalk cacellatio ca be show i Figure 4, which is also suitable for the case of multiple coupled trasmissio lies 4 SIMULATION RESULTS Some simulatios are doe to verify the proposed method Two parallel microstrip trasmissio lies α ad β o PCB are created i the layout iterface of Advaced Desig System (ADS) software The parameters are: w = 40 mil, s = 40 mil, h = mil, t =8mil, ta δ =00, ε r =46, μ r =,l =6i, the metal is copper, ad the characteristic impedace of microstrip lies Z 0 is about 50 Ω The layout of simulatio circuit, the port settigs ad parameters are defied ad show i Figure 5 What s more, the impedace matchig has bee settig Because the elemets i matrix U H ad matrix V are costat, the circuit could be easy costructed accordig to Formula () The total trasfer matrix would be A after circuit structure U H ad V are added, the from the formers of jδkl ad jδkl, which are o-zero elemets i A, we ca kow that addig circuit structure U H ad V is equivalet U H α V - A RC filter 3 v β RC filter 4 v R C Figure 5 Layout of simulatio circuit

5 Progress I Electromagetics Research Letters, Vol 5, (a) (b) Figure 6 Eye diagram for 5 Gbit/s NRZ sigals i W distaces (a) Eye diagram before usig the propsed method (b) Eye diagram after usig the proposed method Table The compariso of performace of eye diagram betwee two crosstalk cacellatio methods at 5 Gbit/s Method I this paper The MIMO-XTC Vertical eye Jitter (ps) diagram [E/H (mv, mv)] [] before 95% UI 0 after 75% UI 775% before 850% UI 73% after 80% UI 655% Jitter improvemets Vertical improvemets 85% 775% 67% 58% to superimpose higher frequecy sigal o each sigal idepedetly So the task of back class A is to filter the sigals superimposed by frot class Cosiderig the realizatio of circuit, two set of RC filter circuits are chose to complete the fuctio The simulatio results are show as eye diagram i Figure 6 Oly diagrams of ˆv are give here because ˆ ad ˆv are very similar The eye diagram of ˆv before ad after addig matrixes U H, V, ad A are illustrated i Figures 6(a) ad (b) respectively The jitter decreases from 85 ps to 5 ps (from 95% UI (uit iterval) to 75% UI) ad the distortio reduces greatly, which is measured with two drive sigals rates of 5 Gbit/s, risig ad fallig time of 0 ps Comparig the eye diagram i referece [3] with Figure 6, it ca be see that the proposed method has a better performace o offsettig jitter ad oise The comparig results with MIMO-XTC method are show i Table, which idicates that jitter improvemets are icreased by 8% ad vertical eye diagram improvemets are icreased by 93% At the same time, the circuit structure of the proposed method is much simpler tha that i referece [3] 5 CONCLUSIONS Crosstalk is oe of the bottleecks i high-speed circuits for rate ad desity icreasig The coceptio of CTL-CTM ad a crosstalk cacellatio method usig uitary trasformatio based o SVD of CTL- CTM are proposed Simulatio results idicate that the method ot oly does well i offsettig shakig ad oise caused by crosstalk but also is easy i circuit desig The crosstalk cacellatio method based o the uitary trasformatio of CTL-CTM could realize greater effect of crosstalk suppressig with lower costs because there is o more limited coditios such as parallel trasmissio lies, spacig of lies with W Stadard, etc, so it could be widely applied However, the proposed method would icrease the cost of circuit, so tradeoff should be made betwee the cost ad effect i reality

6 50 Wag ad Li ACKNOWLEDGMENT This work is supported by the Natioal Natural Sciece Foudatio of Chia (67039), the Geeral Program of Sciece ad Techology Developmet Project of Beijig Muicipal Educatio Commissio (KM05300), the Importatio ad Developmet of High-Caliber Talets Project of Beijig Muicipal Istitutios (CIT&TCD04044) REFERENCES Kudo, Y, T Tobaa, ad T Sasamori, A study of crosstalk ad its suppressio betwee microstrip-lies o a small prited circuit board, IEICE Trasactios o Commuicatios, Vol 9, No, , 009 Hsueh, T, Crosstalk suppressio techique for multi-wire high-speed I/O liks, PhD Defeses, Proquest, A Arbor, 0 3 Hall, S H, G W Hall, ad J A McCall, High-speed Digital System Desig: A Hadbook of Itercoect Theory ad Desig Practices, Joh Wiley & Sos Ic, Hoboke, Bogati, E, Sigal ad Power Itegrity: Simplified, Pretice Hall, New Jersey, Lee, K, H B Lee, H K Jug, et al, Serpetie microstrip lie with zero far-ed crosstalk for parallel high-speed DRAM iterfaces, IEEE Trasactios o Advaced Packagig, Vol 33, No, , 00 6 Mallahzadeh, A R, A H Ghasemi, S Akhlagh, B Rahmati, ad R Bayderkhai, Crosstalk reductio usig step shaped trasmissio lie, Progress I Electromagetics Research C, Vol, 39 48, 00 7 Che, J H ad Z Q Niu, Effect of guard trace o sigal itegrity ad couplig oise of microstrips with differet parameters, Chiese Joural of Radio Sciece, Vol 5, No, 53 58, 00 8 Almalkawi, M ad V Devabhaktui, Far-ed crosstalk reductio i PCB itercoects usig stepped impedace elemets ad ope-circuited, Iteratioal Joural of RF ad Microwave Computer-Aided Egieerig, Vol, No 5, , 0 9 Shiue, G, J Shiu, ad P Chiu, Aalysis ad desig of crosstalk oise reductio for coupled striplies iserted guard trace with a ope-stub o time-domai i high-speed digital circuits, IEEE Trasactios o Compoets, Packagig ad Maufacturig Techology, Vol, No 0, , 0 0 Wu, B P ad T T Mo, Barbed trasmissio lies for crosstalk suppressio, 0 Asia-Pacific Symposium o Electromagetic Compatibility (APEMC), 6 64, Setosa, Sigapore, May 4, 0 Takbiri, M, N Masoumi, M Mehri, et al, Crosstalk reductio usig ope-loop resoators for prited circuit boards traces, 3th Mediterraea Microwave Symposium (MMS), 4, Saida, Algeria, Sep 5, 03 Oh, T ad R Harjai, A 5 Gb/s MIMO crosstalk cacellatio scheme for high-speed I/Os, IEEE 00 Custom Itergrated Circuits Coferece, 4, Sa Jose, USA, Sep 9, 00 3 Oh, T ad R Harjai, A 6-Gb/s MIMO crosstalk cacellatio scheme for high-speed I/Os, IEEE Joural of Solid-State Circuits, Vol 46, No 8, , 0 4 Hill, D A, K H Cavcey, ad R T Johk, Crosstalk betwee microstrip trasmissio lies, IEEE Trasactios o Electromagetic Compatibility, Vol 36, No 4, 34 3, 994