Transmission Parameters of Cascaded Systems

Transcription

1 ! Trasmissio Parameters of Cascaded Systems ^! Mohammed M Al-Asadi,! Alistair P. Duffy, Keeth G Hodge, * Arthur J Willis & * David A Jackso EMTERC Ceter, Faculty of Computig Scieces ad Egieerig, De Motfort Uiversity, The Gateway, Leicester LE 9BH, UK ^ * Brad-Rex Ltd, Glerothes, Fife KY6 RS, Scotlad, UK Priciple Author alasadi@dmu.ac.uk Abstract A equatio for the predictio of the Retur Loss of cascaded systems has bee previously preseted ad validated. This paper further validates this equatio agaist experimetal data obtaied for commuicatio chaels cotaiig log copper cables ad coectors. The paper also presets a aalytical approach to the calculatio of the propagatio costat ad hece the calculatio of both atteuatio ad phase costats for a cascaded system based o kowledge of the impedace ad the propagatio costats of each elemet. Both the impedace ad the propagatio costats used i the proposed aalysis of every idividual compoet may be obtaied aalytically or experimetally ad are frequecy depedet parameters. The atteuatio ad phase predictio ca accout for toleraces i impedace ad i legth of cables ad coectors. The validity of the derived equatios is cofirmed by comparisos preseted with measuremets ad simulatios performed usig the Trasmissio- Lie Matrix (TLM) method. Implicatios for Isertio Loss Deviatio (ILD) are also cosidered. trasmissio chael. This paper addresses the performace of a complete chael. A typical cofiguratio of a copper cable trasmissio chael betwee the source of the trasmitted sigal ad the receivig ed is illustrated i figure. Sigal i Coectio paels Short liks Cross coectios (e.g. coectors) Mai cable Keywords Cable; Coectors; Chaels; Cascaded systems; Retur Loss; Atteuatio; Phase costat; Impedace; Modelig.. Itroductio The icrease i processor speeds has cotiued costatly over the last couple of decades. As a result of this icrease ad higher data volume applicatios, the pressure to commuicate faster has ot dimiished. While optical fiber provides high badwidth chaels, it is geerally oly suited to back-boe operatio. Coaxial cable, a relatively high badwidth choice for the last mile, is relatively expesive ad has greater coectivity problems whe compared to twisted-pair. Hece, a costatly improvig uderstadig of the operatio of structured wire cablig at higher frequecies is fudametal to the ability of commuicatios systems to meet the challeges faced by pressure from the computig ad commuicatios cotet producig sectors. Although calculatios ad modelig of the parameters, e.g. the retur loss, for idividual trasmissio chaels, such as cables uder differet termiatio coditios, have bee a icreasigly ivestigated i the last few years [,,3], relatively little work has bee published o the parameters of a overall cascaded Figure. Typical Chael Cofiguratio icludig short liks ad coectors This chael represets a classic cascaded commuicatio system, where each compoet of the system has its ow trasmissio ad reflectio parameters. The characteristic impedace of ay idividual compoet of such a system may ot always perfectly match the characteristic impedace of the eighborig compoets [4]. This mismatch may result i a sigificat icrease i the retur loss value [3]. The impedace mis-matchig betwee system compoet will also affect the propagatio costat measuremets[5]. Therefore, the desig ad developmet of future facig cablig systems requires a thorough, ad detailed, uderstadig of the secodary trasmissio characteristics of idividual cablig compoets ad their iteractio whe cofigured i a system.

2 This paper presets the developmet of a geeral equatio for the calculatio of the propagatio costat ad, hece, both atteuatio ad phase costats of a cascaded system, based o a kowledge of the impedace, the propagatio costat ad the legth of idividual parameters of the system. The equatio is validated agaist data obtaied by measuremets ad modelig. I additio to this validatio, this paper further validates the retur loss equatio previously preseted agaist experimetal data.. Equatio Developmet. Atteuatio ad phase costats calculatio A trasmissio chael cotaiig, for example, four coectors ad three cables (two patch liks ad oe horizotal lik) ca be represeted by a two port etworks illustrated i figure. Z r i o j + Zo j j = j Zo j + + Zo j Similarly, icidet, reflected ad trasmitted voltages from, ad at, all the chael compoets ca be obtaied. Followig a similar approach to the approach reported i [3], the relatioship betwee the overall voltage icidet ito the far ed of the chael ad the voltage trasmitted from the source ito the st segmet of the chael ca be obtaied as: m= i k = Z + γ = = ok m e T k = Zok + + Z ok m l m (3) (4) Source ed i T r Zo, γ, l Patch lik where is the umber of compoets cascaded i the chael. To aid visualizatio ad aalysis, the chael illustrated i figure ca be replaced by oe segmet of cable havig a legth that is equivalet to the overall legth of the chael as illustrated i figure 3. This ca be achieved uder the coditio that the characteristic impedace of this cable is adjusted so that the relatio betwee the icidet voltage reachig the ed of the cable ad the trasmitted voltage from the source is equivalet to that give i equatio 4. Horizotal lik i T i T i T Load ed r Zo eq, γ eq, l eq r Patch lik Takig ito accout the complex propagatio costat, the icidet voltage at ay part of the system is give as: T j l j i j = γ j + e () where j idicates the j th compoet from the source ed, γ is the propagatio costat of the jth compoet ad l is the physical legth of that compoet. The superscript T implies a trasmitted sigal. Similarly, trasmitted ad reflected voltages at the coectio betwee a chael compoet ad the followig oe are give respectively as: T j r Zo, γ, l Figure. Two-port etwork represetatio of a represetative chael, illustratig the properties of each compoet Z i o j + = j Zo j + + Zo j () Figure 3. Equivalet circuit to the chael illustrated i figure For the above circuit, the relatio betwee the received voltage at the far ed ad the icidet voltage at the ear ed of the circuit is give as: i T γ = e eq l eq where γ eq is the desired equivalet propagatio costat of the whole chael illustrated i figure ad l eq is the equivalet physical legth of the equivalet circuit illustrated i figure 3 ad give as: k = = k = l eq l k Comparig equatios 4 ad 5 leads to: (5) (6)

3 m= = m lm eql k Z γ γ eq e = + = ok m e (7) k = Zok + + Zok Takig the atural logarithm for both sides of the above equatio gives: γ eqleq m= k = Z γ m l = l ok + e m= k = Zok + + Zok Equatio (8) ca be simplified to the followig form: γ eqleq m k = Z m= = l ok + γ m lm k = Zok + + Zok m= Hece the overall propagatio costat of a chael cotaiig compoets ad havig overall legth give i equatio 6, ca be give as: k = Z m= l ok + + γ m lm γ k = Zok + + Z eq ok m= = li (8) (9) () All the elemets of the above equatio are kow, hece the overall propagatio costat ca be obtaied. Sice impedace values of the above equatio ad propagatio costats of all idividual elemets are complex quatities ad are frequecy depedet, the obtaied overall propagatio costat is a complex quatity ad is frequecy depedet. Give that the propagatio costat of ay trasmissio lie is [6]: γ = α + jβ () where α is the atteuatio of that circuit ad β is the phase costat, the atteuatio costat of the whole chael, per uit legth, the isertio loss ca be obtaied, i db, from equatio as: k= Z m ok = l + + m lm k Zok Z γ αeq ok m Re = + + = = l i () ad the overall phase costat of the same chael ca be obtaied from: β eq k = Z m= l ok + + γ m lm k = Zok + + Zok m= = Im li (3). Isertio Loss Deviatio (ILD) calculatio The total atteuatio (isertio loss) of a chael is ormally calculated by addig up the atteuatio of all the compoets: this is referred to as the chael isertio loss or the chael atteuatio [7]. This is oly a approximatio, but oe which is easy to calculate ad relatively accurate if the impedaces of the idividual chaels are close to beig matched. I fact, the chael measured isertio loss (overall atteuatio) is higher tha the result obtaied usig this approximate method. This differece is due to sigal reflectio, ad re-reflectio, betwee chael compoets produced as a result of impedace mis-match. Isertio Loss Deviatio (ILD) is the differece betwee the actual isertio loss as measured o a chael ad that obtaied as a result of addig up the compoets atteuatio. Hece it ca be give as: k = ILD = α eq α k (4) k = It should be metioed here that ILD is a relatively ew term [7] but it is a icreasigly importat parameter that should be take ito accout whe assessig chael performace. Numerical modelig also provides a tool to obtai the overall atteuatio costat as well as other operatioal parameters. This is discussed i the followig sectio. 3. TLM Model Trasmissio-Lie Matrix (TLM) modelig techique is used for the simulatio of twisted pair cables ad the mis-matchig effects o short lik performace [8]. It is a widely used tool for the modelig of microwave devices, circuits ad electromagetic fields simulatios. Here, the method reported i [4,8] is agai used for the calculatio of the atteuatio costat of the trasmissio chael described earlier i this paper. Kowig the icidet ad reflected voltages at both ear ad far eds of the trasmissio chael modeled usig the TLM method, the overall atteuatio costat of the chael ca be obtaied. Due to the fact that TLM is a time domai method, Fourier Trasformatio is used for the calculatio of the frequecy domai data. The overall atteuatio costat is the computed usig the followig equatio: r α = log F (5) i N 3

4 r F is voltage icidet ito the load at the far ed. i N is the icidet voltage from the source at the ear ed of the TLM model. The value obtaied usig equatio 5 ca the be used for the validatio of the overall atteuatio value of the trasmissio chael obtaied usig the developed equatio. 4. alidatio This sectio deals with the validatio of the equatios published i referece [4] ad those developed ad reported i this paper. 4. Retur Loss Equatio Agaist Measuremets The retur loss equatio reported i [4] states that: Z k= k = Zs Z + i Z RL log i Z + Zs k= Zi + Zi Zi + Zi j= k γ j lj j= Z k+ Z e k Zk+ + Zk It was iitially compared with data from a commo equatio obtaied from [6], ad agaist data obtaied usig the TLM approach. This equatio has the bee used for the calculatio of a trasmissio chael cotaiig two patch liks of.7ω impedace ad a horizotal FTP cable (Gigaplus cable) of 99.Ω impedace. The legth of each patch was m while the legth of the horizotal cable was 35m. The effects of the coectors have bee igored i these calculatios. Results obtaied from both measuremets ad calculatios are show i figure 4. For a similar trasmissio chael havig the same legth as both patches ad the horizotal FTP cable, but with a impedace of the patch cable of 5.Ω while the impedace of the horizotal cable was 98.7Ω, the overall retur loss was measured ad calculated usig equatio 6 of referece [4]. Determiatio of the retur loss, geerated as a result of differet termiatios, of a log chael by measuremets may iclude the structural retur loss geerated as a result of coarseess of the cable geometry due to radom maufacturig factors, hadlig, etc. [9]. While this adds extra features (fie-grai detail) to the results, the aalytical solutio predicts the performace evelope with excellet precisio. This is clear from both figures 4 ad 5. Retur Loss (db) Retur Loss (db) Retur Loss Of Gigaplus FTP Cable Tested Through Gigaplus Patch, Date Code5, O Gree Pair (Model calculatios based o.7ohm patch ad 99.ohm horizotal) Cat5e Basic Lik Measured Modelled Frequecy (MHz) Figure 4. Retur loss validatio agaist measuremet for a log 7-segmet chael. Retur Loss Of Gigaplus FTP Cable Tested Through Gigaplus Patch, Date Code999, O Gree Pair (Model calculatios based o 5.ohm patch ad 98.7ohm horizotal) Cat5e Basic Lik Measured Modelled Frequecy (MHz) Figure 5. Reproductio of figure 4 usig cables with differet impedace values 4. Atteuatio Equatio Agaist TLM Detailed derivatio of the TLM model of a regular ad irregular cable is give i both refereces [8] ad [9]. The model developed i these refereces was the used for the predictio of hadlig effects, pig-tailig ad short lik performace uder differet workig coditios. It was also used i referece [4] for the predictio of the overall retur loss of a cascaded trasmissio chael. 4

5 TLM model was used for the calculatio of the overall atteuatio costat of the chael usig equatio 5 for a 3-segmet trasmissio chael cotaiig a Category 5 cable of meter legth coected at both eds via two coectors of cm legth. The omial impedace of both coectors ad the cable was 96Ω. Termiatig with a matched impedace, the overall atteuatio costat was the calculated usig equatio () ad plotted alog with that obtaied usig the TLM model for a rage of frequecies as illustrated i figure 6. Atteutio (db) Atteutio (db)..5 Figure 7. Atteuatio costat for a 7 segmet chael, usig a m cable ad m liks, obtaied usig the ew method (Solid lie) ad the TLM (Dashed lie) Figure 6. Atteuatio costat for a 3- segmet chael (m cable) obtaied usig the ew equatio (Solid lie) ad usig the TLM method (Dotted lie) To calculate the isertio loss deviatio, the overall atteuatio of the trasmissio chael eeds to be calculated usig the traditioal method. Figure 8, shows the overall atteuatio costat of the m chael calculated usig both the traditioal approach ad the ew method..5 Similarly, the overall atteuatio costat of a 7-segmet cascaded chael was obtaied usig both approaches ad plotted i figure 7. The legth of each patch lik is m ad the legth of the horizotal cable is m. The impedace of the patch liks ad the horizotal cables are similar to those used for the productio of figure 6. Both figures 6 ad 7 show a very good agreemet betwee both sets of results, hece they cofirm the validity of the derived equatio. Atteutio (db) Figure 8. Atteuatio costat for a 7 segmets chael, usig a m cable ad m liks, obtaied usig the ew method (Solid lie) ad the addig up method (Dashed lie) 5

6 Figure 9 illustrates the Isertio loss deviatio calculated from the differece betwee both values of figure 8 ad usig equatio ILD (db) Figure 9. Isertio loss deviatio, ILD, for the 7-segmet m chael 5. Implemetatio ad Results After validatig the performace of equatio (), it was the used for the calculatio of the overall atteuatio costat of a practical commuicatio chael cotaiig 7-segmets as described earlier ad for differet termiatio coditios. The isertio loss deviatio ILD was also computed. 5. Matched coditios The atteuatio was obtaied uder matchig coditios, where the impedace of both patch liks illustrated i the 7-segmet chael show i figure, match the impedace of the horizotal cable. Coectors were assumed to have the same impedace. Results for a m patch ad a m cable were reported earlier as plotted as i figures 7 ad 8. For a similar chael havig a m liks ad a m cable, the overall atteuatio costat is computed usig both the ew equatio ad the summatio approach. Results are plotted i figure. Atteutio (db) Figure. Overall atteuatio for a m chael usig the ew equatio (solid lie ad the summatio method (dotted lie). 5. Mismatchig coditios For a chael of two patch liks ad oe horizotal cable where the impedace of both patch liks mismatches the impedace of the cable, the overall atteuatio of the chael ad the ILD were also computed usig both the ew equatio ad the summatio approach. For differet legths of cables ad differet impedace values, the followig tests are carried out, it should be oted that the impedaces used are illustrative ad ot represetative of actual chaels: m-m-m chael, where the impedace of the st lik, the cable ad the d lik are 83,5Ω-96Ω ad 74.5Ω respectively, the overall atteuatio was calculated usig both methods ad plotted as i figure. The ILD was also computed ad plotted as i figure Atteutio (db) Figure. Atteuatio for a 4 m chael, ew equatio (solid lie) ad summatio approach (dotted lie) 6

7 ILD (db).6 ILD (db) Figure. Isertio Loss Deviatio of the results preseted i figure Figure 4. Isertio Loss Deviatio, ILD, for results preseted i figure 3. For the above chael, where the impedaces are.5ω-96ω ad 74.5Ω respectively, the overall atteuatio was also calculated usig both methods ad plotted as i figure 3. The ILD was also computed ad plotted as i figure 4 m-m-m chael, where the impedace of the st lik, the cable ad the d lik are 83,5Ω-96Ω ad 74.5Ω respectively, the overall atteuatio was calculated usig both methods ad plotted as i figure 5. The ILD was also computed ad plotted as i figure Atteutio (db) 6 4 Atteutio (db) Figure 3. Reproductio of figure for differet matchig coditios, ew equatio (solid lie) ad summatio approach (dotted lie) Figure 5. Overall atteuatio for a mis-matched 4m chael, ew equatio (solid lie) ad summatio approach (dotted lie) 7

8 ILD (db) Figure 6. Isertio Loss Deviatio of the results preseted i figure 5 For the same log chael, where the impedaces are agai chaged to.5ω-96ω ad 74.5Ω respectively, the overall atteuatio was also calculated usig both methods ad plotted as i figure 7. The ILD was also computed ad plotted as i figure 8 ILD (db) Figure 8. Isertio Loss Deviatio of the results preseted i figure 7 All the above tests illustrate the eed to uderstad the effects of mismatchig i both short ad log chael o the chael s overall atteuatio costat. Atteutio (db) Discussio ad Coclusio A equatio has bee developed for the calculatio of the propagatio costat of a cascaded system cotaiig may segmets, each havig differet impedace values ad differet propagatio costats. This equatio has led to the developmet of a equatio for the calculatio of the overall atteuatio costat of the system. It has also led to the developmet of a equatio for the calculatio of the overall phase costat of the cascaded system as fuctio of the impedace ad the propagatio costat of each elemet. The ew equatio has bee validated agaist the TLM modelig method Figure 7. Reproductio of figure for differet matchig coditios, ew equatio (solid lie) ad summatio approach (dotted lie) Traditioally, the overall atteuatio costat of a commuicatio chael cotaiig may segmets of differet legths, differet impedace ad differet propagatio costats, was obtaied by summig the atteuatio costats of all the elemets. While this is a simple calculatio, it is oly approximate. With icreasig errors as shorter chaels are cosidered, or where cascaded chaels cosistig of similar compoets is beig cosidered. This is clear from results illustrated i sectio 5. The discussio o Isertio Loss Deviatio (ILD) supports the eed to treat the system atteuatio calculatio with care. Further work is uderway to validate ad apply the phase costat calculatio. 8

9 7. Refereces [] T. Y. Otoshi, Maximum ad miimum retur losses from a passive two-port etwork termiated with a mismatched load May 994, 8 IEEE Tras o MTT, ol.4, No. 5, pp [] A. Umek, Modelig the structural retur loss i twisted pair cables, th IEEE Mediterraea Electrotechical coferece, MeleCo, ol., pp [3] I. T. Sylla, M. Slamai, B. Kamiska, F. M. Hossei ad P. icet, 998, Impedace Mismatch ad Lumped Capacitace effects i High Frequecy Testig 6th IEEE LSI Test Symposium Proceedigs, pp [4] M. M. Al-asadi, A. P. Duffy, K. G. Hodge ad A. J. Willis,, Retur loss predictio for cascaded systems, Proceedigs of the 49 th IWCS symposium, pp [5] D. C. Degroot, D. K. Walker, ad R. B. Marks, 996, Impedace Mismatch effects o propagatio costat measuremets IEEE 5 th Topical meetig, Electrical performace of electroic packagig, pp [6] S. Ramo, J. R. Whiery ad T. a Douzer, Fields ad waves i commuicatio electroics, d ed., 984 [7] P. Kish, April The effect of etwork cablig o Bit Error Rate performace, NORDX/CDT, white paper, pages. [8] M. M. Al-asadi, A. P. Duffy, K. G. Hodge ad A. J. Willis, 999, Aalysig lik performace i high frequecy trasmissio systems, Proceedigs of the 3 th Zurich EMC coferece, pp. 7-. [9] M. M. Al-asadi, A. P. Duffy, K. G. Hodge ad A. J. Willis, 997, Modelig as a tool for aalysig hadlig effects i structured wire cablig, IEE th It. Cof. O EMC, Warwick, UK,, pp Authors Biographies Mohammed M Al-Asadi, Alistair P Duffy, Keeth G Hodge ad Artuhr J Willis: for photos ad biographies, please see paper 4_ i these proceedigs. David A. Jackso holds a BSc(Hos) i Electrical ad Electroic Egieerig from Abertay Uiversity, Dudee, Scotlad. His career has bee domiated by the desig of test systems, iitially as a Research ad Developmet egieer workig o test facilities for microprocessor systems. He has spet over 6 years i the cable idustry desigig ad implemetig radio frequecy test methods. 9