ANALYSIS OF A MULTIPLEX-BUS SYSTEM*

Transcription

1 ANALYSS OF A MULTPLEX-BUS SYSTEM* Syed Masud Mahmud, Devang G. Sheth and Harpreet Singh Eletrial and Computer Engineering Department Wayne State University, Detroit, M 4822, USA. Phone: (313) mahmud%wayne-mts@um..umih.edu Abstrat : A bus is a olletion of one or more wires. A bus is alled a multiplex-bus when it is shared by a number of devies. There are many appliations of a multiplex-bus. For example, a miroproessor-based measurement system may use a bus (say EEE-488, VME, et.) to interonnet a number of miroproessor-based instruments, e.g., voltmeter, ammeter, data aquisition devies, et. All the automobile ompanies are planning to use multiplex-buses (multiplex wiring) in their future vehiles. Advaned eletroni features like antilok braking, eletroni steering, and eletronially ontrolled transmissions and suspensions an improve performane. But the wiring, omponents, and eletroni ontrol units required for these systems must fight for spae in today's small ars, where they may invite diagnosti and repair problems. Multiplexing an redue wiring omplexity and eliminate redundant parts, while simplifying diagnostis. The effetiveness of a multiplex- bus has been reported in a number of papers (1-51. As more and more devies are onneted to a bus, the speed of the bus redues due to apaitive loading effet of the devies. Hene, when too many devies are to be onneted to a bus, it is neessary to know the maximum rate (e.g., bitske) at whih data transfer an our. Pulse width modulation (PWM) tehnique is widely used to transmit digital data in many industrial and onsumer eletronis appliations. We have developed an analytial model for a multiplex-bus system, whih will allow us to determine the shape of the pulses of PWM signals at different nodes of the bus. We have also developed a novel algorithm to onvert our analytial model into a software pakage. Currently we have developed software pakages for both BM and Maintosh personal omputers. The software aepts the following parameters as inputs: eletrial parameters (e.g., apaitane, resistane, et.) of the bus and the devies, bit pattern of the PWM signals, and the harateristis of the bits (e.g., pulse period, pulse widths for logi and 1, et.). The software displays the pulses at different nodes of the bus. By looking at the display one an easily determine whether or not the speed of transmission is too high to detet the bits orretly by the reeiving nodes. Our algorithm is very novel and fast. n this paper we will show our analytial model and the novel algorithm in detail. Our model and algorithm will help other people to develop software pakages for the analysis of multiplex-bus systems. This software pakage will help to determine the maximum number of devies whih ould be onneted to a given bus if a ertain minimum transmission speed has to be maintained.. NTRODUCTON Multiplexing has found wide appliation in many fields in reent years through the power of modern eletronis and miroproessors [l-61. Multiplexing tehnology has developed primarily as the result of the needs of the ommuniations industry. Nearly all multiplexing developments are the result of two major benefits: ost redution and spae saving. A bus is alled a multiplex-bus (multiplex wiring) when it is shared by a number of devies. A miroproessor-based measurement system may use a multiplex-bus to interonnet a number of miroproessor-based instruments, e.g., voltmeter, ammeter, data aquisition devies, et. Multiplex-buses are going to be used in the future automobiles. Advaned eletroni features like antilok braking, eletroni steering, and eletronially ontrolled transmissions and suspensions an improve performane. But the wiring, omponents, and eletroni ontrol units required for these systems must fight for spae in today's small ars, where they may invite diagnosti and repair problems. Multiplexing an redue wiring omplexity and eliminate redundant parts, while simplifying diagnostis. The effetiveness of multiplexing in automobiles are reported in a humber of papers [2,3,5,8]. The use of a multiplex-bus makes a system very flexible. mplementing hanges in ar models and the onsequent funtion and load hanges beome very easy: simply onnet one or more additional proessors (nodes) on the same bus with proper software modifiation. The problem with a multiplex-bus is that the bus speed dereases as the system expands. Beause as the system is expanded by adding more devies (proessors) the apaitive loading effet on the bus inreases. This inreased apaitive loading effet redues the speed of the bus. Hene, when too many devies are to be onneted to a bus, it is neessary to know the maximum rate (e.g., bitske) at whih data transfer an our. Pulse width modulation (PWM) tehnique is widely used to transmit digital data in many industrial and onsumer eletronis appliations. Time or frequeny-domain analysis an be used to evaluate the performane of a multiplex-bus system. Time-domain analysis is very omplex when non-homogeneous devies (i.e., devies with different eletrial harateristis) are onneted to a bus. But time-domain analysis an be more attrative than frequeny-domain analysis when a bus is shared by homogeneous devies. Estin desribed the data handling apaity of a real transmission line (non-multiplex bus) [7]. n this paper we have developed a novel tehnique to determine the performane of a multiplex-bus system whih is shared by similar proessors or proessors with similar eletrial harateristis. We have also developed a novel algorithm to translate our tehnique into a software pakage. Currently we have developed software pakages for both BM and Maintosh 1 personal omputers. The software aepts the following parameters as inputs: eletrial parameters (e.g., apaitane, resistane, et.) of the bus and the devies, bit pattern of the PWM signals, and the harateristis of the bits (e.g., pulse period, pulse widths for logi and 1, et.). The software displays the response of the pulses. By looking at the display one an easily determine whether or not the speed of transmission is too high to detet the bits orretly by the reeiving nodes. Our algorithm is very novel and simple. Our time-domain analysis is verified by frequeny-domain analysis. This researh was supported by a grant from Ford Motor Company (Grant# ). CH294-5/91/-336 $1 C 1991 EEE 336 Authorized liensed use limited to: Wayne State University. Downloaded on Deember 11, 28 at 1:32 from EEE Xplore. Restritions apply.

2 11. MODELNG AND ANALYSS OF A MULTPLEX-BUS An approximate eletrial model of a bus and the devies an be shown by an eletrial iruit with lumped parameters. f the devies are onneted very lose to eah other (say less than a meter), a lumped parameter model of the bus would be as good as a distributed parameter model 191. n order to make the analysis simple we assumed that the devies are uniformly distributed over the bus. A lumped parameter model of a multiplex-bus is shown in Figure 1. Node- 1 Node- 2 Node - n The roots of the polynomial f,(y), shown in Table 1, an be used for any multiplex-bus system whih has a maximum of 16 nodes. For a system with more than 16 nodes, we need the root of f,(y) for n > 16. Sine the same roots an be used for any multiplex-bus system, these roots an be kept in a file to be used by a program to determine the performane of different multiplex-bus systems. Let Yi, 1 2 i 5 n, be a root of the polynomial f,(y). we an write Then L x1 + 2fX1 + gl = (4) 2 RG R C where X = RCD, 1 2 2L' gi = (RG-Y1).RLC L f = and The roots of equation (4) an be written as: Figurel: A lumpled parameter model of a multiplex-bus system..5 x. (2) = -f - (f2 - gi) (5b) Let us define a parameter Y as: Y = (LD + R). (CD + G) d where D means - dt t an be shown that the relationship between the soure voltage, V, and the voltage at node n an be expressed as [lo]: vo = f,(y).vn (2) where f,(y) an be expressed as: where is alled an n-degree multiplex polynomial, and it a (b) a! = (a-b)!.b! (3) Notie that equation (2) is a differential equation, and we must solve this equation in order to write a time-domain expression for Vn. One a time-domain expression is known for Vn, we an easily determine the maximum rate at whih a soure an supply the bits (pulse width modulated signals) suh that ertain predetermined speifiations are satisfied. Two simple speifiations may be as follows: 1) 2) Threshold voltage to detet the presene of a pulse Minimum and maximum widths of a pulse for onsidering the pulse as a logi 1 or logi. Equation (2) an be solved using either frequeny-domain or time-domain tehniques. Sometimes the time-domain analysis ould be very omplex, if not impossible, depending on the omplexity of the equation. This paper presents the performane of multiplex bus systems. The performane "as measured by solving equation (2) using a time-domain tehnique. A novel time-domain analysis of equation (2) exists due to following nie properties of the polynomial f,(y). The roots of the polynomial f,(y) negative numbers, for all n >. are real and When X,(1) and X,(2) are omplex qunatities we an define two terms: Ui and 8i as: The time domain expression for V, the following two algorithms. an then be determined using Alaorithm-1 : Make two matries A and Z as follows: ( n this algorithm the notation A[iJ] is used to mean the element at ith row and jth olumn of matrix A, and the notation Z[i] is used to mean the ith element of matrix Z.) N=O, i=o. i=i+l; F X,(1) and X,(2) ) are omplex numbers THEN N = N + 1. F i = n THEN go to Step #3, OTHERWSE Repeat Step #2. Col =. Col = Col + 1, A[1, Col] = 1, Z[1] = V,(O-)-Vn(m) F Col = 2n - N THEN go to Step #5, OTHERWSE Repeat Step #4. Row = 1, m=o, L=N Row = Row + 1, m = m + 1. F L > THEN L = L- 1 and m = m + 1. Col =, i=o. Col = Col + 1. i = i + 1. F X,(1) and X,(2) are omplex numbers THEN A[Row, Col] = U,mCos(mO,). OTHERWSE A[ ROW, Col ] = Xm(l), Col = Col + 1 and A[ Row, Col ] = X,m(2) F i = n THEN go to Step #9, OTHERWSE Repeat Step #8 Z[ROW] = DmV,(O-) F Row = 2n-N THEN go to Step #O, OTHERWSE Repeat Steps 6,7 and 8. Compute a matrix K as K = A-'.Z, where K = [kl, k2,.., k2,.pjt and the notation.t means the transpose of matrk [.. Use algorithm 2 to determine a time-domain expression for V,. 337 Authorized liensed use limited to: Wayne State University. Downloaded on Deember 11, 28 at 1:32 from EEE Xplore. Restritions apply.

3 Authorized liensed use limited to: Wayne State University. Downloaded on Deember 11, 28 at 1:32 from EEE Xplore. Restritions apply. Alaorithm-2: Proedure To Determine The Time-Domain Expression for V, 1. Determine the values Xl(l) and X( 2), for 1 5 i 5 n, using equation (15). 2. Make matries A and Z using Algorithm Determine the oeffiients kl, 1 s j 5 2n-N, using equation (21). Where N is the number of omplex pairs of Xi(1) and Xi( 2), 1 s i 2 n. 4. i=o, j=. 5. i=i+l, j=j+l. F Xl(l) and Xi(2) are omplex numbers THEN Ui=kl OTHERWSE Pi(1) = kj, j = j + 1, Pl(2) = kj. F i = n THEN go to Step #6, OTHERWSE Repeat Step #5. 6. Determine the time-domain expression for V, using the following equation. e-f.tx LCos (bit) 4 for omplex X (1) & X, (2) 7 1 G = 6.67E-4 mho 2 G = 1.25E-3 mho 3 G = 2.5E-3 mho 12-1 G = 6.67E-4 mho 2 G = 1.67E-4 mho 3 G = 1.E-2 mho P U) Capaitane in pf Figure 4: Data rate versus apaitane (C) for a system with 16 nodes Capaitane in pf Figure 2: Data rate versus apaitane (C) for a system with 4 nodes RESULTS FROM THE ANALYSS Figures show the performanes of multiplex-bus systems for different values of the model parameters : R, C and G. The performane was measured based on the following speifiations. 1 ) Let V, be the amplitude of an undistored pulse. Then the threshold voltage (Vth) to detet the presene of a pulse is 2) assumed to be greater than or equal to.5va, i.e., Vth t O.5Va. The pulse widths of an undistored one and an undistored zero are T and To, respetively. The pulse period T = 3T G = 6.67E-4 mho 6- \ 2 G =7.14E-O4mho -@ 'C m y 4 - C a ' 1 = 1.5T. The threshold value of the width ( T (th) ) for a one was taken as.5 T < T (th) 5 T. Similarly, the threshold value of the width ( To(th) ) for a zero was taken as.5 To < To(th) < To. 338

4 Y v) C= 4 pf Q \ tn 4 * 3 U 111 E 2 Y 'C W k 1 tn 2 C = 4pf Figure 6: Data rate versus the number of nodes (4 to 12 nodes) in a system for lig = 15 ohms Figure 9: Data rate versus the number of nodes (48 to 64 nodes) in a system for 1/G = 15 ohms. \ v, H z P 2 C =4pf 3 C = 6pf 12 1 C=2Pf 2 C= 4bf Figure 7: Data rate versus the number of nodes (12 to 32 nodes) in a system for l/g = 15 ohms Figure 1: Data rate versus the number of nodes (4 to C= 4pf, 5 n 15 1 C=2Pf 2 C = 4 pf U 1C Figure 8: Data rate versus the number of nodes (32 to 48 nodes) in a system for 1/G = 15 ohms. Figure '2 shows the performane of a system with four nodes. This figure shows the data transmission rate (bits/se) versus the model parameter C (apaitane) for some fixed values of G (ondutane). Figures 3, 4 and 5 show similar results for systems having eight, sixteen and thirty two nodes, respetively. Figures 6, 7, 8 and 9 show the data transmission Figure 11: Data rate versus the number of nodes (12 to 32 rate (bitsise) versus the number of nodes in a system for different values of the model parameter C and a value of G = 6.667~1.~ mho, Figures O, 11, 12 and 13 show the similar results but for a value of G = x O - ~ mho. The results presented in this paper will help one to determine the maximum number of devies whih ould be onneted to a T

5 given bus if a ertain minimum transmission speed has to be maintained. Tehnology, vol. 38, No. 3, Aug. 1989, pp [ 41 J. W. Tuska, "Multiplex Wiring with Miroomputer 1 Control," lnternational Congress & Exposition, SAE paper 84495, Detroit, Mihigan, February 27 - Marh 2, U: i\ 3 =4pf C=6pf C=6Df t \ [ 5 ] William J. Evans, "Appliation of S Referene Model to $ 6 Automotive Multiplexing," lnternational Congress 8, eo Exposition, SAE paper Detroit, Mihigan, Y February 25 - Marh 1, ' Y P v, 2 [ 61 "Miroomputer Controls Multiplex Wiring System," SA Automotive Engineering, Vol. 92, No. 1, Otober 1984, pp Figure 12: Data rate versus the number of nodes (32 to C = 4 pf [ 71 Arthur J. Estin, " Data Handling Capaity of a Real Transmission Line in a Noiseless System," / E Trans. on lnstrumentation and Measurement, vol. 39, No. 1, Feb. 199, pp [ 81 W. J. Johnson, D. A. Kowalski, J. R. Volk, and T. Kimber, "Systems onsiderations for inorporating vehile data network (multiplex) into automobiles," in Pro. 5th lnternational Conf. on Automotive Eletronis, UK, 1985, paper C218/85, p. 29. [ 91 Arthur R. Bergen, Power Systems Analysis, Prentie- Hall, n., Englewood Cliffs, New Jersey, 1986, pp [ 1 ] Syed Masud Mahmud, "A Novel Time-Domain Analysis of a Multiplex-Bus System," submitted to the / E Trans. on lnstrumentation and Measurement * i ' '. l ' ' * no. of nodes Figure 13: Data rate versus the number of nodes (48 to 64 V. CONCLUSONS This paper presents a novel time-domain analysis to evaluate the performane of a multiplex-bus system. A novel algorithm is also presented in the paper. Using this algorithm one an easily develop a software to determine the performane of a multiplex-bus. This software will help to determine the maximum number of devies that an be onneted to a system suh that ihe worst ase response of a pulse satisfies some given speifiations at a ertain transmission rate. Similarly, the software an be used to determine the maximum transmission rate of a ertain bus with ertain number of devies. iluwka "Digital Multiplexing Saves Wire and Weight on 747 Superjets," Produt Engineering, July 6, 197, pp Roi aid K. Jurgen, "Coming from Detroit: networks on wheels,'' / E Spetrum, June 1986, pp Abut?S>s,ur, " Digital Simulation of an Automotive Multiplexing Wiring System," / E Trans. on Vehiular Table 1 Roots of!he multiplex-polynomial fn(y), for 1 s n s 16. n 1 Roots of the multiplex-polynomial f,(v) 1-1 oo3 l , , , , , , , - 693, -CO , , , , , , , , -, - 382, ,-35783,-3939, , ,-6454,-2411, , , , , , -1, -5339, lo (-198i, , , , , -2449, , , , ' -4486, 1656, ,-37526,-34579,-3717,-2618,-21256, , , l2-7252,-382,-144, [ , , , , , , , , , , , , , , l ;6275,-329,-126, , , , , , , , , - 548, , - 147, , , , , -3579, , , , , , , ,-2,838, , -2952, l6 1' Authorized liensed use limited to: Wayne State University. Downloaded on Deember 11, 28 at 1:32 from EEE Xplore. Restritions apply.