Circuit models of Lossy Coaxial Shielded cables to Analyze Radiated and Conducted Susceptibilities with unmatched line loads

Transcription

1 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June Circuit model of Loy Coaxial Shielded cable to Analye Radiated and Conducted Suceptibilitie ith unmatched line load M.SAIH 1, H.ROUIJAA 2, A.GHAMMAZ 1, 1 Laboratory of Electrical Sytem and Telecommunication, Department of Phyic, Faculty of Science and Technology, Cadi Ayyad univerity, Marrakeh, Morocco 2 Laboratory of Electrical Sytem and Telecommunication, Department of Applied Phyic, Faculty of Science and Technology, Haan 1er univerity, Settat, Morocco Abtract Thi paper preent a circuit model to analye the variation effect of incident plane ave on hielded coaxial cable, uing Branin method, hich i called the method of characteritic. The model can be directly ued for the time-domain and frequency-domain analye and for all arbitrarily loaded. Thi make it eay to inert in circuit imulator, uch a SPICE, SABER, and ESACAP. The obtained reult are in good agreement ith thoe from other method. Finally, e ill dicu the effect of the variation of the incident plane ave. Index Term Plane ave, hielded coaxial cable, method of characteritic, tranfer impedance, Circuit model. I. INTRODUCTION Shielded coaxial hielded cable are uually ued in RF and microave circuit a reonator [1], VLSI interconnect [2], ave haping [3] analog ignal proceing [4],filter [5] and etc. Neverthele, there exit coupling beteen the exterior and interior of the hield for the reaon that the imperfect nature of the hield. Conequently, electromagnetic interference (EMI) and electromagnetic compatibility (EMC) problem aociated ith cable [6] connecting thee device hould be taken into conideration. Circuit model for multiconductor tranmiion line (MTL) ith and ithout hield [7], [8] have been a ubject of great interet in recent year. Spice model to analye the conducted immunity of coaxial cable have been preented in [9], then ome pice model have preented for the analye of the conducted and radiated immunity of lole hielded cable [1]. Thee model are not inherently capable to analye directly the time-domain, the invere Fourier tranform (IFT) i needed for the model to obtain the time-domain reult. Recently, ome Spice model have been propoed to analye the conducted and the radiated uceptibilitie of lole hielded coaxial cable [8], [11].The principle point of interet of thee model comprie in the likelihood of utiliing them a a part of frequency and time domain, ith linear and non linear load individually, and the dicretiation of hielded cable i not needed. Hoever, thee model cannot be ued to analye loy hielded cable. After Then, ome loy model have been preented to analye the conducted and radiated

2 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June uceptibilitie of Multiconductor Shielded cable [12]. Hoever, a imilarity tranformation i needed to decouple the inner tranmiion-line equation. In thi paper, an equivalent circuit model to analye the radiated uceptibility of uniform hielded coaxial hielded cable i preented. Thee model can be ued to analye both the time-domain and frequency domain and for all arbitrarily loaded. There i a good correlation ith thoe from other method. II. DESCRIPTION OF COAXIAL SHIELDED CABLES A. Model of hielded cable For a coaxial cable over an infinite and perfectly conducting, a illutrated in Fig. 1, the coupling ith external field can be decribed by [8]: Outer ytem Inner Sytem V(, t) I (, t) L R I(, t) V f (, t) t I(, t) V(, t) C GV (, t) I f (, t) t V(, t) I (, t) L R I(, t) Zt I (, t) t I(, t) V(, t) C GV (, t) t (1) (2) Where V i the hield-to-ground voltage, I i the current floing beteen the external hield and the ground, V i the ire-to-hield voltage and I i the current of the ire. L, C, R, and G are the per-unit-lenght (p.u.l) inductance, capacitance, reitance and conductance of the outer ytem, repectively, hile L, C, R and G are the p.u.l inductance, capacitance, reitance, and conductance matrice of the inner ytem. Z t i the tranfer impedance, In cae of braided hield, the tranfer impedance i given by the complex expreion [13-14] Z Z jl (3) t d t Where Z d i the diffuion term, and L t i the inductance hich account for the field penetrating through the braid aperture. The expreion of both Z d and L t in term of the braid eave parameter can be found in [13-14]. In our application, e ued a implified expreion [8] Zt Rt jlt, here R t i the contant p.u.l. tranfer reitance of the hield. V f (,t) and I f (,t) are ditributed ource that repreent external excitation of the tranmiion line. Thee ource term can be ritten olely in term of the incident electric field uing Faraday la. For coaxial hielded cable, hon in Fig. 2, e have:

3 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June h inc inc inc f x V (, t) E ( h,, t) E (,, t) E ( x,, t) dx (4) h inc f x t I (, t) C E ( x,, t) dx (5) inc inc here h i the height of the line, and E ( h,, t ) and E ( h,, t ) are the horiontal and vertical component of the incident electric field, repectively. x The incident field, in the abence of the line, a hon in Fig. 3, can be ritten in the folloing frequency form inc jxx y j E ( x, y,, ) E ( e a e a e a ) e e e (6) x x y y j y Where e x, e y and e are the component of the incident electric field vector along the x, y, and axe, and are given by: ex ine inp ey ine cop cop coe inp (7) e ine cop inp coe cop ex ey e 1 x Shield Inner ire Equipement Equipement y Fig. 1. A Shielded coaxial cable over an infinite and perfectly conducting ground Fig. 2. Definition of the parameter characteriing the incident field a a uniform plane ave

4 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June The angle θ E characterie the polariation ort. The polariation i horiontal if θ E i equivalent to ero and vertical if it i equivalent to 9. The angle θ p decide the rie ith repect to the ground. Thi one i generally called the incident angle. The angle ϕ p give the propagation direction relative to the axi O. The component of the phae contant along thoe coordinate axe are: x cop y inp cop inp inp (8) The phae contant i related to the frequency and propertie of the medium a: r r (9) v Where v 1 i the phae velocity in the pace and the medium i characteried by the permeability r and permittivity r. B. Equivalent Circuit Model for conducted Immunity: Outer ytem In order To olve the equation (1) and (2) e ue the dicrete line model. For thi reaon, the cable i dicretied in the form of cell; the length of each cell i. 1 Uing Branin method, each cell can be ritten in the cae of conducted mode a [12]: V (, t) ZcI (, t) Vbr V (, t) Z I (, t) V c bi (1) In (1), Z c repreent the characteritic impedance of the outer ytem. Uing the firt term of the Taylor erie expanion, e obtain [12] Where Z c R jl 1 Rc R << L ω (11) jc jc R c L C and f C f 2L (12) RR c Eq. (1) become Rc R V (, t) Rc I (, t) I(, t) Vbr 2 ² L R R V (, t) R I (, t) I (, t) V c c bi 2 ² L (13)

5 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June Where Rc R Vbr e V (, t T ) Rc I (, t T ) I (, t T ) 2 ² L Rc R Vbi e V (, t T ) Rc I (, t T ) I(, t T ) 2 ² L (14) The characteritic impedance in thi cae, i preented a a characteritic reitance R c and capacit C a hon in Fig. 4. Where T i the one-ay delay of the hield, and i denoted by T LC With the ame etimation, the contant of propagation get to be: R j j LC (15) 2R c f Fig. 4. Circuit model of each cell of the outer ytem: hield C. Equivalent circuit model for conducted immunity: Inner ytem Uing the ame procedure, the inner ytem can be ritten for each cell a RR c V (, t) RcI (, t) I(, t) V r 2 ² L RR V (, t) R I (, t) I (, t) V c c i 2 ² L Where RR c Vi = e V (, t Tr ) RcI (, t Tr ) I(, t Tr ) ZtI ( ) 2 ² L RR c V e V (,, ) (, ) (, ) ( ) r t t Tr RcI t Tr I t Tr ZtI 2 ² L T L C r (16) (17) (18) Where R c L C (19) and C f 2L (2) RR c Thee relation repreented a hon in Fig. 5.

6 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June Fig. 5. Circuit model of each cell of the inner ytem: ire D. Equivalent Circuit Model for Radiated Immunity of coaxial hielded cable Thi i the ame repreentation a the conducted immunity by adding generator forced of voltage E and E +, hich are repreenting the coupling beteen the hield and the incident ave, a hon in Fig. 6. E x k x C hf R ch R ch C hf Shield Wire I ( + ) - + hield Fig. 6. Equivalent Circuit Model for Radiated Immunity of coaxial hielded cable

7 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June E and E + modeling the influence of the incident field in the time domain. For a perfect ground plane, their expreion are defined by [7] ( t) ( t T T ) E ( T T) (21) ( t T) ( t T) E ( T T) Where ε(t) repreent the amplitude of the electric field in the time domain, α et α + are the coefficient dependent on the parameter of the line defined by: etxyk ( exxk ey yk )( T T ) etxyk ( exxk ey yk )( T T ) (22) ith T T x y k k xyk x (23) y, if a component ave that propagate along the axi T =T, in the opoite cae T =. III. SIMULATION RESULTS AND VALIDATION A. Conducted uceptibility and validation The configuration ued for the conducted uceptibility i hon in Fig. 7. The length L and the height h of the cable are 1m and 1cm, repectively. The hield and the inner ire radiu are r =2.5mm and r =.25mm, repectively. The relative perttivity i ε r = The value of the tranfer reitance and inductance are: R T =1mΩ/m and L T =.5nH/m. The terminal load beteen the hield and the ground are R S1 =1GΩ and R S2 = Ω, hile the inner termination are matched R 2 = R 1 =44 Ω. The lumped current ource adopted for the tranient analyi i a clock ave of unit amplitude characteried by period T 2n, rie and fall time, and duty cycle / 5.. Fig. 8 ho clk the ire-to-hield voltage at the cable end, hich agree ell ith the reult from different method. T clk h I (a) (b) Fig. 7. (a) Geometrical cro-ection of the coaxial cable. (b) Configuration of the imulation for conducted analyi

8 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June Fig.8. Voltage repone of the inner load in the tranient analyi obtained by different method Fig. 9. Magnitude of the frequency repone in decibel of the inner termination The ire-to-hield voltage at the cable end acquired by the propoed model i appeared in Fig.8 together ith the outcome determined by the FDTD [15], here the FDTD implie the finite difference time domain olution to the tranmiion-line equation of the cable, and by the compact circuit model propoed in [1]. They are in very good agreement ith each other. The lumped current ource i et to 1A for the frequency-domain analyi. Fig. 9 demontrate the magnitude of the frequency repone of the inner terminator acquired by the propoed model. The outcome got by the ESACAP tet ytem are in great concurrence ith the analytical olution [16]. A hon in Fig. 9. The coupling into end ide load i clearly tronger than in near ide load, becaue the injection i aymmetrically located on near ide of external hield, the total coupling i under a flat envelop and the anti-reonance frequencie are located a by the folloing formula at f n x., n=1,3,5. B. Radiated Suceptibility Analyi of Coaxial Cable The analyi of the radiated immunity i carried out on the coaxial cable a hon in Fig. 1. The hield radiu and the inner ire radiu are.25mm and.18mm, repectively. The cable characteritic impedance i Zc 5, and the relative permittivity r of the internal dielectric filling i The value of the tranfer impedance i et to R 1 / m and L H / m. The height h and the length L are 5.25mm and 1m, repectively. The internal conductor i adapted ith Za= Zb =5. The incident field i modeled by the double exponential pule E( t) ke exp At exp Bt, auming E 5 KV / m, k 1.3, T T A ,

9 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June B , i ued for the time domain analyi, hile the electric field of 1V/m magnitude for the frequency domain analyi. x E x K y (a) (b) Fig. 1. (a) (a) Geometrical cro-ection of the coaxial cable. (b) Configuration of the imulation for radiated analyi Fig. 11. Current induced on hielded cable in dba excited by uniform Ex- K, obtained by different method (normalied Tot to ZE ). t Fig. 12. Voltage induced at the cable end excited by an incident plane ave Ex- K, obtained by different method

10 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June The hield i hort circuited on the right (Z 2 =.5). At the output of the coaxial e recover the current into dba, hich i matched ith the canonic reult publihed by Smith [16], a hon in Fig.11. When the hield i open on the left (Z 1 =.5) a toering reonance at about /4, a hon in Fig.11. To dratically diminih the coupling to internal ire, a to-ide grounded configuration for the hield mut be utilied. Fig. 12 demontrate the voltage reaction at the inner load of the cable in the time-domain analyi acquired by the divere method, hen Z 1 = Z 2 equivalent to the characteritic impedance of the hield-to-ground (Z 1 =Z 2 =244.5). The arrangement of the ditinctive technique concur exceptionally ell. C. Variation effect of incident plane ave on Coaxial cable ith unmatched line load, over ground plane Fig. 13 ho a coaxial cable of 1m length at 5.25mm above a perfectly conducting ground plane, the hield radiu R h and the inner ire radiu r are.25mm and.716mm, repectively, ith dielectric contant ε r = The load R 1 and R 2 beteen the inner ire and the hield at the to termination are R 1 =1Ω and R 2 =1Ω. The value of the tranfer impedance i et to R T =.1Ω/m and L T =1nH/m. The incident electromagnetic field i a plane ave, hile the incident field E = 1V/m. The Analyi performed for three reference field direction a decribed in Fig. 8 are a follo: a) E x -K : The polariation direction of electric field i along axi. b) E x, K y : The polariation direction of electric field i along y axi c) E, K x : The polariation direction of electric field i along x axi Fig. 13a. Cae 1- Coaxial cable over an infinite and perfectly conducting ground excited by an incident plane ith 9, 9 and 9 p p E. Fig. 14a. Cae 1- Voltage repone at the cable end in the frequency analyi ith the incident ave ith 9, 9 and 9 p p E

11 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June Fig. 13b. Cae 2- Coaxial cable over an infinite and perfectly conducting ground excited by an incident plane ith, 9 and 9 p p E Fig. 14b. Cae 2- Voltage repone at the cable end in the frequency analyi ith the incident ave ith, 9 and 9 p p E Fig. 13c. Cae 3- Coaxial cable over an infinite and perfectly conducting ground excited by an incident plane ith, and p p E Fig. 14c. Cae 3- Voltage repone at the cable end in the frequency analyi ith the incident ave ith, and p p E The to different curve for each cae, ith imilar field illumination, correpond to typical application here the hield i connected to the ground on both ide, or only on one ide, mainly at the receiving end. The internal ire i alay loaded, a typical for real ignal bu, ith lo reitance on the tranmitting ide and high reitance on the receiving ide. In Fig. 14, e compare the voltage at the far-end for three reference field direction. For all cae, it i een that the line reonate at /(3x4) f =225 MH hen the hield load i open at the near-end. The value of the open circuit reitance choen here i 5MΩ. Alo the high impedance reitance value located at oppoite end, for internal line and external hield, provide ome phae compenation, practically eliminating the reonance /4. f =75 MH. Hoever, ith hort circuit at the end, it i een that for cae 1 and 2, eliminate practically all reonance, and the internal immunity i improved more than 2dB. For the cae 3, the ide vertical illumination excite the hield ith maximum efficiency. Thi i the reaon hy the line reonate at /2f=15MH and /(3x2)f=45MH, even under hort circuit condition.

12 Journal of Microave, Optoelectronic and Electromagnetic Application, Vol. 16, No. 2, June IV. CONCLUSION Circuit model ere ued to analye the radiated and conducted uceptibilitie for loy hielded coaxial cable. It require the ubdiviion of cable into everal uniform ection firt. Then the voltage and current ditribution are obtained uing Branin model. The principle point of interet of thee model comprie in the likelihood of utiliing them directly in time and frequency domain analyi. Finally, the introduced approach i verified by comparing it reult ith other method. The propoed model can be alo extended to the MTL in complex ytem. Thi quetion ill be addre in future ork REFERENCES [1] Boick C, Blyler J, and Ajluni C.J: RF circuit deign, 2nd ed. Amterdam ; Boton, 28. [2] Dhaene T, Marten L, and De Zutter D. Tranient imulation of arbitrary nonuniform interconnection tructure characteried by cattering parameter, IEEE Tran. Circuit Syt. Fundam. Theory Appl. 1992, vol. 39, no. 11, pp [3] Burkhart S. C, Wilcox R. B. Arbitrary pule hape ynthei via nonuniform tranmiion line, IEEE Tran. Micro. Theory Tech. 199, vol. 38, no. 1, pp [4] Khalaj-Amirhoeini M. Analyi of coupled or ingle nonuniform tranmiion line uing tepby-tep numerical integration, Prog. Electromagn. Re., 26, vol. 58, pp [5] Robert P.P, and Ton G.E. Deign of microave filter by invere cattering, IEEE Tran. Micro. Theory Tech., 1995, vol. 43, no. 4, pp [6] Lin D.B, Wu F.N, Liu W.S, Wang C.K, and Shih H,Y. Crotalk and dicontinuitie reduction on multi-module memory bu by particle arm optimiation, Prog. Electromagn. Re., 211, vol. 121, pp [7] Mejdoub Y, Rouijaa H, andghamma A. Variation effect of plane-ave incidence on multiconductor tranmiion line, Int. J. Micro. Wirel. Technol., 215, pp [8] Xie H, Wang J, Fan R, and Liu Y. SPICE Model to Analye Radiated and Conducted Suceptibilitie of Shielded Coaxial Cable, IEEE Tran. Electromagn. Compat., 21, vol. 52, no. 1, pp [9] Caniggia S, and Maradei F. Equivalent circuit model for the analyi of coaxial cable immunity, 23, vol. 2, pp [1] Caniggia S, and Maradei F. SPICE-Like Model for the Analyi of the Conducted and Radiated Immunity of Shielded Cable, IEEE Tran. Electromagn. Compat., 24, vol. 46, no. 4, pp [11] Xie H, Wang J, Fan R, and Liu Y. Spice model for radiated and conducted uceptibility analye of multiconductor hielded cable, Prog. Electromagn. Re., 21, vol. 13, pp [12] Saih M, Rouijaa H, and Ghamma A. Circuit model of multiconductor hielded cable: incident plane ave effect, Int. J. Numer. Model. Electron. Net. Device Field, 216, vol. 29, no. 2, pp [13] Teche, F., Iano, M., Karlon, T.: EMC Analyi Method and Computational Model. Ne York, Wiley, [14] Saih, M., Rouijaa, H., Ghamma, A.: Crotalk reduction by adaptation of hielded cable, international Conference on Intelligent Information and Netork Technology, Settat Morocco, (213). [15] Roden, J.A., Paul, C.R., Gedney, W.T.: Finite-difference, time domain analyi of loy tranmiion line, IEEE Tran. Electromagn. Compat., vol. 38, 1996, pp [16] Albert A. Smith, Jr.: Coupling of external electromagnetic field to tranmiion line, (John Wiley & Son, 2nd Edition, 1992).