Practical Measure Of Cable Coupling

Transcript

Practical Measure of Cable Coupling D. W. P. Thomas1, C Christopoulos1 Abstract − In this paper the crosstalk between two parallel coaxial cables is investigated. It is shown that the degree of coupling is strongly effected by the geometry of the system. In many practical situations the geometry of the cable routing is ill-defined so that an exact deterministic solution is not possible or helpful. A simple solution based on the first resonant frequency is proposed which can also be used to provide some statistical analysis of the possible degree of cable coupling. 1 Introduction Coaxial cables with braided shields are a popular form of interconnect in the electronics industry because of they are relatively light and flexible but still possess a high degree of shielding effectiveness. At certain frequencies, however, resonances in the coupling path may occur producing an unacceptable degree of cable coupling. Engineers need to be aware of when and to what degree this occurs so that system EMC compliance and signal integrity is assured. Many accurate models for braided cable transfer impedance and admittance have been proposed [1,2], which is the usual measure of the shielding properties of the cables. When these models of transfer impedance and admittance are combined with a circuit description of the coupling path between cables then this also provides an accurate measure of the cable coupling between the cables [3]. However, in most practical cases the exact geometry of the cable path is not known and it may also vary from system to system so that the prediction of the exact frequency dependence of the cable coupling is not possible or desirable. This paper presents results from simulation and measurement of cable coupling. From these results the important parameters involved in the cable coupling process between coaxial cables are demonstrated and a suitable practical measure, based on the system resonances, is proposed. This will provide the engineer with enough information to make informed decisions for EMC compliance and signal integrity. 2 Theory In this paper the cable coupling due to the transfer impedance alone is considered. The effect of transfer admittance has not been included as for non F. Leferink2 and H Bergsma2 optimized cable sheaths it should only have a small effect [3]. Coupling due to the effect of a transfer impedance will occur between cables when they are laid along a common path. A typical cable arrangement is as shown in Fig. 1 where the cables have approximately the same separation along the majority of their length but diverge at the terminations where they are connected to the equipment connector plate. The nature of the terminations strongly affects the degree of cable coupling at high frequencies due to the stray reactances they introduce. If the cables are connected to a common equipment cabinet then the stray reactance is mostly inductive, however, if the cables are connected to electrically isolated units then the stray reactances will be primarily capacitive. These stray reactances can only be estimated or approximated due to the complexity of the cable geometry or the variability of the construction. The terminations of the cable layout are therefore the main limit to the accuracy to which the cable coupling can be predicted. Connector Connector l I It stray reactances Figure 1: A typical cable layout of two parallel cables showing points where significant stray reactances can effect the coupling. The equivalent circuit for the coupling path created by the cable sheath transfer impedance is shown in Fig. 2. The currents Is along the source cable circuit creates a voltage gradient Eit(x) along the outer sheath of the source cable given by GGIEMR, The University of Nottingham, Nottingham NG7 2RD UK,, e-mail: [email protected], tel.: +44 115 9515594, fax: +44 115 9515616. 1 2 stray reactances THALES, Hengelo, Netherlands e-mail: [email protected]. 978-1-4244-3386-5/09/$25.00 ©2009 IEEE 803 Authorized licensed use limited to: UNIVERSITEIT TWENTE. Downloaded on November 12, 2009 at 09:53 from IEEE Xplore. Restrictions apply. where Eit ( x) = Z ts I s ( x) (1) 1 P( x) = 2Zc where Zts is the transfer impedance of the source cable sheath. There are many models for transfer impedance that compare well with measurement [2]. In this work we have used the model proposed by Kley [4] but other models have been found to provide similar results. Q( x) = 1 2Z c x ∫e Ei (u )du ∫e Ei (u )du γu (3) 0 x −γ u (4) 0 Zc =√(Z/Y) is the characteristic impedance of the tertiary circuit transmission line and K1 and K2 satisfy the boundary conditions at x=0 and x=l which gives source circuit Is Vs It Eti(x) Tertiary circuit Vv0 victim circuit Evi(x) Iv cable braids Vvl I(x) ⎡ ρ Q (0) − P (l ) ⎤ K 2 = ρ 2 e −γ l ⎢ γ1l −γ l ⎥ ⎢⎣ e − ρ1 ρ 2 e ⎥⎦ (6) travelling ρ1 = wave Z 0 − Zc Z0 + Z z reflection (7) Zl − Zc (8) Zl + Z z The transmission line termination impedances Zl and Z0 on the tertiary circuit can incorporate the stray impedance that are due to the geometry of the termination. Equation (2) is first applied to the tertiary circuit to obtain the current on the surface of the cables It and it is then applied to the victim circuit to obtain the currents in the victim circuit Iv. The induced voltages across the victim loads are then. ρ2 = Z Δx V(x) (5) As the boundary coefficients are Figure 2: Equivalent circuit for the cable coupling between two shielded cables via the shield transfer impedance Ei(x) + ⎡ ρ P(l )e−γ l − Q (0)eγ l ⎤ K1 = ρ1 ⎢ 2 γ l ⎥ −γ l ⎥⎦ ⎣⎢ e − ρ1 ρ2 e Y Δx Δx Figure 3. Equivalent circuit of a section Δx of a transmission line with a distributed series voltage source Ei(x). The voltage gradient on the outside of the source cable sheath will then induce a current in the outside of the sheath of the victim cable via the tertiary circuit formed by the electrical connection of the cable sheaths. For the majority of the length of the cable routine the cables have the same separation so the tertiary circuit can be considered to be a wire pair transmission line with a distributed voltage source and the equivalent circuit of an element of which is shown in Fig. 3. The general solution for the currents in the tertiary circuit is then given by Vance [5]: I i ( x) = [ K1 + P( x)]e −γ x + [ K 2 + Q( x)]eγ x (2) Vv 0 = Z v 0 I v (0) Vvl = Z vl I v (l ) (9) (10) In this paper the crosstalk C is defined as the ration of the source voltage to the victim voltage at x=0 i.e in dBs: ⎛V ⎞ C = 20 log10 ⎜ v 0 ⎟ dB ⎝ Vs ⎠ (11) For low frequencies and most coaxial cable types the crosstalk can be of the order of -100 dBs and is not of concern for engineers. For higher frequencies where resonances occur the coupling can be much higher and this occurs when the denominator in (5) and (6) is a minimum. An important measure for cable coupling is therefore the frequency of the first 804 Authorized licensed use limited to: UNIVERSITEIT TWENTE. Downloaded on November 12, 2009 at 09:53 from IEEE Xplore. Restrictions apply. resonance and the peak of the cable coupling at that resonance. The peak of the coupling of the resonance will be limited by the losses in the coupling circuit and the main loss will be the resistance of the outer sheath of the cables. From [5] the internal impedance for an external circuit of a cylindrical is Z e ≈ Rc (1 + j )d δ coth (1 + j )d δ (12) where for the cable sheath: Rc is the DC resistance of the braid d is the wire strand diameter of the braid and δ is the conductor skin depth. A valuable measure of the cable coupling is, therefore, the first resonance frequency and the peak of the coupling at that frequency which can found from the equations (1-12). The problem is nonlinear but the solution can be found through iteration using a Newton-Raphson approach. For most cable layouts, however, the problem is ill defined due to the variability of the instillation or the detail is not known at the design stage. From consideration of equations (5) and (6) it can be seen that the important parameter for cable resonance is the termination impedances and it is these values which need to be estimated and their variance defined so that the full variability of the cable coupling can be quantified. 3 Results To illustrate the problem, and the proposed method of solution, crosstalk measurements were taken between two parallel RG58 coax cables of length 2m. The cable separation was varied but both cables were connected to fixed connector plates where the separation of the connectors was fixed at 20 cm. The general layout was therefore as depicted in Fig. 1. Both cables were terminated by their characteristic impedances (50 ohms) so that the only resonances were due to resonances in the tertiary circuit. Figure 4 shows the measured crosstalk Figure 4. Measurement of crosstalk between two RG58 coax cables of length 2m for separations of: touching, 2 cm, 5 cm and 10 cm. From the results given in Figure 4. It is apparent that only significant coupling occurs at the resonant frequencies. The lowest observed resonant frequency, however, occurs at much lower frequencies than the expected resonant frequency fideal for an ideal tertiary circuit of length 2m (=λ/2): fideal = c / 4 = 75 MHz (13) The reason for the discrepancy is that the extra loop area caused by the connector separation, as depicted in Fig. 1, gives rise to stray inductances at the termination of the tertiary circuit. Approximating the stray inductance Lstray as that due to a loop of radius 10 cm [6] compared with that of perfectly straight cables gives Lstray = 0.4 μH (14) Figure 5 shows the predicted crosstalk assuming the tertiary circuit is terminated by a 0.4 μH inductance. The results given in Fig. 5 agrees well with the measurements given in Fig. 4. Figure 5 Predicted crosstalk between two RG58 coax cables of length 2m for separations of: touching, 2 805 Authorized licensed use limited to: UNIVERSITEIT TWENTE. Downloaded on November 12, 2009 at 09:53 from IEEE Xplore. Restrictions apply. cm, 5 cm an 10 cm. Assuming the tertiary circuit is terminated by inductances of 0.4 μH In general the precise geometry will not be known so that the terminating impedance and even the cable separation can only be estimated. A far more useful measure for the engineer would be an estimate of the frequency of the first resonance and the peak crosstalk at that resonance. This can be found by noting that the peaks occur where the denominators in (5) and (6) are a minimum or by putting: ρ1 ρ 2 = Ae jθ (14) then f res = where n=1,2,3 .. etc. c [ n2π − θ ] 2π l (15) Equation (15) is nonlinear as theta is a function of frequency but it can be solved using a simple NewtonRaphson iteration or similar. The lowest resonant frequency occurs for the condition of touching cables which could be used or a given separation with its variability could be used. If a solution is sought for just the first resonance then it also becomes practical to apply statistical analysis using a Monte Carlo approach also becomes more practical. Assuming the cable separation is 5 cm with a standard deviation of 2 cm and the termination impedances are 0.4 μH with a standard deviation of 0.2 μH then the minimum resonant frequency and peak crosstalk are then: Acknowledgments The authors would like to thank Thales Netherlands for providing the facilities for the project and the EU for providing financial support via the Marie-Currie Fellowship scheme. References [1] E. F. Vance, ”Shielding Effectiveness of braidedwire shields”, IEEE Trans., EMC, Vol. 17, No. 2, 1975, pp 71-77. [2] F. A. Benson, P. A. Cudd and J. M. Tealby, “Leakage from coaxial cables”, IEE Proc-A, Vol. 139, No. 6, 1992, pp 285-303. [3] S. Sali “A circuit based approach for crosstalk between coaxial cables with optimum braided shields” IEEE Trans. EMC, Vol, No. 2, 1993, pp 300-311 [4] T. Kley, “Optimised single braided cable shields” IEEE, Trans. EMC, Vol. 35, No. 1, 1993 pp 1-9. [5] E. F. Vance, ”Coupling of shielded cables”, 1978, Pub. Wiley, ISBN 0-471-04107-6. [6] J. D. Jackson, “Classical Electrodynamics 3rd Edition”, 1998, Pub. J. Wiley & Sons, New York, ISBN 0-471-30932-X Minimum Resonance at 59±4 MHz Resonance Peak value is -58±0.4 dB Notice also that, for these variances, the termination impedance has the greatest influence on the resonant frequency (marginal statistical moment is 93%) but the separation has the greatest influence on the crosstalk amplitude (marginal statistical moment is 92%). These results are then sufficient to describe the maximum crosstalk between two parallel cables in a poorly defined system. 4 Conclusions The degree of crosstalk between two parallel cables has been investigated. It is shown that the amplitude and resonance frequencies in the crosstalk are dependent on the geometry of the system. In most practical systems the cable geometry may be poorly defined so therefore it is shown that sufficient information can be derived by solving for the first resonant frequency and finding the degree of crosstalk at this frequency. Simplifying the problem also enables statistical analysis to be performed. 806 Authorized licensed use limited to: UNIVERSITEIT TWENTE. Downloaded on November 12, 2009 at 09:53 from IEEE Xplore. Restrictions apply.