Grounding, Unbalancing and Length Effects on Termination Voltages of a Twinax Cable During Bulk Current Injection

302 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 46, NO. 2, MAY 2004

an electromagnetic simulator that incorporates the boundary elementmethod (BEM).As it can be seen from these results, the accuracy of this method is

inside a 10% limit of the measured values, caused mainly by the inho-mogeneties present in Section I-A and is more accurate than the ana-lytical method presented in [6], where differences with measurementscan reach 20%. The measurements exhibit a tolerance of around 5%based mainly on the laying of the pair.Finally, the effect of the twist can be incorporated by adapting the

technique described in [8].

IV. SUMMARY

A new method for the calculation of the capacitance of shieldedtwisted-pair cables, with practical shields, has been developed. The useof the two-different methods for the calculation of the conductor toshield and mutual capacitance has added to the accuracy of the methodas in the case of mutual capacitance the conformal transformationsoffer a more accurate value of capacitance. Furthermore, this methodhas been compared with the common cylindrical shield [6] case andhas shown that this common assumption introduces a significant errorin the capacitance calculation.

ACKNOWLEDGMENT

The authors would like to thankD. Jackson of Brand-Rex Ltd., Glen-rothes, Fife, U.K., for providing the measurements used in Table I andthe anonymous reviewers of this brief for their valuable comments andsuggestions.

REFERENCES

[1] “ISO/IEC,” 11801 standard, edition 1.2, Jan. 2000.[2] A. P. Duffy, K. G. Hodge, and A. J. Willis, “Technology forecasting

techniques in communications,” in Proc. 51st Int. Wire Cable Symp.,Lake Buena Vista, Orlando, FL, Nov. 2002, pp. 1–8.

[3] H. G. Sasse, B. G. Tunstall, D. E. Coleby, M. M. Al-Asadi, A. P. Duffy,K. G. Hodge, and A. J. Willis, “A genetic algorithm toolkit for cabledesign,” inProc. 50th Int.Wire Cable Symp., LakeBuenaVista, Orlando,FL, Nov. 2001, pp. 143–150.

[4] P. A. Laura and L. E. Luisoni, “Approximate determination of the char-acteristic impedance of the coaxial line system consisting of a regularpolygon concentric with a circle,” IEEE Trans.Microwave Theory Tech.,vol. MTT-25, pp. 160–162, Feb. 1977.

[5] M. H. Nayfeh and M. K. Brussel, Electricity and Magnetism. NewYork: Wiley, 1985.

[6] S. Zhang, “Calculation of the partial capacitance in an system of con-ductors within the calculable resistor,” IEEE Trans. Instrum. Meas., vol.43, pp. 929–932, Dec. 1994.

[7] B. N. Das, S. B. Chakrabarty, and S. R. Rao, “Capacitance of transmis-sion line of parallel cylinders in the presence of dielectric coating,” IEEETrans. Electromagn. Compat., vol. 37, pp. 94–96, Feb. 1995.

[8] C. D. Taylor and J. R. Castillo, “On the response of a terminatedtwisted-wire cable excited by a plane wave electromagnetic field,”IEEE Trans. Electromagn. Compat., vol. EMC-22, pp. 16–19, Feb.1980.

Grounding, Unbalancing and Length Effectson Termination Voltages of a Twinax Cable

During Bulk Current Injection

G. Antonini, A. Ciccomacini Scogna, and A. Orlandi

Abstract—By means of an equivalent SPICE circuit of a two-parallel-wires shielded cable (twinax), the effects on the induced voltages at thecable’s terminations during a bulk current injection are studied for dif-ferent shield’s grounding, different cable’s asymmetries or unbalancingand different lengths of the cable. The analysis is carried out both in fre-quency and time domain.

Index Terms—SPICE model, two-wires shielded cable.

I. INTRODUCTION

The ever growing use of the bulk current injection (BCI) test[1], [2] and its properties to mimic the exposure of shielded cablesto electromagnetic radiated disturbances has steered in the past[3]–[6], and recently [7]–[12] the attention of several researchers.The induced voltages due to a BCI at the cable’s terminations dependon the grounding condition of the shield, on the cable electrical orgeometrical asymmetry, and on the cable’s length. In order to predictthe effects of these cable’s conditions on the induced voltages, aSPICE model of a shielded cable (coaxial or multiwire but not twisted)has been developed in [13], [14]. This model takes into account thepresence of both the transfer impedance Zt and admittance Yt andallows the analysis in frequency (when the characteristic frequenciesof the cables are sought) and in time domain (when it is of interestthe peaks or the energy associated to the interferences). In this work,such a model is used to perform a parametric analysis of the inducedtermination voltages at the ends of a two-parallel wires shieldedcable (often and also in the following referred as twinax). Startingfrom the evaluation of the frequency response due to the commonshield-to-ground connections then a geometric asymmetry in thecable’s cross section and/or an electrical asymmetry in the Zt or Yt

associated to the internal wires is introduced. Finally, the effects ofdifferent cable’s length on the termination voltages waveforms areanalyzed.

II. MODEL AND CONFIGURATIONS

The model of a twinax cable during a current injection, inducedby a classic current clamp, is formulated by considering an externaltransmission line (TL), whose equivalent SPICE circuit schematic isin Fig. 1(a) having currents flowing on the exterior of the shield andreturning along a reference plane and an internal multiconductor TL(MTL) consisting of two internal conductors referenced to the interiorpart of the shield. The coupling between the external and internal TLsis operated by the transfer impedances and admittances. These transferparameters give rise to induced voltage and current sources (distributedalong the internal conductors) that are represented as lumped voltageand current generators at one of the conductors’ ends. To these lumpedsources, it has been given an exact circuit representation in [13], [14].

Manuscript received May 8, 2003; revised November 28, 2003.The authors are with the UAq EMC Laboratory, Department of Elec-

trical Engineering, University of L’Aquila, I-67040 L’Aquila-Italy, (e-mail:[email protected]; [email protected]; [email protected]).Digital Object Identifier 10.1109/TEMC.2004.826882

0018-9375/04$20.00 © 2004 IEEE

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 46, NO. 2, MAY 2004 303

(a)

(b)

(c)

Fig. 1. (a) Equivalent circuit of the external problem. (b) Equivalent circuit of the internal problem (the reference node “0” corresponds to the shield). (c) Schematicof the left end cable’s termination (the right end termination is specular).


TABLE IGROUNDING CONFIGURATIONS. (CONFIGURTIONS ARE LABELLED AS IN [18])

The remaining part of the internal conductors is modeled as a simplepassive multiconductor TL (MTL). The modal decomposition of theMTL equations is used in conjunction with the SPICE syntax, asproposed in [15], to take into account the mutual coupling betweenthe internal parallel conductors. The global SPICE circuit for theinternal MTL is in Fig. 1(b). In the final global circuit, the impedancesZSH—that connect the external shield to the reference plane at theleft and right ends—and the cable’s terminations represented by thenetwork in Fig. 1(c) can be put in evidence. In this figure, ZDM isthe impedance between the two internal conductors, ZCM1 and ZCM2are those between the internal conductors and the shield. With theseimpedances, it is possible to describe several load and groundingconfigurations as done in Table I where, if not specified, the valuesof the impedance are intended to be resistive and in ohm. The basiccharacteristics of the twinax cable considered along this work are:cable’s length L = 1 m, cable’s height above the reference plane h =

10 cm, external diameter �e = 5 mm, diameter of internal conductors�� = 0.5 mm, center-to-center separation of the internal conductorss = 0.5 mm, relative permittivity of internal dielectric filling �r = 2.4.The two internal conductors are symmetrically placed with respect thecenter of the cable. The transfer impedance and admittance are givenby Zi

t = rit + j!Li

t where ri

t = 10 m m, Li

t = 1.2 nH/m andY i

t = j!Ci

t with Ci

t = 0.041 pF/m for i = 1,2. The injecting clampis placed at d = L=2 from the left end (considered as origin of thedistances, d = 0) forcing an equivalent CW current ISH = 1 + j0 Afrom 1 kHz to 1 GHz.As validation of the used circuit, the numerical solution of the

model’s equations in [13], [14] is compared with the solution obtainedfrom the equivalent circuit. This is done for the loads and groundingconfiguration named TEST in Table I. The four loads ZCMi(i = 1; 2)

at the left and right ends end are equal and balanced with respect toground. As expected the four voltages across the ZCMi impedancesat the cable’s ends, computed by the direct solution of the model’sequations, are equal and shown in Fig. 2. In the same figure, are alsoplotted the same voltages computed by the equivalent circuit. Thesmall values of the maximum difference between the two spectra onall the frequency range is an indication of the reliability of the model.The model uncertainty is a parameter of engineering interest. It can beassessed by comparing the circuit model outputs with other indepen-dent results such as measurements. Fig. 3(a) shows the experimentalsetup of an on going project aimed to evaluate the confidence of theabove mentioned circuit model. Although part of a more extended dataset [16], Fig. 3(b) and (c) show the comparison between measuredand computed voltages at the left termination of a L = 2 m cable[Fig. 3(b)] and at the right cable’s end between the external shield andthe conductive reference plane [Fig. 3(c)]. In the graphs, are also

(a)

(b)

Fig. 2. (a) Magnitude of the frequency response of the voltage across Z :by equivalent circuit and by direct solution. (b) Phase of the frequency responseof the voltage across Z : by equivalent circuit and by direct solution.

indicated the� 2 dB and� 4 dB uncertainty bands with respect to themeasured values. For the most of the considered frequency range, thecomputed voltages are within � 2 dB from the measurements, beingout of the � 4 dB band only at selected frequencies.


(a)

(b)

(c)

Fig. 3. (a) Overview of the experimental setup. (b) Frequency spectrumof the load voltage at the left termination. (c) Frequency spectrum of theshield-to-reference voltage at the right end.

III. EFFECTS OF GROUNDING

The first parametric analysis carried out, is that considering the ef-fects of the shield’s grounding. These effects are measured in terms ofvoltage VDM (or vDM in time domain) across the terminations’ differ-ential impedances ZDM and in terms of common mode voltage VCM(or vCM in time domain) defined as

VCM =2ICMZCM1ZCM2

ZCM1 + ZCM2(1a)

ICM =I1 + I2

2(1b)

where I1 and I2 are indicated in Fig. 1(c).

(a)

(b)

Fig. 4. (a) Magnitude of the frequency response of V at the left terminationfor 6 configurations. (b) Magnitude of the frequency response of V at theright termination for 6 configurations.

For the above mentioned twinax with the six grounding and loadconfigurations in Table I (from A to F), the frequency spectra of themagnitude of VDM at the left and right end side and of the magnitudeof VCM are plotted in Figs. 4(a) and (b) and 5 respectively. Looking atFig. 4(a) and (b), one can observe that the difference in the differentialload impedances has only a small effect on the induced voltages for themost of the configurations. As expected, because balanced with respectto ground, configuration C has the best rejection to the induced inter-ferences due to the injected current on the external shield. The presenceof stray capacitances or decoupling capacitors in configurations E andF (represented by the 100-nF capacitance), is visible in the two markedpeaks at around 1 MHz. After the first resonance of the cable at around50MHz, the cable behaves as a distributed circuit almost independentlyby the grounding and load topology. This is also true for the commonmode voltage VCM, computed as in (1), in Fig. 5.If the longitudinally injected current ISH = 1 + j0 A is considered

as a common mode source of interference, then the plots in Figs. 4 and5 are also a measure of the conversion of common mode currents intodifferential-mode voltages and common-mode voltages, respectively.

IV. EFFECTS OF UNBALANCING

As in all differential signals’ transmitting structures, also for twinaxthe presence of any unbalancing is cause of an increasing of the differ-


TABLE IIEFFECTS OF UNBALANCING

Fig. 5. Magnitude of the frequency response of V for 6 configurations.

Fig. 6. Asymmetric twinax’s cross-section.

ential mode (DM)-to-common mode (CM) conversion [17] and, hencean increasing of the produced interferences. The unbalancing is con-sidered as geometrical or electrical; although related one another theycan be conceptually separated: a geometrical unbalancing is intendedas a asymmetry in the cross section of the cable, an electrical unbal-ancing is intended as a asymmetry in the electrical parameters such asshield-to-ground impedances, loads impedances, transfer parameters.It is considered the twinax described in the Section III, with the

shield’s connections as in configuration TEST of Table I and all theZCMi termination impedances equal to 100 ; a transient trapezoidal

Fig. 7. Transient voltage v (t) for cases (II) to (V) of Table II.

voltage vSH(t) is applied at d = L=2 with the following parameters:amplitude vMAX = 1 V, rise time �r = 5 ns, fall time �f = 5 ns, timewidth � = 100 ns and period T = 200 ns. The transient voltage vDM(t)across ZDM = 1 in Fig. 1(c) is computed for the 5 different casessummarized in Table II. Case (I) is the reference: a perfectly balancedcable in which vDM(t) = 0 V; in case (II) the unbalancing is intro-duced in the cross section (see Fig. 6) leaving artificially unaltered thetransfer parameters Zt and Yt of the two internal wires; case (III) and(IV) consider the unbalancing related to the difference between onlyone transfer parameters at a time leaving the cross section symmetricwith respect the cable’ axis; case (V) shows the effects of a total unbal-ancing: cross section and transfer parameters. Fig. 7 reports the tran-sient waveforms for cases (II) through (V) in a time window of 250 ns;their comparison gives a measure, for this case, of the relative impactof each single unbalancing on the total voltage due to the DM-to-CMconversion.

V. EFFECTS OF CABLE’S LENGTH

It has been recently shown in [18]–[21], the influence of long ca-bles on the levels of conducted emissions: these emissions flowingout of the equipment under test ports may differ significantly fromthose measured at the opposite end, i.e., on a line impedance stabi-lization network. If this happens, it has to be ascribed to propaga-tion and mutual-coupling effects along the cable. Because of this, theanalysis of the cable’s length on the voltages induced at the termi-nation of a twinax during a bulk current injection is the topic of this


(a)

(b)

Fig. 8. (a) Frequency spectrum of V for four different cable’s lengths whend = L=2. (b) Frequency spectrum of V for four different cable’s lengthswhen d = L=2.

section. The main characteristics of the twinax are those describedin Sections II–V, when a symmetric cross section is considered andZ1

t = Z2t and Y

1t = Y 2

t . The shield’s grounding and the load termina-tions are those described in configuration A of Table I and the sourceis an unitary current ISH = 1 + j0 A from 1 kHz to 1 GHz. Fig. 8(a)shows the magnitude of VDM across ZDM = 10 for four differentlengths L = 1, 5, 10, and 50 m when the injecting clamp is always atd = L=2 from one end. The effects of L on the levels of VCM in (1)are visible in Fig. 8(b). As expected at the increasing of the length, thefirst resonance decreases, shortening the frequency range in which aneventual lumped element approximation of the cable would be valid.The position of the injecting clamp along the cable has also effect on

the terminal voltages. Fig. 9 shows the transient voltage vDM(t) at theleft termination for three different cable’s lengths L = 1, 5, and 10 mwhen a double exponential voltage vSH(t) is applied at d = 0:2L andd = 0:8L. The voltage waveform is [22]

vSH(t) = V0(e�t=t

� e�t=t ) (2)

where V0 = 760 V, t1 = 27 ns, and t2 = 17 ns that has a peak valueVpk = 130 V, time-to-peak tpk = 21 ns and time-to-half-value thv =58 ns. The closer the clamp is to the termination, the higher is the ampli-tude of the induced voltages at this termination. For the same lengthsand for the same distances d of the clamp from the left end, Fig. 10shows the transient behavior of vCM(t).

(c)

Fig. 9. v (t) for: (a) L = 1 m, (b) L = 5 m, and (c) L = 10 m.

VI. CONCLUSIONS

By means of an equivalent circuit, the effects due to a localizedcurrent injection on the external shield, on the induced common anddifferential mode voltages at the twinax terminations are studied bothin frequency and time domain. These induced voltages are studied asfunction of the shield’s grounding, of the cable’s length and of the geo-metric and electrical symmetry of the cable.


Fig. 10. v (t) for: (a) L = 1 m, (b) L = 4 m, and (c) L = 10 m.

ACKNOWLEDGMENT

The authors thank R. M. Rizzi for his contribution in performing themeasurements.

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Grounding, Unbalancing and Length Effects on Termination Voltages of a Twinax Cable During Bulk Current Injection