Two-Wire Shielded Cable Modeling for the Analysis of Conducted Transient Immunity Spartaco Caniggia EMC Consultant, Viale Moranti 7, 21 Bareggio (MI), Italy spartaco.caniggia@ieee.org Francesca Maradei DIAEE, Sapienza Univ. of Rome, Via Eudossiana 18, 184 Rome, Italy fr.maradei@ieee.org Abstract A SPICE model is proposed to simulate a typical boxto-box structure when the interconnect is a two-wire shielded cable. The goal is to carry out a very simple circuit that can be easily implemented by any user interested in investigating conducted transient immunity of a parallel-pair (twinax) or twisted-pair shielded cable. The model is based on the classic cable representation as a cascade of lumped element circuit cells obtained considering the cable as a three-conductor transmission line (TL) above a reference plane. Particular attention is here addressed to properly define the mutual inductive coupling between the wires and the shield in order to take into account the penetration through apertures proper of real braided shields. The model is suitable for direct transient analysis and allows modeling any kind of cable terminations. Keywords-Electrostatic discharge; immunity; shielded cable; SPICE I. INTRODUCTION There are many solutions to protect a box-to-box or systemto-system structure when subjected to interfering disturbances such as SURGE, EFT, and ESD. When using shielded cables, it is a common practice to connect the cable shield to the box in order to limit the noise introduced into the internal circuits of the cable. Suitable fixes for EMI reduction depend on how grounding is realized, and specifically on the impedance of the connection for grounding the cable shield: the lowest is the grounding connection impedance the better is the grounding. Box-to-box structure is widely used as setup configuration to test the conducted immunity of shielded cables. Several SPICE models have been presented over the years for coaxial cable connections [1]-[7]. In case of two-wire shielded cables, two compact models are available in literature [4]-[5], both derived by the multiconductor transmission line (MTL) theory, and both based on the separation of the internal and external parts of the shield. Due to this separation, suitable networks are needed to allow modeling of whatever termination. The circuit model proposed in [4] takes into account frequency dependent losses, runs in frequency domain, and time domain results are obtained by Inverse Fourier Transform (IFT). The need of IFT is the main limitation of this model since non linear loads cannot be included in the simulation. The model proposed in [5] is valid under the assumption of negligible losses and is suitable for direct time domain analysis. The equivalent circuit involves several controlled sources to take into account the coupling between the external and internal parts of the cable. The main drawback is that the equivalent circuits for modeling the analytical expressions of the controlled sources are quite complex and only expert users can deal with them. Grounding conductor Box 1 Box 2 Shielded cable V o PCB 1 PCB 2 + - V i Figure 1 Box-to box structure with a two-wire shielded cable connecting PCB 1 and PCB 2. Grounding conductor The goal of this paper is to provide a simple SPICE model to simulate the box-to-box structure when the interconnect is a two-wire shielded cable (i.e., twinax or twisted-pair cable). The configuration of interest is schematically shown in Fig. 1, where the noise produced by an EMI current flowing through the grounding conductor of box 1 is modeled by the voltage source V i. The SPICE circuit that is here proposed is extremely simple and can be easily implemented by any user interested in investigating conducted transient immunity of two-wire shielded cables. The model is based on the classic subdivision of the cable in a cascade of lumped element circuit cells. However, contrary to the usual shielded cable representation based on the separation in internal and external transmission lines coupled through the shield transfer impedance, the cable is here seen as a three-conductor TL above a ground reference. Particular attention is addressed to properly define the mutual inductive coupling between the wires and the shield in order to take into account the penetration through apertures proper of real braided shields. The main limitation of the proposed model is the number of electrically short cells required to simulate interferences up to the maximum frequency of interest. However, in practical immunity test cases, cables are not very long (i.e., some meters) and interfering disturbances of interest (i.e., SURGE, EFT and ESD) are characterized by a maximum frequency less than 1GHz. Therefore, the number of cells required for good accuracy is quite low. The main advantages of the proposed SPICE model are the simplicity, the suitability for direct time domain analysis and the ability to account for arbitrary cable terminations (even non-linear) without any adaptation network as described in [4].
Wire #1 Wire #2 Shield R w1 R w2 R s L w1 L w2 L s C 1s C 12 C 2s C s Inductive Mutual Coupling M 12 L w1 L w2 M 1s M 2s L w1 L s L w2 L s where L t1 and L t2 are the shield transfer inductances for wires 1 and 2 respectively. The derivation of (1) in case of a coaxial cable can be found in [9]. For an ideal cable shield, L t1 = L t2 =, and (1) reduce to the formulas provided in [1]. In practice, the transfer inductances L t1 and L t2 are unknown and no analytical formulas are available. However, they can be derived as described in the next section from the shield transfer impedance measurement. Figure 2 Equivalent lumped circuit of a two-wire shielded cable above a reference ground seen as a MTL with three conductors above ground. R and L per-unit-line parameters R w1, L w1 R w2, L w2 C 12 M 1s M 12 M 2s R s,l s Infinite ground plane Figure 3 Electrical parameters of the lumped circuit model of a two-wire shielded cable above a reference ground. II. SPICE CIRCUIT OF TWO-WIRE SHIELDED CABLES The goal of this section is to present a SPICE model of a two-wire shielded cable above a reference ground easy to implement by anyone interested in investigating the conducted immunity to SURGE, ESD and EFT through a fast prediction tool. The two-wire shielded cable above a reference ground can be seen as a three-conductor transmission line above a metallic ground plane. In case of an electrically short cable (i.e., L cable λ/1=3/f MHz, where λ is the wavelength in meters and f MHz is the maximum frequency of interest in MHz), the three-conductor TL can be modelled by the lumped equivalent circuit shown in Fig. 2. The electrical parameters of the lumped equivalent circuit are visualized in Fig. 3. Since the shield operates an electrostatic separation between the internal and external parts, the wires-to-ground capacitances are not present. The cable capacitances as well as the inductances L w1, L w2, L s and M 12 can be easily calculated as described in [8] for a general MTL. Particular attention needs to be addressed to the mutual inductive couplings M 1s and M 2s between the inner wires and the shield. In fact, in order to take into account the penetration through apertures of realistic cable shields, these mutual inductances are given by: M = L L (1a) 1s s t1 M = L L (1b) 2s s t2 C per-unit-line parameters ε r =1.77 C 1s C 2s C s Infinite ground plane III. MEASUREMENTS OF REAL SHIELD COMMON AND DIFFERENTIAL MODE IMPEDANCES In case of real shields, L t1 and L t2 can be derived from the common and differential mode transfer impedances Z t_cm and Z t_dm that can be measured according to the procedure described in [11]. The measurement setup is schematically shown in Fig. 4a, and the corresponding equivalent SPICE circuit in Fig. 4b, where the left end of the inner wires is connected to ground while the right end is left open. These termination conditions are used for deriving both transfer impedances Z t_cm and Z t_dm. The common mode (CM) transfer impedance Z t_cm can be simply measured with the same method used for coaxial cable by joining the two wires at both cable ends, injecting a current I sh on the cable shield according to a setup reproducing a triaxial structure, and measuring the common mode voltage V cm between one end of the two wires and the shield so that: Faraday cage μv Controlled sources: VFT1=Z t1 I sh VFT2=Z t2 I sh R sg1 V ( f) L +L Zt_cm ( f ) = =R +j ω (2) I R sout I d (,f) R w R w L sout cm t2 t1 t sh( f) 2 G Current probe x L w1 L w2 M 12 I sh Vsource I sh (x,f) Z d=2r w+jω (L w1+l w2-2m 12) VFT1 VFT2 Figure 4 Setup for indirect measurement of differential mode transfer impedance Z t_dm with a current probe, and its equivalent circuit for SPICE. Note that: Z t1=r t+jωl t1 and Z t2=r t+ jωl t1 I d R sg2 R c Vc Open circuit V cm
The differential mode (DM) transfer impedance Z t_dm can be obtained by joining the two wires at each end of the cable and performing the two following measurements: - Measurement of the ratio I d (f)/i sh (f) versus frequency, where I d (f) is the internal loop current of the two wires (see Fig. 4a); - Measurement of the loop impedance of the two wires Z d (f) versus frequency. The differential mode transfer impedance is then derived as: r shield =3 mm d wire =1 mm ε r =1.77 Z( f) I ( f) Z ( ) - ( ) d d t_dm f = = jω Lt2 Lt1 cable Ish ( f) (3) h line =1 cm r wire =.5 mm Cable lenght=1 m Infinite ground plane Indirect measurement of Z t_dm needs two measurements but provides excellent common-mode rejection by using a current probe to measure I d (f). For both measurements, the cable must be electrically short. Therefore we can use I d (f)=i d (,f) and I sh (f)=i sh (,f). R 1ss V 1ss R 1sl R 12s V12s R 12l IV. SPICE MODEL VALIDATION To validate the proposed SPICE model, the cable configuration shown in Fig. 5 was considered assuming the following parameters: Resistance between wires and shield R 1ss =R 2ss =R 1sl = R 2sl =5Ω for both source and load ends; Resistance between the two inner wires R 12s = R 12l =1Ω for both source and load ends; Resistance between shield and infinite ground plane R gnds = R gndl =Ω for both source and load ends; Per unit length (p.u.l.) resistance of internal wires R w1 = R w2 =Ω/m; P.u.l. shield transfer resistance R t =Ω/m; P.u.l. shield transfer inductances L t1 =.8nH/m, L t2 =1.2nH/m. The shield transfer inductances L t1 and L t2 were derived by measurements as described in Section III. The common and differential mode transfer impedances obtained with the above mentioned values of R t, L t1 and L t2 are shown in Fig. 6. It can be noted that the obtained plot is very similar to the measurements shown in Fig. 6.29 of reference [11]. The first validation was performed comparing the results of the proposed low frequency (LF) SPICE model with those obtained through the high frequency (HF) compact model presented in [4] for a cable of length l cable =. The LF SPICE circuit was obtained by cascading 3 cells. Frequency domain simulations were carried out adopting a unit voltage source exciting the cable shield at one end as shown in Fig. 5b. The voltages across the termination resistances at the source end and the current induced on the cable shield are shown in Figs. 7-8. It can be noted a very good agreement for frequencies below 9MHz. Above 9MHz (i.e., high frequency range) the lumped model fails since the section length chosen to discretize the cable is not any longer electrically short. V source 1 1 1 1u 1u 1u 1n 1n R 2ss R gnds I gnds 1 cell Shielded Cable Cable Figure 5 Two-wire cable cross section, and terminations used for the model validation. Transfer impedance (Ohm/m) Common mode transfer impedance Z t_cm Differential mode transfer impedance Z t_dm R 2sl R gndl 1n 1 1 1 1k 1k 1k 1M 1M 1M 1G Figure 6 Simulated common- and differential-mode transfer impedance of a two-wire shielded cable with transfer inductances L t1=.8nh/m, L t2=1.2nh/m derived from measurements.
1 1.1.1 1u.1.1 1u 1u 1n 1n Voltage V 1ss across the load resistance R 1ss (V) HF SPICE model [4] LF SPICE model 9 MHz LF HF 1 1 1 1k 1k 1k 1M 1M 1M 1G Voltage V 12s across the load resistance R 12s (V) HF SPICE model [4] LF SPICE model LF HF 9 MHz 1 1 1 1k 1k 1k 1M 1M 1M 1G 9 MHz Figure 7 Comparison between results obtained with the proposed LF SPICE model and with the HF model [4]: voltages at the source end across resistances R 1ss and R 12s. Current I gnds on the cable shield (A) 1k 1 1 1.1.1 LF 9 MHz HF contains the receiver. The experimental test setup is shown in Fig. 9. The ESD generator MiniZap loaded at 5-kV voltage was used to reproduce typical ESD events. The EMI occurring in the shielded foil twisted pair (SFTP) cable was measured by the current probe Tektronix CT-1 connected to a digital oscilloscope characterized by 1-GHz bandwidth and placed inside a shielded enclosure in order to avoid coupling with the ESD radiated field. Common-mode (CM) interference was measured introducing the two wires of the SFTP cable through the small hole of the current probe, while differential-mode (DM) interference was measured in the same manner but using one wire only. In the following, the interference is represented in terms of induced voltage on the receiver, obtained multiplying the measured current for the CM and DM resistances (i.e., 5 Ω and Ω, respectively). The reference ESD current waveform as provided in the IEC standard [14] has an 85-MHz bandwidth. For the considered 1-m long cable, 3 unit cells provide a suitable approximation up to 1 GHz. The ESD gun used in real testing has been modeled using the ESD generator equivalent circuit provided in []. The induced CM and DM voltages at the receiver end are shown in Figs. 1-11. It is worth noting that the overall behaviour of the calculated and measured CM and DM induced currents is pretty much the same (note that the oscillations depend on the length and position of the green wires simulated as TL with 25-Ω characteristic impedance and 3.3-ns time delay). In addition, not significant differences can be observed in the peak-to-peak values nevertheless the complexity of the setup to be simulated. CM effect due to short pigtails was modelled by a 5-nH inductance at both ends of the cable shield. DM effect due to unbalancing causes was modelled by a 1-μH inductance on one wire at source end. Note also that the height of the line (45cm) from the reference plane is not electrically short for frequencies near 1GHz. Grounding and dissymmetry effects are further investigated in the following.. HF SPICE model [4] LF SPICE model.2m 1 1 1 1k 1k 1k 1M 1M 1M 1G Figure 8 Current on the cable shield I gnds calculated by the proposed LF SPICE model and the HF model [4]. Discharge point MiniZap ESD generator The SPICE model was also validated experimentally by performing a transient analysis in case of an electrostatic discharge (ESD) interference. The configuration used as test is the same that was used in [13], and consists of a two-wire shielded cable of length, placed at 45cm from the ground plane, and connecting differential driver/receiver RS422, both placed inside OPMC shielded enclosures of size 5cm 86cm 3cm. Both the enclosures are positioned on isolating stands of 1-cm thickness, and grounded by green wires. RJ45 shielded connectors are used to link the cable with PCBs. The ESD event in contact mode is assumed to occur on box 1 which Driver enclosure Grounding OPM Flat cable used as ESD strap connected to the metallic floor Figure 9 Experimental setup of ESD testing on a two-wire shielded cable connecting two shielded boxes.
V esd_cm = 47 V Measurements L probe Box 1 Box 2 Shielded cable PCB 1 PCB 2 pigtails L shin L shout 2 ns/div ESD L gnds C gnds C gndl L gndl 45 3 - Common mode voltage (V) V esd_cm = 46 V -3 2 4 6 8 1 (s) Figure 1 Common mode voltage at the cable source end induced by an ESD event occuring on box1: measurements, and simulations. 4.8 3.2 1.6-1.6 V esd_dm =7 V 2 ns/div Differential mode voltage (V) V esd_dm =5.3 V SPICE Measurements SPICE -3.2 2 4 6 8 1 (s) Figure 11 Differential mode voltage at the cable source end induced by an ESD event occuring on box1: measuremenets, and simulations. Metal reference ground: ideal plane Figure 12 Grounding configurations investigated by SPICE simulations in case of an ESD event as EMI source. The SPICE model shown in Fig. 5 was also used to quantify the influence of different grounding practices and undesired dissymmetry effects on wires. A cable of length l cable = was considered and 3 unit cells were cascaded for deriving the equivalent circuit. Assuming an ESD event occurring on Box 1 (see Fig. 12), the following configurations were investigated: 1. Boxes perfectly connected to ground (L gnds = L gndl = and C gnds =C gndl =); 2. Boxes connected to ground by cord (L gnds =L gnds =1μH and C gnds =C gndl =1pF); 3. Boxes grounded by cord and cable shield connected to boxes with pigtails (L sin =L sout =5nH); 4. Boxes grounded by cord, with pigtails and a probe inductance for current measurement on wire 1 (L probe =1nH). The comparison among the different configurations was carried out pointing the attention to the ESD current at discharge point, and to the CM and DM voltages induces across the load at the source end. The ESD currents at discharge point are shown in Fig. 13. In case 1, the ESD current has the same rise time of the reference IEC current for 5kV discharge according to the expectations being L gnd =. This result confirms also that 3 cells are an appropriate approximation for the transient simulation. In cases 2, 3, 4, we can note the same ESD current waveform and a lower first peak. Long oscillations for all cases are due to the 1μH strap inductance of the ESD gun []. The CM and DM voltages induced across the load at the source end are shown in Fig. 14. Note that case 1 gives too low voltages to be distinguishable. The peak-to-peak common and differential mode voltages obtained for the four grounding conditions are summarized in Tab. I, and the following comments can be drawn: When the structure is perfectly connected to the reference ground and cable shield connected to box by a 36-degree contact, the CM and DM noise is very low in the order of μvolt. With boxes isolated (1pF) and connected to ground by a cord of 1-μH inductance, the CM and DM noise rise to some volt.
ESD current at discharge point (A) 2 Cases 2,3,4 IEC 1 Common mode voltage at source end (V) 7.5 Cases 3,4 24 V V s_cm 5 Case 1 1 2 3 4 ESD current at discharge point (A) 2 1 Cases 2,3,4 5 Case 1 1 2 3 4 Figure 13 ESD current at discharge point: full scale, zoom of the peak currents. Table I - Peak-to- peak common and differential mode voltages obtained for the different grounding conditions V esd_cm V esd_dm Case 1: good shielding 35μV 12.5μV Case 2: boxes isolated 2.1V.67V Case 3: boxes isolated + pigtail 24V.59V Case 3: boxes isolated + pigtail + L probe 21V 2.25V With cable shield connected to box by pigtail of 5nH, and boxes connected to ground with cords of about 1μH, the CM noise becomes 1 times higher and the DM noise does not change. With cable shield connected to box by pigtail, boxes connected to the ground by cords, and a dissymmetry due to a probe inductance of 1nH on wire 1, the DM noise becomes 4 times higher and the CM noise does not change. V. CONCLUSIONS The proposed SPICE model of a two-wire shielded cable is suitable for both frequency and direct time domain simulations and for any kind of load conditions at both ends (including nonlinear). The common- and differential- mode transfer impedance concept have been used to derive an RLC network that simulates an electrically short segment of the cable (unit cell). A cascade of cells can appropriately simulate ground loop coupling produced by conducted disturbances such as ESD, EFT and SURGE. The bandwidth of these noises (about 1GHz for ESD, 2MHz for EFT, 2MHz for SURGE) determines the number of unit cell to be used. This number may be much less than 1 in many cases of practical interest where cable lengths are some meters. Problems caused by various grounding IEC -7.5 Case 2-2 4 6 8 1 Differential mode voltage at source end (V) 1.5 Case 4 2.25 V.75 V s_dm -.75 Cases 2, 3-1.5 2 4 6 8 1 Figure 14 Simulated ESD induced effects in a two-wires cable: common mode voltage V S_cm and differential mode voltage V S_dm. topologies such as non-appropriate cable connection to box (i.e., use of pigtails), or dissymmetry in the differential circuit, can be quickly and effectively simulated. REFERENCES [1] S. Caniggia, L. Vitucci, M. Acquaroli, A. Giordano, Measurements and SPICE model for data signal lines under electrical fast transient test, EMC EUROPE 2, Brugge, Belgium, Sept. 2. [2] S. Caniggia, F. Maradei, Equivalent circuit models for the analysis of coaxial cables immunity, IEEE Int. Symp. on Electromag. Compat., Boston, USA, Aug. 23. [3] A. Orlandi, Circuit model for bulk current injection test on shielded coaxial cable, IEEE Trans. on Electromag. Compat., vol. 45, no. 4, Nov. 23, pp. 62-6. [4] S. Caniggia, F. Maradei, SPICE-Like Models for the Analysis of the Conducted and Radiated Immunity of Shielded Cables, IEEE Trans. on Electromag. Compat., Vol. 46, no.. 4, Nov. 24 [5] G. Antonini, A. Orlandi, SPICE Equivalent circuit of a Two-Parallel- Wires Shielded Cable for Evaluation of the RF Induced Voltages at the Terminations, IEEE Trans. Electromag. Compat., vol. 46, no. 2, pp. 189-198, May 24. [6] H. Xie, J. Wang, R. Fan, and Y. Liu, SPICE Models for Prediction of Disturbances Induced by Nonuniform Fields on Shielded Cables, IEEE Trans. Electromag. Compat., vol. 53, no. 1, pp. 185-192, Feb. 211. [7] H. Xie, J. Wang, R. Fan, and Y. Liu, SPICE Models to analyze Radiated and Conducted Susceptibilities of Shielded Coaxial Cables, IEEE Trans. Electromag. Compat., vol. 52, no. 1, pp. 185-192, Feb. 21. [8] Clayton Paul, Introduction to Electromagnetic Compatibility, second edition, John Wiley and Sons, 26 [9] S. Caniggia, F. Maradei, Signal Integrity and Radiated Emission, John Wiley and Sons, 28 [1] Henry Ott, Electromagnetic Compatibility Engineering, John Wiley & Sons, 29 [11] P. Degauque, Joel Hamelin, Electromagnetic Compatibility, Oxford University Press, 1993 [12] SPICE, Spectrum Software, www.spectrum-soft.com. [13] S. Caniggia, F. Maradei, Interference in shielded foil twisted pair (SFTP) cables due to ESD, IEEE 27 International Symposium on Electromagnetic Compatibility, Honolulu (USA), July 9-13, 27, pp. 1-5. [14] IEC 61 Part 4-2 Ed.2: Testing and Measurement Techniques Section 2: Electrostatic Discharge (ESD) Immunity Test, 28-12 [] S. Caniggia, F. Maradei, Circuit and numerical modeling of electrostatic discharge generators, IEEE Trans. Industry Applications, vol.42, no.6, Nov./Dic. 26, pp. 135-1357.