Near-field coupling model between electronic systems and a transmission line

Christelle Leseigneur#1, Priscila Fernández López#2, Christian Arcambal, David Baudry#, Anne Louis#

#IRSEEM / ESIGELEC, Avenue Galilée, 76801 Saint Etienne du Rouvray – France

1 christelle.leseigneur@esigelec.fr, 2 p.fernandez-lopez@esigelec.fr

Abstract— This paper presents an analysis of radiated

electromagnetic disturbances between electronic devices (parasitic emission source) and a transmission line. The study aims to model the coupling and for this purpose, two concepts are combined: the emission source is modelled by an array of elementary dipoles (electric and magnetic) and the induced voltage in the transmission line is calculated from the equivalent sources radiation by two different approaches. The first one is totally analytical and is based on the transmission line theory and Taylor model. The second one uses the insertion of equivalent sources into an electromagnetic simulation tool. To validate our model we apply it for two cases: a passive system and an active one disturbing a transmission line.

I. INTRODUCTION To improve susceptibility of electronic systems, it becomes

essential to consider electromagnetic coupling or crosstalk between electronic devices integrated in a close environment or into the same equipment. To achieve these requirements, it can be necessary to study the parasitic voltages and currents induced in lines of a Printed Circuit Board (PCB) by other electronic devices during the design and integration stages.

In our study, we consider the near-field coupling, representing an often encountered case of interference between closely situated electronic systems. We especially focus on the case of a device in front of a line of another board. For this purpose, we can use, for example, different numerical methods such as the Finite-Difference Time-Domain (FDTD) [1] or the Method of Moments (MoM) [2]. However, these methods have the drawback of requiring long simulation time and significant computing resources. Consequently, we have developed a procedure in order to obtain the coupling that is totally analytical and that allows us to obtain the responses of the line due to an external excitation quickly and with ordinary computing resources. This procedure is composed of two steps: the first one consists in modelling the radiation of a component by equivalent sources (electric and/or magnetic dipoles) [3]-[4]. The second step uses the Taylor model [5] and the set of modelling sources to calculate induced voltages in the victim line. The Taylor model has been already validated using the radiation of three electric dipoles [6].

In this paper, we first present the near-field emission model and the near-field measurement necessary to build it. We deal

with the different parameters of the model and the way to obtain them. Then, we explain how to calculate the voltage induced in the line with transmission line theory and the Taylor model. The procedure is finally applied on a passive device (a Wilkinson power divider) and on an active one (an oscillator). A comparison between simulated results and measurements is shown. We also present an alternative way to calculate induced voltage by the insertion of dipole sources into an electromagnetic simulation software tool. This procedure could be applied to other configurations different from those that Taylor model can solve.

II. RADIATED EMISSION MODEL AND NEAR-FIELD MEASUREMENTS

The model is based on a set of equivalent sources (electric and magnetic dipoles) which radiates the same electromagnetic fields as the component to model [3],[4]. The sources are placed on a XY-plane considered as the upper surface of the component. One model is calculated for each frequency and corresponds to a specific working of the device. Given the topology and the frequency of the device to model, some of the parameters of the dipoles are preliminary fixed by the user: the number, their positions and their lengths. The unknown variables to be determined are consequently the orientations θe and the currents Ie (magnitude and phase) for the electric dipoles and the orientations θm and the currents Im (magnitude and phase) for the magnetic dipoles. To build the model, cartographies of near tangential electric and magnetic fields are required.

An analytical calculation of the field radiated by electric and magnetic dipoles can be used to model the circuit. Another alternative can be used to determine the radiated field. Indeed each electric and magnetic dipole can be designed in commercial electromagnetic software, such as HFSS (High Frequency Structure Simulator from Ansoft) based on finite element method and commonly used in industry. With this numerical approach we can simulate the field radiated by a circuit without designing it. This will be discussed in section III.B.

A. Mathematical Analysis The radiation model is built from the theoretical

expressions of the fields radiated by an electric and a magnetic

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dipole. These fields are calculated from the magnetic vector potential and the electric vector potentialA

rFr

, respectively [3],[7]. As the total electric and magnetic fields are given by the contribution of each elementary dipole, the pr e is expressed as systobl m a matrix em:

, ,

, ,

sincossincos

(1)

where [Ex], [Ey], [Hx] and [Hy] are the near-field tangential components (in amplitude and phase) at a certain distance d above the device. Each α ij depends on the fixed parameters of the model (frequency, length and position of the dipoles), s/2 is the total number of equivalent dipoles and r/4 is the number of points where the field is estimated.

Thus, if fields are known, currents and orientations can be determined. Indeed the least-square inverse method and a division element by element are used to calculate the orientations θe and θm. Next, to obtain the currents, a new matrix [β] is defined, whose elements depend on the fixed parameters of the model and also on the orientations θe and θm.

, ,

, ,

(2)

The least-square inverse method is used again to evaluate Ie and Im.

Once the model is built, we can calculate the electromagnetic field at any other distance above the height where cartographies were done.

As mentioned, to determine all the parameters of the equivalent sources, near-field cartographies of fields are necessary. To get them, near-field measurements are carried out.

B. Near-Field Measurements To obtain the tangential electric and magnetic field

cartographies necessary to build the model, an automated near-field test bench is used. It is based on a single loop for magnetic field and on an electric dipole for electric field [8]-[10]. A 180° hybrid coupler and a low noise amplifier are linked to probes to improve sensitivity and decrease some measurement disturbances.

The phase of fields required for the proposed model is measured with a vector network analyser (or a spectrum analyser in a more complex measurement procedure)[4], [11].

III. NEAR-FIELD COUPLING ONTO A TRANSMISSION LINE The fields predicted by the emission model are then used to

evaluate the disturbances generated by the radiation of an electronic circuit into another one. The key point of this model is that with measurements made on the XY plane at one

particular height, it is possible to evaluate the near field at any other point in space above the XY plane. This avoids making new measurements at corresponding planes.

In this study we consider a transmission line as the victim.

A. Analytical coupling model - Taylor Our approach consists in calculating the disturbance

induced into a transmission line due to the field emitted by different kinds of electronic systems. As previously presented, the disturbance source is replaced by an array of dipole sources. This array is used to calculate the radiated field excitation which is then included in the Taylor model [5], in order to determine the terminal responses of the line. We consider a lossless transmission line structure which is capable of guiding a Transverse ElectroMagnetic (TEM) wave. One of the most important properties of a TEM wave on a transmission line is the fact that the electromagnetic fields can be uniquely related to the voltage and the current via Maxwell's equations. Then we can describe the voltage V’(x) and the current I’(x) by a pair of linear differential equations (T elegrapher's Equation) [12]:

0

0(3)

The capacitor C’ (F/m) represents the per-unit-length capacitance, L’ (H/m) is the per-unit-length inductance and ω is the angular frequency.

Our aim is to calculate the terminal voltages V0 and VL induced by an electronic circuit placed next to the line as shown in Fig. 1.

Fig. 1. A radiation electronic circuit above a transmission line with terminations Z0, ZL.

With the help of transmission-line theory, the line is represented by small sections dx, with the per-unit-length parameters as explained in equation (3). The coupling due to an external excitation on each section of the line can be modelled by a voltage source Vs’ and a current source Is’. The voltage source represents the inductive coupling generated by the exciting normal component of magnetic field Hn

e between the ground line, i.e. plane and the

. (4)

The exciting field is the contribution of the incident wave and the one reflected by the ground plane.

The capacitive coupling can be accounted by the exciting tangential component of the electric field Et

e between the line and the ground plane. It induces an accumulation of positive

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and negative charges on the surface of the cable and the ground plane. The following equation represents the per-unit-l ese charges. ength current due to th

. (5)

From equations (3) to (5) we can deduce the per-unit-length equivalent circuit for the coupling (Fig. 2).

Fig 2. Equivalent circuit including the coupling of an excitation field into a section dx of the transmission line

To take into account the field coupling, the transmission-line equations (3) are modified by inserting the excitation t s ferms (4) and (5) a ollows:

(6)

In the following we use an approximated solution of (6) as a first estimation. It is limited to an electrically short line (L << λ) and termination impedances Z0/L close to the characteristic line impedance ZC. Equations (4) and (5) become then:

·· (7)

in which A=h*L is the area between the centre axis of the line and the ground plane. This simplification is applied for the whole transmission line (not for each section dx). Then the simplified equivalent circuit for the transmission line is shown in Fig. 3.

Fig. 3. Equivalent circuit of the coupling in an electrically short and matched transmission line due to an excitation field

In this case, the voltage due to an electromagnetic excitation at the level of terminal loads Z0/L, can be expressed as follo s w

· ·

· ·

(8)

where, Ete is the exciting tangential electric field, µ0 is the

magnetic permeability in vacuum, Hne is the exciting normal

magnetic field and h the distance between the centre of the wire and the ground plane [13].

According to the analytical expression (8), it is possible to calculate the voltage at both terminals of the line. To do so the exciting electric Et

e and magnetic Hne fields between the

transmission line and the ground plane must be previously determined. In our case the incident field is due to an array of dipole sources and the reflected field is due to the image of the array of dipole sources (using Image Theory) (Fig. 4).

I'(x) L ' dx⋅ 'SV dx⋅

V’(x)

Fig. 4. Image Theory for an electric and a magnetic dipole sources above a perfect electric conductor

According to the Image Theory, horizontal electric and magnetic dipoles at a distance h from a ground plane are equivalent to two dipoles symmetrically located above and below the ground plane. The electric image dipole is counter-directed otherwise the magnetic image one is equally-directed.

Theoretically, the Taylor model is valid for a uniform field distribution. As our exciting field is non-uniform, it is necessary to calculate its 2D-average value on the surface between the centre of the line and the ground plane. For a di ave to calculate: screte number N of field points we h

; ∑ ; (9)

where etE and e

nH are the mean values of the exciting fields and xi is a point on the surface defined by the transmission line and the ground plane.

B. Insertion of the emission model into HFSS Alternatively, the induced voltage can be calculated by

numerical tools; indeed the equivalent set of dipoles which models the emission of a device can be inserted into HFSS. In previous work [3],[4], both types of dipoles (electric and magnetic) were designed in the simulator and their emissions were validated comparing to theory. This numerical aspect of the emission model can be interesting when studying coupling with specific configuration e.g. use of shielding. In this section, we explain the insertion and then we will compare results with the previous analytical procedure.

An electric dipole in HFSS consists of a rectangular structure carrying a uniform current. To insert a magnetic

uivalent electric loop perpendicular to it is e expression which relates both is:

dipole, an eqconsidered. Th

(10) where Im is the magnetic current through the magnetic dipole, l is the length of the magnetic dipole, ω is the angular frequency, μ is the permeability of the material, S is the surface of the loop and Ie0 the electric current through the electric loop. The representation of a magnetic dipole into

Ie’

Ie

Perfect ground plane

h

images

2h

Im0Z Ie ImLZ'SI dx⋅ C ' dx⋅

dx Im’

jωµ0A·Hne

ZZ0

V0 jωC’A·Ete

VL

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HFSS is then an electric loop discretized into four segments (four electric dipoles) with a current value of Ie0.

To insert automatically the set of equivalent sources, a macro in Microsoft Visual Basic has been developed. It reads the parameters of the dipoles from a .txt file to design them into HFSS. The insertion algorithm is presented in [14], [15].

Usually, the set of dipoles which models a device has around two thousands of sources (depending on the dimension of the device) that makes its insertion very difficult, even impossible because of computer limitations. To overcome this problem, a reduction in the number of dipoles is done. Two thresholds on both electric and magnetic currents are defined, so, just dipoles whose current is greater than the threshold are kept for the reduced model. This entails a decrease of the insertion time and less computer memory for simulation.

IV. EXPERIMENTAL AND NUMERICAL VALIDATION In order to validate our procedure we use measurements

and electromagnetic simulations. We focus on the terminal response of the line for different electronic systems. We begin to test the coupling due to a passive electronic system, and then an active electronic system is used.

A. Passive Circuit: Wilkinson power divider The study consists in generating an electromagnetic field

with an electronic circuit and in investigating the coupling through a line above a ground plane. A Wilkinson power divider will be used to generate a local near field which excites the line.

The Wilkinson power divider built in microstrip technology (the relative permittivity of the substrate is εr=4.4 and its thickness h=1.6 mm) and working at 1 GHz is used (Fig. 5). The power divider is excited on its port 1 with an input power Pin=0 dBm, the ports 2 and 3 are matched.

Fig. 5. Wilkinson power divider

The equivalent emission model of this circuit consists of 961 electric dipoles and 961 magnetic dipoles uniformly spread on a surface of 80 mm (x) x 100 mm (y). The reduced model has 140 electric dipoles and 51 magnetic dipoles. This model is built from near-field measurements obtained at 2 mm above the divider [3].

A wire above a ground plane (Fig. 6) is used as a victim circuit and the coupling on its ports is studied. The radius of

the wire is a=0.5 mm and the distance between its central axis and the ground plane is h=0.7 mm. The line is matched. The wire is set up at 5 mm above the divider.

Fig. 6. Wire above a ground plane

To validate the analytical model and the inserted one (i.e. insertion into HFSS), we compare their results with those given by HFSS simulation of the complete system (Fig. 7, the structure of the divider is entirely designed) and measurements (Fig. 8). The comparison aims to study the voltage response variation according to the position of the line above the Wilkinson power divider.

Fig. 7. Coupling between the transmission line and the Wilkinson power divider in HFSS

During the HFSS simulation the line is placed on the y axis at 5 mm above the Wilkinson power divider and is moved along the x axis. To carry out measurements, we built a set-up (Fig. 8) using the near-field test bench presented in section II.B. It permits the displacement of the line above the Wilkinson power divider and enables us to collect the scattering parameters by means of a network analyser.

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Fig. 8. Setup to measure the coupling between the transmission line and the Wilkinson power divider with the help of the near-field test bench.

Fig. 9 presents the results obtained by measurement, by HFSS simulation of the Wilkinson power divider and the line really designed as in Fig. 7 (called HFSS), by HFSS simulation of the line and the set of dipoles instead of the divider (called HFSS inserted model) and by an analytical calculation using the set of dipoles (called Taylor model).

These traces represent the variation of the voltage at the end of the line in function of its position.

Fig. 9. Coupling obtained by measurement, HFSS simulation, inserted model in HFSS and Taylor model in function of the transmission line position.

The good accordance between the numerical simulation and the measurement allows us to validate the set up in Fig. 8.

We notice differences between the results obtained with the Taylor model and the measurements only when the line is close to the border of the micro-strip Wilkinson power divider (beyond ±30 mm). Besides a lack of precision during the measurement, we assume that the idealizations in the analytical model are responsible for the deviations at the borders. This refers especially to the ground plane present in the Wilkinson power divider, where the border effects are not fully taken into account, in contrast to the measurements.

We find some differences in level for the inserted model because of a sharp reduction in the number of equivalent sources although it can predict the variation of the disturbances. We can also note symmetry in the coupling due to the geometry of the aggressed circuit.

This example constitutes the first validation of our approach. The next one is to model the coupling between a line and an active device.

B. Active Circuit: oscillator In this section, we test the coupling between a transmission

line and an electronic circuit oscillator (Fig. 10) which consists of a quartz and some inverters. Its working frequency is 40 MHz and it is power supplied by a 9 V battery.

Fig. 10. Oscillator

The equivalent model of the oscillator consists of 961 electric dipoles and 961 magnetic dipoles uniformly spread on a surface of 60 mm (x) x 60 mm (y). The reduced model has 133 electric dipoles and 64 magnetic dipoles. This model is obtained from measurements at 2 mm above the oscillator [4].

The same victim circuit is used in this case. The wire is set up on the x axis at 5 mm above the higher component of the board and it is moved in the y direction. Fig. 11 shows the radiation model of the oscillator inserted into HFSS with the transmission line. For active circuits, it is not possible to design them into a simulator; therefore the interest is to have such a radiation model.

Fig. 11. Coupling between the transmission line and the radiation model for the oscillator.

Fig. 12 shows the comparison between measurement and the two approaches. They represent the variation of the voltage at the beginning of the line according to its position.

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ACKNOWLEDGMENT The authors wish to acknowledge the assistance and

support of Patrick Aubry, Eric Gaboriaud, Oliver Kröning and Professor Marco Leone. They would also like to thank the program entitled “EMC Platform for Embedded Applications” (EPEA) of the Aerospace Valley Network, Midi-Pyrénées & Aquitaine world competitiveness cluster, and the Haute-Normandie regional council France.

REFERENCES [1] C. Rostamzadeh, B. Archambeault, “Numerical and experimental

investigation of PCB ground-fill on radiated EMI”, IEEE Trans. on EMC, vol. 1, no. 2, pp.79-83, Aug. 2006.

[2] R.F. Harrington, Field computation by moment methods, Macmillan, New York, 1968

[3] P. Fernández López, C. Arcambal, S. Verdeyme, D. Baudry, and B. Mazari, “Near-field measurements to create a model suitable for a commercial simulation tool”, 4th Int. Conference on Electromagnetic Near-Field Characterization and Imaging (ICONIC), pp. 208-213, Taipei, Taiwan, June 2009.

Fig. 12. Coupling obtained by measurement and modelling as a function of the transmission line position.

The Taylor model can predict the disturbance created by the oscillator with slight differences. The difference between the couplings calculated by the inserted model and measurement can be explained by three reasons. Firstly, the reduction of the model can have a little influence. Secondly, as mentioned, to insert the equivalent electric loop it is necessary to discretize it into four segments (electric dipoles). Since the radiation of the discretized equivalent electric loop is slightly different compared to the radiation of the magnetic dipole, we can also have some differences. Finally, the results from our HFSS simulations are less accurate at 40 MHz than at 1 GHz, possibly due to the meshing limitations at low frequencies with the available computational resources. However we can predict a good coupling profile and the analytical model gives fast and satisfying results.

[4] P. Fernández-López, C. Arcambal, D. Baudry, S. Verdeyme, and B. Mazari, “Radiation modeling and electromagnetic simulation of an active circuit”, 7th Int. Workshop on Electromagnetic Compatibility of Integrated Circuits (EMC Compo 09), paper no. 58, Toulouse, France, Nov. 2009.

[5] C. D. Taylor, R. S. Sattewhite and C. W. Harrison, “The response of a terminated two-wire transmission line excited by a nonuniform electromagnetic field”, IEEE Trans. on Antenna Propagation, vol. E, pp. 987-989, Nov. 1965.

[6] C. Leseigneur, O. Kröning, P. Fernández López, D. Baudry, A. Louis, and M. Leone, “Analysis of transmission line coupling with a near-field excitation”, 7th Int. Workshop on Electromagnetic Compatibility of Integrated Circuits (EMC Compo 09), paper no. 62, Toulouse, France, Nov. 2009.

[7] C.A. Balanis, Antenna theory, analysis and design, John Wiley & Sons, Inc. New York, 2nd ed., 1997.

[8] L. Bouchelouk, Z. Riah, D. Baudry, M. Kadi, A. Louis, and B. Mazari, “Characterization of electromagnetic fields close to microwave devices using electric dipole probes”, International Journal of RF and Microwave Computer-Aided Engineering, vol. 18, pp. 146-156, March 2008.

V. CONCLUSION In this paper, an analytical modelling procedure for the near

field coupling into a transmission line has been presented. The use of an array of dipoles to model a radiating device and the Taylor model are the two steps to estimate the induced voltages in a line. To do so we propose the approach of the exciting field mean value. Besides, the array of dipoles modelling the circuit can be inserted into HFSS. This feature allows calculating the coupling between the circuit and the transmission line. The procedures have been validated on a passive device (Wilkinson power divider) and an active one (an oscillator) by comparison with measurements and HFSS numerical simulation for the divider.

The analytical approach is preferred since it takes a few seconds to a minute to calculate the voltage. However, the second approach can be used to calculate the coupling for more complex designs and configurations. Nevertheless, the computational time increases and it can take several hours to obtain the voltage. In spite of this drawback, it remains a good alternative to the analytical calculation.

As perspectives the model will be developed for a transmission line without load-matching restrictions.

[9] D. Baudry, A. Louis, and B. Mazari, “Characterization of the open-ended coaxial probe used for near-field measurements in EMC applications”, Progress In Electromagnetics Research, PIER 60, pp. 311-333, 2006.

[10] D. Baudry, C. Arcambal, A. Louis, B. Mazari, and P. Eudeline, “Applications of the near-field techniques in EMC investigations”, IEEE Trans. on EMC, vol. 49, no. 3, pp. 485-493, Aug. 2007.

[11] Y. Vives, C. Arcambal, A. Louis, F. de Daran, P. Eudeline, and B. Mazari, “Modeling magnetic radiations of electronic circuits using near-field scanning method”, IEEE Trans. on EMC, vol. 49, no. 2, pp. 391-400, May 2007.

[12] Polyanin, A.D., Handbook of linear partial differential equations for engineers and scientists, Chapman & Hall/CRC, 2002.

[13] C.R. Paul, Introduction to electromagnetic compatibility, Wiley Interscience, second edition, 2006.

[14] P. Fernández-López, C. Arcambal, Y. Vives Gilabert, A. Ramanujan, D. Baudry, A. Louis, and B. Mazari, “Development of a magnetic field model and insertion into a commercial electromagnetic simulator”, Turk. J. of Elec. Eng. & Comp. Sci., vol. 17, no. 3, pp. 289-300, 2009.

[15] P. Fernández-López, A. Ramanujan, Y. Vives Gilabert, C. Arcambal, A. Louis, and B. Mazari, “A radiated emission model compatible to a commercial electromagnetic simulation tool”, 20th Int. Symp. on EMC, pp. 369-372, Zurich, Switzerland, Jan. 2009.

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