A Boyer

N Nolhier
email: nolhier@laas.fr

F Caignet
email: fcaignet@laas.fr

S Ben-Dhia

S Ben Dhia

THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

Keywords: Near-field scan, radiated susceptibility, nearfield probe

The work presented in this two-part paper focuses on a prediction method of the radiated susceptibility of integrated circuit and printed circuit board from near-field scan injection, in order to anticipate risks of non-compliance due to design weakness. In Part I, a worst-case estimator of the far-field induced voltage on a PCB trace was proposed. Based on it, an estimator of the radiated susceptibility of a printed-circuit board based on near-field scan results is derived and validated through two validation case studies.

I. INTRODUCTION

EAR-field scan immunity (NFSI) [START_REF]Integrated circuits -Measurement of electromagnetic immunity -Part 9: Measurement of radiated immunity -Surface scan method[END_REF] is a powerful diagnostic tool that reveals coupling areas at the integrated circuit (IC) and printed circuit board (PCB) levels, and that helps electromagnetic compatibility (EMC) experts and designers to identify the root-cause of failures that may trigger during radiated susceptibility (RS) tests. In part I of this twopart paper, several examples of NFSI applications were presented [START_REF] Boyer | Characterization of the Electromagnetic Susceptibility of Integrated Circuits using a Near Field Scan[END_REF]- [START_REF] Wang | The PCB level ESD immunity study by using 3 Dimension ESD Scan System[END_REF]. This research work aims at providing postprocessing methods of NFSI results in order to assess RS risks at the IC and PCB levels. Part I reviewed several attempts to relate the RS level to NFSI results [START_REF] Durier | Comparison of Voltages Induced in an Electronic Equipment during Far Field and Near Field Normative Radiated Immunity Tests[END_REF]- [START_REF] Boyer | A Rigorous Method to extrapolate Radiated Susceptibility from Near-Field Scan Immunity[END_REF]. However, these attempts require preliminary RS test results or the extraction of phase information during NFSI, which make them unpractical.

The first part of this paper clarified the link between far-field (FF) and near-field (NF) coupling on a microstrip line terminated by linear loads. We demonstrated that the precise FF-induced voltage cannot be determined from NFSI results, but a worst-case estimator of the FF-induced voltage can be derived. This may be sufficient for RS risk assessment. The proposed approach relies on accurate knowledge of the field produced by the NF injection probes. It can be obtained by a proper calibration process, which was described and validated in Part I. However, the proposed approach is not perfectly adapted to RS testing, which aims at determining the amount of radiated disturbance that leads to the failure of an electronic device. Moreover, practical electronic systems embed non-This work was supported by the Nanoscan project (CNES No. 200111/00) sponsored by the French National Centre for Space Studies (CNES). linear functions and radiated disturbance simultaneously illuminates several traces of PCB. The effect of this simultaneous coupling cannot be predicted with precision from NFSI results because of local coupling with the NF probe, as pointed out in [START_REF] Pommerenke | Application and Limits of IC and PCB scanning methods for immunity analysis[END_REF].

The second part of this paper addresses these issues and proposes two practical studies to evaluate the impact of these limitations on RS risk assessment. In Section II, the NF-based FF coupling estimator is revised to derive an estimation of the RS level from NFSI results. The underlying assumptions are emphasized. In Section III, the estimator is amended to respond to a practical issue in NFSI testing: determining the maximum excitation power to ensure that the NFSI test is representative of RS test limits. Section IV describes the two case studies (first at the IC level, then at the PCB level) dedicated to validation of the proposed estimator. Finally, results are presented in Section V, where RS measurements in gigahertz transverse electromagnetic (GTEM) cells are compared with the proposed NFSI-based estimator.

II. ESTIMATION OF RADIATED SUSCEPTIBILITY FROM NEAR-FIELD SCAN INJECTION

A. Theoretical Formulation

Let us consider a straight microstrip line of length L terminated by two loads and one of them (Load 1) is an IC input whose susceptibility to radio frequency (RF) disturbance is investigated. The line is excited by harmonic radiated disturbances: either FF disturbance, i.e. plane wave illumination with random angles of incidence and polarization, or NF injection, i.e. an E or H-field probe placed in an arbitrary position above the line. The position of the problem is described in Fig. 1. The purpose is to estimate the RS level from NFSI results, i.e. to determine the minimum amplitude of the incoming plane wave that may induce a failure, here in Load 1. Certain assumptions are made about the nature of the termination Load 1. The impedance is assumed to be linear or quasi-linear, i.e. it does not depend on the induced voltage across the load. In practice, this assumption is valid for IC pins as long as internal electrostatic discharge (ESD) protections are not triggered. However, the internal function that relates the load behavior to the input RF voltage may be non-linear. A failure is triggered if the amplitude of the voltage across the load VL1 exceeds a limit VFail. This model supposes that the failure depends mainly on the RF voltage induced on only one trace. Due to local coupling of the NF injection, the effect of simultaneous radiated coupling on several traces cannot be reproduced during NFSI testing. The risk is overestimation or underestimation of the RS level from NFSI results, depending on how the different coupling contributions combine. 2) defines a cut-off frequency between the low and high frequency regimes of the line illuminated by a plane wave. Below 𝑓 𝐶 , the line portion on which the incoming wave couples is electrically short, so all this line portion is illuminated in phase. Above 𝑓 𝐶 , this line portion becomes electrically long and the incoming wave is not in phase along it.

𝑓 𝐶 = 𝑐 0 2𝜋𝐿 ( √ 𝜀 𝑒𝑓𝑓 -1) (1 - √𝜀𝑒𝑓𝑓 𝜀 𝑟 ) -1 (2)
In the case described in Fig

𝐸 𝑚𝑖𝑛 𝐹𝐹 ≥ 1 2 ( 1 𝐸 𝑍 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅ 𝜀 𝑟 √ 1+( 𝑓 𝑓 𝐶 𝜀 𝑟 √ 𝜀 𝑒𝑓𝑓 ) 2 + 1 𝜂 0 𝐻 𝑌 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅̅ √1+( 𝑓 𝑓 𝐶 ) 2 ) -1 (4) (3)
In this estimator of the RS of a PCB line to a plane wave illumination, the contributions of E and H-field couplings are clearly visible and can be compared. Let ZN be the ratio given by [START_REF] Boyer | Modelling of a Mixed-Signal Processor Susceptibility to Near-Field Aggression[END_REF], which is the normalized wave impedance. The practical interest of this ratio is that it points out the predominance of E or H-field coupling contributions to the induced failure during the RS test. If ZN > 1, the contribution of H-field coupling dominates, while the E-field coupling contribution dominates if ZN <1.

𝑍 𝑁 = 𝐸 𝑍 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅ 𝜂 0 𝐻 𝑌 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅̅ (5)

B. Practical Implementation of the Estimation Method

Equations ( 1), ( 2) and ( 4) have been derived in the case of a straight line. In practical PCB traces or package interconnects, lines can be bended. They are composed of several portions with various directions on which different field components can couple. Thus, the E and H field components of the incoming disturbance couple on different line portions, whose lengths are not necessarily equal to the total length L of the line. The expressions of Section II.A can be extended to the case of a bended line if a new term is introduced: the coupling length LC, which is the line portion on which a field component can couple. Except for a straight line, the coupling length may be different for each field component. For bended microstrip, it is especially true for H-field, which cannot couple along the entire line, but only on line portions that are not parallel to the H-field direction. The coupling length for one H-field component is equal to the total length of these portions.

Let suppose that E and H field components couple on different portions of the line under test. (1) can be rewritten to [START_REF] Dubois | Effect of Low and High-Power Continuous Wave Electromagnetic Interference on a Microwave Oscillator System: From VCO to PLL to QPSK Receiver[END_REF], where LCE and LCH are the coupling lengths associated to E and H-fields. The RS estimator (4) can be rewritten to [START_REF] Durier | Comparison of Voltages Induced in an Electronic Equipment during Far Field and Near Field Normative Radiated Immunity Tests[END_REF].

𝑓 𝐶𝐸 = 𝑐 0 2𝜋𝐿 𝐶𝐸 ( √ 𝜀 𝑒𝑓𝑓 -1) (1 - √𝜀𝑒𝑓𝑓 𝜀 𝑟 ) -1 (7) 𝑓 𝐶𝐻 = 𝑐 0 2𝜋𝐿 𝐶𝐻 ( √ 𝜀 𝑒𝑓𝑓 -1) (1 - √𝜀𝑒𝑓𝑓 𝜀 𝑟 ) -1 (8) 𝐸 𝑚𝑖𝑛 𝐹𝐹 ≥ 1 2 ( 1 𝐸 𝑍 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅ 𝜀 𝑟 √ 1+( 𝑓 𝑓 𝐶𝐸 𝜀 𝑟 √ 𝜀 𝑒𝑓𝑓 ) 2 + 1 𝜂 0 𝐻 𝑌 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅̅ √1+( 𝑓 𝑓 𝐶𝐻 ) 2 ) -1 (9)
A first practical issue is related to the identification of the coupling length for each field component. The practical implementation of (8) to estimate RS requires knowledge of the coupling length for each field component. They have a major influence on the estimated susceptibility level as it appears not only explicitly in [START_REF] Kröning | Near Field-Immunity Scan on Printed Circuit Board Level[END_REF] and [START_REF] Wang | The PCB level ESD immunity study by using 3 Dimension ESD Scan System[END_REF], but also implicitly in [START_REF] Dubois | Effect of Low and High-Power Continuous Wave Electromagnetic Interference on a Microwave Oscillator System: From VCO to PLL to QPSK Receiver[END_REF] for the calculation of the average E or H-fields produced by the injection probe. The coupling lengths are not known from the outset and their extraction relies on the NFSI maps built from NFSI test results. Each point of the NFSI maps gives the required probe excitation to induce a failure when the probe is placed at that point. Sensitive traces or IC package pins can be identified from its analysis, which focuses the RS estimation on these sensitive interconnects.

Once a sensitive trace has been detected from NFSI map analysis, the associated coupling length can be determined. As radiated disturbance couples only on interconnects routed on external board layers, identification of the sensitive traces and extraction of their lengths become obvious. This is the case of interconnects with well-known dimensions, e.g. traces routed on the external layers of PCB. However, the exact dimensions of interconnects are not necessarily available, for example for PCB with an encapsulation protective layer or IC package interconnects. In such a situation, the coupling length can be only extracted from the analysis of the NFSI maps. A sensitive interconnect appears as a local area where a small amount of probe excitation power is required to induce a failure. In this paper, if the coupling length is extracted from NFSI maps, it is defined as the length along which the excitation power remains at less than 6 dB of the minimum required power to induce a failure.

A second practical issue is due to the simultaneous coupling of radiated disturbance on several interconnects. This may happen in FF illumination of a board, but not during local NF injection. NFSI maps will show the different sensitive traces and their length can easily be identified. However, NFSI map analysis cannot provide information on how the contribution of the couplings on the different traces combine, since the NFSI map was built from results of local injection tests. Considering only the coupling on one trace could lead to overestimation of the actual RS, if these contributions counterbalance. Inversely, it could also lead to underestimation of the RS if these contributions add up. For EMC mitigation purposes, overestimation of the RS is better. This choice is made for estimation of the RS in the case studies presented in Section IV.

III. ESTIMATING THE EXCITATION POWER OF THE NEAR-FIELD INJECTION PROBE

An important practical consideration of NFSI testing is defining the required excitation power of an NF injection probe to be representative of an RS test. The probe is assumed to have been calibrated according to the method described in Part I of this paper. In other words, this consists in determining the probe excitation power that generates either the same average E or Hfield as a far-field illumination. It is necessary to dimension the power amplifier used for the NFSI test and make the link between NFSI test results and RS limits. Obviously, the NF injection cannot produce a plane wave whose coupling is distributed along the board under test. Moreover, the susceptibility of the DUT and the contributions of E and H-field couplings are still unknown before the tests. The estimation of the excitation to give to a probe must be done independently of the other probes. An upper bound of the maximum excitation power can be derived.

A. H-field Probe Excitation

Let us consider the tangential H-field injection probe. The maximum E-field amplitude used during the RS test is 𝐸 𝑚𝑎𝑥 𝐹𝐹 .

The FF-induced voltage 𝑉 𝐿1 𝐹𝐹 is upper bounded by ( 6), sum of E and H-field injection results which are unknown before the NFSI tests. The maximum excitation of the H-field probe is determined from (6) by considering only the effect of the Hfield injection (the first term of the right side of ( 6)) and discarding the E-field injection (the second term of the right side of ( 6)). Thus, the excitation to provide to the H-field probe is calculated in such a way that it generates the same average H-field over the DUT than the plane wave with the maximum amplitude that would be used during the radiated susceptibility test. ( 6) is simplified to [START_REF] Boyer | A Rigorous Method to extrapolate Radiated Susceptibility from Near-Field Scan Immunity[END_REF]. When a failure arises, the induced voltage during H-field injection 𝑉 𝐿𝐻 𝑁𝐹 is assumed to be equal to 𝑉 𝐿1 𝐹𝐹 , so the condition [START_REF] Pommerenke | Application and Limits of IC and PCB scanning methods for immunity analysis[END_REF] about the average H-field produced by the probe along the line under test 𝐻 𝑌 𝑁𝐹 ̅̅̅̅̅̅ can be derived.

𝑉 𝐿1 𝐹𝐹 ≤ 𝑉 𝐿1 𝑁𝐹→𝐹𝐹 (𝐸 𝑚𝑎𝑥 𝐹𝐹 ) = 2𝐸 𝑚𝑎𝑥 𝐹𝐹 𝑉 𝐿𝐻 𝑁𝐹 𝜂 0 𝐻 𝑌 𝑚𝑎𝑥 𝑁𝐹 ̅̅̅̅̅̅̅̅̅̅̅ √1+( 𝑓 𝑓 𝐶𝐻 ) 2 (10)
𝐻 𝑌 𝑁𝐹 ̅̅̅̅̅̅ ≤ 2𝐸 𝑚𝑎𝑥 𝐹𝐹 𝜂 0 √1+( 𝑓 𝑓 𝐶𝐻 ) 2 (11)
𝐻 𝑌 𝑁𝐹 ̅̅̅̅̅̅ can be determined from the magnetic dipole model used during probe calibration. Let us consider that the equivalent horizontal dipole is placed at a scan altitude R above the center of a long straight microstrip line oriented along x direction and routed at a height h above an infinitely large ground plane. In case of a straight line, the coupling length to H-field LCH is equal to the total length of the line. In case of a bent line made of several straight portions, the coupling length is the length of the portions on which the probe disturbance can couple. For an actual H-field probe, the center of the equivalent magnetic dipole is placed at R+hinj above the surface of the line, where the injection height hinj was defined in Part I of this paper (Fig. 4) as the distance between the probe extremity and the center of the equivalent dipole. For small scan altitude and from the image theory, the tangential component HY on a point between the trace and the reference plane is given by [START_REF] Altair | Electromagnetic Simulation Software[END_REF]. The magnetic moment mH is related to the excitation power PexcH by the calibration parameters, as given by ( 13), where 𝑚 𝐻 𝑟𝑒𝑓 is the equivalent magnetic moment of the injection probe extracted during the calibration process, and 𝑃 𝑟𝑒𝑓 the used excitation power. The average H-field 𝐻 𝑌 along the line section is given by integral [START_REF] Boyer | Modelling of a Mixed-Signal Processor Susceptibility to Near-Field Aggression[END_REF], whose result is given by ( 16). The function 𝑓 𝐻 ̅ gives 𝐻 𝑌 ̅̅̅̅ along LCH with mH equal to 1 A‧m 2 . Substituting ( 16) into (11) leads to the maximum power PHmax required during H near-field injection (17) to produce the same average field along LCH than an incoming plane wave of amplitude 𝐸 𝑚𝑎𝑥 𝐹𝐹 .

𝐻 𝑌 = 𝜇 0 𝜔𝑚 𝐻 4𝜋𝜂 0 𝑘 0 ( 1 ((𝑥-𝑥 0 ) 2 +𝑅 1 2 ) 3 2 + 1 ((𝑥-𝑥 0 ) 2 +𝑅 2 2 ) 3 2 ) ( 12
)
𝑚 𝐻 = 𝑚 𝐻 𝑟𝑒𝑓 √ 𝑃 𝑒𝑥𝑐𝐻 𝑃 𝑟𝑒𝑓 (13) 𝑅 1,2 = 𝑅 + ℎ 𝑖𝑛𝑗 + ℎ ± 𝑧 (14)
𝐻 𝑌 ̅̅̅̅ = 1 𝐿 𝐶𝐻 ℎ ∫ ∫ 𝐻 𝑌 ℎ 0 +𝐿 𝐶𝐻 2 ⁄ -𝐿 𝐶𝐻 2 ⁄ 𝑑𝑧𝑑𝑥 (15)
Estimating PHmax requires the calibration parameters of the probe and setting various geometrical parameters. Some of them are known from the outset (e.g., h and R). However, the coupling length LCH is known accurately only once the NFSI test is done. In practice, using [START_REF] Boyer | Modelling of a Mixed-Signal Processor Susceptibility to Near-Field Aggression[END_REF] requires us to assume a likely value for LCH, for example based on the dimensions of traces that are suspected to be sensitive.

𝐻 𝑌 ̅̅̅̅ = 𝑚 𝐻 𝑓 𝐻 ̅ = 𝑚 𝐻 𝜋ℎ𝐿 𝐶𝐻 2 ( √ ( 𝐿 𝐶𝐻 2 ⁄ ) 2 +(𝑅+ℎ 𝑖𝑛𝑗 ) 2 𝑅+ℎ 𝑖𝑛𝑗 - √ ( 𝐿 𝐶𝐻 2 ⁄ ) 2 +(𝑅+ℎ 𝑖𝑛𝑗 +2ℎ) 2 𝑅+ℎ 𝑖𝑛𝑗 +2ℎ ) (16
)

𝑃 𝐻𝑚𝑎𝑥 = 𝑃 𝑟𝑒𝑓 1+( 𝑓 𝑓 𝐶𝐻 ) 2 ( 2𝐸 𝑚𝑎𝑥 𝐹𝐹 𝜂 0 𝑚 𝐻 𝑟𝑒𝑓 𝑓 𝐻 ̅ ) 2 (17)
(17) is based on the infinite large ground plane assumption, which may not be met with a practical finite size board. To evaluate the effect of the finite size of the board on the average H-field produced by the injection probe, 3D electromagnetic simulations made with FEKO software [START_REF] Altair | Electromagnetic Simulation Software[END_REF] are performed to compare the field produced by an elementary magnetic dipole placed above either a finite or infinite ground plane. The probe is placed above the middle of a square-shaped board, and the average tangential H-field is computed along the entire board. The relative difference between the H-field computed with the finite and infinite ground planes is plotted vs. the scan height R for three different board sizes Wboard, as shown in Fig. 2-a. The result shows that the relative difference remains less than 5 %, as long as the scanning height is smaller than nearly one fifth of the board width. For practical boards with dimensions larger than several tens of millimeters, the infinite ground plane assumption remains acceptable for a scan height less than several millimeters, which is typically used.

B. E-field Probe Excitation

The same approach can be used to determine the maximum excitation power of the normal E-field probe. Similarly, the maximum excitation of the E-field probe is determined from [START_REF] Dubois | Effect of Low and High-Power Continuous Wave Electromagnetic Interference on a Microwave Oscillator System: From VCO to PLL to QPSK Receiver[END_REF] by considering only the effect of the E-field injection and discarding the H-field injection. Thus, the excitation to provide to the E-field probe is calculated in such a way that it generates the same average E-field over the DUT than the plane wave with the maximum amplitude that would be used during the radiated susceptibility test. ( 6

𝐸 𝑍 𝑁𝐹 ̅̅̅̅̅ ≤ 2𝐸 𝑚𝑎𝑥 𝐹𝐹 𝜀 𝑟 √1+( 𝑓 𝑓 𝐶𝐸 𝜀 𝑟 √ 𝜀 𝑒𝑓𝑓 ) 2 (19)
However, extracting the expression of 𝐸 𝑍 𝑁𝐹 ̅̅̅̅̅ is complex due to the multiple reflections created by the air-dielectric interface and the ground plane. The multiple partial image method [START_REF] Silvester | TEM wave properties of microstrip transmission lines[END_REF] can be used to compute the E-field produced by the injection probe within the substrate. For more details, the reader can refer to Part I of this paper.

Fig. 3. Vertical electric dipole placed above a microstrip line

The normal E-field probe is modeled as a vertical electric dipole (VED). It is placed at scan altitude R above the center of a long microstrip line oriented along x direction and routed at a height h above an infinitely large ground plane, as illustrated in Fig 3 . Initially, let us ignore the effect of the ground plane and the dielectric layer. Only the direct contribution of the VED is considered. For small scan altitude, the normal E-field component Ez is given by (20). The electric moment mE is related to the excitation power PexcE by the calibration parameters (21), where 𝑚 𝐸 𝑟𝑒𝑓 is the equivalent magnetic moment of the injection probe extracted during the calibration process, and 𝑃 𝑟𝑒𝑓 the used excitation power. The average normal E-field 𝐸 𝑍 ̅̅̅ along the line section is given by integral (22), whose result is given by ( 23). The function 𝑓 𝐸 ̅ 𝐸 𝑍 ̅̅̅ along the coupling length LCE produced by the direct contribution of the dipole excited with mE equal to 1 A‧m.

𝐸 𝑍 = 𝑚 𝐸 2𝜋𝜔𝜀 0 (- 3 2 𝑐𝑜𝑠 2 𝜃 𝑟 3 + 1 2𝑟 3 ) = 𝑚 𝐸 2𝜋𝜔𝜀 0 (- 3 2 (𝑧 𝑃 -𝑅-ℎ 𝑖𝑛𝑗 ) 2 (𝑥 𝑝 2 +(𝑧 𝑃 -𝑅-ℎ 𝑖𝑛𝑗 ) 2 ) 5 2 + 1 2(𝑥 𝑝 2 +(𝑧 𝑃 -𝑅-ℎ 𝑖𝑛𝑗 ) 2 ) 3 2
) (20)

𝑚 𝐸 = 𝑚 𝐸 𝑟𝑒𝑓 √ 𝑃 𝑒𝑥𝑐𝐸 𝑃 𝑟𝑒𝑓 (21)
𝐸 𝑍 ̅̅̅ = 1 𝐿 𝐶𝐸 ℎ ∫ ∫ 𝐸 𝑍 0 -ℎ +𝐿 𝐶𝐸 2 ⁄ -𝐿 𝐶𝐸 2 ⁄ 𝑑𝑧𝑑𝑥 ( 22
)
𝐸 𝑍 ̅̅̅ = 𝑚 𝐸 𝑓 𝐸 ̅ 0 = 𝑚 𝐸 𝜋ℎ𝐿 𝐶𝐸 2 𝜔𝜀 0 [2 ( √ ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +𝑧 0 2 𝑧 0 - √ ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +𝑧 1 2 𝑧 1 ) + ( ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +2𝑧 1 2 𝑧 1 √ ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +𝑧 1 2 - ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +2𝑧 0 2 𝑧 0 √ ( 𝐿 𝐶𝐸 2 ⁄ ) 2 +𝑧 0 2 )] ( 23
)
𝑧 0 = -𝑅 -ℎ 𝑖𝑛𝑗 -ℎ (24) 𝑧 1 = -𝑅 -ℎ 𝑖𝑛𝑗 (25)
From the multiple partial image method and (23), the contributions of the reflections due to the ground plane and airdielectric interface can be added together, as given by (26). The first term is the direct contribution of the dipole, the second term is due to the reflection to the ground plane, and the last two infinite sums are the contributions of the secondary images. As suggested in Part I of this paper, 5 to 8 secondary images are sufficient to converge at less than 1 % of the actual E-field value with typical PCB dimensions and scanning height. The authors use 20 images to guarantee the convergence. A simplification of (26) can be made to reduce the number of terms, as the first two terms are dominant for small values of R. Then, (26) can be simplified into (29). For R ranging between 1 and 10 mm, h ranging between 0.2 and 2 mm, and εr between 2 and 5, the maximum relative error introduced by (29) reaches 8 %. The function 𝑓 𝐸 ̅ is the average E-field along the line section for mE equal to 1 A‧m.

𝑓 𝐸 ̅ = 𝐾 ′ 𝑓 𝐸 ̅ 0 (𝑧 0 , 𝑧 1 ) + 𝐾 ′ 𝑓 𝐸 ̅ 0 (-𝑧 0 , -𝑧 0 + ℎ) + ∑[𝐾 ′ (-𝐾) 𝑛 𝑓 𝐸 ̅ 0 (-𝑧 0 + 2𝑛ℎ, -𝑧 0 + 2(𝑛 + 1)ℎ)] + ∞ 𝑛=1 ∑ [𝐾 ′ (-1) 𝑛+1 𝐾 𝑛 𝑓 𝐸 ̅ 0 (𝑧 0 -2𝑛ℎ, -𝑧 1 + 2𝑛ℎ)] ∞ 𝑛=1 (26) 𝐾 = 1-𝜀 𝑟 1+𝜀 𝑟 (27) 𝐾 ′ = 1 + 𝐾 (28) 𝑓 𝐸 ̅ = 2 1+𝜀 𝑟 (𝑓 𝐸 ̅ 0 (𝑧 0 , 𝑧 1 ) + 𝑓 𝐸 ̅ 0 (-𝑧 0 , -𝑧 0 + ℎ)) (29)
Substituting (26) or (29) into (19) leads to the maximum power PEmax required during E near-field injection (30) to produce the same average field along LCE as an incoming plane wave of amplitude 𝐸 𝑚𝑎𝑥 𝐹𝐹 . Using (30) to determine PEmax also requires us to assume a likely value of LCE, which may be based on a preliminary analysis of the possible sensitive traces or pins of the board under test.

𝑃 𝐸𝑚𝑎𝑥 = 𝑃 𝑟𝑒𝑓 1+( 𝑓 𝑓 𝐶𝐸 𝜀 𝑟 √ 𝜀 𝑒𝑓𝑓 ) 2 ( 2𝐸 𝑚𝑎𝑥 𝐹𝐹 𝑚 𝐸 𝑟𝑒𝑓 𝑓 𝐸 ̅ 𝜀 𝑟 ) 2 (30)
(30) is also based on the infinite large ground plane assumption. As in Section III.B, the relative difference between the average E-field computed with the finite and infinite ground planes is plotted vs. the scan height R for three different board sizes Wboard, as shown in Fig 2-b. The result shows that the relative difference remains less than 5 %, as long as the scanning height is smaller than nearly one fifth of the board.

IV. CASE STUDY DESCRIPTION

A. Case Study 1 -Bandgap Reference

In the first case study, NFSI and RS estimation are done at the IC level. A micropower bandgap reference (LTC1798-2.5 from Analog Devices) is considered. It produces a 2.5 V reference voltage from a 5 V input voltage. The IC is mounted on a plastic SO8 package. The exact package encapsulation plastic material and its electrical permittivity are unknown. We assume that standard epoxy molding compound is used, with εr ranging between 3.5 and 4. This circuit is mounted on a 10 cm ×10 cm four-layer board dedicated to TEM cell tests, with a complete ground plane on the top layer. The IC is isolated on the top layer, except short traces connected to the input and output pins, as shown in Fig. 4. The failure criterion is a deviation of +/-10 mV of the output voltage.

B. Case Study 2 -Operational Amplifier

In the second case study, NFSI and RS tests are done at the PCB level. This case consists of an op-amp (LMV651 from Texas Instruments) in non-inverter amplifier configuration. The electrical diagram is shown in Fig. 5. The IC is supplied symmetrically between +/-2.5 V. It is mounted on a 10 cm × 10 cm FR4 four-layer board dedicated to TEM cell tests, with a complete ground plane on internal layers. The IC, the external passive devices, and the PCB traces are placed on the top layer, as shown in Fig. 6. The non-inverting input (V+) is tied to the ground by an RC load through a 40 mm long line. The output voltage is measured by an oscilloscope through a 36 mm long line.

The conducted susceptibility of this op-amp has been studied in a previous study [START_REF] Boyer | A Case Study to apprehend RF Susceptibility of Operational Amplifiers[END_REF]. The circuit is sensitive to RF voltages coupled on both inverting (V-) and V+ inputs of the op-amp, which may lead to positive or negative offset on the output voltage. Up to 100 MHz, the main failure mechanism is related to the slew-rate limitation of the op-amp. It is dependent on the differential-mode (DM) voltage and always results in a positive failure. Above 100 MHz, the offset is mainly linked to a weak distortion due to the input differential pair of the op-amp. The sign and the amount of EMI-induced offset depends on both common-mode (CM) and DM RF voltage amplitude and phase, according to a non-linear relationship. In this study, the failure criterion is set as a maximum deviation of +/-10 mV of the output voltage.

C. Experimental Set-up

The purpose of both case studies is to verify that the RS level measured when the device under test (DUT) is illuminated uniformly can be estimated from NFSI results. A convenient approach adapted to RS testing at the PCB and IC levels is the transverse electromagnetic and gigahertz transverse electromagnetic (TEM/GTEM) cell. Although the polarization of the TEM wave within the cell is fixed, the method is repeatable. The field amplitude within the cell is known with good precision and can reach several hundred V/m with an excitation of only a few watts. The board under test can be oriented to the GTEM input connector according to four directions: 0°, 90°, 180° and 270° according to the orientation of the DUT to the cell septum. RS tests are carried out with a GTEM cell model Schaffner GTEM250. 0° and 90° directions of the case studies in the GTEM cell are shown in Figs. 4 and6. In 0° and 180° orientation, the H-field produced in the GTEM cell is oriented along the Y-axis, while it is oriented along the X-axis in 90° and 270° orientation.

The calibrated E and H-field injection probes described in Part I of this paper are reused. NFSI tests are done with three field components: Ez, which refers to the test with normal Efield probe made of a 4 mm long tip at the end of a semi-rigid coaxial cable, and Hx and Hy with the tangential H-field probe oriented along x and y directions consisting of a 5 mm diameter circular loop that terminates a semi-rigid coaxial cable. In both case studies, the scan altitude is set at 2 mm above the PCB surface. The scan altitude is chosen to place the injection probe as close as possible to the board under test, without any risk of contact with mounted components. The scan step is 2 mm along the X-axis and 1 mm along the Y-axis. NFSI and GTEM cell tests are done from 10 MHz to 3 GHz. Two power amplifiers are used for the range 10 MHz to 1 GHz and 1 to 3 GHz, with power capability limited to 46 dBm and 44 dBm, respectively. During the GTEM cell tests, the maximum E-field is limited to 1,000 V/m and 800 V/m in each frequency range. The maximum power during the NFSI tests is limited to 40 dBm in order to avoid overheating of the injection probes.

V. EXPERIMENTAL RESULTS

A. Experimental Results of Case Study 1 1) GTEM cell results

Fig. 7 presents the susceptibility levels of the bandgap reference measured in the GTEM cell. Results from 10 to 100 MHz are not shown as no failures were detected. Failures trigger between 200 MHz and 1.2 GHz, and around 1.7 GHz. Regardless of the frequency, the disturbance induces a negative offset voltage on the bandgap reference output. Depending on the orientation of the DUT in the GTEM cell, susceptibility peaks arise either around 300 MHz or 600 MHz. Some conclusions can be drawn about the nature of the coupling. The differences between the susceptibility levels measured in 0° and 90° (or 180° and 270°) orientations indicate that the H-field coupling contributes significantly. If only E-field couples, susceptibility levels will be similar regardless of the DUT orientation. However, E-field coupling also contributes to the observed failures because of the differences measured between the orientations 0° and 180° (or 90° and 270°).

2) NFSI results

NFSI tests produce a massive amount of data that needs to be carefully analyzed to clarify the coupling mechanisms that lead to a failure. Only specific significant results are shown in this paper in order to clarify the coupling mechanisms. Figs. 9 to 11 present the susceptibility maps obtained with the three tested field components at three different frequencies. The positions of the susceptibility maxima change with the frequency. Fig. 8 shows the minimum probe excitation power required to induce a failure in the susceptibility maxima positions.

Irrespective of the frequency, a negative offset is generated on the DUT output. During Hy injection, the coupling is mainly located on the output pin up to 350 MHz, and then extends to the input pin. At 300 MHz, although the coupling is maximum when the H-field probe is placed above the die (Fig. 10 on the left), the coupling arises both on the input and output package leads and bonding wires. Because of the limited spatial resolution of the injection probe, simultaneous couplings arise on both package interconnects and their contribution tends to add up. The contribution of individual coupling on each package interconnect cannot be separated. Above 500 MHz, the coupling is localized between the input and the ground pins. An interesting observation is that there is nearly no offset when the probe is placed in-between these pins. The RF voltages induced on both pins tend to counterbalance. Depending on the frequency, the coupling may appear mainly on the input or the ground pin (e.g. at 1 GHz). During Hx injection, the coupling area is localized above the y-oriented parts of the input and the ground pins within the IC package (package leads and bonding wires). However, contrary to Hy injection, no offset compensation is observed. During Ez injection, the coupling area is localized above the center of the IC package, regardless of the frequency. The coupling is certainly mainly concentrated on the die pad.

Fig. 8. Susceptibility level of the bandgap reference in NFSI tests

There are some correlations between GTEM cell and NFSI results. The susceptibility peak around 300 MHz in GTEM cell tests for the 0° and 180° directions is also visible in the Hy injection test. In the 0° and 180° orientations, only the Hy component is seen in the GTEM cell. Similarly, the susceptibility peak around 600 MHz in GTEM cell tests for 90° and 270° directions is also visible in the Hx injection test. The peak around 1.7 GHz appears both in GTEM cell and Ez injection results. However, the post-processing of NFSI results is required to verify the link between GTEM cell and NFSI results. Moreover, the direct comparison between the power excitation during E and H-field injection could be misleading as probe moments are different. The extent of E and H-field couplings cannot be determined without post-processing.

3) Radiated susceptibility estimation from NFSI results

The methodology described in Section II is used to estimate the RS level from NFSI results. It requires the identification of the minimum probe excitation power from NFSI maps, probe calibration data, and geometrical and electrical information concerning the DUT. However, the exact information about the internal geometry of the IC package and die is unknown in practice. The identification of coupling areas and geometry rely only on the NFSI maps and external dimensions of the IC package. For H-field, NFSI maps show that the coupling arises package leads. As shown in [START_REF] Boyer | Modelling of a Mixed-Signal Processor Susceptibility to Near-Field Aggression[END_REF] and [START_REF] Boyer | Modeling Magnetic Near-Field Injection at Silicon Die Level[END_REF], radiated coupling on IC package pins can be modeled similarly as for a twoconductor transmission line, formed by the package lead and the ground plane below. The equivalent line structure is a microstrip line. As the Taylor model is considered in this study, only coupling on the horizontal parts of the package is considered. Only two geometrical parameters are required to compute the average field produced by the injection probe in the estimator (9): the coupling length, which is deduced from the NFSI maps, and the distance to the ground. According to the external dimensions of the package provided by the manufacturers which give the height of the lead frame, the package leads are assumed to be placed a constant height of 0.8 mm above the top layer of the PCB. Fig. 11 shows that the coupling of Ez arises above the die pad. As no internal details about the IC package are available, the following E-field coupling model is assumed: the die pad and the ground plane on the PCB top layer form a two-conductor line. The separation between both conductors is also supposed to be equal to 0.8 mm and the coupling length is extracted from the NFSI maps.

From NFSI maps, the sensitive pins are identified at each frequency and the coupling length is extracted according to the approach described in Section II.B. Depending if the field couples on the input and the ground pins, the coupling length is set to 4 mm for Ez, 3 or 6 mm for Hx, and 4 or 8 mm for Hy. The exact permittivity of the package is unknown so εr and εeff are assumed to be equal to 4. Finally, the contributions of couplings of the E and H-fields on different areas are added. This is a limitation of the proposed approach, since the phase of each coupling contribution cannot be measured in NFSI. If the incoming wave couples simultaneously on several pins or traces, and if the induced effects counterbalance, this effect cannot be measured accurately in NFSI since the injection is local. The risk is overestimation of the predicted RS. To prove the validity of the RS estimation method, the estimated RS level is compared with GTEM cell results. However, the H-field is oriented either along x or y directions in the GTEM cell, as explained in Section IV.C. Therefore, Hx and Hy NFSI results should not be combined. RS in 0° and 180° orientations is estimated from Ez and Hy NFSI results, whereas Ez and Hx NFSI results are used to estimate RS in 90° and 270° orientations.

Initially, (17) and (30) are used to determine the maximum probe excitation power to produce the same effect as a 1,000 V/m plane wave on the DUT. From the geometrical parameters of the board, the scan altitude, and the calibration parameters of the probes, the maximum power for E and H-field injections (PEmax and PHmax) are equal to 36 dBm and 32 dBm, respectively using a coupling length of 8 mm. These power limits are plotted on Fig. 8. Proving their validity by a direct comparison between GTEM and NFSI results is not straightforward, since E and H field coupling may coexist during GTEM cell test. These limits are relevant in a RS risk assessment only if a failure arises at least during one NFSI test below the power limit. This relevance is confirmed by the comparison between Figs. 7 and8. As shown in Fig. 7, in GTEM cell, failures arise under less than 1000 V/m between 170 MHz and 1 GHz. Although failures arise in E-field injection below PEmax only between 270 and 700 MHz, an excitation below PHmax is enough to induce failure during H-field injection between 100 MHz and 1 GHz. As no failures are missed between 170 MHz and 1 GHz, the RS risk assessment from NFSI results is possible based on PEmax and PHmax. The lack of failure during E-field injection below PEmax between 170 and 270 MHz and between 700 MHz and 1 GHz suggests that the DUT is not sensitive to E-field coupling on these frequency ranges.

A first validation step of the proposed estimator of RS consists in combining Ez and Hy injection results according to [START_REF] Durier | Comparison of Voltages Induced in an Electronic Equipment during Far Field and Near Field Normative Radiated Immunity Tests[END_REF] to estimate the RS level for the 0 and 180° orientations, as only Hy couples to the DUT in the GTEM cell. Similarly, as only Hx couples for the 90° and 270° orientations, Ez and Hy injection results are combined to estimate the worst-case RS level in these orientations. Results are presented in Fig. 12. Up to 350 MHz, the coupling is essentially magnetic (ZN exceeds 2) and becomes electric between 1.5 and 2.7 GHz (ZN is less than 0.5). Relatively good correlation between the GTEM cell for 0° orientation and the NFSI-based estimator is observed up to 400 MHz. For the 0° orientation, E and H-field contribution tends to add up, contrary to the 180° orientation. However, NFSI-based estimation tends to overestimate the RS level between 400 and 950 MHz. This can be explained by the simultaneous coupling of H-field on the input and ground pins during the GTEM cell test, which tends to counterbalance. This effect is illustrated in Figure 13, which shows a simplified geometrical description of the package pins. In 0° and 180°, the H-field in the GTEM cell is oriented along the Y-axis and couples on the X-oriented part of the pins. Due to the orientation of the electromotive forces induced on both pins, the RF voltage generated between the input and the ground pins tends to be attenuated. This type of effect does not appear for the 90° and 270° orientation as the H-field in the GTEM cell is oriented along the X-axis. The effect of the electromotive force induced on input and ground pins tends to add up and increase the RF voltage generated between the input and the ground pins. In 90° and 270°, good agreement between GTEM cell results and the NFSI-based estimator is obtained between 400 and 1100 MHz. The susceptibility peak at 1.7 GHz is also predicted by the NFSI-based estimator with the correct order of disturbance level. The NFSI-based estimator tends to overestimate the RS level in GTEM between 1.1 and 1.6 GHz, and above 2.4 GHz. An offset tends to appear in this frequency range during the GTEM cell test, but the power limit of the amplifier is reached. This difference may be explained by compensation between E and H-field coupling in the GTEM cell. For the same reason, the proposed method underestimates the RS level in the 90° and 270° orientations between 300 and 400 MHz. The cumulative effect of the simultaneous couplings of E and H fields on several IC pins is not correctly determined from NFSI maps. Secondly, a worst-case estimation of the RS level is made by considering the minimum value between the two previous NFSI-based estimators. This worst-case estimator is compared with the minimum RS level in the GTEM cell, regardless of the orientation, as shown in Fig. 14. Relatively good correlation is observed between 150 and 1500 MHz, where the maximum difference does not exceed 100 V/m. The estimator also correctly predicts the lack of failures below 150 MHz and between 1.9 and 2.5 GHz. Differences can be explained by uncertainty about the permittivity and the internal geometry of the IC package, but also by the differences between NFSI and TEM cell set-ups. They can also be explained by the compensation between E and H-field coupling during GTEM cell tests. However, this result shows that, even though compensation effects arise due to simultaneous coupling on several pins, this does not exist for all incoming wave orientations. As a result, the proposed NFSI-based estimator can determine the worst-case situations without excessive overestimation.

B. Experimental Results of Case Study 2 1) GTEM cell results

Fig. 15 presents the susceptibility levels of the op-amp board measured in the GTEM cell. Depending on the frequency and board orientation, failures are related to positive or negative offset. Except around 100 MHz for the 0° orientation, the main susceptibility peak is around 700 and 800 MHz, regardless of the board orientation.

Fig. 15. Susceptibility level of the op-amp in the GTEM cell

Above 1 GHz, the susceptibility level tends to vary abruptly with frequency and board orientation, with numerous changes of the offset sign. This effect can be explained by the long electrical dimensions of the board above 1 GHz and its relative complex geometry, that leads to a complex relationship between the CM and DM RF voltages applied on the op-amp inputs. Up to 1 GHz, susceptibility is larger in 0° and 180°, where the V-input and output traces are parallel to the GTEM septum which optimizes H-field coupling, contrary to the 90° and 270° orientations. The measurement differences between the four orientations reveals that both E and H-field couplings contribute to failure generation.

2) NFSI results

Figs. [START_REF] Boyer | Modeling Magnetic Near-Field Injection at Silicon Die Level[END_REF], 17 and 18 present the susceptibility maps obtained for Hx, Hy and Ez components at two different frequencies. The positions of the susceptibility maxima change with the frequency. Fig. 19 shows the minimum probe excitation power required to induce a failure in the susceptibility maxima positions. During H-field injection, the coupling is mainly visible on the V+ input trace and leads to a negative offset, except below 180 MHz. In low frequency, H-field coupling is also seen on the output and feedback traces, resulting in a positive offset. At higher frequencies, for Hy injection, some coupling is also found on the V-input trace (around 1 and 3 GHz). For Hx injection, coupling is mainly done on the V-input trace and leads to a positive offset. During E-field injection, coupling appears on the V-input up to 550 MHz and leads to positive offset. Then, E-field coupling appears mainly on the V+ input between 600 and 900 MHz. At higher frequencies, E-field coupling arises on both op-amp inputs, resulting in changes of the offset signs with frequency. This complex behavior confirms the influence of the couplings of E and H-fields on opamp inputs, which has an influence on the offset sign. This clarifies the strong variability of the RS in GTEM, according to the frequency and board orientation. NFSI results show that several coupling areas exist on the board, which may capture either E or H-field and lead to positive or negative offset. During a global illumination by a plane wave, the resulting effect on the offset varies strongly depending on how these different coupling contributions are combined on V+ and V-. There are also some correlations between GTEM cell and NFSI results. The susceptibility peak around 700 MHz in the GTEM cell is also visible in E and H-field injection. However, the link between NFSI and GTEM cell results is not obvious and postprocessing of NFSI results is required.

3) Radiated susceptibility estimation from NFSI results

The RS estimation methodology previously applied is reused. In this case study, the coupling arises mainly on PCB traces. Due to the small size of the IC package, its influence on coupling is disregarded. The height of the traces to reference ground plane is 0.42 mm and the board εr is set to 4.5. From NFSI maps, the sensitive traces are identified at each frequency. As the exact dimensions of PCB traces are known exactly, the coupling lengths are based on the dimensions of the identified sensitive traces. Depending if the field couples on the input, feedback and output traces, the coupling length is set to 8 or 16 mm for Ez, 8 or 11 mm for Hx, and 40 mm for Hy. Similar to the first case study, the contributions of couplings of E and Hfields are added, since the measurement of the phase of the induced RF voltage due to E and H-field coupling at trace ends is difficult in a real application board. Moreover, Ez NFSI results are combined either with Hx or Hy NFSI results, depending on the orientation of the board in the GTEM cell.

Initially, ( 17) and (30) are used to evaluate the maximum probe excitation power to produce the same effect as a 1,000 V/m plane wave on the DUT. From the geometrical parameters of the board, the scan altitude and the calibration parameters of the probes, the maximum power for 17) and (30), which remains unknown before the NFSI tests. In practice, an additional margin is recommended to compensate the uncertainty about the coupling length on the estimation of PEmax and PHmax.

A first validation step of the proposed estimator of RS consists in combining Ez and Hy injection results according to [START_REF] Durier | Comparison of Voltages Induced in an Electronic Equipment during Far Field and Near Field Normative Radiated Immunity Tests[END_REF] to estimate the RS level for the 0° and 180° orientations. Similarly, as only Hx couples for the 90° and 270° orientations, Ez and Hx injection results are combined to estimate the worstcase RS level in both orientations. Results are presented in Fig. 20. Relatively good correlation between the GTEM cell for the 180° orientation and the NFSI-based estimator is observed between 180 MHz and 1 GHz. E and H-field contribution tends to add up, contrary to the 0° orientation. However, above 1 GHz, the estimation overestimates the RS level, due to the simultaneous coupling of E and H-field on V+ and V-, which tends to counterbalance the induced offset. Similarly, NFSI-based estimation tends to underestimate the RS level below 150 MHz. In this range, the simultaneous coupling on V+ and V-during GTEM cell testing adds up to generate a positive offset. This cumulative effect cannot be produced during NFSI due to local coupling. Nevertheless, underestimation does not exceed 25 % of the actual RS level, and the susceptibility peak around 100 MHz is correctly predicted. Although this peak is not clearly visible on NFSI results (Fig. 19), NFSI post-processing reveals this effect because the H-field couples to both V+, V-and output traces around 100 MHz, while it couples only on V+ above 180 MHz. The widening of the coupling length reduces the required field to induce a failure. The same conclusions can be drawn from the comparison between GTEM results in 90° and 270° and the NFSI-based estimator. Above 400 MHz, the post-processing of NFSI results provides an acceptable of the RS level. Below 400 MHz, the proposed estimator tends to overestimate the susceptibility level because of the simultaneous coupling on V+ and V-. Nevertheless, the estimator predicts a high immunity level below 400 MHz for the 90° and 270° orientations, which is verified by GTEM cell measurement.

Second, as in the first case study, a worst-case estimation of the RS level is made by considering the minimum value between the two previous NFSI-based estimators, and is compared with the minimum RS level in the GTEM cell. As shown in Fig. 21, relatively good correlation is observed between 180 MHz and 1 GHz. The differences below 180 MHz and above 1 GHz are mainly due to simultaneous coupling on several PCB traces during GTEM cell testing. However, underestimation of the RS level does not exceed 25 % of the actual RS level, and the proposed NFSI post-processing provides the correct RS level estimate. It may be sufficient to assess the RS risks at the PCB level at the end of NFSI investigation. The second part of this two-part paper has presented an estimator of the radiated susceptibility of a circuit or a PCB from NFSI results. The proposed post-processing method of NFSI results has been applied to two practical studies. In spite of the presence of non-linear devices and the simultaneous couplings on several traces or IC pins, the method provides a correct estimate of the worst-case radiated susceptibility level, at least up to 3 GHz. When simultaneous couplings arise, the precision of the estimator degrades, but it remains acceptable for susceptibility risk assessment purposes, since the estimated susceptibility level is determined correctly, and susceptibility peaks are detected. With this type of tool, a PCB designer can evaluate at the end of a preliminary NFSI campaign whether the PCB will introduce excessive non-compliance risk during susceptibility testing, or whether design improvements are required.

The problem of the simultaneous coupling is an intrinsic issue of any estimation method of the radiated susceptibility from NFSI results, since it is related to a fundamental difference between far-field illumination and local near-field injection. Without any measurements or models of the different contributions of the incoming field coupling, determining how they should be combined is not straightforward. It constitutes one limitation of the proposed approach. Further research is required to find a method to determine from NFSI results how the different contributions of simultaneous radiated couplings actually combine. It is of major importance to improve the accuracy of the radiated susceptibility estimation for more complex PCB design with multiple traces connected to the same sensitive IC pins.

One advantage of NFSI in this risk assessment process is the reduced amount of excitation power compared to other radiated susceptibility tests, such as the Absorber-Lined Shield Enclosure or TEM cell. The NFSI user can make use of the formulations proposed in this paper to evaluate the amount of excitation power according to the calibration results of the injection probe and basic geometrical of the DUT. One drawback of the proposed approach is that it is limited to investigation at the board or circuit level. The impact of cables or enclosures, which have a major impact on radiated susceptibility of electronic equipment, has not been considered in this study. These issues should be investigated in future studies.

publications in peer-reviewed journals and conference proceedings, and supervised 14 PhD theses and 9 MSc theses.

Fig. 1 .

 1 Fig. 1. Equivalent model of the illuminated line terminated by an integrated circuit input (Load 1)In Part I of this paper, the estimator 𝑉 𝐿1 𝑁𝐹→𝐹𝐹 of the worst-case FF-induced voltage based on NFSI results was derived[START_REF]Integrated circuits -Measurement of electromagnetic immunity -Part 9: Measurement of radiated immunity -Surface scan method[END_REF]. It provides an upper bound of the maximum induced voltage along the line terminal illuminated by a plane wave whose Efield amplitude is E0, regardless of the plane wave incidence direction and polarization. 𝑉 𝐿𝐸 𝑚𝑎𝑥 𝑁𝐹

Fig. 2 .

 2 Relative difference between the average field computed above a finite and an infinite ground plane: (a) Tangential Hfield produced by a magnetic injection probe, (b) Vertical Efield produced by an electric injection probe

Fig. 4 .

 4 Fig. 4. Scan area and orientation of case study 1 (Bandgap reference)

Fig. 5 .Fig. 6 .

 56 Fig. 5. Electrical diagram of case study 2 (op-amp board)

Fig. 7 .

 7 Fig.7. Susceptibility level of the bandgap reference in the GTEM cell

Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .

 9101112 Fig. 9. Hx NFSI maps of the reference bandgap: 300 MHz (left), 600 MHz (center), 1 GHz (right)

Fig. 13 .

 13 Fig. 13. Effect of board orientation in the GTEM cell on H-field coupling: (a) 0° and 180° orientation, (b) 90° and 270° orientation

Fig. 14 .

 14 Fig. 14. Comparison between worst-case susceptibility levels measured in the GTEM cell and NFSI-based susceptibility estimator

Fig. 16 .Fig. 17 .Fig. 19 .

 161719 Fig. 16. Hx NFSI maps of the op-amp board: 200 MHz (left), 1000 MHz (right)

  E and H-field injection are PEmax = 35 dBm (LCE = 8 mm) and PHmax = 40 dBm (LCH = 40 mm), respectively. As shown in Fig. 15, in GTEM cell, failures arise under less than 1000 V/m between 34 MHz and 1 GHz. In Fig. 19, failures arise in E-field injection below PEmax between 40 MHz and 3 GHz, and in H-field injection below PHmax between 50 MHz and 3 GHz. Except between 34 and 40 MHz, no failures are missed during NFSI tests with the selected PEmax and PHmax and RS risk assessment is possible. The discrepancy between 34 and 40 MHz can be explained by the guess of coupling length in ((

Fig. 20 .

 20 Fig. 20. Comparison between susceptibility levels measured in the GTEM cell and NFSI-based susceptibility estimator: for the 0°/180° orientation (top), and 90°/270° orientation (bottom)

Fig. 21 .

 21 Fig. 21. Comparison between worst-case susceptibility levels measured in the GTEM cell and NFSI-based susceptibility estimator VI. CONCLUSION

  1, this estimator can be used to determine VL1 as the termination impedances are assumed to be linear. The relationship (3) between the worst-case FF-induced voltage 𝑉 𝑤𝑜𝑟𝑠𝑡

	𝐹𝐹	for the E0 field illumination and the estimator (1)
	can be written. Let us consider 𝐸 𝑚𝑖𝑛 𝐹𝐹 to be the minimum
	amplitude of the plane wave illumination that leads to a failure,
	i.e., in the worst-case coupling situation. When a failure arises,
	regardless of the type of radiated disturbance, VL1 is equal to
	VFail. If the failure is triggered during E and H-field injection,
	the terms 𝑉 𝐿𝐸 𝑚𝑎𝑥 𝑁𝐹	and 𝑉 𝐿𝐻 𝑚𝑎𝑥 𝑁𝐹	are equal to VFail. If the failure
	arises during the RS test in the worst-case coupling situation,
	𝐹𝐹 𝑉 𝑤𝑜𝑟𝑠𝑡 leads to (4), which gives the lower bound of 𝐸 𝑚𝑖𝑛 is also equal to VFail. Substituting VFail into (1) and (3) 𝐹𝐹 according to
	the average E and H-field produced by the injection probes
	when a failure arises during NFSI measurements.
		𝑉 𝑤𝑜𝑟𝑠𝑡 𝐹𝐹	(𝐸 0 ) ≤ 𝑉 𝐿1 𝑁𝐹→𝐹𝐹 (𝐸 0 )


Javier Castro-Jimenez

Y Aminot

C Pollono

B Idjaton

L Bizzozero

O Pierre-Duplessix

N N Phuong

Johnny Gasperi

Environmental occurrence of organophosphate esters and micro-plastics in sediments and benthic organisms

from the Loire Estuary (France)

Environmental occurrence of organophosphate esters and microplastics in sediments and benthic organisms from the Loire Estuary (France)

INTRODUCTION AND OBJECTIVES

Organophosphate ester (OPE) flame retardants and plasticizers and microplastics (MPs) are emerging threats to the marine environment, presenting multiple sources in the environment and being widely distributed in sea and ocean of the planet [START_REF] Van Der Veen | Phosphorus flame retardants: properties, production, environmental occurrence, toxicity and analysis[END_REF][START_REF] Xie | Organophosphate ester pollution in the ocean[END_REF][START_REF] Schmidt | Export of Plastic Debris by Rivers into the Sea[END_REF] . Marine sediments are thought to be a sink for both OPEs and MPs. In addition, leaching from MPs could constitute in-situ sources of OPEs [START_REF] Xie | Organophosphate ester pollution in the ocean[END_REF] . Therefore, determining their environmental occurrence in sediments becomes crucial to better understand their current stocks, the exposure of benthic organisms, and possible impacts on the global functioning of marine ecosystems. The Loire is the longest river in France representing an important freshwater discharge to the North-East Atlantic Ocean. Its estuary is considered as an ecosystem of high ecological value as well as an ocean/land interface for sea trade and associated industrial activities.

Fig. 2 .

 2 Fig. 2. Mean concentrations (ng/g d.w and distribution patterns (%) of tri-OPEs and di-OPEs in sediments (upper and mid panels, respectively) and tri-OPEs in Scrobicularia plana (lower panel). Vertical bars are standard deviation.

Fig. 1 .Fig. 3 .

 13 Fig. 1. Study area, sampling zones and detail on Scrobicularia plana individuals collected in Zone A (a) and sediments from Zone B (b)

Acknowledgements

We would like to acknowledge Nadège Bely and Lauriane Ledieu for their help in the sampling campaign Surface sediment (1-5 first cm) was collected at four different zones from the Loire Estuary subjected to different anthropogenic pressures (Fig. 1). Five sites were collected in each zone following a grid pattern. The benthic organism Scrobicularia plana (SP) was only present in two zones (A, D). Both sediment and SP were freeze-dried. Sediments were sieved (500µm), spiked with OPE labelled standards, and ultrasound extracted (1 g d.w.). Separated extractions were performed for tri-OPE analysis (EtOAc/Cyclohexane 80/20) and di-OPE (MeOH). Clean-up was performed using SPE-NH2 (500mg, 6 ml Discovery® DSC-NH2) and SPE-HLB (500mg, 6 ml Oasis HLB) cartridges for tri-OPE and di-OPE, respectivelly. SP samples (1 g d.w.) were processed by accelerated solvent extractaction (ASE) with in-cell florisil clean-up and followed by sequential SPE-NH2 and SPE-ENVI-Carb cartridges (500mg, 6 ml, Supelclean™ ENVI-Carb™). Twenty-one tri-OPEs (eleven in SP) and seven degradation metabolites (di-OPE, only in sediments) were quantified by isotopic dilution LC-MS/MS (UPLC coupled with a triple quadrupole Xevo TQS-µ from Waters, Milford, MA, USA) . MP abundance was determined after sediment digestion (10g w.w.) with H 2 O 2 (30%) and polymer isolation (NaI) and the fragments were characterized by µ-FTIR (Thermo_nicolet iZ10). Method median recoveries varied from 29 to 130% and limits of quantification ranged from 0.01 to 1.2 ng/g d.w depending on the specific OPE.

METHODS


Philippe Guilpain

Clément Le Bihan

Vincent Foulongne

Patrice Taourel

Nathalie Pansu

Alexandre Thibault

Jacques Maria

Boris Jung

R Larcher

Kada Klouche

Vincent Le Moing

Response to: 'Severe COVID-19 associated pneumonia in 3 patients with systemic sclerosis treated with rituximab' by Avouac et al

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Ron-Angevin Ricardo

Beasse Joseph

Clément Adrien

Dupont Clara
email: cdupont013@ensc.fr

Gall Le

Maïwenn

Juliette Meunier
email: jmeunier@ensc.fr

Lespinet-Najib Véronique
email: veronique.lespinet@ensc.fr

André Jean-Marc
email: jean-marc.andre@ensc.fr

Comparison of Two Paradigms Based on Stimulation with Images in a Spelling Brain-Computer Interface

Keywords: Brain-Computer Interface (BCI), P300, speller, stimuli, RCP paradigm. I

A BCI Speller is a typical Brain-Computer Interface (BCI) system for communication purposes. This technology can provide users with severe motor disability with an assistive device controlled by brain activity. The present preliminary study, with only four subjects, is focused on the control of a 5x5 P300-based speller matrix for communication purposes. In this work, we study the effect of flashing stimuli used to highlight the letters in two conditions: pictures and red famous faces (that is, famous faces coloured in red). These preliminary results, based on performance and the Information Transfer Rate (ITR), showed that both conditions are similar, obtaining very good performance compared to conventional P300-speller. In this sense, the use of pictures does not make the performance worse, allowing to develop more attractive and usable interfaces. More tests would confirm if there is a difference in performance between the two conditions proposed.

INTRODUCTION

A Brain-Computer Interface (BCI) is based on analysis of the brain activity recorded during certain mental activities in order to control an external device. It helps to establish a communication and control channel for people with serious motor function problems, but without a cognitive function disorder [START_REF] Wolpaw | Brain-computer interfaces for communication and control[END_REF]. Currently, the most commonly used BCI systems are those based on electroencephalographic (EEG) signals, mainly because they can be recorded in a noninvasive manner and show adequate temporal resolution.

A BCI Speller is a typical brain-computer interface system for communication purposes. This technology can provide users with severe motor disability as, for example, patients suffering from Amyotrophic Lateral Sclerosis (ALS), with an assistive device controlled by brain activity.

Most of the BCI spellers are based on the P300 Event-Related Potential (ERP). The P300 signal is a positive deflection in voltage occurring about 300 ms after an infrequent or significant stimulus is perceived [START_REF] Wolpaw | Brain-computer interfaces for communication and control[END_REF]. The P300 wave amplitude is typically between 2μV and 5μV and is symmetrically distributed around the central scalp areas, showing greater amplitude in the occipital rather than the frontal region [START_REF] Krusienski | Toward enhanced P300 speller performance[END_REF]. Most of these spellers are based on the P300 speller first developed by Farwell and Donchin [START_REF] Farwell | Talking off the top of your head: toward a mental prosthesis utilizing event-related brain potentials[END_REF]. In this BCI, a 6 x 6 matrix of letters, arranged in rows and columns, is shown to the subject. The user focuses his/her attention on the matrix element he/she wishes to select as each row and column is flashed (i.e., intensified) randomly, one after the other. After a number of flashes, the symbol that the user has supposedly chosen is presented on the screen. This paradigm is known as Row-Column Presentation (RCP) paradigm.

In order to increase the performance of a BCI Speller based on the RCP paradigm, different stimulus presentation have been proposed. One of the stimuli which has resulted in improved BCI performance is the use of familiar faces [4] [5]. Effectively, regarding the nature of stimuli, it has been demonstrated that the presentation of Famous Faces (FF) instead of letters leads to an improvement in performance. Specifically, in [START_REF] Kaufmann | Flashing characters with famous faces improves ERP-based brain-computer interface performance[END_REF], the stimulus used was composed of famous faces. In [START_REF] Li | Use of a green familiar faces paradigm improves P300-speller brain-computer interface performance[END_REF], the use of green familiar faces improves the BCI performance compared to the famous face paradigm. Carrying on this research line based on the use of stimuli with familiar faces, news studies have been recently proposed. In [START_REF] Li | Comparison of the ERP-Based BCI Performance Among Chromatic (RGB) Semitransparent Face Patterns[END_REF], the effects of a combinations of face stimuli with three primary colors (RGB) on BCI performance have been explored. The highest online averaged accuracy (93.89%) and (ITR) Information Transfer Rate (28.68 bits/min) were obtained with red semitransparent faces. Based on this study, very recently the same research group showed that using a stimulus combining a famous face coloured in red (red famous face) with a white rectangle could improve the performance [START_REF] Zhang | Evaluation of color modulation in visual P300-speller using new stimulus patterns[END_REF], getting an online average accuracy of 96.94%. It is important to notice that, in all these propositions, the stimuli used are always the same for all the symbols of the matrix.

Besides, a study carried out by the research group of the University of Málagathe UMA-BCI groupshows that the use of a set of varied different pictures (e.g., photographs of things, people or places) as flashing stimuli could also have a significantly improvement in the usability of a BCI-speller based on RCP [START_REF] Fernández-Rodríguez | Evaluation of emotional and neutral pictures as flashing stimuli using a P300 braincomputer interface speller[END_REF]. Unlike the previous studies based on familiar faces, in this study, different images were used for each symbol of the matrix. This can have a great advantage in the design of a BCI-P300 speller. Effectively, the use of different images to stimulate the different symbols of the speller, allows to develop BCI speller based on pictograms or commands, increasing the options of communications and control.

Due to the advantage of using images, the main objective of this preliminary study was to study if the performance of a BCI-P300 speller based on pictures stimulus presentation was similar to those based on red famous faces with a white rectangle.

This paper is organized as follows: Section 2 describes the experimental setup, and presents details about the spelling paradigms. The results and discussion are presented in Section 3, followed by the conclusion and future works in Section 4.

II. MATERIAL AND METHODS

A. Participants

Four healthy French university students (S1-S4) participated in this study. None of them had previous experience using a BCI system. The study was approved by the Ethics Committee of the University of Malaga and met the ethical standards of the Helsinki Declaration. According to self-reports, all participants had no history of neurological or psychiatric illness, had normal or corrected-to-normal vision, and gave informed consent trough a protocol reviewed by the ENSC-IMS (Ecole Nationale Supérieur de Cognitique -Intégration du Matériau su Systéme) Cognitive and UMA-BCI teams.

B. Data acquisition and Signal Processing

The EEG was recorded using the electrode positions: Fz, Cz, Pz, Oz, P3, P4, PO7 and PO8, according to the 10/20 international system. All channels were referenced to the right earlobe, using FPz as ground.

The EEG was amplified through a 16 channel biosignal amplifier gUSBamp (Guger Technologies). The amplifier settings were from 0.5 Hz to 100 Hz for the band-pass filter, the notch (50 Hz) was on, and the sensitivity was 500 μV. The EEG was then digitized at a rate of 256 Hz. EEG data collection and processing were controlled by the UMA-BCI Speller software [START_REF] Velasco-Álvarez | UMA-BCI speller: an easily configurable P300 speller tool for end user[END_REF], a BCI speller application developed by the UMA-BCI group which provides end users with an easy to use open source P300 speller. This software is based on the widely used platform BCI2000 [START_REF] Schalk | BCI2000: a general-purpose braincomputer interface (BCI) system[END_REF] so, it takes advantage of the reliability that such a platform offers. The UMA-BCI Speller wraps BCI2000 in such a way that its configuration and use are much more visual and, therefore, easier. Users can configure their speller more appropriately using characters, images or sound cues, and they can navigate through different layouts, thus opening the door to complex speller configurations. As with a P300 speller developed with BCI2000, a Stepwise Linear Discriminant Analysis (SWLDA) of the data was performed to obtain the weights for the P300 classifier and calculate the accuracy. A detailed explanation of the SWLDA algorithm can be found in the P300Classifier user reference [START_REF]P300Classifier[END_REF].

C. The spelling paradigms

Two different paradigms were evaluated in this study. Both paradigms were based on the previously mentioned row-column lighted paradigm developed by Farwell and Donchin [START_REF] Farwell | Talking off the top of your head: toward a mental prosthesis utilizing event-related brain potentials[END_REF], however, the current proposal used a 5 x 5 matrix (25 symbols, i.e., letters "A" to"Y").

The first paradigm employed a flash stimulus based on the study developed by [START_REF] Zhang | Evaluation of color modulation in visual P300-speller using new stimulus patterns[END_REF], that is, red famous faces with a white rectangle (the same stimulus for all the symbols).

The second paradigm, our proposal, used a flash stimulus based on pictures: one image for each symbol (that is, 25 pictures). All the images were obtained from the International Affective Picture System (IAPS; [START_REF] Lang | International Affective Picture System (IAPS): Technical Manual and Affective Ratings[END_REF]). The images were selected according two conditions: 1) neutral pictures (low arousal and medium valence images) and 2) images with the same proportion, that filled all the space and did not have black paddings. Both conditions are represented in Figure 1.

For both paradigms, a Stimulus Onset Asynchrony (SOA) of 304 ms and an Inter-Stimulus Interval (ISI) of 96 ms were used, so each stimulus was presented for 208 ms.

D. Procedure

The experiment was carried out in an isolated room. Participants sat at a distance of, approximately, 60 cm from the screen. Each participant participated in one session to evaluate the two paradigms. The order of the paradigms was counterbalanced across participants. Each session consisted of a calibration phase and a copy-spelling phase.

We used three words for calibration purpose and each one had four letters, having a total of 12 characters per condition, with a short break between words (variable at the request of the user). Each letter flashed 20 times and the user was asked to count these flashes to maintain the attention. The writing time for each character in this phase was 30.4 s. The specific French words were: "FEUX" (fire), "CHAT" (cat) and "PURE" (pure). In this phase, there was no feedback, and the recorded EEG was used to train the classifier.

The copy-spelling phase started after the calibration and training of the classifier. In this phase, the number of trials used to select a target was dependent on the offline classification accuracies. The used criterion was that the number of trials should be one trial more than the minimum number of trials required to obtain 100% accuracy in the calibration phase. In the copy-spelling phase, participants had to spell four four letters French words: "ABRI" (refuge), "LUNE" (moon), "YOGA" (yoga) and "CHEF" (boss). In case of incorrect selection, the participants were instructed not to correct and to continue with the next target. During this phase, the selected symbols were shown at the top of the screen.

E. Evaluation

Two parameters were used to evaluate the effect of the paradigm and stimulus type on the performance: i) the accuracy in the copy-spelling phase (i.e., the number of correct selections divided by the total number of characters, that is, 16) and ii) the Information Transfer Rate (ITR, bits/min) based on the following formula [14].

ITR = {log2 N + P log2 P + (1 -P) log2 [(1 -P)/(N -1)]}/T
where P denotes the classification accuracy, N denotes the number of targets (N was 25 in this experiment) and T denotes the time interval per selection (that is, the number of sequences to select a symbol in the copy-spelling phase).

It should be advised that the pause between selections was not considered to calculate the ITR.

Due to the small sample size, non-parametric analyses were carried out. Due to the preliminary nature of the present study, no correction method was applied for multiple comparisons. Thus, the obtained conclusions should be considered carefully, being admitted that more tests will be necessary to be carried out, increasing the number of participants and the number of characters in the copy-spelling phase.

III. RESULTS AND DISCUSSION

Table 1 summarizes the obtained results for the accuracy and the Information Transfer Rate (ITR) in the copyspelling phase, for each condition and subject.

Figure 2 and Figure 3 show, respectively, the mean classification accuracy and the ITR achieved by users for each paradigm (condition), in the copy-spelling phase.

Despite the low number of users, these preliminary results show some trends that are worth to be mentioned. Firstly, the mean classification accuracy and the ITR obtained for the red famous faces with a white rectangle (T1) condition (93.75% and 27.33 bits/min, respectively) are similar to those obtained in [START_REF] Zhang | Evaluation of color modulation in visual P300-speller using new stimulus patterns[END_REF] (96.94%) and [START_REF] Li | Comparison of the ERP-Based BCI Performance Among Chromatic (RGB) Semitransparent Face Patterns[END_REF] (28.68 bits/min). In this sense, we can consider that we have correctly replicated the experiment carried out in [START_REF] Zhang | Evaluation of color modulation in visual P300-speller using new stimulus patterns[END_REF].

However, the most interesting results is that, even lightly lower, the obtained results when using neutral pictures as stimulus (T2) are almost the same as those obtained for the red famous faces with a white rectangle (T1). Effectively, the mean number of flashes used in the online copy-spelling phase are 3 for both conditions.

TABLE TYPE STYLES

Regarding the mean accuracy, we obtained 93.75% for the red famous faces with a white rectangle and 92.18% for the neutral image condition. A similar difference is obtained for the mean ITR (27.33 bits/min and 26.6 bits/min for red famous faces with a white rectangle and neutral image conditions, respectively).

Even if these results are preliminary due to the low number of participants, they indicate that using neutral pictures as flashing stimuli does not make the performance worse. This paradigm has a huge advantage compare to the one proposed by [START_REF] Zhang | Evaluation of color modulation in visual P300-speller using new stimulus patterns[END_REF]. If in the first condition (T1) the stimuli are the same for each element of the speller (a red famous face with a white rectangle), in the proposed paradigm, a different image is used for each element. These images can be used to develop more attractive and usable interfaces, allowing to create a speller based on pictogram or control systems in which each figure corresponds to a specific command.

IV. CONCLUSION AND FUTURE WORK

The present preliminary study about the effect of different sets of flashing stimuli based on images has shown some trends that should be further explored in future proposals. The main finding is that the use of neutral pictures does not worsen the performance compared to one of the most effective BCI-spellers recently proposed in the literature and based on red famous faces with a white rectangle. Moreover, it would be necessary to increase the number of symbols in the copy-spelling phase and to use a larger sample of participants in order to carry out a statistical comparison and to obtain stronger results and conclusions.

Figure 1 .

 1 Figure 1. Spelling paradigms used in the experiment: a) Red Famous Faces with a white rectangle (T1) with white rectangle, b) Images (T2).

Figure 2 .

 2 Figure 2. Classification accuracy (mean ± standard error) of the two paradigms during copy-spelling phase (T1: Red Famous Faces with a white rectangle, T2: Images).

Figure 3 .

 3 Figure 3. Information Transfer Rate (ITR; mean ± standard error) of the two paradigms during copy-spelling phase (T1: Red Famous Faces with a white rectangle, T2: Images).

TABLE I .

 I

Copyright (c) IARIA, 2022. ISBN: 978-1-61208-980-5 BRAININFO 2022 : The Seventh International Conference on Neuroscience and Cognitive Brain Information

ACKOWLEDGMENT

This work was partially supported by the project SICCAU: RTI2018-100912-B-I00 (MCIU/AEI/FEDER, UE) and by the University of Malaga. Moreover, the authors would like to thank all participants for their cooperation. This work has been carried out in a framework agreement between the University of Málaga and the University of Bordeaux (Bordeaux INP).