Andrew S S Wilson

Michael S Hill

Mary F Mahon

Chiara Dinoi

Laurent Maron
email: laurent.maron@irsamc.ups-tlse.fr

Dehydrohalogenation of halobenzenes and C(sp(3))-X (X = F, OPh) bond activation by a molecular calcium hydride

Keywords:

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

Introduction

From the synthesis of medicinal compounds to agrochemicals, aromatic substitution reactions provide a broadly useful platform for the modification of aromatic ring scaffolds and are of pivotal importance in many organic transformations. Although a majority of such transformations operate by the addition of appropriate electrophiles to electron-rich arene π systems (i.e. electrophilic aromatic substitution), [START_REF] Smyth | Chapter 11 in March's Advanced Organic Chemistry: Reactions, Mechanisms and Structure[END_REF] it has long been recognised that alternative nucleophilic substitution (SNAr) pathways are also accessible, particularly for arene systems bearing electron withdrawing substituents. [START_REF] Bunnett | [END_REF]3 Although a majority of SNAr processes require the stepwise formation of a discrete, non-aromatic Meisenheimer intermediate, a number of studies have lent credence to the operation of alternative concerted substitution (cSNAr) pathways. 4,5 Of particular relevance to the current contribution, are Chiba's report of the hydrodehalogenation of haloarenes with a sodium hydride-iodide composite and Tuttle and Murphy's recent account of the role of potassium hydride in haloarene reduction (Scheme 1). [6][7][8] -2-Foreshadowed by an earlier empirical study by Pierre and co-workers, 9 this latter study employed a combination of experimental and computational techniques to demonstrate that concerted displacement of halide from haloarenes is initiated by attack of the naked hydride donor at the π* orbital of the aromatic ring. Although evidence for single electron transfer was observed for reactions performed in benzene, the formation of benzyne intermediates was discounted under all conditions, and a cSNAr mechanism was deduced to predominate in procedures carried out in THF. In contrast, although documented examples are sparse, related reports of the reactivity of molecular lanthanide or d 0 transition metal hydrides with halobenzenes are typically complicated by the formation of the reactive benzyne intermediate via ortho-metalation and cleavage of the C-halogen bond. 10 Scheme 1: Concerted nucleophilic aromatic substitution (cSNAR) by potassium hydride and the hydrodehalogenation of iodobenzene. 8,4,9 Our current interest in these processes derives from recent advances arising from the chemistry and reactivity of heavier alkaline earth hydride derivatives. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] Our particular focus has been provided by the molecular β-diketiminato calcium hydride, [(BDI)CaH]2 (1; BDI = HC{(Me)CN-2,6-i-Pr2C6H3}2), which serves as a potent source of the hydride nucleophile. [30][31][32][33][34][35][36][37][38] We have previously reported that that the hydride ligands of compound 1 react in a stepwise fashion and through retention of its dimeric structure during their nucleophilic addition to accessible C=C bonds in alkenes and even the high energy π systems of aromatic hydrocarbons. 38,34 While the former reactions give rise to a range of calcium alkyl derives, which are themselves sufficiently reactive to effect the nucleophilic activation of H2 and benzene, 31,30,39 the outcome of hydride addition to a range of polyaromatic hydrocarbons dis[played an apparent dependence on the energy of the relevant π* system and could be correlated with the arene reduction potential (E 0 ). 34 Whereas degenerate Ca-H/C-H exchange between benzene (E 0 = ca. -3.4 V) and compound 1 was calculated to involve a high energy nucleophilic attack of hydride (∆H ‡ 35.5 kcal mol -1 ), similar disruption of the aromaticity of tetracene, anthracene or naphthalene induced facile loss of atomic hydrogen and the formation of a radical anion intermediate en route to the ultimate arene dianion products of two electron reduction. While the reduction of naphthalene (E 0 = ca. -3.4 V), in particular, indicates that compound 1 presents as a highly potent molecular reducing agent, the reaction with benzene may be viewed as broadly analogous to the dehalogenative processes depicted in Scheme 1b. In this study, therefore, we report our initial observations of the reactivity of compound 1 with the monohalobenzenes, C6H5X (X = I, Br, Cl, F) and related transformations with α,α,α-trifluorotoluene and anisole.

Results and Discussion

Hydrodehalogenation of halobenzenes. Immediate analysis of a reaction between compound 1 and two equivalents of iodobenzene in C6D6 at room temperature provided a 1 H NMR spectrum comprising two predominant compounds. The dicalcium hydride-iodide (2) was tentatively identified by the emergence of a γ-methine BDI signal at 4.76 ppm, while the formation of the dimeric calcium iodide [3, δ 4.84 (γ-CBDI) ppm] was subsequently confirmed by its independent isolation in analytically pure form (vide infra). The signals arising from compounds 2 and 3, along with a minor quantity of [(BDI)2Ca] (δ 4.94 (γ-C) ppm), 40 were observed to integrate in an approximate ratio of 2:3:1, while the production of additional C6H6 was evidenced by a clear increase in intensity of the signal associated with the residual protio resonance of C6D6 (Scheme 2). An analogous reaction of two equivalents of bromobenzene and 1 similarly afforded a 1 H NMR spectrum containing a mixture of unreacted 1, an intermediate species cautiously assigned as the dicalcium hydride-bromide [4, δ 4.76 (γ-CBDI) ppm] and the dimeric calcium bromide, [(BDI)CaBr]2 [5, δ 4.82 (γ-CBDI) ppm] (Scheme 2). Although the 1 H NMR spectrum of this reaction mixture was effectively unchanged after one day at room temperature, a further reaction of 1 with a ca. 100-fold excess of bromobenzene afforded a 1 H NMR spectrum that consisted predominantly of compound 5 after three days at room temperature. In contrast to the facility of the reactions with its heavier halide congeners, initial analysis of a reaction performed with two equivalents of chlorobenzene and 1 provided a 1 H NMR spectrum arising entirely from the unreacted starting materials. After one week at room temperature, however, the consumption of ca. 50% of the initial quantity of 1 was accompanied by the emergence of the dicalcium hydride-chloride (6), which could be identified in the 1 H NMR spectrum by the appearance of a new γ-CHBDI resonance at δ 4.85 ppm, and which integrated in an approximate 2:1 ratio with an accompanying hydride signal at δ 3.95 ppm. A subsequent reaction between 1 and an excess of chlorobenzene afforded almost exclusive formation of compound 6 after one day at room temperature.

In a similar manner to the reaction with C6H5Cl, addition of two equivalents of fluorobenzene to a C6D6 solution of 1 provided a 1 H NMR spectrum solely indicative of the unreacted starting materials at the first point of analysis. Storage at room temperature for four days, however, afforded an intractable mixture of unidentified compounds. Although residual unreacted fluorobenzene could -4-be identified in the 19 -5-Table 1: Selected bond (Å) and angles (°) of 3, 5, 6, 7 and 8.

(X

= I) 5 (X = Br) a 6 (X = Cl) b 7 (X = F) b 8 (X = OPh) c
Ca1-N1

1-x, 1-y, -z; b 1-x, -y, -z; c -x, -y, 1-z.
The veracity of the deductions arising from the in situ analysis of these reactions was supported by the characterisation of pure samples of compounds 3, 5 and 6, which were isolated as single crystals suitable for X-ray diffraction analysis either from the reaction mixture (3) or from toluene/hexane solutions (5, 6). Calculations were carried out at the DFT level (B3PW91) in order to get some insights onto the formation of complexes 4, 5 and 6 from the reaction of either bromo-or chloro-benzene with 1. For clarity, only the reaction of 1 with bromobenzene, that is the formation of 4 and 5, will be discussed in detail. The formation of 6 is presented in the ESI (Figure S24).

The lowest energy profile in presented in Figure 2 but other possible reactions were computed and were found to be higher in energy (see Figure S25). As was the case in previous observations of compound 1, 30,31 the reaction is found to occur at the dicalcium complex since the dimer disruption energy is more than 40.4 kcal mol -1 . After the formation of a loosely bonded bromobenzene adduct (BBr, +0.4 kcal mol -1 ), a SNAr-type transition state (TS-BCBr) has been located. Consistent with the relatively slow reaction observed, the associated barrier is 32.0 kcal mol -1 . Following the intrinsic reaction coordinate yields the formation of the very stable benzene solvated complex 4 (CBr), whose formation is exothermic by 67.7 kcal mol -1 . The latter reaction energy indicates that the experimental time scale for the completion of the reaction is s direct consequence of the height of this barrier.

Subsequent benzene to bromobenzene exchange is athermic but allows complex 4 to undergo a further SNAr-type reaction via a similar barrier of 34.0 kcal mol -1 . From this perspective, therefore, the remaining hydride in complex 4 appears to be almost as reactive as that invoked in its own generation from complex 1. Although the formation of the solvated version of complex 5 (EBr) is again highly exothermic (-135.6 kcal mol -1 with respect to the entrance channel, -67.9 kcal mol -1 , -7-from CBr), the barriers associated with the production of both 4 and 5 are effectively identical, irreversible and consistent with the experimental observations of relatively slow reactions. It is noteworthy that the inclusion of dispersion effect led to a similar profile as that reported in Figure 2.

The associated barriers, however, are too low and inconsistent with a reaction needing three days at room temperature for completion (see Figure S26). We ascribe this observation as an artefact resulting from an overestimation of the attractive interactions in the bimetallic species and a resultant lowering of the barriers.

The formation of complex 6 was computed to follow a similar pathway as that shown in Figure 2 (Figure S24) with similar barrier. The lack of formation of the chloride equivalent of complex 5 is, thus, attributed to the rapid crystallisation of complex 6 (CCl in Figure S24), which prevents further reaction.

Reactivity of compound 1 and α,α,α-trifluorotoluene and anisole. The contrasting reactivity of 1 with fluorobenzene was tentatively ascribed as a consequence of initial ortho-metalation and subsequent benzyne formation. Similar processes have previously been deduced for reactions between the range of halobenzenes utilised herein and [Cp*2YH]2. 10 This reactivity is also reminiscent of directed ortho-metalation (DoM) chemistry, in which aromatic substituents such as an amide or methoxy group are employed to direct the site of metalation by organolithium reagents, and which continues to be a widely employed strategy to effect the regioselective functionalisation of substituted aromatic and heteroaromatic compounds. [44][45][46][47] The trifluoromethyl substituent of α,α,α-trifluorotoluene is known to induce pronounced increases in the acidity of the aryl-hydrogen bonds. This is particularly acute at the ortho positions, which are readily deprotonated by s-block organometallics such that, for example, the regioselective ortho-metalation of α,α,α-trifluorotoluene has been achieved

with n-butyllithium, 48,49 n-butylsodium, 50 the alkali metal zincate [NaZn(TMP)t-Bu2] (TMP = 2,2,6,6tetramethylpiperidide), 51 the aluminate [LiAl(TMP)t-Bu3] 52 and the magnesiate [(PMDETA)2K2Mg(CH2SiMe3)] (PMDETA = N,N,N',N'',N''-pentamethyldiethylenetriamine). 53 Notably, the sodium magnesiate inverse crown complex [Na4Mg2(TMP)6(n-Bu)2] selectively ortho,meta-dimetalates α,α,α-trifluorotoluene via a templating motif. 54 In a similar manner, the methoxy substituent of anisole effects predominant ortho-metalation via inductive and complex-induced proximity effects. 55 DoM of anisole was initially observed with n-BuLi and PhLi during the seminal studies of Gilman 56 and Wittig. 57 Directed ortho-lithiation has since been investigated with NMR spectroscopy, 58 computational calculations, 58,59 isotopically labelled experiments 60 and X-ray crystallography. 61 Similarly, ortho deprotonation with alkali metal zincate, [(THF)LiZn(TMP)(t-Bu)2], 62 aluminate, [(THF)LiAl(TMP)2(i-Bu)2], 63 and magnesiate, [(PMDETA)KMg(TMP)2(CH2SiMe3)], 64 complexes has been readily achieved.

Based on these significant precedents, therefore, it was postulated that the basicity of compound 1 may enable the deprotonation of α,α,α-trifluorotoluene and anisole in a similar fashion.

-8-Immediate assessment of a reaction between two equivalents of α,α,α-trifluorotoluene and 1 in C6D6 toluene afforded single crystals of 7 suitable for X-ray diffraction analysis (Figure 1d and Table 1).

Although the bridging fluoride and hydride ligands are again disordered, the centrosymmetric Ca-µ2-F-Caʹ bridged structure of compound 7 is comparable to those of the previously reported β- by the appearance of a further singlet resonance at δ 0.16 ppm, which was readily attributed to methane. 68 The origin of these observations was resolved by removal of deuterobenzene and -9-crystallisation of the solid residue from toluene. The resultant single crystal X-ray analysis confirmed the identify of 8 as the calcium phenoxide derivative, [(BDI)CaOPh]2 (Figure 3, Table 1), and the overall stoichiometry of the reaction shown in Scheme 3. The calcium centres of the centrosymmetric structure of 8 are coordinated by typical calcium-nitrogen interactions from the β-diketiminate ligand In summary, the β-diketiminato calcium hydride (1) effects the dehydrohalogenation of iodobromo-and chlorobenzene under mild conditions. Furthermore, compound 1 is able to activate strong bonds of α,α,α-trifluorotoluene (C-F; ~500 kJmol -1 ) and anisole (C-O; 273 kJmol -1 ). Although the outcome of both these latter processes is striking, their viability may be attributed to the resultant thermochemical strength of the resultant Ca-F (557 kJ mol -1 ) and Ca-O (348 kJ mol -1 ) bonds.

diketiminato calcium fluorides, [ (BDI

Synthesis of [{(BDI)Ca}2(µ-F)(µ-H)] (7)

α,α,α-trifluorotoluene (500 µL) and C6D6 (50 µL) was added to 1 (60 mg 0.065 mmol) and stored at room temperature overnight (ca. 16 hrs) affording an orange solution. The resulting solution was evaporated to dryness, redissolved in toluene (ca. 0.5 ml), layered with hexane (ca. 0.5 ml) and cooled to -35 °C to yield 7 as colourless single crystals (13 mg, 11%). [START_REF] Smyth | Chapter 11 in March's Advanced Organic Chemistry: Reactions, Mechanisms and Structure[END_REF] H NMR (500 MHz, benzene-d6) δ (NC(CH3)CH) ppm. 19 F NMR (470 MHz, benzene-d6) δ -42.0 ppm ( 2 JHF = 37. 3 Hz). Repeated attempts at elemental analysis failed to provide meaningful results.

Synthesis of [(BDI)CaOPh]2 (8)

Scheme 2 :

 2 Scheme 2: Reaction of 1 with halobenzenes.

  F{ 1 H} NMR spectrum (δ -112.9 ppm), this resonance was observed alongside a series of similar but unassignable fluorine resonances at δ -75.5, -74.3, -72.8, -72.2, -70.3 and -44.7 ppm.

Figure 1 :

 1 Figure 1: ORTEP s of compound (a) compound 3, (b) compound 5, (c) compound 6 and (d) compound 7 with thermal ellipsoids at 30%. Hydrogen atoms, except H1 of compounds 6 and 7, have been omitted for clarity. Symmetry operations to generate primed atoms: (5) 1-x, 1-y, -z; (6, 7) 1-x, -y, -z.

Figure 2 :

 2 Figure 2: Computed enthalpy (Gibbs free energy in parenthesis) profile for the reaction of bromobenzene with complex 1 at room temperature.

Scheme 3 :

 3 Scheme 3: Synthesis of compound 8.

[ 2 . 72 Figure 3 :

 2723 Figure 3: ORTEP representation of compound 8 with thermal ellipsoids at 30%. Hydrogen atoms have been omitted for clarity. Atoms with primed labels related to those in the asymmetric unit by the -x, -y, 1-z symmetry operation.

7.10 - 7 .

 7 03 (m, 12H, Ar-H), 4.83 (s, 2H, NC(CH3)CH), 3.83 (d, 3 JHF = 37.3 Hz, 1H, CaH), 3.11 -3.03 (m, 8H, CH(CH3)2), 1.66 -1.65 (m, 12H, NC(CH3)CH), 1.14 (d, 3 JHH = 6.8 Hz, 24H, CH(CH3)2), 1.05 (d, 3 JHH = 6.8 Hz, 12H, CH(CH3)2), 1.02, 0.98 (d, 3 JHH = 6.8 Hz, 6H, CH(CH3)2) ppm. 13 C{ 1 H} NMR (126 MHz, benzene-d6) δ 165.4, 165.4, 165.3(NC(CH3)CH), 144.5, 143.9, 143.5 (Cipso), 141.9, 141.9, 141.7 (Cortho), 125.0, 125.0, 124.8 (Cpara), 124.5, 124.3, 123.6 (Cmeta), 94.6, 94.4, 94.3 (NC(CH3)CH), 28.4, 28.3, 28.3 (CH(CH3)2), 25.0, 24.7, 24.6, 24.2, 24.2, 24.2 (CH(CH3)2), 23.6, 23.6, 23.5

  afforded a 1 H NMR spectrum containing only unreacted starting materials. Continued monitoring over 7 days, however, demonstrated the slow formation of the calcium hydride-fluoride [{(BDI)Ca}2(µ-F)(µ-H)] (7), which was identified by the appearance of diagnostic doublet resonances at δ 3.84 ppm and δ -42.0 ppm in both the 1 H and19 F NMR spectra ( 2 JHF = 37.3 Hz). Although the mechanism of fluoride abstraction was not investigated in detail, the absence of a19 F resonance attributable to C6H-5CHF2 [δ( 19 F) -111 ppm]65 and the appearance of unidentified singlet resonances in the19 F NMR spectrum at δ -63.0, -72.8 and -83.8 ppm indicates that the reaction is unlikely to be predicated solely on a direct metathetical Ca-H/F-C exchange process.Despite the apparent complexity of the reaction, and in a similar manner to the reactions with halobenzenes described above, treatment of 1 with a ca. 100-fold excess of α,α,α-trifluorotoluene

afforded a solution that contained predominantly compound 7 [δ 4.83 (Ca-H), 3.84 (γ-CBDI) ppm] after only one day at room temperature. Monitoring of this solution by 1 H and

19

F NMR spectroscopy confirmed that compound 7 persisted in solution and provided no detectable evidence for redistribution to either compound 1 or [(BDI)CaF]2. Crystallisation of the reaction mixture from

74

  Experimental SectionAll manipulations were carried out using standard Schlenk line and glovebox techniques under an inert atmosphere of argon. NMR experiments were conducted in J Young tap NMR tubes prepared and sealed in a Glovebox. NMR spectra were collected on an Agilent ProPulse spectrometer operating at 500 MHz ( 1 H), 126 MHz ( 13 C), 470 MHz ( 19 F). The spectra were referenced relative to residual protio solvent resonances or an internal standard. Solvents (toluene, hexane) were dried by passage through a commercially available (MBraun) solvent purification system, under nitrogen and stored in ampoules over 4Å molecular sieves. C6D6 was purchased from Sigma-Aldrich Corp., dried over a potassium mirror before vacuum distilling under argon and storing over molecular sieves. Calcium , redissolved in toluene (ca. 0.5 ml), layered with hexane (ca. 0.5 ml) and cooled to -35 °C to yield 5 as colourless single crystals (11 mg, 30%).[START_REF] Smyth | Chapter 11 in March's Advanced Organic Chemistry: Reactions, Mechanisms and Structure[END_REF] H NMR (500 MHz, benzene-d6) δ 7.17 -7.11 (m, 6H, Ar-H), 4.84 (s, 1H, NC(CH3)CH), 3.06 (hept, 3 JHH = 6.7 Hz, 4H, CH(CH3)2), 1.66 (s, 6H, NC(CH3)CH), 1.18 (d, 3 JHH = 6.7 Hz, 12H, CH(CH3)2), 1.11 (d, 3 JHH = 6.7 Hz, 12H, CH(CH3)2) ppm. Chlorobenzene (500 µL) and C6D6 (50 µL) was added to 1 (30 mg 0.033 mmol) and stored at room temperature overnight (ca. 16 hrs) affording a pale-yellow solution. The resulting solution was evaporated to dryness, redissolved in toluene (ca. 0.5 ml), layered with hexane (ca. 0.5 ml) and cooled to -35 °C to yield 6 as colourless single crystals (8 mg, 25%).[START_REF] Smyth | Chapter 11 in March's Advanced Organic Chemistry: Reactions, Mechanisms and Structure[END_REF] H NMR (500 MHz, benzene-d6) δ 7.13 -7.06 (m, 12H, Ar-H), 4.84 (s, 2H, NC(CH3)CH), 3.95 (s, 1H, CaH), 3.08 -3.00 (m, 8H, CH(CH3)2), 1.66 -1.65 (m, 12H, NC(CH3)CH), 1.15 -1.05 (m, 48H, CH(CH3)2) ppm. 13 C{ 1 H} NMR (126 MHz, benzene-d6) δ 166.0, 165.7 (NC(CH3)CH), 143.0, 143.0 (Cipso), 142.2, 142.1 (Cortho), 125.5, 125.3 (Cpara), 124.5, 124.5 (Cmeta), 94.1 (NC(CH3)CH), 28.8, 28.6 (CH(CH3)2), 25.2, 24.9, 24.7, 24.4 (CH(CH3)2), 23.7, 23.7 (NC(CH3)CH) ppm. Elemental analysis for C58H83Ca2ClN4: C, 73.18; H, 8.79; N, 5.89%. Found: C, 73.12; H, 8.92; N, 5.85%.

	13 C{ 1 H} NMR (126 MHz, benzene-d6) δ 166.2 (NC(CH3)CH), 143.2 (Cipso), 142.2 (Cortho), 125.5
	(Cpara), 124.5 (Cmeta), 95.4 (NC(CH3)CH), 28.9 (CH(CH3)2), 25.2, 24.6 (CH(CH3)2), 23.9
	(NC(CH3)CH) ppm. Elemental analysis for C58H82Ca2Br2N4: C, 64.79; H, 7.69; N, 5.21%. Found: C,
	64.51; H, 7.57; N, 5.18%.
	Synthesis of [{(BDI)Ca}2(µ-Cl)(µ-H)] (6)
	Single crystals suitable for X-ray diffraction analysis were obtained directly from the analogous NMR
	scale reaction of iodobenzene with 1 in C6D6. 1 H NMR (500 MHz, benzene-d6) δ 7.18 -7.14 (m, 6H,
	Ar-H), 4.84 (s, 1H, NC(CH3)CH), 3.10 (hept, 3 JHH = 6.8 Hz, 4H, CH(CH3)2), 1.65 (s, 6H,
	NC(CH3)CH), 1.25 (d, 3 JHH = 6.8 Hz, 12H, CH(CH3)2), 1.13 (d, 3 JHH = 6.8 Hz, 12H, CH(CH3)2) ppm.
	13 C{ 1 H} NMR (126 MHz, benzene-d6) δ 166.5 (NC(CH3)CH), 142.1 (Cortho), 125.5 (Cpara), 124.5
	(Cmeta), 95.2 (NC(CH3)CH), 29.0 (CH(CH3)2), 25.9, 24.6 (CH(CH3)2), 24.2 (NC(CH3)CH) ppm.
	Elemental analysis for C58H82Ca2I2N4: C, 59.58; H, 7.07; N, 4.79%. Found: C, 59.75; H, 7.18; N,
	4.76%.

iodide (99.95%) and organic reagents were purchased from Sigma-Aldrich Corp. and either distilled or recrystallised prior to use. [(BDI)CaH]2 (1) was synthesised by a literature procedure.

30

Synthesis of [(BDI)CaI]2 (3)

Iodobenzene (7.27 µL, 0.065 mmol) was added to an unstirred toluene (ca. 0.5 ml) solution of 1 (30 mg, 0.033 mmol). After 16 hrs at room temperature hexane (ca. 0.5 ml) was added to the resultant pale-yellow solution which was stored at -35 °C to afford colourless crystals of 3 (18 mg, 45%).

Synthesis of [(BDI)CaBr]2 (5)

Bromobenzene (500 µL) and C6D6 (50 µL) were added to 1 (30 mg 0.033 mmol) and stored at room temperature for three days affording a pale-yellow solution. The resulting solution was evaporated to -11-dryness

Ackknowledgements

We thank the EPSRC (UK) for the provision of a DTP studentship (ASSW) and the University of Bath. LM is a senior member of the Institut Universitaire de France. CalMip is acknowledged for a generous grant of computing time

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Graduate Student Member, IEEE, Frédéric Lafon , Senior Member, IEEE Oskari Leppäaho

Frederic Lafon

Priscila Fernandez-Lopez

Marine Stojanovic

Member, IEEE Tim Claeys

Richard Perdriau

Senior Member, IEEE Mohamed Ramdani

Triaxial Cell for Determining Shielded Cable Transfer Impedance During Environmental Stress

Keywords: Electromagnetic compatibility, cable shielding, transfer impedance, aging, reliability

I. INTRODUCTION

S HIELDED CABLES have been used for data transmission for over a hundred years after Heaviside's first patent of a coaxial cable [START_REF] Heaviside | Improvements in Electrical Conductors and in the Arrangement and Manner of Using Conductors for Telephonic and Telegraphic Purposes[END_REF]. While some modern data transmission has shifted to unshielded twisted pairs (UTP) and optical links, a major part of high-speed data transmission still relies on shielded cables.

In automotive, the future trends of electrification and advanced driver-assistance systems (ADAS) still rely heavily on the use of shielded cables in one form or other: shielded twisted pairs, twinaxial (an impedance controlled non-twisted shielded pair) or traditional coaxial cables for data [START_REF] Rusch | Robust Connectivity Solutions for Next-Generation Automotive Data Networks[END_REF] and shielded power cables for electrification.

In aerospace, data transmission is moving towards fiber optics [START_REF] Nguyen | Fiber-optic communication links suitable for on-board use in modern aircraft[END_REF], but electrification keeps shielded cables on the agenda. Especially, shielding the new medium-voltage power distribution systems remains a concern [START_REF]Funding Opportunity Announcement[END_REF].

In the manufacturing industry, the fourth industrial revolution is increasing data usage that drives communication needs. Some of those communication links will be wireless, some optical, but some part will remain in shielded cables. Similarly to mobility industry, the advent of power electronics is constantly increasing the amount of variable frequency drives that will have applications that need shielded cables for EM disturbance [START_REF] Skibinski | Generation, control and regulation of EMI from AC drives[END_REF] and bearing current control [START_REF] Weicker | Review on system parameters in variable speed AC-induction motor drives with parasitic electric bearing currents[END_REF].

With the aforementioned advent of the increased electrification on many industries, it has become more crucial to characterize the performance of shielded cables over their lifetime to ensure that systems using them remain reliable. One important performance parameter of a shielded cable is its transfer impedance [START_REF] Vance | Shielding effectiveness of braided-wire shields[END_REF]. Transfer impedance of typical shielded cables can be defined per unit-length as

z T = r T + jωl T (1)
consisting of transfer resistance r T and transfer inductance l T , where both r T and l T are complex, frequency dependent variables due to skin-effect. This model covers all the cables studied in this paper. For solid shields, only r T is relevant [START_REF] Schelkunoff | The Electromagnetic Theory of Coaxial Transmission Lines and Cylindrical Shields[END_REF], and l T = 0. In case they have openings, l T is not zero, and depends on the shape and amount of the openings [START_REF] Kaden | L.3. Kopplungswiderstand von Leitungsschirmen[END_REF]. For helical shields, as most foil shields are wound, r T and l T are derived from solid shield's r T and its internal impedance with some helix specific coefficients applied to them [START_REF] Kaden | L.3. Kopplungswiderstand von Leitungsschirmen[END_REF]. For braided shields, both terms can be defined for a single braid [START_REF] Kley | Optimized single-braided cable shields[END_REF] or a combination of two braids [START_REF] Vance | Shielding Effectiveness of Braided Wire Shields[END_REF]. A theory to combine arbitrary shield configurations is also available [START_REF] Kaden | L.3. Kopplungswiderstand von Leitungsschirmen[END_REF]. Often, accurate definitions add unnecessary complexity, and both r T and l T are commonly treated as frequency independent real values without significant loss of accuracy [START_REF] Vance | Shielding effectiveness of braided-wire shields[END_REF]. However, this approach is not valid for shields with low l T as skin-effect reduces r T before the inductive impedance is large enough to compensate for it.

Many methods have been used to characterize transfer impedance along the years, the most important ones being lineinjection [START_REF] Eicher | Very Low Frequency To 40 GHz Screening Measurements On Cables And Connectors; Line Injection Method And Mode Stirred Chamber[END_REF], triaxial [START_REF] Kley | Measuring the coupling parameters of shielded cables[END_REF], and reverberation chamber [START_REF] Démoulin | Shielded Cable Transfer Impedance Measurements in the Microwave Range of 1 GHz to 10 GHz[END_REF] methods. A fairly recent listing of other methods can be found in [START_REF] Deschenes | Effect of gland quality on the screening effectiveness of cable-connector assemblies[END_REF]. While it has been shown that the line-injection method has the widest frequency range starting from DC [START_REF] Démoulin | Shielded Cable Transfer Impedance Measurements High frequency range 100 MHz-1 GHz[END_REF], the triaxial method has been a go-to method for many practitioners due to its robustness and homogeneous field excitation. The aforementioned methods have been complemented by the reverberation chamber method that is valid from a few hundred of megahertz to at least 10 GHz.

©2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The effect of environmental stresses to shielded cables has been studied on the level of dielectrics to understand the dependency of RF losses [START_REF] Bur | Dielectric properties of polymers at microwave frequencies: A review[END_REF] and dielectric strength on temperature [START_REF] Montanari | Progress in electrothermal life modeling of electrical insulation during the last decades[END_REF], and other stresses like radiation [START_REF] Nakamura | Degradation of Dielectric Properties of Polyethylene by Combined Y-Irradiation and Thermal Stresses[END_REF]. Now, the authors extend these studies to evaluate the dependency of shielded cable transfer impedance on thermal and vibration stresses.

In this paper, the authors present a new triaxial cell design intended for environmental testing of shielding effectiveness (SE) and transfer impedance of shielded cables. The cell design is discussed in Section II. A comparison of RF performance against a commercial cell in laboratory ambient conditions is drawn in Section III, and in Section IV the cell design is verified during highly accelerated life tests (HALT) [START_REF] Charki | Robustness evaluation using highly accelerated life testing[END_REF]. Section IV presents typical transfer impedance responses of shielded cables to steady-state and cyclic thermal stress, random vibration, as well as combined cyclic thermal stress and random vibration. Finally, aging is evaluated by comparing measurement results of fresh samples to the ones that have undergone the environmental test cycle.

II. TRIAXIAL CELL

Different configurations of the triaxial cell for measurement of shielded cable transfer impedance have been analyzed [START_REF] Kley | Measuring the coupling parameters of shielded cables[END_REF], and some of them are standardized [START_REF]Metallic Communication Cable Test Methods -Part 4-3: Electromagnetic Compatibility (EMC) -Surface Transfer Impedance -Triaxial Method[END_REF]. An overview of the measurement principle is given in Fig. 1, where a transmission S-parameter S 21 is measured between P1 and P2. Measurements can be done either by using a combination of a signal generator and a spectrum analyzer, or with a vector network analyzer (VNA). In the measurements of this paper, a VNA is exclusively used.

Transfer impedance can be derived from measured S 21 , length L c , and termination R load of the cable-undertest (CUT) [START_REF]Metallic Communication Cable Test Methods -Part 4-3: Electromagnetic Compatibility (EMC) -Surface Transfer Impedance -Triaxial Method[END_REF]

z T = R load + Z 0 2L c S 21 , (2)
where Z 0 is the impedance of the VNA. This corresponds to the short-circuited near-end configuration assuming high optical coverage of the shields and electrically short L c , so that transfer admittance y T and propagation effects can be omitted.

The design of the environmental triaxial cell is shown in Fig. 2. The main characteristics of the cell are gathered in Table I. The given transfer impedance measurement frequency range can be extended to cover the full shielding effectiveness frequency range by extrapolating through the first resonance points due to the sample length [START_REF]Metallic Communication Cable Test Methods -Part 4-1: Electromagnetic Compatibility (EMC) -Introduction to Electromagnetic Screening Measurements[END_REF].

The cell was constructed from 3 mm thick aluminum sheet metal with 15 mm thick end terminations. Its nominal internal diameter was set to 90 mm. That is the same as the one of a commercial cell available to the authors. Thus, it enabled direct comparisons at laboratory ambient conditions. The diameter selection is not critical to measurement results, as the measured transfer impedance has been shown to be independent of the triaxial cell diameter, as long as the TEMwave condition is sustained [START_REF] Leppäaho | Sensitivity of Shielded Cable Transfer Impedance Measurement to Triaxial Cell Diameter[END_REF]. Critical design choices are discussed in Sections II-A and II-B, where the cell body and CUT termination design are respectively addressed.

A. Hexagonal cross-section and perforations

To enable fast CUT change, the triaxial cell was designed to be split into two halves. For light weight, the cell design was based on an aluminum sheet metal structure. After iterations, the traditional round design was substituted with a hexagonal design to ease the manufacturing.

The most important features of the overall cell design are:

1) Stable characteristic impedance 2) Uniform field around the cable sample

To assess these features of the hexagonal design, a 3D FEMsimulation was carried out. There, the hexagonal design was compared to a round one, and E-field results at 1 GHz are reported in Fig. 3. As the simulation result ended up with only the TEM-mode present up to the maximum frequency of 3 GHz, the H-field magnitude can be calculated from the presented results with the help of the free-space wave impedance [START_REF] Pozar | Chapter 2: Transmission Line Theory[END_REF]. The field distribution and strength close to the cable sample are equal with both cross-sections. The hexagonal cross-section shows some different field strength pattern close to its boundaries. It means that the free air-space between the CUT and the cell wall should be larger than the cable diameter for all CUTs. This condition is satisfied for all the samples that the authors plan to test in this cell. Following the successful cross-section change, the next challenge authors wanted to address was to improve the airflow in the triaxial cell. A traditional closed cell will trap air inside acting as a good insulator during thermal tests. Thus, most of the heat would be conducted to the sample through its mounting at the terminations. However, one of the terminations connects the cable shield just to the center pin of the Nconnector as plastic mounting hardware and dielectric insulate the termination structure limiting any thermal conduction to the cable. This is a very ineffective way of thermal energy transfer resulting in long time constants to reach thermal equilibrium.

To improve thermal transfer by introducing proper airflow around the CUT, a 10-by-10 mm grid of 5 mm holes was drilled on the covers of the hexagonal cell as can be seen in Fig. 2. The effect of this perforation was also studied with 3D FEM-simulation. The results on E-field strength at 1 GHz across the cell in Fig. 4 show that the perforations have minimal effect on the field distribution inside the cell, and thus, to the characteristic impedance of the cell. Only a small difference is seen close to the cell wall, where the E-field magnitude decreases earlier than with the solid designs. However, it will not have a practical effect on the measurements performed. Again, the H-field results follow the E-field as indicated above. The reference field strength for the circular design was analytically calculated as shown in the Appendix following an approach given in [START_REF] Pozar | Chapter 2: Transmission Line Theory[END_REF] to confirm the accuracy of the simulations.

B. Terminations and ferrules

The second topic in the cell design deserving special attention is the cable shield mounting into the body of the triaxial cell. The quality of this joint is assessed by looking at three design parameters:

1) Stable and low contact resistance 2) Mechanically robust structure 3) Ease of changing the sample A stable and low contact resistance is paramount at the end where the CUT is fed as, at that end, the termination makes a short-circuit between the cable shield and the triaxial cell body. Any resistance of that contact will be seen as the resistance of the braid, and thus, as error in the measured transfer resistance. Mechanically robust structure is needed, not only to ensure the stability of the contact resistance during environmental stress, but also to withstand all the stresses that the hanging cable will exert to the terminations during vibration testing. Last, test time at environmental testing laboratories is generally expensive. In order to exploit it the best way possible, the CUT sample should be easy and fast to change.

Against these requirements, four termination methods are graded in Table II: 1) Soldering the cable shield is a robust method, but it is difficult to make and disassemble when used with parts that have large thermal masses, like the termination plates in Fig. 5. 2) BNC-connector or similar quick-connect type would provide very fast sample change possibility, but would Ease of sample change ---+ + + + + + + + + Excellent, + + Very Good, + Good, -Fair, --Poor, ---Bad

TABLE III MEASURED CONTACT RESISTANCES

Contact

Resistance-to-Connector Short-circuit termination 185 µΩ N-center-pin termination 1.87 mΩ lack robustness. An N-connector could fare better, but would still not reach the quality of the solder joint. 3) Pressure contact can be made with pressure plates like in the commercial cell that is used as a reference in this paper. 4) Ferrule method uses widely available hydraulic fittings to connect the cable shield to the triaxial cell. Cable shield is crimped and soldered into a specifically designed ferrule that is then joined to the hydraulic fitting. Grading was made by the authors to help in the selection of the best termination, but it is not intended to be an absolute reference. Based on it, the ferrule termination method was selected. Fig. 5a shows the exploded view drawing of the short-circuited termination. Fig. 5b shows the floating termination, where a similar structure is used with the exception that the adapter is now replaced with a blind termination that is supported with a high-temperature (HT) plastic isolating it from the termination plate. Note, that the thin copper rod is subject to vibration stress, and for the sake of longevity of the test setup, a small part of it should be replaced with a braid to provide sufficient stress relief.

Measured contact resistances of both termination assemblies in Fig. 5 are gathered in Table III. They were measured from the ferrule to the N-connector body for short-circuited termination, and from the ferrule to the center pin of the Nconnector for the floating termination. The measurements were done with a BK Precision 2841 DC resistance meter. The values achieved correspond to very good contact performance and enable reliable operation of the test system.

III. RF TESTING

Initial testing of the developed triaxial cell was performed at ambient laboratory conditions. There, two important facets of the cell operation were tested. The cell performance with a copper pipe calibration piece is discussed in Section III-A. The copper pipe is of the same diameter as the rod used in the simulation studies in Section II-A. In Section III-B, the cell

A. Cell Results

The reflection coefficient measurement of the outer cell is shown in Fig. 6. From the magnitude measurement comparison it can be seen that there is no excess attenuation or radiation from the hexagonal perforated cell below 1 GHz, but the magnitude starts to deteriorate above it. In fact, the performance is even better than that of the commercial cell up to 1 GHz. After 1 GHz, the phase angle does not show strong resonances in the cell, but instead changes slowly as a function of frequency with only minor resonances indicated at multiples of the first resonance frequency. It indicates that after 1 GHz there are frequencies, where either most of the incident power actually reflects from an impedance discontinuity between the copper rod and the blind termination shown in Fig. 5b or radiates from the perforation structure. The differences seen on the reflection coefficient phase between the commercial and perforated hexagonal cells below 1 GHz are due to slightly different length of the cells, and are thus expected.

As a conclusion, the perforated hexagonal cell design of this paper works comparably to the reference commercial cell up to 1 GHz. At higher frequencies, the perforated hexagonal cell does not illuminate the CUT correctly either due to the termination design or the perforations as explained in the previous paragraph. The commercial cell offers adequate performance up to 3 GHz, where the measurement range ended.

B. Cable Results

The transfer impedance measurements of a generic RG-58C/U-cable are shown in Fig. 7. Below 1 MHz, the commercial cell shows a higher measurement value. This is mainly due to the pressure clamp contacts employed in it to interface with the cable shield. These clamps do not always fit perfectly, and can exhibit an increased contact resistance. From 1 MHz to 100 MHz the fit is excellent between the two cells. At higher frequencies there are some discrepancies, where first the perforated hexagonal cell seems to perform better with the resonance peaks at the transfer inductance envelope up to 1 GHz. The resonance points between the two measurements are very close to each other as the measured cable length was very similar: 30 cm for the commercial, and 25 cm for the perforated hexagonal cell. Afterwards, the findings of Section III-A are confirmed as the measurement result of the perforated cell starts to suddenly drop likely due to the weakened illumination. The results match well with the state-of-the-art model [START_REF] Kley | Optimized single-braided cable shields[END_REF].

As a conclusion, both cells are capable of measuring the transfer impedance up to 30 MHz without resonances, and the perforated hexagonal cell seems to follow the envelope of the increasing transfer impedance better up to 1 GHz. Neither one of the cells seems to provide any reliable transfer impedance measurement above 1 GHz.

IV. ENVIRONMENTAL TESTING

Environmental testing applied in the scope of this paper is HALT [START_REF] Gray | Next Generation HALT and HASS: Robust Design of Electronics and Systems[END_REF]. In the field of mechanical reliability, it has controversial nature as the test chambers are generally not designed for absolute repeatability of the tests, but more to provide extreme test conditions and to withstand them. As a consequence, large uncertainty between the set and measured values as well as thermal gradients need to be tolerated. This means that absolute testing is better done with other methods [START_REF] Charki | Robustness evaluation using highly accelerated life testing[END_REF], but for the purposes of this paper the HALT method provides great value for rapid assessment on the feasibility of the developed triaxial cell in environmental testing. Moreover, it can be used to do comparative tests between different technological solutions, like different cable shielding structures. Pictures of the evaluated cables are presented in Fig. 8 with their shield construction highlighted in the captions. The type markings for cables (d) to (f) have been replaced with generic terms due to confidentiality reasons. For each cable, the analysis of environmental dependency is evaluated at two distinct frequencies on the transfer impedance curve so that the first one represents an area, where transfer resistance dominates, and the second one an area, where transfer inductance dominates. The selected frequencies per cable are shown in Table IV. For three cables, transfer inductance needed to be extracted from the shielding effectiveness region as discussed in Section III-B. The first anti-resonance point was used for RG-58, and the second anti-resonance point was used for coaxial and LVDS cables.

The triaxial cell installed in a HALT chamber is shown in Fig. 9. The chamber was setup to run a test cycle that consisted of four distinct phases as shown in Fig. 10: A) Temperature steps from ambient temperature to -50°C, and then to 120°C, or to the minimum and maximum tolerable temperature of the CUT according to its datasheet, whichever was more limiting, and no vibration B) Five cycles between the temperature extremes used in the previous phase with a 5-minute dwell-time at each extreme, and no vibration C) Increasing vibration level with a 10g rms step up to 80g rms with a 5-minute dwell-time at each level, and at ambient temperature D) B and C phases combined with a 10-minute dwelltime per vibration level, and a 5-minute dwell-time per temperature level Generally, the cable jacket temperature followed the set temperature according to a first order thermal equivalent circuit [START_REF] Strickland | The Thermal Equivalent Circuit of a Transistor[END_REF] with a 1-minute time constant, whereas the triaxial cell temperature followed the set-temperature similarly with a 3-minute time constant. Such systems are considered to have reached a steady state after five time constants [START_REF] Storey | Chapter 9 -Transient Behaviour[END_REF]. This means that the cable jacket reached thermal equilibrium during cyclic testing, whereas the triaxial cell did not. The exact vibration energy transmission to the cable was too challenging to determine reliably, and thus, it is only assumed that the 25 cm mounting span of the cable in the triaxial cell is representative of a typical use case, like vehicle mounting. A more thorough analysis of the achieved temperatures and vibration levels is given in [START_REF] Leppaaho | Including Experimental Aging of Shielded Cables into Bulk Current Injection Simulations[END_REF].

A. Thermal Tests

Representative results from thermal step tests are shown in Fig. 11. The upper plot shows the transfer impedance of a copper pipe with a 4 mm hole drilled on the side of the pipe to introduce a small constant transfer inductance. Otherwise, it is similar construction as introduced in Section III.

Below 100 kHz, the transfer impedance curves vary proportionally to 1/f . This is not due to the CUT the triaxial cell, but due to a well-known return-current division [START_REF] Kley | Measuring the coupling parameters of shielded cables[END_REF] that depends on the transfer resistance of the test cables, and on the loop inductance of the whole measurement setup. As both measurement ports (P1 & P2) are connected to the same ground reference at VNA, return current is divided between the test cable shields proportionally to their resistance at low frequencies causing an erroneous measurement result. As the frequency increases, the increasing loop impedance forces the return current to follow the smallest loop i.e. the shield of the injecting cable. This effect could be minimized by using shorter test cables with better transfer resistance characteristics, or by adding ferrites on top of the test cables to increase loop inductance. Unfortunately, none of these methods were available to the authors during HALT testing.

Between 100 kHz and 10 MHz, the VNA dynamic range limited the measurement accuracy. Above 10 MHz no change in the measurement result is seen for the 8 mm copper pipe with a 4 mm hole. It means that the triaxial cell does not show temperature dependency on its measurement result. A representative transfer impedance thermal dependency graph is given in the bottom part of Fig. 11 for the high voltage cable.

Further results for the evaluated cables are given in Table V. There, linear regression with least squares approach was used to arrive at the temperature coefficients that can be used as a simple model. These coefficients were then normalized to enable comparison between different cables with different magnitudes of transfer resistance and inductance. The extracted coefficients were sufficiently over different frequencies as demonstrated in Fig. 12.

Transfer resistance thermal dependency was generally between that of a copper (0.40%/ • C) and an eutectic SnPb alloy (1.0%/ • C) [START_REF] Gancarz | Thermal Expansion, Electrical Resistivity, and Spreading Area of Sn-Zn-In Alloys[END_REF]. The results were within this interval for all the other samples except the coaxial sample. Its variation could be explained by e.g. NiCr (0.008%/ • C) [START_REF] Majumder | A computational study of the impact of the Wiedemann-Franz-Lorenz law on the thermal response of nichrome cylinders[END_REF] impurities in the braiding causing reduced thermal dependency.

Transfer inductance thermal dependency from cable to cable was less uniform with both positive and negative temperature coefficients. To consider thermal expansion of materials as an explanation for the transfer inductance change, Kleymodel [START_REF] Kley | Optimized single-braided cable shields[END_REF] was used to calculate the difference in transfer inductance as the braid diameter varied. As the Kley-model is for single-braided cables, RG-58C/U cable was selected as an example. Its dielectric consists of polyethylene [START_REF] Nexans | RG 58 -Coaxial cable with characteristic impedance 50 ohm[END_REF], which has a worst-case linear thermal expansion coefficient of 3.5 • 10 -4• C -1 [START_REF] Exsource | Thermal and Electrical Properties of PE[END_REF] for the low-density variant. With this value, Kley-model gives an average transfer inductance decrease of 0.15%/ • C. Thus, thermal expansion of the dielectric seems to explain approximately one-half of the observed transfer inductance decrease as a function of temperature. A further study will be needed to tie the transfer inductance better into the physical behavior of the cable.

With regards to the cell performance during rapid thermal cycling (phase B in Fig. 10), Fig. 13 shows identical data to Fig. 11, but just at the extreme temperatures. It must be noted that during cycling in phase B, temperature control has a larger error than in phase A. Generally, a ±5 • C error is expected. All the dependencies were linear, and thus, any value that is lower in the cyclic columns of Table V than the one in the temperature dependency columns is considered to present no cyclic dependency. It can be concluded that cyclic thermal stress does not have an effect on the transfer resistance of shielded cables with a small uncertainty on the high voltage cable that showed slightly larger cyclic dependency than expected. However, it has also the largest thermal mass, which could have affected the measured results. From transfer inductance point of view it is evident that thermal cycling will have an effect on it with the exception of cables whose shields consist of braid only. The reason for the inductance change could be the movement of the foil shield, but it has not been studied in this work.

Cable R T (%/ • C) L T (%/ • C) R T (%/cycle) L T (%/

B. Vibration Tests

Representative transfer impedance results from random vibration tests are shown in Fig. 14. Here, the cell verification was done with an RG-58C/U cable as the inner conductor in the copper pipe moved relative to the drilled hole during vibration making the cell validation impossible. It is seen that the triaxial cell does not have an effect on the transfer impedance measurement result within the random vibration range used. Here, the representative cable sample was also changed to the coaxial one that reacted more visibly to vibration.

Linear least squares fitted coefficients for transfer impedance vibration dependency modeling are gathered in

C. Combined Tests

Representative results from combined vibration and thermal cycling tests are shown in Fig. 15. The thermal transient extremes for the coaxial cable were reduced to -40 • C and 105 • C due to its ratings. The copper pipe with a 4 mm hole was used again as a reference sample. As the center conductor was not completely fixed, transfer inductance showed some dependency on vibration. However, the measurement results also show the immense stress that this last test step causes to the triaxial cell assembly. At frequencies lower than 100 kHz, several test points show an increased measurement result. Those increased measurement results indicate a loosened test cable at either of the N-connectors. That slight change was the first sign of an imminent cable detachment. Thus, during these tests, the setup needed to be repaired several times.

The coefficients for linear least squares fits of combined transfer impedance vibration and thermal dependency are gathered in Table VII for all the evaluated cables. They are formatted as vibration dependencies at T min and T max temperatures. Again, the cables with braided shields seem to be fairly immune to the combined stress, whereas the same cables as in pure vibration tests show exponential dependency on both their transfer resistance and transfer inductance. Interestingly, at low temperatures, the dependency is closer to linear than exponential. This could be linked to the fact that at low temperatures the cable structure contracts being able to hold the shield better in place without space for it to move due to vibration. This effect could be seen to be confirmed by comparing all the transfer inductance results, which show higher linear dependency to vibration at high temperatures.

D. Aging During HALT

After HALT tests were finished, cables were cooled down back to the ambient temperature as they were measured at the beginning of the tests. Then, an additional transfer impedance measurement was done to determine if any aging effects could be seen on the shielding performance. The results of these measurements are shown in Table VIII, and they can be directly used to model the cable behavior before and after the test cycle given in Fig. 10. Values in the "Increase"columns have been calculated before rounding, and might deviate slightly from what can be calculated from the rounded values presented. Transfer impedance graphs for two corner cases: the high voltage cable and the LVDS cable are shown in Fig. 16. They confirm the values reported in Table VIII. No practical difference on transfer resistance between fresh and aged samples is seen, but the transfer inductance for the aged high voltage cable is slightly lower than that of the fresh cable, whereas the shielding effectiveness region result for the LVDS cable shows significantly decreased performance for the aged cable due to increased transfer inductance. Results for the coaxial cable have been previously published in [START_REF] Leppaaho | Including Experimental Aging of Shielded Cables into Bulk Current Injection Simulations[END_REF].

The r T increase over the test cycle was within measurement uncertainty except for the coaxial cable. More significant changes were seen in the l T measurements, where only the RG-58C/U cable can be considered completely immune to the applied aging stress. The LVDS cable with the worst aging result was analyzed after the tests. Fig. 17a shows the cable with jacket removed and Fig. 17b with the braiding removed. It was observed that the braid wires had disorientation due to motion related stress, but they were all intact. The foil shield had teared apart completely close to both mounting points, and had smaller tears along the cable making the foil damage as the most probable cause of the increased l T . V. CONCLUSION In this paper, a hexagonal triaxial cell for environmental testing was presented. The design was analyzed with 3D FEMsimulation, and later verified to provide good results compared to a commercial cell at ambient laboratory conditions. Then, it was verified to work well under both thermal stress between -50°C and and under random vibration up to 80g rms . The temperature swing was mainly limited by the coaxial cables used to connect the triaxial cell to the VNA as they were limited to -55°C and 125°C. The vibration level was close to the maximum of HALT system that was used. Thus, it is possible that the cell design could be used above the aforementioned stress levels.

It was shown that typical shielded cables can have either no dependency on environmental stress, like was the case for RG-58C/U under vibration stress, a limited dependency on the environmental parameter, like for the high voltage CUT under thermal stress, or a high dependency, like for the coaxial CUT during vibration as well as combined vibration and thermal stress. After the tests, some cables, like the RG-58C/U, did not show any signs of aging. On the other hand, some cables with foil shield, like the LVDS cable, showed more than a ten-fold increase in transfer inductance, which was related to tearing of the foil shield.

A logical next step from these results would be to develop better models than the linear ones shown in this paper -possibly taking into account more of the physical cable features. Then, these models could be easily integrated into system simulation to predict product EMC performance during development. This responds to the emerging need to address increasing safety and reliability requirements that modern electronics systems face throughout their lifetime.

APPENDIX TRIAXIAL CELL E-FIELD STRENGTH CALCULATION

The E-field strength

E(z, ρ) = -∇ t Φ(z, ρ) (3)
is calculated with the help of scalar potential

Φ(z, ρ) = V (z) ln b 2ρ ln b a , ( 4
)
where ρ is the distance from the center of the cell, b is the inner diameter of the triaxial cell, and a is the diameter of the copper rod. To arrive at the correct voltage V (z) along the line, the incident voltage wave amplitude needs to be calculated as

V + = V (z) e -jβz -e jβz = 2P in Z 0 e -jβz -e jβz , (5)
where z = -385mm, input power P in = 1W, and Z 0 = L/C, β = 2πf √ LC are the characteristic impedance and propagation constant of the triaxial cell configuration, respectively. The distributed inductance and capacitance are calculated as

L = µ 0 2π ln b a (6a) C = 2πϵ 0 ln b a , (6b)
respectively with µ 0 and ϵ 0 as vacuum permeability and permittivity.

Then, the voltage V (z) in ( 4) can be calculated as

V (z) = V + e -jβz -e jβz , (7)
and the field strength in Fig. 4 can be calculated by setting z = -195mm and sweeping ρ. As seen in Fig. 4, the analytical result matches perfectly with the FEM-simulation result.

Fig. 1 .

 1 Fig. 1. Overview of the triaxial measurement principle

Fig. 2 .

 2 Fig. 2. Triaxial cell overview as (a) fully assembled and (b) cover removed

Fig. 3 .

 3 Fig. 3. E-field strength at circular and hexagonal cross-sections of the triaxial cell at 1 GHz

Fig. 4 .

 4 Fig. 4. E-field strength at cross-sections of different cell designs at 1 GHz

Fig. 5 .

 5 Fig. 5. Exploded view drawings of the (a) short-circuited termination and (b) floating termination

Fig. 6 .Fig. 7 .

 67 Fig.6. Reflection coefficient of the outer circuit (P2 in Fig.1) with an 8-mm copper pipe

Fig. 8 .

 8 Fig. 8. Overview of the evaluated cables

Fig. 9 .

 9 Fig. 9. Triaxial cell in the HALT chamber

Fig. 10 .Fig. 11 .

 1011 Fig. 10. HALT cycle temperature and vibration set-points

Fig. 12 .

 12 Fig. 12. Temperature of transfer resistance and inductance of a high voltage cable

Fig. 13 .

 13 Fig. 13. Transfer impedance over rapid thermal cycles of phase B

Fig. 17

 17 Fig. 17. LVDS cable with (a) jacket removed and (b) braid removed after the test cycle

  Fig. 17. LVDS cable with (a) jacket removed and (b) braid removed after the test cycle

TABLE I TRIAXIAL

 I

	CELL CHARACTERISTICS
	Parameter	Symbol	Value
	Major diameter	b	90 mm
	Sample length	Lc	25 cm
	Cell length	-	40 cm
	Temperature range	-	-50°C -120°C
	Vibration range	-	0 -80grms
	Frequency range for shielding effectiveness	-	0 -1 GHz
	Frequency range for transfer impedance	-	0 -30 MHz

TABLE II COMPARISON

 II OF THE CABLE SHIELD TERMINATION METHODS

	Characteristic	Soldering Connector Pressure	Ferrule
	Initial contact resistance	+ + +	--	-	+ +
	Contact resistance stability	+ + +	---	-	+ +
	Mechanical robustness	+ +	+	+ +	+ + +

TABLE IV

 IV

	EXTRACTION FREQUENCIES FOR TRANSFER IMPEDANCE
		ENVIRONMENTAL DEPENDENCY
	Cable	f for r T extraction	f for l T extraction
	RG-55/U	50 kHz	30 MHz
	RG-58	10 kHz	500 MHz
	RG-58C/U	50 kHz	10 MHz
	Coaxial	300 kHz	960 MHz
	LVDS	300 kHz	930 MHz
	High voltage	300 kHz	10 MHz

TABLE V TRANSFER

 V IMPEDANCE THERMAL DEPENDENCY (TEST PHASES A AND B)

  cycle)T min Tmax T min Tmax

	RG-55/U	0.44	0.11	-0.2	-0.5	3.3	1.1
	RG-58	0.58	0.79	0.3	0.0	-10	-8.1
	RG-58C/U	0.48	-0.28	-0.1	0.1	-0.4	0.5
	Coaxial	0.32	-0.48	-0.2	0.2	4.7	2.9
	LVDS	0.42	-0.81	0.3	0.0	-4.9	-5.5
	High voltage	0.41	-0.40	1.0	0.9	-2.7	-3.6
		1	8 mm Copper Pipe with a 4 mm Hole
							SE only
	Impedance (	10m 100m
	Transfer	10
		10k	100k	1M	10M	100M	1G
		1		High Voltage Cable
			1 . cycle -50 °C	1 . cycle 120 °C
	(
	Transfer Impedance	1m 10m 100m	2 . cycle -50 °C 3 . cycle -50 °C 4 . cycle -50 °C 5 . cycle -50 °C	2 . cycle 120 °C 3 . cycle 120 °C 4 . cycle 120 °C 5 . cycle 120 °C		SE only
		10k	100k	1M	10M	100M	1G
				Frequency (Hz)

Table

  VI for all the evaluated cables. It is found out that only the transfer resistance of the coaxial cable has significant linear dependency on vibration amplitude. Transfer inductance wise, the regression results are more divided with some cables, like the RG-58C/U, demonstrating practically no linear or other dependency to vibration, to other cables like the coaxial cable demonstrating exponential dependency. The exponential dependency means in practice that the shield has failed during the test in one way or another. The aging results shown in Section IV-D are likely to explain the reason for the exponential dependency of the transfer inductance.

8 mm Copper Pipe with a 4 mm Hole

		1
							SE only
	Impedance (	10m 100m
	Transfer	10	10k	100k	1M	10M	100M	1G
			10g rms -50°C	30g rms -50°C	50g rms -50°C	70g rms -50°C
			10g rms 120°C	30g rms 120°C	50g rms 120°C	70g rms 120°C
			20g rms -50°C	40g rms -50°C	60g rms -50°C	80g rms -50°C
			20g rms 120°C	40g rms 120°C	60g rms 120°C	80g rms 120°C
		10			Coaxial Cable
							SE only
	Impedance (	10m 100m 1
	Transfer	100	10k	100k	1M	10M	100M	1G
					Frequency (Hz)
	Fig. 15. Transfer impedance dependency on combined vibration and thermal
	cycling measured during phase D.

TABLE VIII z

 VIII T MEASUREMENT RESULTS OF FRESH AND AGED SAMPLES

	Cable	r T (mΩ/m)		l T (pH/m)
			Fresh	Aged	Increase	Fresh	Aged	Increase
	RG-55/U	7.8	8.0	+3%	7.2	10	1.4×
	RG-58	107	112	+5%	4.9	28	4.7×
	RG-58C/U	15.6	16.5	+6%	1100	1000	0.9×
	Coaxial	44.4	57.5	+30%	21	230	10×
	LVDS	20.8	21.7	+4%	2.1	84	40×
	High voltage	3.4	3.7	+8%	220	130	0.6×
	( /m)	1	High voltage cable -Fresh High voltage cable -Aged
	Transfer impedance	1m 10m 100m	LVDS cable -Fresh LVDS cable -Aged			SE only
		10k	100k		1M	10M	100M	1G
					Frequency (Hz)
	Fig. 16. Fresh and aged transfer impedance measurement comparison

ACKNOWLEDGMENT

Authors would like to thank O. Maurice of ARIANE Group for fruitful discussions on shielded cable transfer impedance under environmental stress. Equally, they would like to thank B. Pichereau of Arts et Métiers Angers Campus for providing mechanical design help and improvements, and A. Maire of Valeo Thermal Systems, La Verrière for his excellent design improvement suggestions during initial vibration testing. The authors faced some unexpected failures that could have taken significantly longer to solve without A. Maire pointing out typical fixes for the weak spots found in the design. During HALT, Rohde & Schwartz provided a VNA for the first author to capture the results reported in Section IV.

The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 812.790 (MSCA-ETN PETER). This publication reflects only the authors' view, exempting the European Union from any liability. Project website: http://etn-peter.eu/.

Oskari Leppäaho (GS '20) was born in Seinäjoki, Finland, in 1987. He received the B.Sc.(tech.) and M.Sc.(tech.) degrees in electromagnetics from Tampere University of Technology, Tampere, Finland, in 2014 and 2015, respectively.

From 2013 to 2017, he was with Vacon Oy, Vaasa, Finland. From 2017 to 2019 he was with Danfoss Drives, Loves Park, IL, USA. He is currently working towards a Ph.D. degree at Valeo, Créteil, France and he is affiliated with INSA Rennes, Rennes, France. His current reserach interests include system level modelling, shielded cables and connectors, EMC related grounding structures, and highly accelerated life testing.

Frédéric Lafon (M'14-SM '15) was born in Chennevieres, France in 1974. He received the M.Sc. degree in electromagnetic compatibility (EMC) from the University of Clermont-Ferrand, France, in 2004, the Ph.D. degree in electronics from the Institut National des Sciences Appliquees, Rennes, France, in 2011, and the "Habilitation a Diriger des Recherches" (Accreditation Degree) in Electronics from Universite de Rennes 1, France, in 2016.

In 2000, he joined Valeo, Créteil, France, where he is currently an EMC Master Expert and the Group EMC discipline manager. His current research interests include the characterization and modeling techniques of integrated circuits, for emissions, immunity, and transients (electrostatic discharge), as well as the different techniques to manage EMC at the system level through a bottom-up approach.

Priscila Fernández-López was born in Oviedo, Spain, in 1982. She received the degree in telecommunication engineering from the University of Oviedo, Spain, in 2007 and the Ph.D. degree in electronics from the University of Rouen, France, in 2011.

From 2006 to 2011, she was with Embedded Electronic Systems Research Institute (IRSEEM), Saint-Etienne-du-Rouvray, France. In 2012, she joined Valeo, Créteil, France, where she is an EMC expert at present. Her current research interests include electromagnetic compatibility at integrated circuit and system levels, in particular the integrated circuit characterization and modelling techniques in order to predict the electromagnetic compatibility performance of systems.

Marine Stojanovic was born in Creil, France, in 1992. She received the Engineering degree in electronics and electrotechnics from the Engineering School ESIEE, Amiens, France, in November 2015, the Ph.D. degree in electronics from the Institut National des Sciences Appliquees, Rennes, France, in 2018.

In 2015 she joined Valeo, Créteil, France, where she is currently an EMC Expert. Her current research interests include electromagnetic compatibility, filter design, and EMC simulations.

Tim Claeys (M'20) was born in 1990. He received the M.S. degree in industrial engineering sciences, option electronics, from the University College Katholieke Hogeschool Sint-Lieven Gent, Ghent, Belgium, in 2013, and the Ph.D. degree in electrical engineering from Katholieke Universiteit (KU) Leuven, Leuven, Belgium, in 2018.

Since 2018, he has been a Postdoctoral Researcher with the M-Group Research Group (Lab FMEC), KU Leuven, Bruges, Belgium. His current research interests include near-field scanning, the development of characterization methods for shielding materials and gaskets, electromagnetic interference resilience of wireless protocols, and global reliability of electronic systems.

Dr. Claeys is a member of the IEEE EMC Society Benelux chapter executive committee as the treasurer and communication manager. From 1991 to 2008, he was an Associate Professor with ESEO, Angers, France, in the fields of microelectronics and microwave electronics. Since 2008, he was a Full Professor. His research interest includes EMC of integrated circuits and integrated circuit design. He has authored several book chapters and many peer-reviewed scientific papers.

Dr. Ramdani was the General Chair of EMC Europe 2017, which was held in Angers, France. He was elected the Vice Chair of the IEEE France Section, in 2016.