Minon ' Tsikpo

Kossi Kodji

Emilie Lanoy

Lise Giorgis-Allemand

Bernard Laumon

Anne-Sophie Sophie Evrard

Minon'tsikpo Kossi Kodji

Émilie Lanoy

Kodji

The role of noise annoyance and noise sensitivity in the effect of aircraft noise on self-reported health: the results of the DEBATS longitudinal study in France

Keywords: epidemiology, aircraft noise exposure, general health, self-reported health, mediation analysis

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

Introduction

According to recent systematic WHO reviews, transportation noise (road traffic noise, aircraft noise and railway noise) exposure is associated with impaired subjective health (self-reported health status (SRHS), general health, wellbeing, mental health) and impaired quality of life [START_REF] Guski | WHO environmental noise guidelines for the European region: a systematic review on environmental noise and annoyance[END_REF][START_REF] Clark | WHO Environmental Noise Guidelines for the European Region: A Systematic Review on Environmental Noise and Cognition[END_REF][START_REF] Clark | Evidence for Environmental Noise Effects on Health for the United Kingdom Policy Context: A Systematic Review of the Effects of Environmental Noise on Mental Health, Wellbeing, Quality of Life, Cancer, Dementia, Birth, Reproductive Outcomes, and Cognition[END_REF] . However, only few studies have investigated the relationship between aircraft noise and impaired SRHS in adult populations. SRHS is often used in health research as a predictor of mortality and overall health status [START_REF] Idler | Self-Rated Health and Mortality: A Review of Twenty-Seven Community Studies[END_REF] . SRHS is defined as a subjective measure of health in which an individual considers all aspects of their health [START_REF] Idler | Self-Rated Health and Mortality: A Review of Twenty-Seven Community Studies[END_REF][START_REF] Miilunpalo | Self-rated health status as a health measure: the predictive value of self-reported health status on the use of physician services and on mortality in the working-age population[END_REF] . A study conducted in the USA in 2000 showed that residents exposed to aircraft noise had worse general health than unexposed residents [START_REF] Meister | The Impact of Commercial-Aircraft Noise on Human Health: A Neighborhood Study in Metropolitan Minnesota[END_REF] . This result is consistent with those of two other cross-sectional studies in which increased aircraft noise levels were found to be associated with impaired SRHS [START_REF] Franssen | Aircraft noise around a large international airport and its impact on general health and medication use[END_REF][START_REF] Baudin | Self-rated health status in relation to aircraft noise exposure, noise annoyance or noise sensitivity: the results of a cross-sectional study in France[END_REF] . The study conducted by Schreckenberg et al. in Germany in 2010 also showed that higher aircraft noise levels were associated with poorer quality of life, such as poor vitality and poor physical health [START_REF] Schreckenberg | Aircraft noise and quality of life around Frankfurt Airport[END_REF] . A longitudinal study in Switzerland in 2020 found no association between aircraft noise levels and quality of life [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF] . These results regarding aircraft noise seem to confirm those obtained with road traffic noise [START_REF] Brink | Parameters of well-being and subjective health and their relationship with residential traffic noise exposure-A representative evaluation in Switzerland[END_REF][START_REF] Welch | Road traffic noise and health-related quality of life: A cross-sectional study[END_REF][START_REF] Halonen | Associations of traffic noise with self-rated health and psychotropic medication use[END_REF][START_REF] Héritier | The association between road traffic noise exposure, annoyance and health-related quality of life (HRQOL)[END_REF] and those with all transportation noise combined [START_REF] Ou | Self-rated health and its association with perceived environmental hazards, the social environment, and cultural stressors in an environmental justice population[END_REF][START_REF] Dzhambov | Pathways and contingencies linking road traffic noise to annoyance, noise sensitivity, and mental Ill-Health[END_REF] .

It has been suggested that observed health effects of noise could be partly mediated by other factors related to noise exposure. A mediator in the relationship between noise levels and health is an intermediate variable through which noise affects health. Noise annoyance has been found to mediate the health effects of noise such as impaired SHRS or quality of life [START_REF] Schreckenberg | Aircraft noise and quality of life around Frankfurt Airport[END_REF][START_REF] Welch | Road traffic noise and health-related quality of life: A cross-sectional study[END_REF][START_REF] Héritier | The association between road traffic noise exposure, annoyance and health-related quality of life (HRQOL)[END_REF] , depression [START_REF] Benz | Examination of the causal relationship between aircraft noise exposure, noise annoyance and diagnoses of depression using structural equation modelling[END_REF] , mental well-being [START_REF] Schreckenberg | The relationship between aircraft sound levels, noise annoyance and mental well-being: An analysis of moderated mediation[END_REF] , and potentially the incidence of hypertension [START_REF] Babisch | Road traffic noise and cardiovascular risk[END_REF][START_REF] Kourieh | Incident hypertension in relation to aircraft noise exposure: results of the DEBATS longitudinal study in France[END_REF] . Indeed, in the WHO systematic review on environmental noise annoyance, a direct association was found between noise levels and noise annoyance [START_REF] Guski | WHO environmental noise guidelines for the European region: a systematic review on environmental noise and annoyance[END_REF] , which in turn negatively affects health.

Noise sensitivity is considered an aspect of personality that increases the degree of reactivity to noise, whatever the noise level [START_REF] Job | Noise sensitivity as a factor influencing human reaction to noise[END_REF] . Noise sensitivity seems to be the most important non-acoustic factor influencing noise annoyance [START_REF] Job | Noise sensitivity as a factor influencing human reaction to noise[END_REF][START_REF] Guski | Personal and social variables as co-determinants of noise annoyance[END_REF] . Previous studies showed an association between noise sensitivity and impaired SRHS or health-related quality of life [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF][START_REF] Dzhambov | Pathways and contingencies linking road traffic noise to annoyance, noise sensitivity, and mental Ill-Health[END_REF][START_REF] Schreckenberg | The associations between noise sensitivity, reported physical and mental health, perceived environmental quality, and noise annoyance[END_REF][START_REF] Baliatsas | Noise sensitivity: Symptoms, health status, illness behavior and co-occurring environmental sensitivities[END_REF] . The more noise sensitive participants were, the more they reported impaired perceived health. It has also been suggested that noise sensitivity may moderate the health effect of noise [START_REF] Baudin | Self-rated health status in relation to aircraft noise exposure, noise annoyance or noise sensitivity: the results of a cross-sectional study in France[END_REF][START_REF] Baliatsas | Noise sensitivity: Symptoms, health status, illness behavior and co-occurring environmental sensitivities[END_REF][START_REF] Shepherd | Exploring the relationship between noise sensitivity, annoyance and health-related quality of life in a sample of adults exposed to environmental noise[END_REF][START_REF] Stansfeld | Road traffic noise, noise sensitivity, noise annoyance, psychological and physical health and mortality[END_REF] . In other words, the association between noise levels and health issues may be higher in people who are highly sensitive to noise compared to those who are not. In a study conducted in Japan in 2009, Kishikawa et al. found that road traffic noise exposure was associated with poorer self-reported health in the noise-sensitive group, while no association was observed in the non-sensitive group [START_REF] Kishikawa | Noise sensitivity and subjective health: questionnaire study conducted along trunk roads in Kusatsu, Japan[END_REF] .

Only few studies have investigated the relationship between aircraft noise and impaired SRHS, and even fewer have studied the mediating and moderating roles of aircraft noise annoyance and noise sensitivity in this association. Furthermore, all of the aforementioned studies that investigate these roles were cross-sectional studies.

In this context of lack of longitudinal studies, we propose to explore the relationship between aircraft noise exposure and impaired SRHS by considering the mediating and moderating roles of aircraft noise annoyance and noise sensitivity using data collected in the DEBATS longitudinal study conducted between 2013 and 2017 near three French airports.

Methods

Study population

The DEBATS (Discussion on the health effects of aircraft noise) study investigated the health effect of aircraft noise exposure. Participants were residents living near one of three major French airports (Paris-Charles de Gaulle, Lyon Saint-Exupéry, and Toulouse-Blagnac). They were randomly selected from a phone directory after stratification on four aircraft noise levels in terms of Lden: <50, 50 to 54, 55 to 59 and ≥ 60 dBA. Lden is the day-evening-night noise level.

It is a descriptor of noise level based on energy equivalent noise level over a whole day [6.00 -18.00] with a penalty of 10 dBA for night time noise [in France: 22.00 -6.00] and an additional penalty of 5 dBA for evening noise [in France: 18.00 -22.00] 28 . This indicator is used by the European Union for environmental noise management [START_REF]Directive 2002/49/EC of the European Parliament and of the Council of 25 June 2002 relating to the assessment and management of environmental noise[END_REF] . It is therefore one of the most used in epidemiological studies of the health effects of noise.

Participants were older than 18 years at inclusion and had lived in their dwelling for at least 1 year and for at least six months during the year. They completed a questionnaire administered during a face-to-face interview with an investigator at their home at inclusion in 2013, then at the first follow-up in 2015, and finally at the second follow-up in 2017. Demographic (sex, age, marital status), and socio-economic characteristics of the participants as well as information on their lifestyle (alcohol consumption, smoking, physical activity) were collected. They were also asked to assess their health status, their annoyance due to aircraft noise, and their sensitivity to noise.

Aircraft noise levels

Noise maps were used to estimate aircraft noise levels outside the participants' residence by linking noise levels to participants' addresses through a geographic information system. These noise maps were produced by Paris Airports and the French Civil Aviation Authority with the Integrated Noise Model [START_REF] He | Integrated Noise Model (INM) version 7.0 user's guide[END_REF] , which allows the calculation of aircraft noise levels near airports. In our study, participants' exposure to aircraft noise was characterized using two energetic indicators: Lden and LAeq24h. LAeq24h is an unweighted indicator which corresponds to the energy equivalent noise level over a 24-hour period.

Self-reported health status

Participants self-assessed their health status by answering the following question: "In general, would you say that your health is excellent, good, fair, or poor?" For statistical analyses, this variable was dichotomized: participants who reported fair or poor health were compared to those who reported good or excellent health (reference).

Aircraft noise annoyance

Participants' aircraft noise annoyance was assessed with the following question recommended by the International Commission on the Biological Effects of Noise (ICBEN) [START_REF] Fields | Standardized generalpurpose noise reaction questions for community noise surveys: Research and a recommendation[END_REF] : "Thinking about the last 12 months, when you are here at home, how much does aircraft noise bother, disturb, or annoy you: extremely, very, moderately, slightly or not at all?". Following ISO/TS recommendations [START_REF] Clark | Revising ISO/TS 15666-The noise annoyance standard[END_REF] , we considered participants reporting "extremely" or "very" to this question to be highly annoyed by aircraft noise (severe annoyance), and those reporting "moderately", "slightly" or "not at all" to be not highly annoyed.

Noise sensitivity

Participants rated their sensitivity to noise by answering the following single question: "Regarding noise in general, compared to people around you, do you think that you are: much less sensitive than, or less sensitive than, or as sensitive as, or more sensitive or much more sensitive than people around you?" We considered participants who reported being more or much more sensitive than people around them to be highly sensitive to noise, and those who reported being much less sensitive than, or less sensitive than, or as sensitive as people around them to be not highly sensitive to noise. Because noise sensitivity can be considered a stable personality trait [START_REF] Stansfeld | Noise, noise sensitivity and psychiatric disorder: epidemiological and psychophysiological studies[END_REF][START_REF] Zimmer | PSYCHOMETRIC PROPERTIES OF FOUR MEASURES OF NOISE SENSITIVITY: A COMPARISON[END_REF] , only the level of noise sensitivity reported in 2013 at study inclusion was considered in the statistical analyses.

Confounding factors

Factors associated with impaired SRHS in univariate analyses with a p<=0.2 and that modified the association between aircraft noise and impaired SRHS were considered as potential confounders The following variables were included in the models as confounders of the association between aircraft noise levels and impaired SRHS: age (in six categories: 18 to 34, 35 to 44, 45 to 54, 55 to 64, 65 to 74 and ≥ 75 years old), the number of people in the household (in four categories: 1, 2, 3 , more than 4 people), occupational activity (yes/no), income per consumption unit (CU) (in three categories: < 1550, 1550 to 2750 and ≥ 2750 euros per month; according to the definition of CU by Insee 35 , the first adult in the household counts for 1 CU, other persons of 14 years or older count 0.5 CU and children under 14 years count for 0.3 CU), country of birth (France versus other country), and smoking habits (in three categories : never smoke, current smoker, smoker). Others variables such as sleep duration, alcohol consumption and education were also found in previous studies as potential confounders. But, in our study, these variables were not included in the final model because they did not modify the association between aircraft noise and impaired SRHS in the multivariate analysis including other confounders listed above.

Statistical analysis

The Pearson khi2 test (for categorical variables) and the Friedman test (for continuous variables) were used to compare the distributions of variables over the three visits.

To address the fact that the data analyzed came from the same participants at all three time points of the DEBATS longitudinal study (inclusion, first and second follow-up), generalized linear mixed models with a random intercept at the participants level were used (Glimmix procedure in SAS software). All analyses were conducted separately for men and women. Indeed, previous studies have shown that women in France tend to judge their health more severely than men [START_REF] Goldberg | Longitudinal study of associations between perceived health status and selfreported diseases in the French Gazel cohort[END_REF] .

Sensitivity analyses were conducted to assess the robustness of the results: 1) the study population was limited to participants who participated in all three visits, 2) the study population was limited to participants who had resided in their dwelling for more than 5 years at inclusion and who had not moved during the two follow-ups if they had not been lost to follow-up, 3) the analyses were conducted considering noise levels in two categories in terms of Lden: ≥ 50 dBA versus < 50 dBA. The results of these sensitivity analyses are reported in the online supplemental tables. The mediating role of aircraft noise annoyance in the association between aircraft noise levels and impaired SRHS was investigated according to Baron and Kenny's recommendations [START_REF] Baron | The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations[END_REF] , by comparing the results from the following three regression models that include confounding factors. The M1 model evaluated the association between aircraft noise levels and aircraft noise annoyance. The M2 model evaluated the association between aircraft noise annoyance and impaired SRHS after controlling for aircraft noise levels. The M3 model evaluated the association between aircraft noise levels and impaired SRHS. According to Baron and Kenny's recommendations, the mediation role hypothesis was validated if, i) aircraft noise levels were associated with the potential mediator (ie aircraft noise annoyance) (M1), ii) the potential mediator (ie aircraft noise annoyance) was associated with impaired SRHS after controlling for aircraft noise levels (M2) , and iii) the association between aircraft noise levels and impaired SRHS was weaker after controlling for the mediator (ie aircraft noise annoyance)(i.e. weaker in M2 than in M3).

We also evaluated the association between noise sensitivity and impaired SRHS after controlling for aircraft noise levels and all confounding factors (M4 model).The moderating role of aircraft noise annoyance and noise sensitivity in the relationship between aircraft noise levels and impaired SRHS was investigated by introducing an interaction term between aircraft noise levels and the potential moderator (aircraft noise annoyance or noise sensitivity) in the M2 model and in the M4 model respectively (M5 Model).

The associations between aircraft noise levels and aircraft noise annoyance or between aircraft noise levels and impaired SRHS were evaluated for a 10 dBA increase in aircraft noise levels.

The corresponding odds ratios (OR) will be noted OR10dBA. Unless otherwise stated, only the ORs for Lden are reported in the text. The linearity of the relationship between aircraft noise levels and impaired SRHS was tested using the cubic spline function [START_REF] Royston | Multivariable modeling with cubic regression splines: a principled approach[END_REF] . All statistical analyses were conducted using SAS software version 9.4. We considered 5% as the threshold for statistical significance.

Results

Table 1 shows the study population characteristics for the three visits. Among the 4,202 individuals eligible for the study, 1,244 (695 women and 549 men) agreed to participate and were included in the study at baseline (T0). Of these, 992 (549 women and 443 men) participated in the first follow-up (T2) in 2015 (80%) and 811 (438 women and 373 men) participated in the second follow-up (T4) in 2017 (82%).

For all three visits, aircraft noise levels ranged from 44 to 67 dBA in terms of Lden, for both men and women. The distributions of aircraft noise levels were relatively similar across the three visits for both men and women. The proportion of men/women reporting impaired SRHS was similar for all three visits (around 15%).

The proportion of participants who reported being highly annoyed by aircraft noise was similar for men and women at T0 (18%). This proportion increased over the two follow-ups (T2 and T4) for both men and women, and was slightly higher for women. Women were more likely to report being highly sensitive to noise than men. This proportion remained stable over time: about 34% for women and 25% for men. The proportion of participants who reported an income per consumption unit below 1,550 euros per month decreased from about 43% at baseline to 32% at T4, for women, and from about 37% at baseline to 25 % at T4 for men. The distribution of age, number of people in the household, and smoking habits changed slightly over time for both men and women. The Pearson khi2 test for categorial variables and the Friedman test for continuous variables were used for comparing characteristics during the three visits for both men and women 2 n (%) Table 2 presents the adjusted OR and their 95% confidence intervals (95% CI) for the three mediation analysis models described in the methods section. Aircraft noise levels were associated with severe annoyance due to aircraft noise, for both, men (OR10dBA = 2.78, 95% CI = (1.97, 3.92), M1 model) and women (OR10dBA = 2.69, 95% CI = (2.01, 3.61), M1 model).

Severe annoyance due to aircraft noise tent to be associated with impaired SRHS (OR = 1.57, 95% CI = (0.98, 2.44), M2 model for men and OR = 1.35, 95% CI = (0.92, 1.98), M2 model for women).

No association was observed between aircraft noise levels and impaired SHRS for women (OR10dBA = 1.00, 95% CI = 0.73, 1.37, M3 model). Aircraft noise levels were associated with impaired SHRS only in men (OR10dBA = 1.47, 95% CI = (1.02, 2.11), M3 model). When aircraft noise annoyance and aircraft noise levels were both included in the M2 model, the OR for the association between aircraft noise levels and impaired SRHS decreased compared to the OR in model M3 (OR10dBA = 1.36, 95% CI = (0.94, 1.98), M2 model). [START_REF] Guski | WHO environmental noise guidelines for the European region: a systematic review on environmental noise and annoyance[END_REF] For a 10 dBA increase in aircraft noise levels [START_REF] Clark | WHO Environmental Noise Guidelines for the European Region: A Systematic Review on Environmental Noise and Cognition[END_REF] Severe aircraft noise annoyance was modeled [START_REF] Clark | Evidence for Environmental Noise Effects on Health for the United Kingdom Policy Context: A Systematic Review of the Effects of Environmental Noise on Mental Health, Wellbeing, Quality of Life, Cancer, Dementia, Birth, Reproductive Outcomes, and Cognition[END_REF] Impaired SRHS was modeled M1 model was adjusted for age, number of people in the household, occupational activity, economic dependency on airport activities, use of the noise source, fear of a plane crash, homeownership, type of housing, residential satisfaction, source-and authority-related attitudes, and noise sensitivity Noise sensitivity was associated with impaired SRHS both in men (OR = 1.68, 9)5% CI = (1.00, 2.80), M4 model) and in women (OR = 1.48, 95% CI = (1.00, 2.17), M4 model) (results not shown).

Table 3 shows the results of the M5 model including an interaction term between aircraft noise levels and aircraft annoyance (left), and an interaction term between aircraft noise levels and noise sensitivity (right), for men and women separately. No association was observed between aircraft noise levels and impaired SRHS for either highly annoyed or not highly annoyed men.

But for both, the ORs were relatively greater than 1 and very similar (OR10dBA = 1.37, 95% CI = (0.64, 2.91), for men who were highly annoyed and OR10dBA = 1.36, 95% CI = (0.89, 2.07), for men who were not highly annoyed). For women, no association was observed between aircraft noise levels and impaired SRHS, for either highly annoyed or not highly annoyed women.

Aircraft noise levels seems to be associated with impaired SHRS. This association, even if it was not significant, was slightly higher for men who reported high noise sensitivity (OR10dBA = 1.84, 95% CI = (0.92, 3.70), versus OR10dBA = 1.39, 95% CI = (0.90, 2.14), for men who were not highly sensitive to noise) even in absence of interaction (p = 0.50). For women, aircraft noise levels were not associated with impaired SHRS and there was no interaction between aircraft noise levels and noise sensitivity (p = 0.74). Similar results were observed in sensitivity analyses when the study population was limited to participants who participated in all three visits, or to participants who had resided in their dwelling for more than 5 years at inclusion and who had not moved during the two follow-ups (online supplemental Table 1 andTable 2). When the analyses were conducted considering noise levels in two categories in terms of Lden (≥ 50 dBA versus < 50 dBA), aircraft noise levels were associated with impaired SRHS in men (OR = 1.84, 95% CI = (1.11, 3.06), M3 model) (online supplemental Table 3). When aircraft noise annoyance and aircraft noise levels were both included in the M2 model, the OR for the association between aircraft noise levels and impaired SRHS decreased (OR = 1.59, 95% CI = (0.99, 2.54), M2 model) (online supplemental Table 3). The association between aircraft noise levels and impaired SRHS was higher for men who were highly annoyed (OR = 2.71, 95% CI = (1.43, 5.14)) than for those who were not (OR = 1.64, 95% CI = (0.94, 2.85), M5 model), compared to the same reference group (men who were exposed to aircraft noise levels below 50 dBA and not highly annoyed) (online supplemental Table 4). The association between aircraft noise levels and impaired SRHS was also higher for men and women who were highly noise sensitive than for those who were not, compared to the same reference group (men or women who were exposed to aircraft noise levels below 50 dBA and not highly noise sensitive) (OR =3.00, 95% CI = (1.46, 6.18) for men who were highly noise sensitive and OR = 1.58, 95% CI = (0.87, 2.87) for men who were not; OR = 1.47, 95% CI = (0.81, 2.66) for women who were highly noise sensitive and OR = 1.05, 95% CI = (0.60, 1.81) for women who were not, M5 model) (online supplemental Table 4).

Discussion

This study is one of only a few longitudinal studies to investigate the relationship between aircraft noise levels and impaired SHRS. In addition, it is among the few studies to assess the role of aircraft noise annoyance and noise sensitivity in this association.

Aircraft noise levels were associated with aircraft noise annoyance (OR10dBA = 2.78, 95% CI = (1.97, 3.92), M1 model, in men and OR10dBA = 2.69, 95% CI = (2.01, 3.61), M1 model in women). This result is in line with the exposure-response curve the percentage of people highly annoyed by aircraft noise in cross-sectional analyses previously conducted by Lefèvre et al. using only participant information collected at inclusion in the DEBATS study in 2013 [START_REF] Lefèvre | Understanding the relationship between air traffic noise exposure and annoyance in populations living near airports in France[END_REF] .

The percentage of people highly annoyed by aircraft noise was also found as an increasing function of aircraft noise levels in the European Union standard curve [START_REF]Directive 2002/49/EC of the European Parliament and of the Council of 25 June 2002 relating to the assessment and management of environmental noise[END_REF] and in the WHO systematic review on environmental noise and annoyance [START_REF] Guski | WHO environmental noise guidelines for the European region: a systematic review on environmental noise and annoyance[END_REF] .

This study found that aircraft noise annoyance was associated with impaired SRHS (OR = 1.57, 95% CI = (0.98, 2.44), in men and OR = 1.35, 95% CI = (0.92, 1.98), in women, M2 model, Table 2). This result is consistent with the one of a study investigating the association between severe aircraft annoyance and impaired health-related quality of life near Frankfurt airport in 2010: people highly annoyed by aircraft noise had lower vitality (OR10dBA= 1.25; 95% CI: (1.13, 1.37)) and physical health scores (OR10dBA =1.13; 95% CI: (1.01, 1.26)) than those who were not highly annoyed [START_REF] Schreckenberg | Aircraft noise and quality of life around Frankfurt Airport[END_REF] . In addition, it was also consistent with those found by two cross-sectional studies that examined the association between road traffic noise annoyance and impaired SRHS or quality of life [START_REF] Welch | Road traffic noise and health-related quality of life: A cross-sectional study[END_REF][START_REF] Héritier | The association between road traffic noise exposure, annoyance and health-related quality of life (HRQOL)[END_REF] .

In this study, aircraft noise levels were associated with impaired SRHS in men (OR10dBA = 1.47, 95% CI = (1.02, 2.11), M3 model). This result is consistent with those of the few cross-sectional studies investigating the association between severe aircraft annoyance and impaired general health, impaired SRHS or health-related quality of life [START_REF] Meister | The Impact of Commercial-Aircraft Noise on Human Health: A Neighborhood Study in Metropolitan Minnesota[END_REF][START_REF] Franssen | Aircraft noise around a large international airport and its impact on general health and medication use[END_REF][START_REF] Schreckenberg | Aircraft noise and quality of life around Frankfurt Airport[END_REF] . The only one that did not find an association was also the only longitudinal study on the subject (Swiss cohort study SALPADIA) [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF] . The gender difference observed in the present study was also found in some previous studies investigating the association between road traffic noise levels and impaired self-rated health [START_REF] Clark | WHO Environmental Noise Guidelines for the European Region: A Systematic Review on Environmental Noise and Cognition[END_REF][START_REF] Halonen | Associations of traffic noise with self-rated health and psychotropic medication use[END_REF] . The authors suggested that this gender difference may be due to a higher threshold for reporting poor health in men than in women. Indeed, some studies have shown that self-rated health may be a better predictor of severe health outcomes, such as mortality, in men than in women [START_REF] Idler | Survival, Functional Limitations, and Self-rated Health in the NHANES I Epidemiologic Follow-up Study, 1992[END_REF] . In the present study, the proportion of participants reporting poor health was similar for men and women. In addition, the distributions of aircraft noise levels were also similar for men and women. Further research is needed to better understand the observed gender differences.

After controlling for aircraft noise annoyance, the association between aircraft noise levels and impaired SRHS in men decreased. This result suggests that this effect would be partly due to aircraft noise annoyance and thus confirms the mediating role of aircraft noise annoyance in the relationship between aircraft noise levels and impaired SRHS [START_REF] Schreckenberg | Aircraft noise and quality of life around Frankfurt Airport[END_REF][START_REF] Welch | Road traffic noise and health-related quality of life: A cross-sectional study[END_REF][START_REF] Héritier | The association between road traffic noise exposure, annoyance and health-related quality of life (HRQOL)[END_REF] .

There was no interaction between aircraft noise levels and aircraft noise annoyance (p >0.05).

The association between aircraft noise levels and impaired SRHS was similar in men who were highly annoyed and in those who were not. When the analyses were conducted considering noise levels in two categories in terms of Lden (≥ 50 dBA versus < 50 dBA), the effect of aircraft noise on impaired SRHS was higher in people who were highly annoyed than in those who were not. This result suggests a moderated mediation of aircraft noise annoyance in the relationship between aircraft noise levels and impaired SRHS [START_REF] Preacher | Addressing Moderated Mediation Hypotheses: Theory, Methods, and Prescriptions[END_REF][START_REF] Valeri | Mediation analysis allowing for exposure-mediator interactions and causal interpretation: Theoretical assumptions and implementation with SAS and SPSS macros[END_REF] .

Noise sensitivity was associated with impaired SRHS: the more noise sensitive people were, the more they reported impaired SRHS. This finding is in line with the results of studies that have investigated this association, although the methods for assessing noise sensitivity were different [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF][START_REF] Dzhambov | Pathways and contingencies linking road traffic noise to annoyance, noise sensitivity, and mental Ill-Health[END_REF][START_REF] Schreckenberg | The associations between noise sensitivity, reported physical and mental health, perceived environmental quality, and noise annoyance[END_REF][START_REF] Baliatsas | Noise sensitivity: Symptoms, health status, illness behavior and co-occurring environmental sensitivities[END_REF] . Accounting for an interaction between aircraft noise levels and noise sensitivity in the models showed a higher association between aircraft noise levels and impaired SRHS for men who were highly noise-sensitive compared to those who were not. This was also the case when the analyses were conducted considering noise levels in two categories in terms of Lden (≥ 50 dBA versus < 50 dBA). This result suggests and confirms a moderating role of noise sensitivity in the relationship between aircraft noise levels and impaired SRHS [START_REF] Baudin | Self-rated health status in relation to aircraft noise exposure, noise annoyance or noise sensitivity: the results of a cross-sectional study in France[END_REF][START_REF] Baliatsas | Noise sensitivity: Symptoms, health status, illness behavior and co-occurring environmental sensitivities[END_REF][START_REF] Shepherd | Exploring the relationship between noise sensitivity, annoyance and health-related quality of life in a sample of adults exposed to environmental noise[END_REF][START_REF] Stansfeld | Road traffic noise, noise sensitivity, noise annoyance, psychological and physical health and mortality[END_REF][START_REF] Kishikawa | Noise sensitivity and subjective health: questionnaire study conducted along trunk roads in Kusatsu, Japan[END_REF] . The lack of interaction in this case could be due to an insufficient number of participants in each category, the interaction test being very sensitive to the size of the study samples.

The main strength of our study is its longitudinal design. Indeed, it involved information collected for the same participants on three successive times (at inclusion and then at two follow-ups), considering the different variations of the variables over time. Furthermore, the results of these longitudinal analyses strengthened the results previously obtained from a crosssectional analysis using only inclusion data [START_REF] Baudin | Self-rated health status in relation to aircraft noise exposure, noise annoyance or noise sensitivity: the results of a cross-sectional study in France[END_REF] . All but one 10 of the epidemiological studies that have investigated the relationship between noise levels, noise annoyance, noise sensitivity and perceived health status were cross-sectional studies. Potential bias related to lost to follow-up that is a major problem in longitudinal studies is very unlikely in the present study. Indeed, the rate of loss to follow-up was relatively low, with 65% of the 1244 recruited participants attending the last follow-up. Moreover, the results of a sensitivity analysis limiting the study population to the 811 participants who participated in all three visits remained relatively similar (online supplemental Table 4). Finally, baseline characteristics of participants lost to follow-up were similar to those of participants who remained in the study (results not shown).

Selection bias cannot be ruled out in this study but seems limited. Indeed, in the DEBATS study, the demographic characteristics of 40% of non-participants who completed a short questionnaire and those of participants were relatively similar [START_REF] Evrard | Does exposure to aircraft noise increase the mortality from cardiovascular disease in the population living in the vicinity of airports? Results of an ecological study in France[END_REF] . However, these nonparticipants were probably not representative of all non-participants. In addition, people who believe they have a poor general health or who consider themselves sensitive to noise or potentially annoyed if exposed to high noise levels would avoid living in areas with high noise levels, especially near airports. Under these conditions, the results may be biased because of the under-representation of these people in noise-exposed areas around airports leading to an underestimation of the real associations observed in the present study.

A main weakness of the study is that the assessment of noise annoyance and noise sensitivity was based on a single question, which may not be specific enough, and could lead to misclassification. It has been shown that a single question does not adequately capture noise sensitivity in its various aspects [START_REF] Kishikawa | Noise sensitivity and subjective health: questionnaire study conducted along trunk roads in Kusatsu, Japan[END_REF][START_REF] Welch | What is Noise Sensitivity?[END_REF] . The use of items with multiple questions related to noise sensitive seems to be more accurate (e.g., the Weinstein noise sensitivity scale [START_REF] Weinstein | Individual differences in reactions to noise: a longitudinal study in a college dormitory[END_REF] or the NoiSeQ [START_REF] Schutte | The development of the noise sensitivity questionnaire[END_REF] ). In addition, an international standard was used for the annoyance assessment using a single item, with annoyance rated on a 5-point verbal scale. The fact that this is a standard does not prevent the annoyance assessment from having the same psychometric weakness as discussed for noise sensitivity. However, multi-question questionnaires were not introduced into the DEBATS questionnaire because it was already nearly an hour long and consideration of noise sensitivity in particular was not part of the original primary objectives of the study.

Exposure misclassification also cannot be ruled out in this study. Indeed, participants' noise exposure was estimated at home, outdoors. No information was available on their exposure to aircraft noise inside their home or during the day when they were outside their home, including at their workplace. This lack of information could have led to an underestimation of the association between aircraft noise exposure and impaired SRHS. It was not possible to estimate aircraft noise exposure indoors for the 1,244 participants in the longitudinal study, but , information was collected regarding the type of housing and the presence of windows or roof insulation. However, since these variables were not associated with either a degradation of SRHS or severe annoyance, they were not included in the final model. Finally, acoustic measurements were also performed for one week outside and inside the bedroom of a subsample of 112 participants in the DEBATS longitudinal study. The average relative difference between outdoor noise level estimates based on the noise maps produced by the Direction Générale de l'Aviation Civile using the INM model [START_REF] He | Integrated Noise Model (INM) version 7.0 user's guide[END_REF] and those calculated from the measurements was only 5% and the 95 th percentile of that difference was 11% [START_REF] Nassur | The impact of aircraft noise exposure on objective parameters of sleep quality: results of the DEBATS study in France[END_REF] .

Another limitation concerns the standard statistical methods (the GLMM and the Baron & Kenny's approach) used in this study to explore mediation and moderation. They may be insufficient to control for all confounding factors, thus leading to confounding bias. Both annoyance and sensitivity to noise were found to be associated with self-reported health impairment. As mentioned in previous studies [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF][START_REF] Benz | Examination of the causal relationship between aircraft noise exposure, noise annoyance and diagnoses of depression using structural equation modelling[END_REF][START_REF] Schreckenberg | The relationship between aircraft sound levels, noise annoyance and mental well-being: An analysis of moderated mediation[END_REF] it is also conceivable that health status may influence future reactions to noise such as noise annoyance and noise sensitivity [START_REF] Cerletti | The independent association of source-specific transportation noise exposure, noise annoyance and noise sensitivity with health-related quality of life[END_REF] . This temporality of noise exposure, mediator/moderator (noise annoyance and noise sensitivty), and impaired SRHS was not considered with the standard method used, which may lead to bias and prevent a causal interpretation of the observed association. Causal inferences methods such as marginal structural models [START_REF] Vanderweele | Effect decomposition in the presence of an exposure-induced mediator-outcome confounder[END_REF][START_REF] Vanderweele | Mediation analysis with time varying exposures and mediators[END_REF] are thus needed for identifying causal effect of exposure, mediator and moderator.

Conclusion

With its longitudinal design, this study confirms the mediating role of aircraft noise annoyance and the moderating role of noise sensitivity in the relationship between aircraft noise levels and impaired SRHS. These findings strengthen those of the few cross-sectional studies that have explored the association between transportation noise exposure and subjective health outcomes.

For future research, we suggest the use of causal inference methods to better control for confounding factors in order to perform a causal interpretation of the results. and LGA. The analyses were interpreted by MK with EL, LGA and ASE. MK and ASE drafted the initial report. All co-authors revised the report and approved the final version. ASE is responsible for the overall content as the guarantor of this paper.

Supplemental Table 1: Adjusted odds ratios for the association between aircraft noise levels and impaired SRHS in participants

  who participated in the three visits, and in those who had resided in their dwelling for more than 5 years at inclusion and had not moved

Table 1 : Characteristics of the study population for the three visits (T0, T2 and T4)

 1

	Baseline (T0)	First follow-up (T2)	Second follow-up (T4)	p-value 1 p-value 1
	Women	Men	Women	Men	Women	Men	Women	Men

Table 2 : Adjusted odds ratios for the association between aircraft noise levels and aircraft noise annoyance, between aircraft noise annoyance and impaired SRHS, and between aircraft noise levels and impaired SRHS

 2

	Women	Men

Table 3 : Adjusted odds ratios for impaired SRHS in relation to aircraft noise levels in highly annoyed/noise-sensitive men and women compared to those who are not (M5 model) Not highly annoyed Highly annoyed Not highly noise-sensitive Highly noise-sensitive

 3 adjusted for age, number of people in the household, occupational activity, income per consumer unit, country of birth, and smoking habits

		OR10dBA	95% CI	OR10dBA	95% CI	p-value 2	OR10dBA	95% CI	OR10dBA		95% CI	p-value 2
	Women	N §	569/404/318			126/145/120		459/352/291			234/197/147
		LAeq24h 1	0.87	0.58	1.31	1.13	0.59	2.18	0.49	1.06	0.68	1.65	0.92	0.52	1.63	0.70
		Lden 1	0.91	0.64	1.51	1.06	0.57	1.31	0.67	1.05	0.70	1.56	0.94	0.56	1.57	0.74
	Men	N §	448/340/292			99/103/81			405/331/277			135/112/96
		LAeq24h 1	1.45	0.90	2.34	1.45	0.65	3.23	0.99	1.39	0.86	2.26	2.31	1.06	5.03	0.28
		Lden 1	1.36	0.89	2.07	1.37	0.64	2.91	0.99	1.39	0.90	2.14	1.84	0.92	3.70	0.50
	1 For a 10-dBA increase in aircraft noise levels
	2 p-value of interaction
	§ N for T0/T2/T4
	All models were

.72 1.13 2.63 1

  For a 10 dBA increase in aircraft noise levels[START_REF] Clark | WHO Environmental Noise Guidelines for the European Region: A Systematic Review on Environmental Noise and Cognition[END_REF] Severe aircraft noise annoyance was modeled[START_REF] Clark | Evidence for Environmental Noise Effects on Health for the United Kingdom Policy Context: A Systematic Review of the Effects of Environmental Noise on Mental Health, Wellbeing, Quality of Life, Cancer, Dementia, Birth, Reproductive Outcomes, and Cognition[END_REF] Impaired SRHS was modeled M1 model was adjusted for age, number of people in the household, occupational activity, economic dependency on airport activities, use of the noise source, fear of a plane crash, homeownership, type of housing, residential satisfaction, source-and authority-related attitudes, and noise sensitivity M2 and M3 models were adjusted for age, number of people in the household, occupational activity, income per consumer unit, country of birth, and smoking habits Supplemental

										T4 : N=298)
	Outcome		OR	95% CI	OR	95% CI	OR	95% CI	OR	95% CI
	M1 model
	Aircraft noise annoyance 2 LAeq24h 1	2.88 1.97 4.20	3.45	2.23 5.34	2.46	1.74 3.48 2.86 1.88	4.34
		Lden 1	2.69 1.89 3.82	3.11	2.09 4.64	2.30	1.67 3.17 2.58 1.76	3.80
	M2 model
		LAeq24h 1	1.01 0.65 1.58	1.53	0.93 2.52	0.92	0.61 1.38 1.67 1.04	2.70
	SRHS 3	Aircraft noise annoyance	1.56 1.00 2.43	1.41	0.80 2.48	1.37	0.90 2.07 1.44 0.86	2.43
		Lden 1	0.98 0.66 1.46	1.41	0.90 2.19	0.92	0.63 1.33 1.62 1.05	2.50
		Aircraft noise annoyance	1.57 1.01 2.44	1.42	0.81 2.51	1.37	0.90 2.07 1.44 0.85	2.43
	M3 model
	SRHS 3	LAeq24h 1	1.11 0.72 1.72	1.66	1.02 2.66	0.98	0.66 1.46 1.79 1.12	2.85
		Lden 1	1.06 0.72 1.58	1.50	0.98 2.31	0.97	0.68 1.40 1

Table 2 : Adjusted odds ratios for impaired SRHS in relation to aircraft noise levels in highly annoyed/noise-sensitive men and women compared to those who are not (M5 model) in participants who participated in the three visits, and in those who had resided in their dwelling for more than 5 years at inclusion and had not moved during the two follow-ups Participants who participated in the three visits Not highly annoyed Highly annoyed Not highly noise-sensitive Highly noise-sensitive

 2

			OR10dBA	95% CI	OR10dBA	95% CI	p-value 2 OR10dBA	95% CI	OR10dBA	95% CI	p-value 2
	Women N	360			78		287				149
		LAeq24h 1	0.94	0.57 1.58	1.21	0.57 2.55	0.57	1.14	0.66	1.96	1.12	0.55 2.33	0.99
		Lden 1	0.94	0.60 1.48	1.10	0.54 2.24	0.71	1.07	0.66	1.75	1.09	0.56 2.11	0.97
	Men	N	305			68		282				88
		LAeq24h 1	1.46	0.83 2.56	1.80	0.68 4.72	0.71	1.44	0.82	2.54	2.34	0.92 5.96	0.39
		Lden 1	1.34	0.82 2.20	1.68	0.66 4.24	0.67	1.40	0.85	2.32	1.82	0.78 4.25	0.60

Participants who had resided in their dwelling for more than 5 years at inclusion and had not moved during the two follow-ups

  T4All models were adjusted for age, number of people in the household, occupational activity, income per consumer unit, country of birth, and smoking habits

	Women N §	447/303/249		104/125/104		362/279/235			187/147/116
		LAeq24h 1	0.86	0.54	1.38	1.07	0.54 2.15	0.59	1.09	0.65	1.81	0.86	0.45 1.65	0.58
		Lden 1	0.86	0.58	1.35	1.03	0.53 1.98	0.69	1.05	0.66	1.67	0.89	0.50 1.61	0.67
	Men	N §	352/254/226			88/91/72		331/263/229			103/78/66
		LAeq24h 1	1.69	0.98	2.92	1.62	0.67 3.91	0.93	1.61	0.93	2.77	2.57	1.01 6.51	0.39
		Lden 1	1.62	0.99	2.65	1.62	0.70 3.74	0.99	1.66	1.01	2.73	2.12	0.91 4.96	0.62
	1 For a 10-dBA increase in aircraft noise levels
	2 p-value of interaction
	§ N for T0/T2/

and women compared to those who are not (M5 model) considering aircraft noise levels in binary (< 50 dBA versus ≥ 50 dBA)

  N for T0/T2/T4 All models were adjusted for age, number of people in the household, occupational activity, income per consumer unit, country of birth and smoking habits

			Not highly annoyed		Highly annoyed	Not highly noise-sensitive	Highly noise-sensitive
			OR	95% CI	OR	95% CI	OR	95% CI		OR	95% CI
	Women	N §	569/404/318			126/145/120	459/352/291		234/197/147
		Lden < 50dBA	Ref	-	-	1.62	0.61	4.34	Ref	-	-	1.74	0.81	3.78
		Lden ≥ 50dBA	0.94	0.59 1.50	1.25	0.74	2.13	1.05	0.60	1.81	1.47	0.81	2.66
	Men	N §	448/340/292			99/103/81	405/331/277			135/112/96
		Lden < 50dBA	Ref	-	-	1.38	0.39	4.93	Ref	-	-	1.03	0.37	2.92
		Lden ≥ 50dBA	1.64	0.94 2.85	2.71	1.43	5.14	1.58	0.87	2.87	3.00	1.46	6.18

§

Acknowledgements

The Airport Pollution Control Authority (Acnusa) requested the French Institute of Science and Technology for Transport, Development and Networks (ex Ifsttar) to carry out this study. The authors would like to thank them for their confidence.

The authors are grateful to all the participants in the study and their interviewers.

The authors also thank Paris Airports and the French Civil Aviation Authority for providing noise exposure maps, and are also grateful to Inès Khati and Marie Lefèvre for her participation in the implementation of the study. This work has been conducted in the framework of CeLyA (Lyon Center for Acoustics, ANR-10-LABX-0060).

Funding

The present study was supported by funds from the French Ministry of Health, the French Ministry of the Environment, the French Civil Aviation Authority, the Airport Pollution Control Authority (Acnusa) and the Gustave Eiffel University. The authors would like to thank them for their kind assistance.

The funders had no role in the design of the study and collection, analysis, and interpretation of data and in writing the manuscript.

Competing interests

The authors declare that they have no competing interests.

Authors' Contributions

Anne-Sophie Evrard (ASE) and Bernard (BL) conceived and designed the study. ASE conducted the study. Minon'tsikpo kossi Kodji (MK) and Lise Giorgis Allemand (LGA) did data preparation. MK performed the statistical analyses, supervised by ASE, Émilie Lanoy (EL) The participants signed and returned an informed consent by mail.

Ethics approval and consent to participate

Supplemental Table 3: Adjusted odds ratios for the association between aircraft noise levels and aircraft noise annoyance, between aircraft noise annoyance and impaired SRHS, and between aircraft noise levels and impaired SRHS considering aircraft noise levels in two


Nicolas Roussel

Lucile Lallemant

Jean -Yves Chane-Ching

Sophie Guillemet-Fristch

Bernard Durand

Vincent Garnier

Guillaume Bonnefont

Gilbert Fantozzi

Lionel Bonneau

Sandrine Trombert

Domingo Garcia-Gutierrez

Highly Dense, Transparent a-Al 2 O 3 Ceramics From Ultrafine Nanoparticles Via a Standard SPS Sintering

Using discrete, ultrafine alumina, highly dense transparent (71% real in-line transmission, RIT, k = 640 nm) ceramics were achieved with grain size as small as 260 nm using standard SPS sintering. We show that use of La 3+ as a dopant greatly reduces sensitivity to the sintering temperatures. Transparent alumina were achieved in a large range of sintering temperatures, 1140°C<T < 1200°C, thus providing better reliability and flexibility into the fabrication of large sintered transparent ceramic bodies.

I. Introduction

D ENSE, refractory transparent ceramics are of technologi- cal importance in high-temperature light transmitting materials, [START_REF] Apetz | Transparent Alumina: A Light-Scattering Model[END_REF] armor, [START_REF] Krell | Advanced Spinel and Sub-lmA l 2 O 3 for Transparent Armour Applications[END_REF] IR emitters envelopes,etc [START_REF] Krell | Transmission Physics and Consequences for Materials Selection, Manufacturing, and Applications[END_REF] Indeed, ideal process routes to the fabrication of such materials will involve use of ultrafine nanoparticles along specific forming and sintering process routes. Large-scale development of such materials has been hindered by the availability of discrete, refractory nanoparticles. Their synthesis represents a challenging task face to the high driving force for sintering and coarsening existing at the high temperatures required for structure crystallization of the nanocrystals. In this context, highly transparent alumina ceramics were developed [START_REF] Krell | Transparent Compact Ceramics: Inherent Physical Issues[END_REF][START_REF] Grasso | Highly Transparent Pure Alumina Fabricated by High-Pressure Spark Plasma Sintering[END_REF][START_REF] Kim | High-Pressure Spark Plasma Sintering of MgO-Doped Transparent Alumina[END_REF][START_REF] Stuer | Transparent Polycrystalline Alumina Using Spark Plasma Sintering: Effect of Mg, Y and La Doping[END_REF] because they combine transparency and high mechanical properties. Indeed, sintered transparent a-Al 2 O 3 ceramics displaying RIT values of 72% (e = 0.8 mm) [START_REF] Krell | Advanced Spinel and Sub-lmA l 2 O 3 for Transparent Armour Applications[END_REF] were achieved in a two-step process route including presintering under vacuum to close porosity followed by final densification using hot isostatic pressing. Another interesting transparent alumina ceramic displaying a real in-line transmission of ~69% (e = 0.80 mm) [START_REF] Kim | High-Pressure Spark Plasma Sintering of MgO-Doped Transparent Alumina[END_REF] was obtained by high-pressure spark plasma sintering involving a uniaxial pressure of 400 MPa and an in-house experimental setup including graphite dies and WC disks. Because the best results to date require sintering processes involving several stages or specific conditions, fabrication of transparent alumina through standard densification process route is highly desirable.

With this objective, routine fabrication of transparent alumina ceramic requires availability of ultrafine Al 2 O 3 nanocrystals with controlled physicochemical properties. Various process routes were recently proposed for the fabrication of ultrafine refractory nanoparticles. [START_REF] Chane-Ching | Size and Morphology Control of Ultrafine Refractory Complex Oxide Crystals[END_REF][START_REF] Li | One-Step Synthesis of Luminescent Nanoparticles of Complex Oxide, Strontium Aluminate[END_REF] Indeed, discrete, a-Al 2 O 3 ultrafine nanoparticles were recently developed and commercialized. Here, we show that using discrete, ultrafine highly pure a-Al 2 O 3 nanoparticles, careful control of feature characteristics such as surface chemistry, interparticle interactions during green body forming, and grain growth during sintering will allow the formation of highly dense a-Al 2 O 3 transparent ceramic through standard SPS sintering technique. Interestingly, using a specific dopant addition procedure, we demonstrate that La 3+ , a dopant previously used to improve transmittance of transparent Al 2 O 3 ceramics, [START_REF] Zhan | Polycrystalline optical window materials from nanoceramics[END_REF][START_REF] Watanabe | Translucent alumina sintered body and a process for producing the same[END_REF] enlarges the temperature range for achieving high RIT values, providing higher flexibility for the fabrication of transparent refractory alumina ceramics. 3+ was determined by ICP analysis on the resulting dispersion. TEM observation of the nanocrystals was performed on the purified dispersions using a JEOL JEM 1011 (JEOL, Tokyo, Japan). HRTEM was carried out on samples prepared from a small volume of sample (6-7 lL) deposited on a lacey carbon membrane supported on TEM copper grids, followed by room-temperature drying. Images were recorded at 200 KV on a FEI TITAN G2 60-300 microscope (FEI Europe, Eindhoven, the Netherlands).

II. Experimental Procedure

High-density green compact (D = 20 mm) was achieved using a liquid forming procedure. [START_REF] Lallemant | Transparent Polycrystalline Alumina Obtained by SPS: Green Bodies Processing Effect[END_REF] The slurry was slip cast onto 20 mm diameter porous alumina molds to avoid any contamination. All the green bodies were manually polished to obtain 2 g cylindrical samples.

Densification of the resulting compacts was performed using a standard SPS technique (HP D 25/1, FCT System, Rauenstein, Germany). Samples were sintered with the following cycle: applied uniaxial pressure of 80 MPa throughout the cycle, rapid heating up to 800°C, heating rate of 10°C/min from 800°C to 950°C followed by a slower heating rate (1°C/min) up to the final sintering temperatures. The final sintering temperature was in the 1060°C-1200°C range.

After sintering, the samples (D = 20 mm) were carefully mirror-polished on both sides using diamond slurries (to 1 lm) and the transparency in the center of the pellet (spot size 5 mm 9 2 mm) was determined by a (Jasco V-670, JASCO Easton, MD). Real in-line transmittance (RIT) measurements were conducted using a shield with an appropriate aperture placed between the sample and the detector to avoid scattered light with angle > 0.5°. All the RIT values reported in this article were measured for k = 640 nm and the RIT were normalized at similar thickness of t 2 = 0.80 mm using the following equation RIT (t 2 )= (1ÀR S ) [(RIT(t 1 )/(1ÀR S )] t2/t1 where R S denote the total normal surface reflectance (0.14 for transparent alumina), RIT (t i ) is the RIT for a sample of thickness t i .

III. Results and Discussion

(1) a-Al 2 O 3 Ultrafine Nanoparticles and Dispersion Properties Highly pure a-Al 2 O 3 nanoparticles dispersions were prepared by HNO 3 peptization followed by post purification using ultracentrifugation and redispersion. Consistently, increased repulsive interparticle interactions as revealed from zeta potential measurement are achieved from complete removal of the residual Al 3+ cations from the dispersions. Thus, highly concentrated a-Al 2 O 3 dispersions displaying volume fractions, Φ v up to 0.33 were obtained due to the high degree of nanoparticles individualization.

A similar approach was adopted to the preparation of highly individualized La 3+ -doped a-Al 2 O 3 nanoparticle dispersions. Fine tuning of the interparticle interactions involves absorption of La 3+ cations on a-Al 2 O 3 nanoparticles surfaces followed by post removal of the non absorbed La 3+ cations from the dispersions. Although divalent and trivalent metal cation do not exhibit a high absorption affinity to the Al 2 O 3 surface in the pH range, 3 < pH < 4, [START_REF] Zimmermann | Treatment of Magnesium Ion Adsorption at the Gamma-Al 2 O 3 -Water Interface Quantitative[END_REF] (2) Forming, Sintering and Optical Properties Forming of the green body was carried out by slip casting from the concentrated dispersions. Hg porosimetry performed on green compacts reveals a quasi-monodisperse pore size distribution with a mean pore diameter of 18 nm (Fig. 2). Interestingly, a green density of 58% is achieved on compacts formed from these individualized nanoparticles. Note that the reference sample composed of nanoparticles displaying a less isotropic morphology exhibits a lower green density, larger pore size distribution and a much higher mean pore size value of 32 nm.

Sintering of the slip-cast green bodies was performed by standard SPS sintering. Our temperature profile was designed with the objective to achieve full densification while inhibiting grain growth. Although activation energy of densification is generally higher than that of grain growth 14 our temperature profile involves a rather low densification temperature associated with a low heating rate. [START_REF] Aman | Spark Plasma Sintering Kinetics of Pure a-Alumina[END_REF] Indeed, heating rates were shown to strongly influence the spark plasma sintering mechanism of a-Al 2 O 3 and grain coarsening was greatly minimized when sintering using the designed temperature profile. Highest RIT values of the non-doped (RIT = 68%) and La 3+ -doped (RIT = 71%) a-Al 2 O 3 compacts were achieved at 1100°C and 1140°C [Fig. 3(a)], respectively. To the best of our knowledge, these values are the highest values obtained in standard SPS sintering. As lower RIT values, RIT = 53% were obtained in similar forming and sintering conditions [START_REF] Lallemant | Transparent Polycrystalline Alumina Obtained by SPS: Green Bodies Processing Effect[END_REF] using the reference powder, characteristic features of the ultrafine a-Al 2 O 3 powder such as ultrafine size, size monodispersity, and isotropic morphology are crucial parameters facilitating the formation of a-Al 2 O 3 transparent ceramics.

Comparison of our experimental RIT values to theoretical RIT 1 values determined at different grain sizes [Fig. 3(b)] suggests a full densification for the compacts sintered at 1100°C for the nondoped samples. Using the same argument, La 3+ -doped samples sintered between 1140°C and 1200°C display full densification. Indeed, a higher sintering temperature [START_REF] Fang | Effect of Yttrium and Lanthanum on the Final Stage Sintering Behavior of Ultrahigh Purity Alumina[END_REF] was observed for the La 3+ -doped samples indicating diffusion blocking in the presence of La 3+ . Note that this shift in sintering temperature for the La 3+ -doped a-Al 2 O 3 material was previously observed in natural sintering. This shift was attributed [START_REF] Harmer | Fast Firing -Microstructural Benefits[END_REF] to reduced grain-boundary diffusivity arising from strong segregation of La 3+ to the grain boundary. From a HRTEM investigation carried out on La 3+doped a-Al 2 O 3 materials at various La 3+ content, a similar effect of the La 3+ dopant in a-Al 2 O 3 spark plasma sintering was found. Indeed, presence of secondary phase LaAl 11 O 18 at triple junction and along some grain boundaries was only observed on samples doped at high La 3+ content (600 ppma) while no inclusion was observed on samples doped below that concentration.

More interestingly, compared with the non-doped samples, a larger plateau of sintering temperatures yielding RIT values higher than 67% was observed with La 3+ dopant. Although similar RIT values were determined in the range of sintering temperatures, 1140°C<T < 1200°C, fine inspection of the corresponding microstructures [Fig. 4(a)] reveals a grain growth with average grain sizes ranging from 260 to 390 nm with increased sintering temperature. In contrast, a smaller window of sintering temperatures, 1080°C<T < 1100°C, was determined for non-doped materials. Indeed, for these latter samples sintered at 1060°C and 1120°C, large variations of RIT values were observed inside a same sample, depending on the region investigated. These variations of RIT values were shown to arise from different grain size probably due to slight local variations of green density. All these observations highlight the beneficial use of La 3+ reducing sensitivity to sintering temperature.

From these results, future work aimed to the fabrication of high RIT transparent a-Al 2 O 3 ceramics will involve dispersion of agglomerate-free, mono-crystalline, ultrafine, La 3+ -doped a-Al 2 O 3 building blocks.

IV. Conclusions

Highly dense transparent (RIT 71%) a-Al 2 O 3 ceramics were achieved using discrete, ultrafine high purity a-Al 2 O 3 nanoparticles sintered by standard SPS technique. Crucial effects of the nanoparticle characteristics, such as size monodispersity, isotropic morphology, and surface chemistry were emphasized. We demonstrate the beneficial use of La 3+ as a dopant, reducing the sensitivity of sintering temperature, thus increasing flexibility to fabricate large homogenous transparent a-Al 2 O 3 ceramics.

Fig. 1 .

 1 Fig. 1. TEM images of a-Al 2 O 3 nanoparticles. (a) Low magnification image showing perfectly discrete Al 2 O 3 nanoparticles. (b) High magnification TEM images showing primary crystallites of 80 nm. Inset: Electronic diffraction pattern showing crystalline a-Al 2 O 3 structure. (c) HRTEM image revealing highly crystallized interface. (d) Low magnification image of a reference powder showing non-isotropic aggregated particles.

Fig. 2 .

 2 Fig. 2. Pore diameter distribution of a-Al 2 O 3 green body formed from 80 nm nanoparticles showing monodisperse pore distribution and a mean pore diameter of 18 nm. Pore distribution of the reference powder (140 nm) is also given for comparison. Inset: Pore volume suggesting a higher green density when using discrete, isotropic ultrafine a-Al 2 O 3 nanoparticles.

Fig. 3 .

 3 Fig. 3. (a) Dependence of RIT of nondoped and La 3+ -doped sintered a-Al 2 O 3 on sintering temperature showing a larger range of densification temperatures with La 3+ dopant. Inset: photographs of samples taken at 2.8 cm above the text (i) non-doped sample sintered at 1100°C. (ii) La 3+ -doped sample sintered at 1140°C. (b) RIT and grain size of sintered alumina. RIT model curves calculated from Ref. 1 versus grain size are reported suggesting full densification of our sintered a-Al 2 O 3. The model curves (continuous line: 0.00 vol% porosity, dotted line: 0.01 vol% porosity) were obtained with an average refractive index change Dn = 0.005 with a pore diameter = 100 nm. RIT values from literature were renormalized for e = 0.80 mm.

  h

Fig. 4 .

 4 Fig. 4. SEM images showing pure and La 3+ -doped a-Al 2 O 3 microstructures. (a) nondoped Al 2 O 3 sintered at 1100°C, (b) La 3+ -doped a-Al 2 O 3 sample sintered at 1140°C, (c) 1160°C, (d) 1200°C.

Acknowledgments

The authors acknowledge support from the Agence Nationale pour la Recherche, ANR, France. This work was done through the CERATRANS project.


Hugot Pichon
email: hugot.pichon@g2elab.grenoble-inp.fr

Yves Lembeye

Jean-Christophe Crebier

Influence of DMC EMI Optimization on CMC EMI for DC-AC Isolated Power Converter Array

This paper focuses on the EMC disturbances generated by converter networks (PCA). After recalling the interest of the interleaving for the reduction of the differential mode current (DMC), the impact of the interleaving strategy on the common mode current (CMC) is studied. For this purpose, a PCA model allowing the evaluation of the CMC is proposed. This model, confronted with measurements carried out on a prototype PCA, has shown its good accuracy. Based on this model, several interleaving strategies of the PCA converters are evaluated according to the conducted EMC disturbances they generate. The interleaved control strategies are therefore studied according to their induced CMC but also according to the impact they have on the DMC. The work is based on simulations and modelling of a multi-stage DC-AC converter. The modelling of the CMC sources as voltage hotspots exploited by the interleaved control strategy is developed. An analysis is performed to highlight the opportunity of common mode recycling at the multistage converter and ends with the presentation of a control strategy allowing CMC recycling inside the PCA.

Introduction

Initially used on high power, high voltage applications [START_REF] Rodriguez | Multilevel Converters: An Enabling Technology for High-Power Applications[END_REF], modular converters are today considered in low-medium power (100W up to 100kW) low-medium voltage (10V up to 1kV) systems to increase converters performances, dynamics and densities [START_REF] Jung | Control Strategy for Improved Dynamic Performance of Variable-Speed Drives With Modular Multilevel Converter[END_REF]- [START_REF] Ronanki | Modular Multilevel Converters for Transportation Electrification: Challenges and Opportunities[END_REF] Modular converters are made of vectors or matrices of identical conversion modules working together to answer conversion specifications. Many different topologies and architectures have been proposed in the literature [START_REF] Perez | Modular Multilevel Converters: Recent Achievements and Challenges[END_REF], all based on the association in parallel and or in series of several, and even numerous conversion cells [START_REF] Kolar | Novel Three-Phase AC-AC Sparse Matrix Converters[END_REF]. Among them, multicellular, multi-levels power converter arrays are gaining in interest [START_REF] Andreta | A High Efficiency and Power Density, High Step-Up, Non-isolated DC-DC Converter Based on Multicell Approach[END_REF]. In particular, these conversion architectures are helping sharing voltage and current constraints, distributing losses while offering potential benefits from their multi cell organization in terms of conducted EMI but also modularity, fault tolerance or efficiency [START_REF] Kolar | Extreme Efficiency Power Electronics[END_REF]. A further step in modularity is related to the concept of power converter arrays [START_REF] Huang | High-Frequency High-Efficiency GaN-Based Interleaved CRM Bidirectional Buck/Boost Converter with Inverse Coupled Inductor[END_REF], [START_REF] Liserre | Power Routing: A New Paradigm for Maintenance Scheduling[END_REF]. Power Converters Arrays (PCA) are made of Conversion Standard Cells (CSC) working together, connected in series and or in parallel, to achieve the global conversion. The main difference is about the structure of the sub module. In PCA, each CSC is an individual isolated converter contributing to the overall conversion effort as illustrated in Fig. 1. By associating them in series and parallel, it is possible to accommodate the PCA to almost any range of conversion specifications, opening the opportunity to address a wide range of converter specifications with a limited variety of components, design and manufacturing options. Multicellular converters open up the opportunity to implement multi-levels which can be used to interleave voltage steps in series associations or current ripples in parallel associations, both leading to significant differential mode current (DMC) conducted EMI reductions [START_REF] Lamorelle | Handling Differential Mode Conducted EMC in Modular Converters[END_REF]. If the literature is extensively investigating DMC in multicell converters, it is not focused on its impact on Common mode currents (CMC). CMC are parasites currents flowing from the converter through ground. They are also subjected to conducted EMI limitations [START_REF] Chen | Common-mode interference study of a auxiliary power supply based on the serialization of SiC MOSFETs for MMC-HVDC system[END_REF] and must be carefully addressed in low and medium power levels. This paper is investigating how interleaved control strategies can also provide an interesting benefit from the CMC point of view.

The paper is organized as follows. First, DC to AC PCA converter architecture considered in this paper is recalled, since it is fundamental to address conducted EMI issues to clearly define it. Then the main benefits of interleaved control strategy optimization with respect to DMC are recalled. Its impact on CMC is then analyzed before considering the control strategy options that can be implemented to limit CMC levels. The analysis is carried out thanks to equivalent models and time domain simulations.

DC to AC, PCA inverter topology

The Such a converter topology provides the opportunity to interleave the voltage steps of each full bridge through interleaved control signals, as illustrated in the Fig. 2. By reducing the amplitude of the HF voltage steps while multiplying the apparent frequency of the HF voltage pattern, the interleaving control offers a significant reduction in differential mode filtering needs as described in [START_REF] Rodriguez | A Review of Control and Modulation Methods for Matrix Converters[END_REF]- [START_REF] Crebier | DC-AC Isolated Power Converter Array[END_REF].

Experimental behavior

A prototype was designed in order to evaluate in practice the benefits of interleaving multicell converters. The DMC filter was designed accordingly to regulation compliance. The prototype displayed on Fig. 3 is made out of 2 parallel converters of 6 CSCs in series. Table 1. Pro-vides a few essential data related to the hardware implementation. The prototype was tested under conducted EMI measurement standard conditions. As it can be seen in Fig. 4 where EMI normative measures are presented with DMC filter and without CMC filter, significant EMI levels are still preventing the prototype from regulation compliance. This is mainly due to CMC disturbances that are still very high and have to be filtered out. have a different effect on the common mode current due to the electrical series connections. The resulting conducted EMI harmonics are multiple of the switching frequency. This behavior will be detailed in section 4.

The very flat envelop for conducted EMI levels is characteristic of conducted CMC. It shows that traditional interleaved control strategies, if effective on DMC, is not effective on CMC, at least for multicell series associations. It is therefore interesting to investigate further, how interleaved control signals could be considered in order to limit as well CMC disturbances. For this purpose, the following section is introducing an original modeling of PCA converters in order to study and analyze its CMC EMI signature.

Common mode equivalent model

In order to represent the behavior of each CSC in terms of CMC conducted EMI source, CSCs are simplified as illustrated in Fig. 5. In this equivalent model, the DC/DC converter stage is totally neglected from the modeling effort. This is made possible since the switching frequency of the DC/DC converter stage is different from the H Bridges and its corresponding CMC EMI can be discriminated. As a result, the DC/DC conversion stage is represented as a perfect voltage source VDC connected to the DC link. To account for the parasitic propagation paths offered by the DC stage to CMC, two parasitic capacitances (B1 & B2) are added to the equivalent circuit, both connected to ground on one side and each to a terminal of the DC link as illustrated in Fig. 5. The H bridge is still represented with its four switches plus two common mode capacitances between each middle point and ground (A and C).

An additional modeling stage proposed in [START_REF] Crebier | DC-AC Isolated Power Converter Array[END_REF] is introduced in Fig. 6 in order to consider only HF signals. The H bridge switches and the DC link voltage source are substituted then by two voltage sources representing the HF voltage patterns of each H bridge middle point as illustrated in Fig. 6. Each voltage source VA and VC is a two level HF square wave with the magnitude of the DC link voltage source VDC. In this equivalent model, the two parasitic capacitors (B1 & B2) have been summed up in HF to a single named (B). In the analysis parasitic capacitance CB of B, is expected to be significantly larger than capacitances CA and CC of capacitors A and C. Also the AC side loop is connected to a resistor that represents the LISN HF equivalent model. This is necessary to close the common mode path loop. Please note the color code that has been used in Fig. 5 and 6 in order to ease the comprehension.

The right side of Fig. 6 represents the two stable states of an H bridge operated in bipolar control strategy. A stable state occurs between switching transitions, when no voltage variation is visible at the output of the H bridge. It is then possible to set the voltage across the various components of the HF equivalent circuit.

States "+" and "-" are used to name the two stable state in bipolar control strategy. In "+" state, the CSC adds VDC to the output AC loop. When in "-" state, it adds -VDC. [START_REF] Crebier | Common mode disturbance reduction of PFC full bridge rectifiers[END_REF].

With the use of this model, the next part will present the analysis of CMC generation when several CSC are associated in series on their AC sides.

4 Analysis of driving signal strategies on serial conversion interleaving conducted EMI.

Command strategies analyzed

As reminded in part 2, the interleaving of series connected PCA reduces the magnitude of the HF voltage steps, reducing the need of DM filtering. However, it produces high CMC. In this part this CMC is analyzed when an interleaved control strategy is used in a PCA converter with 4 CSC associated in series on the AC side. This analysis is carried out considering first a bipolar control strategy. Similar analysis can be carried out for unipolar control strategy and only main conclusion will be provided for that case.

Based on the analysis, a specific interleaving strategy for the driving signal will be proposed and analyzed to cancel out CMC disturbances in PCA converters. Please note that the analysis can be generalized to any number of CSCs, odd or even and any type of control strategy. where the first CSC (on the left) is in Sate "-" and the 3 others are in the Sate "+". Similarly to Table 1Table 2, Table 3 presents in orange columns, for each transition, the evolution of the voltage across each parasitic capacitor and, in grey columns, their fixed voltage for each stable state. The last line, in dark grey is the sum of the resulting CMC contribution for each capacitor type (Ax, Bx and Cx). One can see that in contrary with the analysis and results obtained in Table 2, here the sum of the CMC flowing through the parasitic capacitors is no more cancelled. As previously introduced in section 2, each CSC is inducing a specific CMC current, avoiding the opportunity of CMC cancelation at PCA level. The CMC wave at PCA level will not be a unique signal generated at 4 times the switching frequency but a complex signal due to unequal contributions.

Effect on common mode generation

Symmetrical bipolar command

Common mode current recycling

Common mode current recycling is a method to cancel CMC outside the converter [START_REF] Crebier | Common mode disturbance reduction of PFC full bridge rectifiers[END_REF]. In single-phase H bridges, designed and operating with two symmetrical switching cells, the resulting parasitics may cancel each other. For PCA inverters with DC/AC stage associated in series, in addition to the symmetrisation of the physical hardware thanks to modular approach, it is necessary to symmetrize the control signals in order to provide CMC cancellation. This is analysed in the following section. It is shown that if the same control signal are applied to two "electrically" symmetrical CSCs, the switching effect of one cell is cancelled by the other. By "electrically" symmetrical, one must understand opposite in the series association (top one and bottom one in the string for example or first one with fourth one and second one with third one in Fig. 7).

Effect on common mode current generation

In the following, CSCs 1 and 4 are supposed to be symmetrical due to their respective positions in the serial connexion. It is the same for CSCs 2 and 3. Let's consider that, cells 1 and 4 have opposite driving signals and it is the same for 2 and 3. With this approach at each switching transition during the period, CMC current flowing through B capacitors of a CSC is cancelled by the opposite CMC generated by the physically and electrically symmetrical CSC. Similarly, the CMC from capacitor C of one CSC is cancelled by the CMC through capacitor A of the symmetric CSC. This allows to expect a perfect recycling of the CMC into the PCA, equivalent to the natural recycling in a regular two levels H bridge voltage source inverter. This is outlined in Table 4 where stable states and evolutions of the hot spots voltages in a 4 cells PCA are described. 4 switching event per period are considered in bipolar control strategy. It is shown that with the symmetrization of driving signals at PCA level, it would lead to a perfect cancellation of the switching transitions.

Unipolar command

The same analyse can be done with a unipolar control strategy. It is known that using unipolar control in VSI allows reducing DM filtering effort by 4, it is also known that it also causes higher CMC emissions since it is less suitable for CMC cancelation [START_REF] Crebier | Common mode disturbance reduction of PFC full bridge rectifiers[END_REF]. However in the case of interleaved PCAs, the analyse shows the same opportunity of improvement as it is the case for bipolar control strategy. Also by using 180° shifted signals to drive physically and electrically symmetrical cells, the "symmetrised unipolar control strategy" has the same behaviour than "symmetrical bipolar command" having a possible perfect CMC recycling.

For the lack of place, the illustration with a table is not depicted here but the reader can easily understand that it works as well for any type of driving signal strategy as long as two physically and electrically symmetrical switching cells are switched at the same time.

Effect on differential mode current

The proposed driving signal approach has an effect on the differential mode filtering need. For the symmetrization needs, it reduces the number of CSCs that can be interleaved by a factor of two. It is well known that interleaving N CSCs the output inductor value will be reduced by a N² factor, no matter the control strategy considered (bipolar or unipolar or other). Therefore, symmetrized driving signals at PCA level will induce a reduction of 4 in the benefits of interleaving, no matter the number of CSC considered. This may be the price to pay in order to reduce CMC levels. The next section will present the spectrum analysis of a simulated PCA. This analysis will compare the CMC spectrum of the PCA according to the different interleaved control and driving signals strategies (bipolar, symmetrical bipolar, unipolar and symmetrical unipolar)

5 Time based simulation

Simulation parameters

The time domain simulation parameters must be set according to a realistic case study. For that purpose, the prototype depicted in Section 2 is considered. The electrical and dynamic behaviour of the main components of the DC/AC stages are represented to account for switching times, as well as filtering effects. In these simulations the PCA is supposed made out 6 pairs of interleaved CSCs, 12 in total, as the prototype one. Bipolar control strategy is considered. The switching events location are considered perfect (no dead time). Only the DCR of the filtering inductors and transistors are considered with the Coss and common mode (A B and C) capacitors.

A and C capacitors are estimated equal to 10 pF, and B capacitors are estimated equal to 200 pF. The Fig. 8 presents in blue the simulated CMC spectrum using the same bipolar command mode as in the prototype. The image of the produced CMC is observed looking at the voltage across the pair of 50 Ω resistors of the LISN model. The simulation result having the similar behaviour as the prototype (see Fig. 4 Normative measure of the conducted EMI from the PCA converter prototype (including DMC filter and no CMC filter)), the model is considered representative of CMC generated by the PCA converter. One can compare the natural reduction of the 6th and 12th harmonic in both the simulation and measurement. The red curve is the envelope of the spectrum. This envelop will be used in the following to compare the CMC spectrum generated by each control and driving signal strategy.

Analysis of the common mode spectrum

The Fig. 9 presents four envelops of CMC spectrums, the red one is the previously presented spectrum for the interleaved bipolar non symmetrized control strategy. The green one is the unipolar interleaved non-symmetrized spectrum.

The doted red and doted green are respectively the spectrum generated by symmetrized bipolar and unipolar control strategies. The level of these two last doted spectrums are comparable with numerical calculation noises. These time domain simulation results demonstrate the great interest of symmetrized driving signal at PCA level to cancel and to solve the CMC issue.

Sensibility to imperfection

One knows that without imperfections and dispersion, there would be no need of common mode filtering on regular VSI as discussed in [START_REF] Crebier | DC-AC Isolated Power Converter Array[END_REF][START_REF] Crebier | Common mode disturbance reduction of PFC full bridge rectifiers[END_REF]. However, the parasitics and component dispersions, associated with switching time location dispersion affect the perfect CMC recycling and cancelation. Taking into account all the imperfections is a complex task which should nevertheless be carried out if one wants to verify the effectiveness of the proposed symmetrical controls.

Conclusion

This work has exposed the incompatibility between standard interleaving control methods into series connected multinodular inverters and CMC conducted EMI mitigation. After a description of the CMC origin and causes into PCA topologies, a new symmetrized driving signal approach has been presented. It has been demonstrated the opportunity to cancel CMC. Considering components and parasitic dispersion, the time domain simulations of the PCA under symmetrized driving signal has shown significant benefits. This whole approach remains to be demonstrated in practice.

  multicell inverter topology used in this work consists of an association of isolated DC-AC conversion standard cells (CSC) connected in parallel on the DC side and in series on the AC side. The CSCs shown in dashed green boxes on the Fig. 1, are made out of a Dual Active Bridge (DAB) DC/DC conversion stage with galvanic isolation, cascaded with an H bridge DC/AC conversion stage. Two inductors LDM are placed on the AC side of this DC/AC conversion stage to filter out high frequency (HF) voltage patterns.

Fig. 3 Fig. 1

 31 Fig. 3 PCA prototype with 12 CSCs (6 series of 2 cells parallels) used to characterize the impact of interleaving driving signals on conducted EMI disturbances.

Fig. 2 Fig. 5 Fig. 4

 254 Fig. 2 Comparison between HF output voltage waveforms of a series non-interleaved and interleaved bipolar control strategy at 75% duty cycle

  The measured CMC is the current flowing through RLISN, and the Kirchhoff laws show that the current flowing through this resistor is the sum of the current flowing through the parasitic capacitors. Considering CA = Cc, and the equivalence of the impedance of different current path, the CMC is equal IRLISN in the following equation. The common mode current is always proportional to the sum of the voltage variation on A, B and C.

Fig. 7

 7 Fig.7introduces the equivalent HF model of the PCA with 4 DC/AC CSCs connected in series on their AC side. The control signal configuration displayed in Fig.7corresponds to state "-+++" where the first CSC (on the left) is in Sate "-" and the 3 others are in the Sate "+". Similarly to Table 1Table 2, Table3presents in orange columns, for each transition, the evolution of the voltage across each parasitic capacitor and, in grey columns, their fixed voltage for each stable state. The last line, in dark grey is the sum of the resulting CMC contribution for each capacitor type (Ax, Bx and Cx). One can see that in contrary with the analysis and results obtained in Table 2, here the sum of the CMC flowing through the parasitic capacitors is no more cancelled. As previously introduced in section 2, each CSC is inducing a specific CMC current, avoiding the opportunity of CMC cancelation at PCA level. The CMC wave at PCA level will not be a unique signal generated at 4 times the switching frequency but a complex signal due to unequal contributions.

Fig. 6

 6 Fig. 6 HF equivalent model of a full bridge inverter and the two stable states voltage distribution for bipolar control strategy.

Fig. 7

 7 Fig. 7 HF equivalent model of the 4 CSCs for the stable State "-+++"

Fig. 8

 8 Fig. 8 Spectrum and envelop of the simulated CMC measured on standard LISN impedance (2X50 Ω)

Fig. 9

 9 Fig.[START_REF] Huang | High-Frequency High-Efficiency GaN-Based Interleaved CRM Bidirectional Buck/Boost Converter with Inverse Coupled Inductor[END_REF] Comparison of four CMC EMI spectrum envelops with respect to control strategy choices.

Table 2

 2 Stable states and magnitudes of A, B and C capacitor voltage steps in a single H bridge.

	The Table 2 presents the way the analysis is go-
	ing to be carried out to analyze CMC generation
	across each parasitic capacitance A, B and C.
	The analysis approach is introduced here for a
	single H bridge operating in bipolar control strat-
	egy. Each switching cell has two stable states +
	and -and two transitions, represented in the Fig.
	6 by arrows and in the table by k*VDC. The grey
	columns account for the stable voltage states of
	the switching cells (between switching transi-
	tions) and the orange columns describes the
	voltage transition magnitude across each ca-
	pacitance at each switching transition.
	The last line of the table (dark grey) shows the
	sum voltage swing across CA and CC for each
	switching transition. If equal and opposite, the
	CMC cancelation is observed and no CMC cur-
	rent flows to the LISN

Table 3

 3

stable states and evolutions of the parasitic capacitors voltages in a 4 cells converter. A 4 CSC bipolar converter has 8 switching events per period.

Table 4

 4

	stable states and evolutions of the hot
	spots voltages in a 4 cells PCA. 4 switching event
	per period are considered in bipolar control strat-
	egy.