A Probabilistic Approach to Susceptibility Measurement in a Reverberation Chamber

Transcription

1 A Pobabilistic Appoach to Susceptibility Measuement in a Revebeation Chambe Emmanuel Amado, Chistophe Lemoine, Philippe Besnie To cite this vesion: Emmanuel Amado, Chistophe Lemoine, Philippe Besnie. A Pobabilistic Appoach to Susceptibility Measuement in a Revebeation Chambe. Asia Pacific Symposium on EMC, May, Singapoe, Singapoe. pp.-4,. <hal-7388> HAL Id: hal Submitted on 4 Jun HAL is a multi-disciplinay open access achive fo the deposit and dissemination of scientific eseach documents, whethe they ae published o not. The documents may come fom teaching and eseach institutions in Fance o aboad, o fom public o pivate eseach centes. L achive ouvete pluidisciplinaie HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau echeche, publiés ou non, émanant des établissements d enseignement et de echeche fançais ou étanges, des laboatoies publics ou pivés.

2 A Pobabilistic Appoach to Susceptibility Measuement in a Revebeation Chambe Emmanuel Amado, Chistophe Lemoine, Philippe Besnie IETR, UMR CNRS 664, INSA Rennes, Fance emmanuel.amado@insa-ennes.f Abstact In this aticle, we popose an altenative appoach fo measuing the susceptibility level of an equipment unde test in a evebeation chambe. Instead of using a statistical estimation of the maximum, ou estimation is based on an estimation of the pobability of failue of the equipment unde test. We show though Monte Calo simulations that the pobability of failue of an equipment unde test allows to pedict with a good accuacy its susceptibility level. An expeimental validation with a simple equipment unde test shows that the susceptibility levels measued in a evebeation chambe ae consistent with measuements pefomed in a GTEM cell. [ V/m] E(E m) 95% CI of E(E m) E(E M ) 95% CI of E(E M ) I. INTRODUCTION Susceptibility measuements in a evebeation chambe (RC) ae based on a statistical estimation of the maximum level an equipment unde test (EUT) may have eceived ove a numbe N of independent stie positions []. A lot of wok [], [3], [4], [5], [6], [7] has been done in the community to chaacteize statistically the estimation of the maximum value of a ectangula E-field component o the maximum powe in an RC. Exteme value theoy is used to detemine the pobability density function of the maximum powe [] o the maximum of a ectangula component of the E-field[4] in the chambe. Let X a andom vaiable with a density pobability function f X (x) and a cumulative distibution function F X (x). The cumulative distibution function of the maximum value ove N independent samples F N is given by: F N (x) = F X (x) N () and thus the density pobability function of the maximum is given by: f N (x) = NF X (x) N f X (x). () The maximum value of the powe o the maximum value of a ectangula component of the E-field is a N-ode statistics. It is deived fom the size N of the sample measued (e.g the numbe of independent stie positions o the numbe of independent fequency used duing the measuement) and the powe injected in the RC. It means that by using an estimation of the maximum, an intinsic quantity like the susceptibility level of an EUT is a function of the numbe of stie positions used duing the test. Moeove, the uncetainty of the estimation of the maximum of a ectangula E-field component is lage and deceases slowly with the size of the sample N as shown in continuous line in figue. In this aticle we popose a new appoach based on the pobability N Fig.. Monte Calo simulations ( 5 expeiments), showing the expected value and the 95 % confidence inteval (CI) of both the mean value of the magnitude of a ectangula E-field component E m and the maximum magnitude of ectangula E-field component E M fo diffeent values of N. The mean value of the ectangula component is set to V.m in these simulations. of failue of the EUT. This appoach uses an estimation of the mean value of a component of the E-field duing the measuement and an estimation of the pobability of failue of the EUT duing the testing. As shown in blue in figue, the uncetainty of an estimation of the mean value of a ectangula E-field component deceases moe apidly. Afte pesenting the theoetical backgound of ou appoach, we show that it can be used to measue with a good accuacy the susceptibility level of an EUT. The appoach is confimed by an expeimental validation and the values obtained ae consistent with measuements pefomed in a guided wave setup like a GTEM cell. II. MEASUREMENT OF THE SUSCEPTIBILITY BASED ON THE PROBABILITY OF FAILURE OF AN EUT In this section, we popose a method that allows to deive the susceptibility of the EUT fom the pobability of failue measued in an RC. The statistical distibution followed by a ectangula E-field component in an ovemoded and wellstied RC is a Rayleigh distibution. The mean value of a Rayleigh distibution is σ π [8]. The cumulative pobability function of a Rayleigh distibution with scale paamete σ

3 Cumulative pobability ces and 95% CI fo Es = V/m, ( 4%) [V/m] ces and 95% CI fo Es = V/m, ( 46%) No failue E s Failues Magnitude of the E-field Fig.. Cumulative density function of a Rayleigh distibution. Above the susceptibility level E s, failues ae detected with a pobability. (shown in figue ) is given by [8]: F (x) = e x /σ, with x. (3) When the mean value of the E-field E m in the chambe equals the susceptibility level E s of the EUT, the pobability of failue m can be deived by posing: ( ) π m = F (E s ) = F σ = e π/4 46 % (4) If a default is detected fo m = 46 % of the stie positions, the susceptibility level E s of the EUT is diectly given by the mean value E m of a ectangula component of the E-field in the chambe. Let define the susceptibility level E s of an object in an RC as the mean value of a ectangula component fo which e π/4 46 % of the stie positions povoke a failue on the EUT. We will deive a geneal elation that allows to deduce the susceptibility level E s fom a measuement with an abitay mean value of a ectangula component of the E-field E m and a coesponding pobability of failue of the EUT. If >.46, the mean value of a ectangula E-field component E m is geate than the susceptibility level E s of the EUT, and if <.46, we can deduce that E m < E s. The knowledge of the pobability of failue, the mean value of the E-field E m in the chambe, and the theoetical CDF of an E-field component allow to pedict the susceptibility level E s. Fom (4), we can wite: = F (E s ) = e E s /σ (5) We can wite the two following equations: { Es = σ ln(/) and thus: E m = σ π/. E s = E m ln(/) π (6) (7) ces and 95% CI fo Es =.3 V/m, ( 9%) N Fig. 3. Mean value and 95 % CI of the estimato Ês fo diffeent values of susceptibility E s and fo diffeent values of N. The mean value of a ectangula component E m is set to V.m. Monte Calo simulations with 4 expeiments fo each value of N. We can extact the level of susceptibility of an EUT fom its pobability of failue, oughly given by = N f /N and fom an estimation of the mean value the magnitude of a ectangula component of the electic field duing the measuement Êm. III. MONTE CARLO SIMULATIONS OF OUR APPROACH In this section we study the statistical popeties of ou appoach by using Monte Calo simulations. The goal is to have an indication of the quality of the estimato Ês of the level of susceptibility E s. Fom equation (7), we can note that the estimato Ês is a function of two estimatos, Êm and. As these two estimatos ae estimated by computing an aveage ove a sample of size N, the confidence inteval (CI) should decease with the sample size N. A. Effect of the sample size N on the confidence inteval Figue 3 shows the estimation of the susceptibility level fo thee diffeent levels of susceptibility E s as a function of the numbe of stie positions N. In these simulations, the mean value of the E-field is set to V.m. Fist in ed, the susceptibility level equals the mean value of the E- field. As pointed out in (4), 46 % of the stie positions povoke a failue on the EUT. The statistics of Ês is simila to the statistics of E m pesented in figue. We can note that the uncetainty of the estimation vaies with the level of susceptibility measued. This is mostly due to the estimation of the pobability of failue. If E s =.3E m, as depicted in blue in figue 3, the pobability of failue equals 9 %. The CI emains lage when the numbe of stie positions inceases and the mean value of Ês conveges to E s when N >. If E s = E m, as depicted in geen in figue 3, the pobability of failue equals 4 %. The CI emains significant when the If the quality facto of the chambe with the EUT is known, E m can be deived diectly fom it.

4 3 E s/e m (susceptibility of the EUT ) E(Ê s/e m) 95% C I of Ê s/e m Ê s/e m Fig. 6. Extenal view of the equipment unde test. Metallic enclosue Fig. 4. Mean value and 95 % CI of the estimato Ês nomalized by Em as a function of the pobability of failue with N = 3 stie positions. Monte Calo simulations with 5 expeiments fo each value of. Antenna _ 9V k max. V - V V s _ 9V.4 k.3. Ês/E s. Fig. 7. Schematic view of the equipment unde test and its electonic boad Mean value (N=3) 95% CI (N=3) Mean value (N=) 95% CI (N=) Fig. 5. Mean value and 95 % CI of Ês/Es as a function of the pobability of failue with N = 3 and N = stie positions. Monte Calo simulations with 5 expeiments fo each value of. numbe of stie positions inceases and the mean value of Ê s conveges to E s if N > 4. These Monte Calo simulations show that a pobabilistic measuement of the susceptibility gives good esults as long as the values of o ae not too small. Unlike an estimation based on the maximum value of the E-field, this estimation based on its mean value does not incease with N. B. Effect of the pobability of failue on the confidence inteval Figue 4 shows the mean value and the 95 % CI of Ês/E m when N = 3. We can note that with N = 3 the mean value of the estimato is coect fo a pobability of failue between.5 and.95. Fo a coect estimation of the susceptiblity level, one can use the following ule of thumb N N. Figue 4 shows that the absolute width of the CI inteval of Ê s /E m is not vaying with. It means that elative eo is inceasing when the susceptibility level E s is deceasing. Figue 5 shows the CI of the elative estimato Ês/E s fo N = 3 stie positions and N =. If N = 3, the elative eo of 95 % of the Monte Calo expeiments does not exceed ± % as long as.6. If N =, should not exceed.8. These Monte Calo simulations show that the estimation of a susceptibility level based on the pobability of failue of an EUT is possible and may be a good altenative to measuements based on the maximum value. The uncetainty of the estimation is elatively well contolled and deceases moe apidly when N is inceasing than the estimation based on the maximum. A. Expeimental setup IV. EXPERIMENTAL VALIDATION In ode to validate ou appoach, we designed an EUT. This EUT consists of an electonic boad with an opeational amplifie (op-amp) acting as a compaato. The boad is placed in a metallic enclosue. A 5 cm long monopole extenal antenna is connected to the cicuit as shown in figue 6. A schematic of the electonic cicuit is given in figue 7. The antenna is associated with an envelope detecto fo filteing the high fequency and fo ectifying the signal. Without any distubance, since V > V the op-amp delives V s = 9 V. With distubances leading to V > V, the op-amp povides V s = 9 V indicating a default. The signal V s is ecoded with a digital oscilloscope and a home made pogam that

5 [V/m] 5 5 Measuement in a GTEM cell Susceptibility based on the max (N = 5) Pobabilistic susceptibility (N = 3) diffeent levels of powe injected in the chambe. We estimate the susceptibility if and only if the estimated pobability of failue is between /N and /N. These cuves show that ou pobabilistic appoach of the susceptibility levels give esults that ae consistent with the levels measued in the GTEM cell. If the EUT is not pone to be damaged easily, this appoach can educe the duation of the testing by detemining almost immediately the susceptibility level of the EUT instead of inceasing gadually the level of powe injected in the chambe Fequency [MHz] Fig. 8. Measuements of the susceptibility in an RC with ou pobabilistic appoach fo vaious injected powe (o E m) as calculated fom (7) (in ed), with the method based on an estimation of the maximum value of the E-field (in blue) and measuements of the susceptibility pefomed in a GTEM cell (in black). contols all the expeimental setup. The pogam etuns eithe the value in the case of no susceptibility, o the value if a susceptibility is detected. The measuements ae pefomed between 85 MHz and 5 MHz. At these fequencies, the behavio of ou chambe is ideal and measuements have shown that the ectangula E-field components follow a Rayleigh distibution. We choose to use N = 5 stie positions and the powe injected in the chambe is inceased gadually allowing to each a magnitude of V.m fo the ectangula components of the E-field. Susceptibility measuements wee pefomed with the same setup in a GTEM cell at diffeent positions in the test volume. Since the levels obtained fom one position to anothe wee simila, we choose to keep only the minimum value of the susceptibility among the diffeent positions. B. Results Figue 8 shows the diffeent susceptibility levels measued in the RC and in the GTEM cell of ou laboatoy. Ou setup did not allow to get an E-field magnitude geate than V.m in the GTEM cell. It explains the lack of susceptibility detection below GHz. The measuements of the susceptibility based on an estimation of the maximum magnitude of the E-field in the evebeation chambe with N = 5 stie positions ae given by the blue cuve. In compaison with the measuements made in the GTEM cell, the susceptibility measued is geneally highe and fo some fequencies, the levels measued ae supeio by a facto of 4. This susceptibility measuement exhibits oscillations that cannot be explained physically given the length of the antenna. The oscillations ae mainly due to the statistical uncetainty in the estimation of the maximum value as explained in section I and pesented in figue. The ed cuves in figue 8 show the susceptibility of the EUT by using ou appoach with only N = 3 stie positions. These cuves coespond to the V. CONCLUSION This aticle gives an altenative appoach fo measuing the susceptibility in an RC. This appoach based on an estimation of the pobability of failue of an EUT allows to pedict with accuacy the level of susceptibility of an EUT. We based ou investigation on a ectangula component of the electic field in an ideal evebeation chambe. Thus we used a Rayleigh distibution to build ou appoach. The tansposition of this method with othe distibutions is staightfowad, we can use Weibull distibutions to pefom susceptibility measuements at lowe fequencies o exponential distibutions if the quantity measued is the powe eceived. The vaious Monte Calo simulations show that the CI of this method deceases with the numbe of stie positions. The measuements on an EUT show that the susceptibility levels obtained with this pobabilistic appoach ae consistent with measuements made in a GTEM cell and that the statistical dispesion of the values is educed in compaison with measuements based on a statistical estimation of the maximum. ACKNOWLEDGMENT This wok was suppoted by the Fench Ministy of Defence DGA (Diection Généale de l Amement), with a Ph.D. gant deliveed to Emmanuel Amado. REFERENCES [] Revebeation Chambe Test Methods. Intenational Electotechnical Commission (IEC) Standad 6-4-, 3. [] T. Lehman and G. Feye, Chaacteization of the maximum test level in a evebeation chambe, in Electomagnetic Compatibility, 997. IEEE 997 Intenational Symposium on, Aug. 997, pp [3] G. Koepke and J. Ladbuy, New electic field expessions fo EMC testing in a evebeation chambe, in Digital Avionics Systems Confeence, 998. Poceedings., 7th DASC. The AIAA/IEEE/SAE, vol., 998, pp. D53/ D53/6. [4] K. Haima, Statistical chaacteistics of maximum E-field distibution in a evebeation chambe, in Electomagnetic Compatibility, 4. EMC 4. 4 Intenational Symposium on, vol., 4, pp [5] M. Hoije, Maximum powe available to stess onto the citical component in the equipment unde test when pefoming a adiated susceptibility test in the evebeation chambe, Electomagnetic Compatibility, IEEE Tansactions on, vol. 48, no., pp , May 6. [6] M. Hoije, H. Kauthäuse, and J. Ladbuy, On maximum powe available to stess onto the citical component in the equipment unde test when pefoming a adiated susceptibility test in the evebeation chambe, Electomagnetic Compatibility, IEEE Tansactions on, vol. 5, no. 4, p., nov. 8. [7] G. Ojubin, Maximum field inside a evebeation chambe modeled by the genealized exteme value distibution, Electomagnetic Compatibility, IEEE Tansactions on, vol. 49, no., pp. 4 3, 7. [8] A. Papoulis, Pobability, Random Vaiables, and Stochastic Pocesses, 4th ed. New Yok: Mc Gaw Hill,.