The Failure of Coaxial TEM Cells ASTM Standards Methods In H.F. Range

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1 The Failure of Coaxial TEM Cells ASTM Standards Methods In H.F. Range Mihai Badic HV/EMC Laboratory, Research Institute for Electrical Engineering - ICPE Bucharest, ROMAN badic@icpe.ro Mihai-Jo Marinescu HV/EMC Laboratory, Research Institute for Electrical Engineering - ICPE Bucharest, ROMAN j@icpe.ro Abstract The paper deals with one of the ost used and reliable ways to characterize the shielding capability of aterials, based on the Schelkunoff isoorphis. This ethod uses the physical-atheatical equivalence of equations describing SE in the case of infinite plane shield, respectively in the case of aterial saple introduced in the easuring coaxial TEM cell ( ), and it resulted into the ASTM standards ES7-83 and D The paper shows that these standards (and Schelkunoff isoorphis) are not valid for electrically thick saples; there is no identity between shielding effectiveness and insertion attenuation/insertion loss in H.F. range. Keywords Shielding effectiveness, TEM cells, easuring standards. INTRODUCTION The goal of SE easureents - using coaxial TEM cells or other ethods - is the evaluation of shielding capability of aterials (hoogeneous, coposite, ultilayer) in the ideal case of infinite plane shield placed in free space illuinated by a plane electroagnetic wave. The theory of Schelkunoff and the isoorphis between this case and the one of the coaxial line was accurately deonstrated [1], [] for the configuration entioned in ASTM ES7-83. In certain situations, as shown in [3], [4], ASTM D ay be reduced to the one entioned before. Results that if isoorphis withstands to a theoretical analysis taking into account all phenoena, the experiental ethod is validated, at least theoretically, for both standards. The paper deonstrates theoretical and experiental that this is not possible: Schelkunoff isoorphis is affected by a basic error that liits its applicability just in the area of axiu interest: electrically thick saples, eaning the H.F. range. ANALYTIC BACKGROUND As it is known, by perforing two successive easureents, one is able to deterine: ref U1 T = SE (1) load U T The two easureents are siilar in the case of the two standards entioned above (being identical for surface conducting aterials), as follows: - for ASTM ES7-83: U 1 is the voltage easured at the output of the cell without aterial saple and U is the voltage easured at the output of the cell with aterial saple. - for ASTM D : T ref is the transission coefficient when the reference saple is ounted inside the TEM cell T load is the transission coefficient easured with the load saple. These easureents allow deterining SE and the coparison of the data with the theoretical curves plotted according to: SE = log 1 + log ( + ) log e -ãd 1 e ád = R + + A + B where R =reflection loss, A =absorption loss, B =rereflection correction, =free space wave ipedance, =wave ipedance of aterial, γ=α+jβ=propagation constant and d=shield thickness [5]. In order to obtain accurate results (errors less then %) soe technical conditions ust be fulfilled: 5 Ω ipedance atching for all devices (source, TEM cell, receiver, cables, a/o.); easureent prefored below the liit frequency of TEM cell (usually 1-1.5GHz); good contact between the saple and the cell. The last condition, the ost difficult to fulfil, was avoided by applying ASTM D standard (flanged version developed by NBS). This holder uses flanges, rather then continuous conductors, thus avoiding the influence of contact resistance. Moreover, this standard allows the easureent of surface insulated aterials and ultilayer shields. If the plot of equation () in Fig.1 is considered, it ay be easily observed that there are two distinct areas: area A - ()

2 the flat part of the curve corresponding to electrically thin saples (d<<δ), respectively area B - the fast rising part of the curve corresponding to electrically thick saples (d>>δ). SE [] where E 1, E represent electric field in the absence of the infinite plane shield in free space respectively in its presence, and H 1 and H the sae for agnetic field. Subscript c refers to application of and γ equations to the transission line with dielectric, respectively with washer shaped saple on a length equal to the shield thickness d. AREA B γ AREA A E 1 H 1 E H, γ a) d << δ d >> δ U 1 U Frequency IN a b OUT Figure 1. Area A-verification of test equipent; Area B-verification of Schelkunoff isoorphis. c, γ d c γ c b) Measureents in Area A check the technical conditions already entioned. For ost of the aterials the curves are flat in this area, being described by the approxiate equation (characteristic to electrically thin saples, d<<δ): σd SE log ; SE = F d (3) ( ) 1 σ, Conductivity σ ay be easily easured using classical ethods, (3) becoing calibration ethod for any TEM easuring coaxial cell [1]. On another hand, easureents in Area B give inforation on behavior of aterials exposed to high frequency. This is the ost iportant area for experients (usually the curve has a rapidly increasing shape). The ain proble is that there are no published results showing a good atch between theory and easureents, in this area, using the ethods prooted by the already entioned standards. This indicates a basic error regarding the validity of Schelkunoff isoorphis, the subject of this paper. For ASTM ES7-83 equations (1) and () are valid, as well as configuration in Fig.. For this configuration, the following relations express isoorphis: U 1 E 1 H 1 U E H c c (4) γ γ c SE 377Ω; c = 5Ω Figure. Measuring ethod of ASTM ES7-83 based on Schelkunoff isoorphis: a) infinite plane shield in free space; b) TEM cell with and without saple. It is easy to deonstrate that γ γ c, and the shape factor (1/π)ln(b/a) is reduced in expression () so that SE. In [5], [6] is shown that for electrically thin saples (d<<δ low frequency) with µ r 1 equation () becoes: A) THIN SAMPLE - PROPAGATION INSIDE CELL (l λ ) = log e d δ 4 γd ( 1 e ) d log 1 + γd 4 δ γd σ d log = log = log R B) THIN SAMPLE - NO PROPAGATION INSIDE CELL (l << λ ) d log 1 σ + sq = + log 1 R sq (6) where l represents the total length of the easuring line (including cell), σ is aterial conductivity and R sq is square resistance [7], eaning the resistance on a aterial square having thickness d. It ay be observed that if we write the above equations as function of characteristic ipedance of line/cell, results for the two cases: (5)

3 c log (7) L respectively + c log 1 (8) L where L is purely resistive ipedance of the washer/disk shaped saple introduced in the easuring cell. For ASTM D is valid expression (1), but working equations are calculated with expressions characteristic to luped constants circuits. The structure of easuring cell is shown in Fig.3, and the equivalent circuit is presented in Fig.4. IN Figure 3.Measuring ethod in case of ASTM D : a) reference saple easureent; b) load saple easureent. C d Annular shaped piece Disk Load K C where b is the inner diaeter of outer conductor and a is the diaeter of inner conductor. Conditions (1) and (13) correspond, for usual diensions of TEM cells, to the values λ H11 c respectively λ E1 5c. The ost rea) b) OUT According to this equivalent network (Fig.4), results: A = log 1 + (9) B A B c ( C + K ) + C ( R + C ) ( + + R) C = c + R (1) C K K R K = L + R (11) + R K = 5Ω The above equations result fro [3] for the case when contact resistance and capacitance in the equivalent network are equal towards transversal and longitudinal syetry axis. If C are considered negligible, then A= c. If also contact resistance are null (R=), then equation (9) becoes (6) because the shape factor in both expressions ( c and L ) is reduced in (8). So, it ay be said, based on the deonstrations accopanying the two ASTM, that in the ideal (technically) case they offer the sae solution. It ust be highlighted that this is valid for the case of electrically thin saples (d<<δ) and cells without propagation (l<<λ ). This observation is obvious because the working equations are deduced based on a luped constants circuit (Fig.4). ASTM D is not odeling the behavior of electrically thick saples and there is no theoretical basis for region B of SE =F(w) in Fig.1. On another hand, ASTM ES7-83 is odeling apparently accurate the behavior of infinite plane shield in free space, both in areas A and B, even if it involves difficulties in eliinating the influence of contact resistance. It ay be assued that for certain aterials with good surface conductivity (which ay be checked by eans of copleentary ethods) an identical characteristic or close to the theoretical one (Fig.1) can be obtained. It will be deonstrated further on that this is ipossible both in theory and practice. c R R R C Figure 4. Equivalent network for calculation of working equations of a flanged coaxial transission line holder (ASTM D ). L K R C c INCONGRUITY OF METHODS The axiu frequency condition of the TEM cell, entioned before, is deduced fro the condition of the lack of overoding [8], [9]: - for H 11 (TE 11 ) ode: π λh 11 = ( b + a) ; λ λh 11 (1) - for E 1 (TM 1 ) ode: λ ( b a) λ λ 1 = (13) E 1 ; E

4 strictive condition (1) leads to the axiu working frequency (1.5GHz) entioned before. The basic error, giving the incongruity of the two ethods, consists of neglecting the odification of wavelength inside the conductor/seiconductor saple because of conductivity σ, as it is shown in Fig.5. As consequence, overoding appears at uch lower frequency then 1GHz. λ<<λ Actually, the axiu frequency of using the TEM cell for the saple's aterial is considerably higher because there is another condition for the appearance of higher odes (longitudinal fields), this being the propagation condition inside the aterial saple having thickness d: 1 f < (15) π d σ µ For this particular case considered, the two conditions are fulfilled siultaneously at frequencies below 5.6MHz (for d=3). This phenoenon of waves with longitudinal fields that can exist as higher odes in coaxial lines is presented in Fig.6. The liit frequency depends on all acroscopic paraeters ε, µ, σ, but the ost iportant is conductivity σ. λ / λ / d ε,µ,σ Figure 5. The phenoenon of wavelength odification when a far field electroagnetic radiation illuinates a seiconductor shield with absorption. Thus, supposing a aterial having a oderate conductivity (5Ω -1-1, close to certain synthetic Graphite types), results: Table 1.Wavelength shift inside seiconductor saple Frequency 1kHz 1MHz 1MHz 1GHz Free space λ free space = 3k λ Material saple λ saple v f saple 1413/s 54.7k/s 447k/s 1413 critical frequency for TEM ode 5kHz k/s Data in Table 1 were calculated with the following equations (valid for conductors): ω f v f = 316 ; β σ v v c (14) λ = saple v saple λ saple a) b) Figure 6. Higher odes in coaxial line: electric field agnetic field a)te 11 ode;b) TM 1 ode.

5 PRECISION AND ACCURACY Precision is linked to easuring errors leading to ore or less reproducible easureents, while accuracy refers to systeatic deviations due to basic or technical reasons. In the case of the two standards brought into discussion, both need to be analyzed. ASTM ES7-83 PRECISION: very good for conductors and seiconductors when contact resistance is less iportant. ACCURACY: very good for area A (d<<δ). ASTM D PRECISION: very good for any kind of saple (hoogeneous, coposite, ultilayer), no atter of contact resistance (such a reference easureent allows one to cancel the effect of contact resistance between saple and etallic waveguide). ACCURACY: very good only for area A (d<<δ). Experients were perfored for easuring =F(ω), on different saples, having conductivity within the range 1Ω Ω -1-1 and thickness of µ 5, with or without agnetic properties. None of these tests was able to provide a shape siilar to the one in Fig.1 - the theoretical behavior of the infinite plane shield placed in free space. Many other authors obtained this negative result [1], [11], [1]. On another hand, it is always obtained a correct value of SE in the region A (flat), deonstrating that errors are not due to contact resistance. The accuracy of these results is checked by easuring conductivity σ by eans of copleentary ethods and applying equation (3) to calculate. Also, fro the way of checking 5Ω ipedance atch for all devices (source, TEM cell, receiver, cables, a/o.) [1] is deduced that errors don't proceed either fro an ipedance isatch. Because tests were perfored at frequency up to 1GHz results that all technical conditions were fulfilled. The only reaining cause of errors - analytically deonstrated - is the appearance of higher odes inside the aterial saple, because of severely reduced wavelength in conductive aterials. The ost significant tests are those perfored on Synthetic Graphite (Fig.7) and Si p(b) Monocrystal (Fig.8) respectively Polycrystal (Fig.9). Thus, Synthetic Graphite has a oderate conductivity ( Ω -1-1 ), leading to appearance of region B starting fro approxiately 1MHz. Even so, experiental results do not atch theoretical predictions, although in region A errors are of only 1% (Fig.7). Experients perfored on Si p(b) and Si Polycrystal intended to highlight how useful is the ethod in region A of shielding characteristic (relatively low frequency). It ay be observed a Schottky type phenoenon on the characteristic, due to etal (Ag deposit) - seiconductor (Si). After Schottky barrier breakdown (using a relatively high voltage), the flat part of characteristic has significantly increased (apparent σ increases). At higher frequency ( Hz) is practically identical to the one obtained by calculation - equation (3) - using for σ the value deterined by the ethod of 4 points probe. Figure 7. Insertion attenuation for Synthetic Graphite [] : teoretical ο, experiental 34,3; σ=54 f=18 MHz f[khz] Figure 8. for Si onocrystal p(b); sae saple before (x) and after (o) Schottky etal-seiconductor interface breakdown (d=5.1) [] : teoretical experiental 7,7 ; σ=458 d=5 f[khz] [] : teoretical ο, experiental 11,9; σ=4, f=, MHz f[khz] Figure 9. Sae test for Si polycrystal (d=4.95).

6 CONCLUSIONS In order to analyze the practical cases that occur in shielding technique we ust take into account a reference odel. This is the infinite plane shield in free space (hoogeneous, coposite or ultilayer aterials). For a hoogeneous aterial, the theoretical proble was solved by Schelkunoff (1943) based on the wave ipedance concept and reflection and absorption phenoena. It is also considered that inside conductors the plane wave conserves the TEM ode. This theory undisputed up to present by anyone, shows that the variation of SE versus frequency looks like Fig.1. The fact that the shield is considered, initially, infinite, has no special iportance, because phenoena is conserved also for a finite shield if it is illuinated by strait directive patterns antennas, for exaple, with respect to the plane waves (far field) condition. The proble is that no experiental validation was obtained up to present, except area A, where the ost iportant phenoenon is reflection. The fact that in area B - where absorption is decisive - there is no atch between theory end experient leads to suspicion over the easuring ethods prooted by ASTM ES7-83 and ASTM D , both based on the Schelkunoff isoorphis. As consequence, this isoorphis ust be re-analyzed fro theoretical point of view. It is the goal of this paper, deonstrating both theoretical and experiental that these ethods are not valid in the H.F. range because of neglecting a physical phenoenon: appearance of higher odes in the coaxial line, phenoenon that does not occur in the case of plane shield placed in free space or in other cases et in practice. No theory ay be considered valid if is not experientally checked. In order to apply with good results the standards entioned above also in the H.F. range (area B of shielding characteristic), should exist at least one saple ade up by hoogeneous conductive aterial (for exaple Cu, Bisuth, etc.) showing a =F(ω) characteristic identical/siilar to the theoretical one. In conclusion, the paper deonstrates both theoretical and experiental that the ethods proposed by the two ASTM standards discussed here are useful only in the electrically thin saples area (having accuracy up to 1%), and result in considerable errors in the thick saples area, for theoretical and not technical reasons, as considered up to present. Measureents in this area should be avoided and testing labs should propose new ethods for deterining SE in d>>δ region. REFERENCES [1] Schelkunoff, S.A., Electroagnetic Waves, D. Van Nostrand Copany, Inc., (1943). [] Lauri Hale, "Screening Theory of Metallic Enclosures", 199 IEEE International Syposiu on EMC, Anahei, California, USA, (199). [3] Wilson, P.F., Ma, M.T., A Study of Techniques for Measuring The Electroagnetic Shielding Effectiveness of Materials, NBS Technical Note 195, (1986). [4] ASTM D , Standard Test Method for Measuring the Electroagnetic Shielding Effectiveness of Planar Materials (1989). [5] White, D.R.J., Electroagnetic Shielding Materials and Properties, Don White Consultants, Inc., (198). [6] Badic,M., Marinescu, M.-J., "On the Coplete Theory of Coaxial Te Cells", Proceedings of IEEE International Syposiu On Electroagnetic Copatibility, Washington, DC, USA, (August 1-5, ). [7] Nagao, H. a/o., "Approxiation and Accuracy of Shielding Effectiveness Calculated by Sheet Resistivity", Tokyo Institute of Technology. [8] Harley, A.F., Microwave Engineering, Acadeic Press, (1963). [9] Neubauer, H., Huber, F.R., "Higher Modes in Coaxial RF Lines", The Microwave Journal, (June 1969). [1] Haitao,Y., Ying, L., "Calibration and Analysis of Coaxial Holder for Measuring Shielding Effectiveness of Materials", 199 IEEE International Syposiu on EMC, Anahei, California, USA, (199). [11] Sarto, Maria Sabrina, Di Michele, S., Leekerkap, P., Thuis, H., "An Innovative Shielding Concept for EMI Reduction", IEEE EMC Society Newsletter, Issue No. 19, (Suer 1). [1] Schwab, A., Benz, Th., Herold, J., "Messung der Schirdäpfung leitfähiger Kunststoffe - Eine neue TEM-Meßzelle", Kongreß EMV in Karlsruhe, (13-15 März 199).