The scattering and transfer matrix of screening effectiveness, modeling of the triaxial setup Thomas Hähner Nexans Draveil, France +33 6 80 12 55 04, [email protected] Abstract The method described in the literature to model the triaxial setup to measure the screening attenuation in the case of different coupling sections is based on the principle of (voltage) wave propagation and (multiple) reflections. This approach leads to cumbersome formulae. The following article describes a more versatile way based on the theory of cascaded multi-ports and the introduction of the scattering and transfer matrix for the electromagnetic coupling through the screen. In that way also the impact of impedance variations in the device under test can be investigated. Furthermore a method is described to extend the frequency range for transfer impedance and screening attenuation measurements. Note that the symbols used in the following text are described in paragraph 7. cable sheath cable under test input voltage U cable screen coupling length app. 2m 1 tube terminating resistor R1= Z1 calibrated receiver or network analyzer signal generator U1 U2 Figure 1: triaxial setup Keywords: transfer impedance; screening attenuation; screening effectiveness, scattering matrix, transfer matrix, cascaded multiports, Mason’s gain formula, triaxial set-up, IEC 62153-4 series 2. Scattering matrix S of screening attenuation 1. Introduction The coupling between two lines (the inner and the outer circuit) can be depicted as a four port coupling device (see Figure 2). Ports 1-3 represent the inner circuit (device under test) and Ports 2-4 represent the outer circuit (surrounding). The screening effectiveness of screened cables, connectors and cable assemblies is described by the (surface) transfer impedance  and screening attenuation . The relation between the transfer impedance and the screening attenuation of the screen, for a uniform device under test (DUT) is well described in the literature . At IWCS 2017 the first time a paper was presented dealing with non uniform devices like cable assemblies or connecting hardware . That paper presented formulae which allow to take into account variations of the impedance (and velocity) in the outer circuit (cable surrounding). However the given formulae are limited to 4 segments and exclude impedance variations in the inner circuit (DUT). A new, more versatile and elegant approach is based on the theory of cascaded multi-ports and the use of the scattering matrix S and transmission matrix T. It allows to evaluate the impact of variations of the impedance and velocity in the inner and outer circuit for any number of segments. Today the triaxial method (see Figure 1) is the preferred method to measure the transfer impedance  and screening attenuation . Other methods are the line injection method  for transfer impedance and the absorbing clamp  or injection clamp  method for screening attenuation. The maximum frequency up to which the transfer impedance can be measured depends on the load conditions of the test configuration and the test length . In general the frequency is limited to about 100MHz. The IEC standard 62153-4-16  describes a method to extrapolate the test results to higher frequencies for transfer impedance or to lower frequencies for screening attenuation. But the method is only applicable in the case of a matched inner circuit (device under test). However transfer impedance measurements are often made with a mismatched inner circuit. A new approach applicable to any load conditions is presented. 2.1 Coupling matrix S42 Port 2 Port 4 S21 S41 Port 1 Port 3 S31 Figure 2: 4-port coupling device For passive and reciprocal devices like cables, cable assemblies or connecting hardware the forward scattering parameters Sxy equal the reverse scattering parameters Syx . The coupling between the inner and outer circuit is loose therefore the forward and reverse scattering parameters of the inner circuit (S31=S13) and outer circuit (S42=S24) equal the (wave) attenuation of the inner respectively outer circuit: S IC S 31 S13 e 1 l (1) SOC S 42 S 24 e 2 l (2) For matched circuits the reflection coefficients are zero: S11 S 22 S 33 S 44 0 (3) In the case of matched conditions in the inner and outer circuit ,  describe the formulae for the voltages coupled from the inner to the outer circuit at the near end and the far end. But scattering parameters are ratios of (square root) of power waves. Therefore the formulae for the voltage ratios need to be extended by introducing the square root ratio of the impedances in the inner and outer circuit: CN ZT Z F 1 1 e 1 2 l 2 Z1 1 2 CF Z F ZT 1 l 1 e 1 2 e 2 l 2Z1 1 2 Z1 (4) Z2 (5) Z2 (6) C F S14 S 41 S 32 S 23 (7) The scattering matrix for the coupled four port device is then expressed by: SC CN S IC 0 CF CF 0 S OC CN Z 2 Z 2n Z 2 Z 2n rOC , f Z2 f Z2 Z2 f Z2 (12) 2.3 Transfer matrix T Z1 C N S12 S 21 S 34 S 43 0 C N S IC CF rOC , n CF S OC CN 0 (8) It is important to note that the reference impedance of this scattering matrix is not the reference impedance of the vector network analyzer, in general 50 Ohm. But the reference impedance of the inner circuit (port 1 to 3) equals the impedance of the inner circuit. The reference impedance of the outer circuit (port 2 to 4) equals the impedance of the outer circuit. Hence the Sxx of the coupling matrix equal zero (see formula (8)) The conversion from the scattering matrix S to the transfer matrix T (also known as cascade matrix or transfer scattering matrix) is well known for two ports. Recent work extended the T-Matrix of 2-ports to multi-ports . It is interesting to note that already in 1961 Wilhelm Klein described the conversion between the scattering matrix and transfer matrix for M x M multi-ports  (page 90 ff). In the following the notations described by Wilhelm Klein are used. Here the conversions for a 4-port are shown: S I , I S II1,I S II1,I (13) TI , I TI , II TII,1II TII , I TII,1II TII , I (14) S S I , I S II1,I S II , II T I , II S II1,I S II , II T T 1 S I , II II , II TII,1II Where the S-Matrix and T-Matrix are split into 4 sub-matrices: S11 S S 21 S 31 S 41 S12 S 22 S 32 S 42 S13 S 23 S 33 S 43 The coupling matrix is valid for matched circuits. To take into account impedance variations between different cascaded segments or the load conditions of the triaxial setup1 a junction matrix is introduced. T11 T T 21 T31 T41 T12 T22 T32 T42 T13 T23 T33 T43 The formulae given in  (page 61 ff) for a two port can be extended to a 4 port device and leads at the near end to: 2.4 Triaxial set-up as a cascade of near end junction, coupling and far end junction rIC, N 0 S JN 2 1 rIC, N 0 The resulting transfer matrix T of the triaxial set-up and consequently resulting scattering matrix is obtained from a simple matrix multiplication: 2.2 Junction matrix 0 1 rIC, N 2 rOC, N 0 0 rIC, N 1 rOC, N 2 0 0 1 rIC, F 2 1 rOC, N 2 0 rOC, N (9) 1 rOC, F 2 0 rOC, F (10) 0 rOC, N 0 0 rIC, F 1 rOC, F 2 0 0 Where the reflection coefficients r are obtained for a wave propagating from the near end (generator side) to the far end (receiver side): rIC , n Z Z1 n 1 Z1 Z1n rIC , f Z1 f Z1 Z1 f Z1 T14 T24 TI , I T34 TII , I T44 S I , II S II , II TI , II TII , II Ttriax TJN TC TJF And at the far end to rIC, F 0 S JF 2 1 r IC, F 0 S14 S 24 S I , I S 34 S II , I S 44 (11) (17) It is to note, that the short circuit at the near end of the outer circuit, i.e. rOC,N=1, leads to a sub-matrix SII,I of the near end junction matrix which is singular. Thus the matrix inverse does not exist and the conversion to a T-matrix is not possible (formula (13). Therefore a value close to zero, e.g. 10-9 Ohm, shall be taken for Z2,n. Figure 3 shows simulation results for the configuration indicated in Table 1: Table 1: parameters for simulation of triaxial set-up Z0=50Ω ; L=2m Z2=150Ω ; Z2,n=0Ω ; Z2,f=Z0 ; εr2=1,0 ; α2=0 In the triaxial method the outer circuit is short circuited at the near end and mismatched at the far end. (16) For the determination of the reflection factors [formulae (11)(12)] of the junction matrices [formulae (9)(10)] one has to consider that the outer circuit has a short circuit at the near end (Z2,n=0) and a mismatch at the far end (Z2,f=Z0). For the inner circuit (device under test) the load at the near is in general Z1,n=Z0 and at the far end depending on the used method Z1,f=0 or Z1,f=Z1 or Z1,f=Z0. Z1= Z0 ; Z1,n= Z0 ; Z1,f= Z0 ; εr1=2,25 ; α1=0 1 (15) RT=13,6mΩ/m ; MT=0,93nH/m ; CT=0,04pF/m 0 0 cascaded multi‐port classical formulae ‐20 ‐20 ‐30 ‐30 ‐40 ‐50 ‐60 ‐40 ‐50 ‐60 ‐70 ‐70 ‐80 ‐80 ‐90 ‐90 ‐100 ‐100 0 500 1000 1500 2000 frequency in MHz 2500 3000 0 Figure 3: cascaded multi-port vs. classical formulae The results of the resulting coupling Striax,41=Striax,14 are in perfect concordance with the results obtained from the classical formulae described in . 2.5 Cascading of different segments A non uniform device under test like a cable assembly, with connectors at the cable ends, or a cable junction, with connectors between two cable segments, may have variations of the impedance (and propagation constant) in the outer and inner circuit. In that case the resulting coupling can be obtained by cascading the different uniform segments. The impedance variations between the different segments are taken into account by the junction matrix. The resulting transfer matrix T of the cascaded segments and consequently resulting scattering matrix S is obtained from a simple matrix multiplication; see Figure 4 and formula (18). Junction Near end Segment 1 Junction S1,2 Segment 2 … Segment n‐1 Junction Sn‐1,n Segment n Junction Far end Figure 4: cascaded multiports (18) TR TJ N TC , s1 TJ , s1s2 TC , s2 ... TJ , sn1 , sn TC , sn TJF IWCS 2018 IWCS 2017 ‐10 coupling in dB coupling in dB ‐10 500 1000 1500 2000 frequency in MHz 2500 Figure 5: cascaded multiport approach vs. wave propagation and multiple reflections 3. Extrapolation of measurement results to higher frequencies for transfer impedance and lower frequencies for screening attenuation The triaxial set-up can be used to measure both the surface transfer impedance  and the screening attenuation . The transfer impedance is in general measured with a coupling length of 0,5 m resulting in an upper frequency limit of around 100 MHz whereas the screening attenuation is in general measured with a coupling length of 2 m to 3 m resulting in a upper frequency limit for the transfer impedance of around 10 MHz and a lower frequency limit for the screening attenuation of around 100 MHz (see also  clause 8 and 9). Figure 6 shows the grey zone between electrically short (measurement range for the transfer impedance) and electrically long (measurement range for the screening attenuation). In the example, the transfer impedance can be measured up to around 30 MHz using a coupling length of 50 cm and the screening attenuation can be measured starting from 150 MHz using a coupling length of 200 cm. 10000 0 Figure 5 shows simulation results for the triaxial configuration indicated in Table 2: Table 2: parameters for simulation in triaxial set-up S21 ‐ 50cm ‐10 Zt grey zone ‐20 1000 ‐30 ‐40 mOhm/m Z0=50Ω 4 segments S21 ‐ 200cm dB reference segments 3000 100 ‐50 # 1 2 3 4 Z2 150Ω 100Ω 50Ω 150Ω inner circuit L 1m 0,25m 0,5m 0,25m Z1= Z0 ; εr1=2,25 ; α1=0 ; equal for all segments outer circuit εr2=1,0 ; α2=0 ; equal for all segments screen RT=13,6mΩ/m ; MT=0,93nH/m ; CT=0,04pF/m ; equal for all segments The results of the resulting coupling SR,41=SR,14 are in perfect concordance with the results obtained from the approach presented at IWCS 2017 . I.e. the results and conclusions presented there are confirmed and valid! ‐60 ‐70 10 ‐80 ‐90 ‐100 1 0,01 0,1 1 MHz 10 100 1000 Figure 6: simulation of the scattering parameter S21 (left hand scale) and the transfer impedance (right hand scale) for a single braid screen The IEC standard  describes a method to extrapolate the test results of transfer impedance to higher frequencies and the test results of screening attenuation to lower frequencies. But the method is limited to a matched inner circuit, whereas transfer impedance measurements are often made with a mismatched inner circuit (device under test) P1 S JN31 SC41 S JF42 The first idea was to use the described approach of cascaded multi-ports to extract (de-embed) the coupling matrix (TC respectively SC) from the measured resulting S-Matrix (SM) and the corresponding resulting T-Matrix (TM): P3 S JN31 SC31 S JF11 SC43 S JF42 TC TJN 1 TM TJF 1 (19) However in the triaxial setup the scattering parameters can only be measured from two ports, i.e. port 1 and port 4 (see Figure 2). Although with the short circuit at the near end of the outer circuit (port 2) we know S21=S12=S23=S32=S24=S42=0 and S22=1, we have the problem that in the case of an inner circuit which is matched at the far end (S33=0) we do not know S34=S43. In the case of an inner circuit with a short circuit at the far end we know S31=S13=S43=S34=0 and S33=1 and the measured matrix could be written as: S11 0 0 S14 0 1 0 0 SM 0 0 1 0 S 41 0 0 S 44 (20) But the sub-matrix SII,I is singular and the matrix inverse does not exist and the conversion to a T-matrix is not possible. Simulations revealed that it is not sufficient to replace the zeros by a value close to zero. Therefore a new approach is based on the signal flow graph of the triaxial setup and Mason’s gain formula. 3.1 Signal flow graph of the triaxial setup and Mason’s gain formula The signal flow graph of the triaxial setup is illustrated in Figure 7. The middle section corresponds to the coupling between both circuits and the sections at the left and the right correspond to the load conditions of the measurement setup. For screened devices the coupling is loose (weak) between the inner circuit (DUT) and the outer circuit (environment). Therefore it is reasonable, for the sake of simplification, to neglect the feedback from the disturbed circuit to the disturbing circuit. P2 S JN31 SC21 S JN 44 SC42 S JF42 (21) P4 S JN31 SC31 S JF11 SC23 S JN 44 SC42 S JF42 The signal flow graph contains 6 loops: L1 S JN33 SC11 L4 S JN44 SC22 L2 SC33 S JF11 L5 SC44 S JF22 (22) L3 SC31 S JF11 SC13 S JN33 L6 SC42 S JF22 SC24 S JN44 Applying Mason’s formula and taking into account that in SC, the coupling matrix, S11= S22= S33= S44=0 leads to the resulting S41 of the triaxial setup: S R41 P1 P2 P3 P4 1 L3 L6 L3 L6 (23) After some further conversions and taking into account the short circuit at the near end of the outer circuit one obtains: S R41 1 r1n 2 1 r2 f 2 CF 1 r1 f e 1 2 L C N e 2 L 1 r1 f e 1 2 L 2 L 1 r1n r1 f e 2 1L r2 f e 2 2 L r1n r1 f r2 f e 1 2 (24) Figure 8 shows the comparison between the results obtained from the approach of cascaded multiports (with the conversion between S and T matrix and multiplication of the T matrices) with the results obtained using Mason’s formula. The configuration of the triaxial setup is shown in Table 3 with a mismatched inner circuit having a short circuit at the far end. Table 3: parameters for simulation of triaxial set-up Z0=50Ω ; L=2m Z1= 75Ω ; Z1,n= Z0 ; Z1,f= 0 ; εr1=2,25 ; α1=0 Z2=150Ω ; Z2,n=0Ω ; Z2,f=Z0 ; εr2=1,0 ; α2=0 RT=13,6mΩ/m ; MT=0,93nH/m ; CT=0,04pF/m 0 Mason's formula cascaded multiport ‐10 resulting S41 in dB ‐20 ‐30 ‐40 ‐50 ‐60 ‐70 ‐80 ‐90 ‐100 0 Figure 7: signal flow graph of the triaxial setup To obtain the resulting scattering parameter S41 one has to find in the signal flow graph all paths (P) from port 1 to port 4 and all loops (L). It exist 4 paths to get from port 1 to port 4: 500 1000 1500 2000 frequency in MHz 2500 3000 Figure 8: cascaded multi-port vs. Mason’s formula The results of both approaches are in perfect concordance. Thus formula (24) obtained from Mason’s gain formula can be used to convert the measured scattering parameter SR41 to the transfer impedance ZT. 3.2 Conversion between resulting (measured) scattering parameter SR41 and transfer impedance ZT 4. Measurement versus simulation results In most cases the capacitive coupling through the cable screen can be neglected. This is in particular true for screens composed of metal foils, dense single braids or double braids. In this case formula (24) can be rearranged to obtain the transfer impedance ZT: ZT Z F 0 S R41 2 Z1Z 2 1 r1n 2 1 r2 f 2 1 r1n r1 f e21L r2 f e 2 2 L r1n r1 f r2 f e 21 2 L L 1 e 1 2 L 1 e 1 2 L L e 2 L 1 r1 f e 1 2 1 r1 f e 1 2 1 2 1 2 (25) For low frequencies (L<<1) formula (25) can be rewritten as: ZT S R41 Z 2 f Z1n Z1 f In formula (25) it is necessary to know the propagation constant of the inner and outer circuit. A method to obtain them from measurement is described in IEC 62153-4-16 . (26) 2 L Z1n Z 2 f Figure 9 shows the comparison between the results of transfer impedance obtained from formula (25) and the commonly used conversion formula between the measured forward transfer scattering parameter and transfer impedance as described in IEC 62153-4-3 . The configuration of the triaxial setup is shown in Table 3 with a mismatched inner circuit having a short circuit at the far end. Table 4: parameters for simulation of triaxial set-up Figure 10 shows the results of the conversion from the measured scattering parameter SR41 to the transfer impedance for a RG59 type cable. The DUT was matched at the near end (generator side) and far end. The conversion was done using a relative dielectric permittivity of the inner circuit (DUT) of 2,3 (PE dielectric) and 1,1 of the outer circuit (PVC jacket in tube). The blue line and the green line show the transfer impedance when measured with a 2m coupling length respectively 0,5m and using the standard conversion formula as described in  and formula (26). One can see that the upper frequency limit for the validity of the transfer impedance is 10MHz for the 2m length and 40MHz for the 0,5m length. The red line shows the conversion to transfer impedance of the 2m length using formula (25). Here the upper frequency limit for the validity of the transfer impedance is 200MHz. The observed peaks at higher frequencies are due to the capacitive coupling impedance ZF which is not exactly zero (single braid with “low” coverage) and due to uncertainties in the dielectric permittivity used in the conversion formula (25). Z0=50Ω ; L=0,5m Z1= 75Ω ; Z1,n= Z0 ; Z1,f= 0 ; εr1=2,25 ; α1=0 Z2=150Ω ; Z2,n=0Ω ; Z2,f=Z0 ; εr2=1,0 ; α2=0 RT=13,6mΩ/m ; MT=0,93nH/m ; CT=0 The transfer impedance obtained from formula (25) corresponds, as expected, to the transfer impedance obtained from the screen parameter (RT, MT, and CT). But using the formula described in IEC 62153-4-3 to convert the measured forward transfer scattering parameter to transfer impedance limits the upper frequency for the transfer impedance to about 30MHz. transfer impedance in milli‐Ohm/m 100 000 ZT of screen ZT from S41 ZT from IEC62153‐4‐3 10 000 Figure 11 shows the test results of transfer impedance for a single braided coaxial cable with 50Ω impedance. The DUT is short circuited at the far end (Z1f=0). The results are shown for 3 different coupling lengths 35cm, 100cm and 200cm. The conversion from the measured scattering parameter SR41 to the transfer impedance was done according to IEC 62153-4-3 . The results show that the cut-off frequency for the transfer impedance is decreasing with increasing length from 60MHz for 35cm to 10MHz for 200cm. 1 000 100 10 1 0 0,01 0,1 1 10 frequency in MHz 100 Figure 10: Example for the conversion of measured scattering parameter SR41 to the transfer impedance of a RG59 type cable; inner circuit matched; assuming relative dielectric permittivity of 2,3 and 1,1 for the inner, respectively outer circuit 1000 Figure 9: comparison of formulae for conversion between forward transfer scattering parameter and transfer impedance The IEC standard 62153-4-16  to extend the frequency range is only applicable for a matched DUT and cannot be used for a DUT with a short circuit at the far end. The newly introduced equation (25) however can be used for any load conditions. This is shown for the above cable in Figure 12. The results for the coupling length of 100cm and 200cm have been extrapolated using equation (25). The conversion was done using a relative dielectric permittivity of the inner circuit (DUT) of 2,3 (PE dielectric) and 1,0 of the outer circuit (cable jacket was removed). The cut-off frequency has been increased from 10MHz for 200cm respectively 20MHz for 100cm to 200MHz. The observed residual peaks at higher frequencies are due to the capacitive coupling impedance ZF which is not exactly zero and due to uncertainties in the dielectric permittivity used in the conversion formula (25). Furthermore a method is described to extrapolate measurement results of transfer impedance to higher frequencies respectively screening attenuation to lower frequencies. This covers now the grey zone between electrically short and long devices and extends the method described in  to any load conditions. 6. Outlook A future project is to model the coupling attenuation of screened balanced cables as a 6 port. The coupling attenuation is the resulting coupling between first the differential mode to the common mode and second between the common mode and the surrounding. 7. Symbols The symbols used throughout the paper are presented in Table 5. Table 5: symbols Figure 11: measurement of transfer impedance of a single braided cable with 50Ω impedance; inner circuit short circuit; coupling length 35cm, 100cm, 200cm Figure 12: conversion of measured scattering parameter SR41 to the transfer impedance of a single braided cable with 50Ω impedance; equation (25); inner circuit short circuit; assuming relative dielectric permittivity of 2,3 and 1,0 for the inner, respectively outer circuit 5. Conclusions In this paper I have presented the scattering matrix S and transfer matrix T for the coupling between two lines. The introduction of the scattering matrix for the junction allows to model the different test configurations (i.e. load conditions) for the measurement of the transfer impedance and screening attenuation. By using the theory of cascaded multi-ports it is possible to evaluate the resulting screening attenuation of composed (non uniform) devices like cable assemblies where the local impedance in the inner circuit (device under test) and outer circuit (surrounding) may be varying. The results presented at IWCS 2017  are confirmed and in addition it is now possible to take into account impedance variations in the inner circuit (device under test). CN, F coupling transfer function at the near respectively far end CT capacitive coupling through the screen DUT device under test f frequency in MHz L coupling length MT magnetic coupling through the screen rIC,n, f reflection coefficient of the inner circuit at the near respectively far end rOC,n, f reflection coefficient of the outer circuit at the near respectively far end RT DC resistance of the screen S scattering parameter matrix SC scattering parameter matrix of the coupled four port SIC forward (reverse) transfer scattering parameter of inner circuit S31, S13 SJ N, JF scattering parameter matrix of the load conditions at the near respectively far end SJ, sn-1,sn scattering parameter matrix of a junction between section n and n-1 SOC forward (reverse) transfer scattering parameter of outer circuit S42, S24 SR41 resulting forward coupling scattering parameter of the triaxial setup Sxy scattering parameter of multiport T transfer parameter matrix TJ N, JF transfer parameter matrix of the load conditions at the near respectively far end TJ, sn-1,sn transfer parameter matrix of a junction between section n and n-1 Z1 impedance of the inner circuit Z1n, f load impedance at the near respectively far end of the inner circuit Z2 impedance of the outer circuit Z2n, f ZF ZT load impedance at the near respectively far end of the outer circuit capacitive coupling impedance Z F jCT Z1Z 2 transfer impedance ZT RT jM T α1 attenuation in the inner circuit α2 attenuation in the outer circuit γ1 propagation constant in the inner circuit γ2 propagation constant in the outer circuit εr1 relative dielectric permittivity of the inner circuit εr2 relative dielectric permittivity of the outer circuit circular frequency (=2f) 8. Acknowledgments This paper has been written in memory to Otto Breitenbach (†2003) the father of the triaxial setup to measure the screening attenuation of cable screens . Otto Breitenbach was the head of R&D at Kabelmetall Nuremberg (today Nexans) and had the idea to extend the triaxial method – at that time used for transfer impedance measurements up to 100MHz – to the GHz frequency range for the measurement of the screening attenuation. Thanks also to Lauri Halme, Thomas Schmid and Bernhard Mund and the members of IEC TC46 WG5 for encouraging this laborious work which is the continuation of the work presented at IWCS 2017 . 9. References  IEC TS 62153-4-1 2014: Metallic communication cable test methods - Part 4-1: Electromagnetic compatibility (EMC) Introduction to electromagnetic screening measurements  IEC 62153-4-3: Metallic communication cable test methods Part 4-3: Electromagnetic compatibility (EMC) - Surface transfer impedance - Triaxial method  IEC 62153-4-4: Metallic communication cable test methods Part 4-4: Electro Magnetic Compatibility (EMC) - Test method for measuring of the screening attenuation as up to and above 3 GHz, triaxial method  L. Halme and B. Szentkuti, The background of electromagnetic screening measurements of cylindrical screens, Technische Mitteilung PTT Nr. 3 1988  O. Breitenbach and T. Hähner, Kabelschirmung im Übergang von MHz zu GHz-Frequenzen, NTZ Bd. 46 Heft 8 1993  O. Breitenbach, T. Hähner, B. Mund, Screening of cables in the MHz to GHz frequency range, extended application of a simple measuring method, Colloquium on screening effectiveness measurements, Savoy Place London, 6 May 1998, Reference No: 1998/452  T. Hähner and T. Schmid, Modeling of the triaxial setup to measure the screening attenuation in the case of different coupling sections, IWCS proceedings 2017  IEC 62153-4-16: Metallic communication cable test methods Part 4-16: Electro Magnetic Compatibility (EMC) - Extension of the frequency range to higher frequencies for transfer impedance and to lower frequencies for screening attenuation measurements using the triaxial set-up  IEC 62153-4-6: Metallic communication cable test methods Part 4-6: Electromagnetic compatibility (EMC) - Surface transfer impedance – Line injection method  IEC 62153-4-5: Metallic communication cable test methods Part 4-5: Electromagnetic compatibility (EMC) - Coupling or screening attenuation - Absorbing clamp method  IEC 62153-4-2: Metallic communication cable test methods Part 4-2: Electromagnetic compatibility (EMC) – Screening and coupling attenuation - Injection clamp method  W. Klein, Die Theorie des Nebensprechens auf Leitungen, Springer Verlag 1961  Hans-Jürgen Michel, Zweitor-Analyse mit Leistungswellen, Teubner Studienbücher, Stuttgart, 1981  James Frei, Xiao-Ding Cai, Stephen Muller, Multiport SParameter and T-Parameter Conversion With Symmetry Extension, IEEE Transactions on Microwave Theory and Techniques, Vol. 56, No. 11, November 2008  Janusz A. Dobrowolski, Scattering Parameters in RF and Microwave Circuit Analysis and design, Artech House, 2016  W. Klein, Grundlagen der Theorie elektrischer Schaltungen, Akademie Verlag Berlin, 1961 10. Author Thomas Hähner received in 1989 his Diploma in Electrical Engineering (Dipl.Ing. (FH)) with emphasis on Telecommunications Technology from the Georg Simon Ohm University of Applied Science in Nuremberg (Germany) and in 2000 his Diploma in Business Administration (Dipl. Wirt.-Ing. (FH)) from the University of Applied Science in in Wildau (Germany). Thomas Hähner is in the cable business since 1990 where he joined Nexans in Nuremberg (Germany) as an R&D engineer of radio frequency and data transmission cables and manager of the RF test laboratory. Today he is still with Nexans and since September 2015 Technical Manager for Aerospace-DefenseMedical based in Paris area (France). He is active since more than 20 years in standardization committees. In 2010, Thomas Hähner was granted for the 1906 IEC Award in recognition of his outstanding technical contribution in developing, writing and finalizing TC 46’s IEC 62153-4 series (Metallic communication cable test methods Electromagnetic compatibility). Thomas is Chairman of IEC technical committee TC46 (Cables, wires, waveguides, R.F. connectors, R.F. and microwave passive components and accessories) and Chairman of CENELEC technical committee TC46X (Communication Cables).