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1 Publication Kontantin S. Kotov and Jorma J. Kyyrä nertion lo and network parameter in the analyi of power filter. n: Proceeding of the 008 Nordic Workhop on Power and ndutrial Electronic (NORPE 008). Epoo, Finland June page. 008 by author

2 1 nertion Lo and Network Parameter in the Analyi of Power Filter Kontantin S. Kotov and Jorma J. Kyyrä Abtract - The inertion lo (L) i regarded a the bet interference uppreion characteritic of power filter or uppreion component. The L definition are conidered and a an alternative the paper ugget the ue of network parameter. t i a known fact that the tandard L meaurement do not provide reliable information about the operational performance of a uppreor. Thi i largely due to the ource and load mimatch, which i typical in power line. Argument are preented, howing that network parameter allow for more complete and reliable characterization of power filter and component. The L would not be abandoned, becaue the network parameter provide enough information to obtain not only the tandard L, but alo the L in a non 50 Ω ytem. A new treatment of wort cae or minimum L i propoed, which i alo baed on network parameter. Furthermore, input, output, or tranfer impedance, imulation model, and other characteritic, can be obtained from the network parameter, but not from the currently publihed tandard L data. ndex Term - Electromagnetic interference, interference uppreion, power filter, cattering parameter. T. NTRODUCTON HE inertion lo (L) i ued a a meaure of the interference uppreion capability of paive power filter and component. Sometime the L i confued with voltage attenuation, which could be in part due to the different definition in the technical literature. To avoid ambiguity the following Section conider thoe definition. n Section the equation for L in term of two-port network parameter are lited. Thee include chain, impedance, and cattering parameter, which we find mot ueful. f needed, imilar L equation in term of admittance, or hybrid h- and g- parameter, can be derived eaily. There are alo different idea of wort cae L. Some think of it a the L meaurement in 0.1 Ω/100 Ω and the revere ytem. Other undertand it a the theoretical minimum L provided by the filter or component. n Section we ugget the minimum L to be the lower of the two chain parameter: c 11 and c. n theory, the L can be even Manucript received May 15, 008. K. S. Kotov i with the Electrical Engineering Department at the Helinki Univerity of Technology, P.O.Box 3000, F-0015 HUT, Finland (phone: ; fax: ; Kontantin.Kotov@tkk.fi). J. J. Kyyrä i with the Electrical Engineering Department at the Helinki Univerity of Technology, P.O.Box 3000, F-0015 HUT, Finland ( jorma.kyyra@tkk.fi). le than that, but that can happen in very rare cae, which require pecial attention and more careful analyi. Section dicue the argument in favor of publihing the filter network parameter, intead of tandard L only. There are alo the meaurement upporting thoe argument. The concluion are ummarized in Section.. NSERTON LOSS DEFNTONS A. Claical Definition The L i defined in [1] a the ratio, in db, of two power in accordance with the following equation: 0 L = 10 lg P, db (1) P where P 0 i the power delivered to the load impedance, which i the input impedance of the meaurement intrument receiver, connected to the ignal generator a in Fig. 1a and P i the power delivered to the ame impedance by the ame generator, but with a filter inerted between them, a hown in Fig. 1b. n the figure, 1 and are repectively the input and output voltage of the filter. Similarly, 1 and denote the input and output current. For the definition of L the direction of the output current i irrelevant, but it matter in the definition of network parameter. Sometime in the literature the direction of i revered, but in the more general cae of n-port network, it i more enible to uniformly define a port current a flowing into the port. n the reference meaurement, Fig. 1a, ideally 10 = 0 and 10 = 0. n the oldet ource [] known to u, the L i defined a the inertion ratio (R) in db: R = L 0 lg 0 lg = = = () t i eay to how that definition (1) and () are equivalent: P 0 Re 0 { YL } 0 L = 10 lg 10 lg 0 lg P = Re{ YL } = (3) and imilarly: P 0 Re 0 { ZL} 0 L = 10 lg 10 lg 0 lg P = Re{ ZL} = (4) Notice that the requirement in the claical definition of L i that the ource impedance Z and load impedance are ame in both meaurement - with and without the filter. Z and do not have to be reitive, equal to each other, or contant. NORPE/008, Nordic Workhop on Power and ndutrial Electronic, June 9-11, 008

3 10 0 P 0 Z 10 0 Signal Generator (a) 1 P Z 1 EM Filter Signal Generator (b) Fig. 1. nertion lo definition: a) reference meaurement (filter replaced by hort circuit), b) meaurement with the filter inerted. B. CSPR 17 Definition The international CSPR 17 tandard [3] require that the ource and load impedance are equal to the reference impedance Z 0 = 50 Ω. When Z = the load voltage 0 = / and (3) become: L = 0 lg (5) which i the L equation given in the tandard [3]. According to CSPR 17, the L i meaured both with and without load current, in three different tet circuit: aymmetrical (common-mode), hown in Fig. a; ymmetrical (differential-mode), hown in Fig. b; and unymmetrical tet circuit, which i hown in Fig. c. n the lat tet circuit all line that are not connected to the port of the meauring intrument, mut be terminated to ground reference through impedance, equal to the reference impedance Z 0, which i pecified to be 50 Ω. Probably the primary concern of CSPR 17 i the reliability and repeatability of the meaurement. Thi could be why the tandard emphaize that the ource and load impedance mut be equal to the reference impedance and define the L by (5), which i a pecial cae of the claical definition (1). ndeed, whenever Z, (5) doe not yield L. CSPR 17 alo give intruction for L meaurement in non 50 Ω ytem. Thee are not mandatory and hould be done in the frequency range from 1 khz to 300 khz with 0.1 Ω/100 Ω ource/load impedance a well a in the revere ytem. The impedance tranformation can be achieved with two wideband tranformer connected a hown in Fig. 3. The tandard ugget turn ratio of 1.4:1 to get the 100 Ω, and :1 to obtain 0.1 Ω impedance, een by the filter when both the generator and the receiver have 50 Ω impedance. Thee turn ratio are obviouly calculated from: Fig.. Matched ytem inertion lo meaurement tet circuit: a) aymmetrical (common-mode), b) ymmetrical (differential-mode), c) unymmetrical. Z n = (6) Z0 where Z i the deired Z or, een from the input or output port of the filter, and Z 0 = 50 Ω i the meaurement ytem impedance. n theory, (6) i correct, but in practice the reulting impedance are far from the target value, a it will be hown later. Then it i not clear whether engineer hould Z 0 HF Signal Generator Z 0 HF Signal Generator 1:n n L :1 Z (a) 1:n n L :1 Z EM Filter Z 0 EM Filter Z 0 (b) Fig. 3. Tet circuit for meauring inertion lo in non 50 Ω ytem: a) common-mode, b) differential-mode.

4 3 adjut the turn ratio, to get cloer to the 0.1 Ω/100 Ω target, or keep the turn ratio contant. n either cae, the mimatched L of a filter, meaured with one pair of wideband tranformer, would not match that meaured with another pair of tranformer. C. Other Definition There can be alo other definition of L in different tandard and publication, e.g. [4], but it i doubtful that they can reveal ome hidden qualitie, or improve the characterization of electromagnetic interference (EM) filter or component.. NSERTON LOSS N TERMS OF TWO-PORT NETWORK PARAMETERS By definition the concept of L i applicable to two-port network, and therefore, it can be expreed in term of twoport network parameter. A derivation of the following expreion for L in term of chain c-parameter (often called ABCD-parameter) can be een in [5]: c11zl + c + c1 + c1zl L = 0 lg (7) + ZL where c 11, c 1, c 1, and c are the c-parameter of a linear twoport network, defined a: 1 c11 c1 = 1 c1 c (8) with port voltage and current a defined in Fig. 1b. n a imilar manner, equation for the L in term of other port parameter can be derived. The R in term of z- and c- parameter have been publihed in [1], but referred to a L, which apparently confue the R and L in (). The L in term of z-parameter i: ( + z11 )( ZL + z ) z1z1 L = 0 lg (9) Z + Z z ( ) where z 11, z 1, z 1, and z are the impedance z-parameter of a linear two-port network, defined a: 1 z11 z1 1 (10) = z1 z f needed the L can be expreed in term of other network parameter by uing the converion table found in the related literature, e.g. in [6]. The eaiet and mot accurate way to meaure two port parameter nowaday i via the cattering -parameter, which are meaured with vector network analyzer (NA) and are defined a: b a1 (11) b = 1 a where 11, 1, 1, and are the cattering -parameter of a linear two-port network; the a 1 and a are incident, and b 1, b reflected power wave. The equation for L in term of - parameter ha alo been publihed [7]: L 1 L = 0 lg ( 1 )( 1 ) ( 1 ρρ ) ρ ρ ρ ρ 11 L L 1 1 L 1 (1) where ρ and ρ L are the ource and load reflection coefficient, defined a: Z0 ZL Z0 ρ = and ρl = (13) Z + Z Z +Z 0 L 0 Equation (1) can be derived by uing ignal flow graph [6], or the power gain equation [6] and [7]. Equation (7), (9), and (1) relate the L in the ene of the claical definition, to the two-port network parameter, which characterize the filter for a given conduction mode commonmode or differential mode. n the pecial cae of matched ource and load impedance, i.e. when ρ = ρ L = 0, (1) implifie to: L = 0 lg 1 (14) which i the L equation in term of -parameter, given in CSPR 17 tandard [3].. MNMUM NSERTON LOSS n [8] the L meaurement in 0.1 Ω/100 Ω and the revere ytem are called the approximate wort cae. According to [1] there are different wort cae inertion loe, which are achieved, at different ource and load mimatch cae. n the next Section, it i hown that the approximate wort cae L, meaured according to CSPR 17 guideline for non 50 Ω ytem, i a lot higher than the minimum L. The theoretical minimum L can be found via the chain parameter. Equation (7) can be rewritten in the following form: ZL c1 c11 + c + + c1zl L = 0 lg (15) ZL 1+ When Z, i.e. in the cae of an ideal current ource, it follow from (15) that the L become: c1zl Lc = 0 lg c + c1zl = 0 lg c + 0 lg 1+ (16) c From (16), the larger, the larger the L c would be, unle ( { ZL Z, } ) ( { ZL Z, } Re m < 1 (17) ) where Z, = c /c 1 i the open-circuit output impedance. Therefore, the minimum of L c i when = 0, i.e. when hort-circuiting the output, except in the rare cae when (17) i fulfilled. n mot practical cae the minimum of L c i: Lc,min = 0 lg c (18) When Z = 0, i.e. in the cae of an ideal voltage ource, from (7) it follow that: c1 c1 L 0 v lg c 11 0 lg c11 0 lg 1 Z L c11zl (19) A long a the following condition i not fulfilled: Re Z Z m Z Z ) < 1 (0) ( {,0 L} ) ( {,0 L}

5 4 where Z,0 = c 1 /c 11 i the output impedance with horted input, the minimum L v i when, and it i: Lv,min = 0 lg c11 (1) t can be concluded that in mot practical cae, the lover limit for the L curve can be contructed by plotting the maller of the c 11 and c coefficient over the frequency range of interet. However, if condition (17) and (0) are fulfilled, then even lower L i poible.. MEASUREMENTS AND DSCUSSON Publihing the full et of -parameter, i.e. both commonand differential-mode, would give cutomer the mot complete, accurate and reliable information about filter and component. The -parameter can be converted to any other et of network parameter, depending on the need. Uing (7), (9), or (1), deigner could predict the inertion lo of a filter in any line where it would be inerted, provided they have etimation of the line impedance. The full et of network parameter can alo be utilized to build circuit imulation model of uppreion component or filter another advantage of network parameter over L data. The tandard L data, which are currently publihed by manufacturer, would not be lot, becaue according to (14), 1 coefficient i the tandard L curve with an oppoite ign. A an example, the common-mode -parameter of the filter in Fig. 4 are hown in Fig. 5, where the 1 ubplot i a mirror image of Fig. 6a, which i the meaured tandard commonmode L of the ame filter. The tandard L meaurement do not provide ufficient information to determine the L at mimatched ource and load impedance. The latter can be eaily calculated, if the four network parameter for a given conduction mode are known. For example, Fig. 6b how the mimatched commonmode L of the ame filter (Fig. 4) with -parameter in Fig. 5, but with Z and a hown in Fig. 7. Equation (7), (9), and (1) are equivalent and any of them would yield the ame mimatched L (Fig. 6b), for a given et of network parameter, ource, and load impedance. A wideband tranformer WBT1.5-1SLB [9] wa ued to increae the ource impedance. With a 1:1.5 turn ratio, one would expect Z 11.5 Ω according to (6), but the reult i very far from that (Fig. 7) although WBT1.5-1SLB ha a very wide bandwidth from 40 khz to 350 MHz. WBT16-1SLB, which ha a bandwidth from 100 khz to 100 MHz [9], wa ued to lower the load impedance. Again Fig. 5. Common-mode -parameter of the filter in Fig. 4, meaured with NA. Reference impedance Z 0 = 50 Ω. there i a large dicrepancy between theoretical and meaured impedance. From (6), with turn ratio of 1:16, the load impedance een from the output of the filter hould be 0. Ω, but it i more than 3 Ω for all frequencie above 50 khz. Fig. 6c repreent the mimatched common-mode L meaured a in Fig. 3a, with the above mentioned impedance changing tranformer. t differ ignificantly from Fig. 6b, which wa calculated from the meaured tandard commonmode -parameter according to (1). Obviouly, the impedance tranformation depend on the characteritic of the tranformer. Thi make it impoible to have reliable and repeatable mimatched L meaurement, which i probably the reaon, why thee are not mandatory. n contrat, if the network parameter meaurement of a filter are reliable and repeatable, one would expect reliable and repeatable mimatched L from (7), (9), or (1). Therefore, the value of L meaurement in non 50 Ω ytem i Fig. 4. An example of a ingle-phae power filter: R = 1 MΩ, C X1 = C X = 100 nf, L CM = 1.8 mh, C Y1 = C Y = 3.3 nf. Fig. 6. Common-mode inertion lo of the filter in Fig. 4: a) Standard meaurement in 50 Ω ytem. b) Calculated from network parameter with Z and a in Fig. 7. c) Meaured in tet circuit Fig. 3a, with Z and a hown in Fig. 7. d) Minimum L, which i contructed from (1) up to 700 khz, and (18) for the remaining frequencie up to 90 MHz.

6 5 Fig. 7. The ource and load impedance een from the input and output port of the filter. quetionable. ntead, what i needed i the complete et of network parameter for common- and differential-mode. t wa mentioned earlier that the definition of L i applicable only to two port network. However, even the implet ingle-phae filter are in fact 4-port network (Fig. 4), a 3-phae filter would be a 6-port network, etc. Thi neceitate the ue of the tet circuit, hown in Fig., the realization of which require ome auxiliary network - connecting wire, balanced-unbalanced tranformer (balun) [7]. Thee auxiliary network are not part of the filter itelf and affect the meaurement reult. n other word, they add meaurement error. n thi repect network parameter obtained with NA can have an advantage over L data meaured with EM tet receiver due to the following reaon: 1) A NA ue more ophiticated calibration, which can take into account the connecting wire. ) f the -parameter of the auxiliary network are meaured, deembedding [10] can be ued to remove the error due to thee network. 3) The tandard n-port -parameter can be meaured in the unymmetrical tet circuit Fig. c and converted to mixedmode network parameter [11], which contain the commonand differential-mode -parameter. Unymmetrical tet circuit meaurement do not require auxiliary network, thu, eliminate the aociated meaurement error. To ummarize, the tandard L data alone are incomplete and it i impoible to analyze the filter or uppreing component in greater detail. They do not provide enough information to predict the L under mimatched ource and load condition. Furthermore, it i impoible to contruct the minimum L curve, to find the input, output, or tranfer impedance, or imulate the performance of a component or a filter, if only it L i known.. CONCLUSON The claical L definition wa compared with the definition, given in the CSPR 17 tandard. The equation for L in term of network parameter were given a well. Many of the advantage of network parameter were pointed out. Nowaday, any et of network parameter i uually calculated from the meaured cattering -parameter, which are accurate, reliable and repeatable. Therefore, publihing the - parameter, intead of L data, would provide the neceary information to obtain any et of network parameter that a cutomer might need. Thoe ued to the tandard L would not loe anything, becaue it i viible from the -parameter. However, thoe who need the L in mimatched condition are currently unable to get it. t wa hown that the CSPR 17 recommended procedure for mimatched L meaurement do not produce reliable and repeatable reult. With the network parameter, it i poible to obtain the L for arbitrary ource and load termination. Furthermore, the tandard L doe not give any idea of how the performance of an EM filter could deteriorate in extreme cae of mimatch, but with network parameter the minimum L can be obtained. Finally, the input, output, or tranfer impedance, imulation model, and other characteritic of the uppreor, can be obtained from the network parameter, but not from the currently publihed tandard L data. ACKNOWLEDGMENT We are grateful to Mr. Jari Heininen and Mr. Antti Jäälinoja from Schaffner Oy, Finland, for haring their experience and providing ome of the equipment ued in thi work. REFERENCES [1] L. Tihanyi, Electromagnetic Compatibility in Power Electronic, EEE Pre, 1995, pp [] W. C. Johnon, Tranmiion Line and Network, McGraw-Hill nc., 1950, pp [3] Method of meaurement of the uppreion characteritic of paive radio interference filter and uppreion component, CSPR 17 Standard, 007. [4] S. M. akil, ML-STD-0A veru Claical Meaurement of Filter nertion Lo in a 50-Ω Sytem, EEE Tran. on EMC, ol. 5, pp , November [5] K. S. Kotov, J. J. Kyyrä, and T. Suntio, Analyi and Deign of EM Filter for DC-DC Converter Uing Chain Parameter, 10th European Conference on Power Electronic and Application, EPE 003, Touloue, France, - 4 September 003, pp. 10. [6] G. Gonzalez, Microwave Tranitor Amplifier Analyi and Deign, Prentice-Hall nc., 1984, pp. 45. [7] L. Beer, and R. Gilmore, Practical RF Circuit Deign for Modern Wirele Sytem, ol. 1, Paive Circuit and Sytem, Artec Houe nc., 003, pp [8] Application Note A, CSPR 17 Meaurement, Schaffner, March 1996, pp. 1. Available: [9] Document 45, Wideband Tranformer, Coilcraft, nc. 008, pp. 5. Available: [10] M. Hiebel, Fundamental of ector Network Analyi, Rohde & Schwarz GmbH & Co. KG, 005, pp [11] D. E. Bockelman and W. R. Eientadt, Combined differential and common-mode cattering parameter: theory and imulation, EEE Tran. on Microwave Theory and Technique, vol. 43, pp , July 1995.