Estimation of the EMI Filter Circuitry from the Insertion Loss Characteristics

Transcription

1 RADIOENGINEERING, VOL. 19, NO., JUNE Estmaton of the EMI Flter Crcutry from the Inserton Loss Characterstcs Zdeněk KEJÍK 1, Jří DŘÍNOVSKÝ, Václav RŮŽEK 3 Dept. of Rado Electroncs, Brno Techncal Unversty, Purkyňova 118, Brno, Czech Republc 1 xkejk01@stud.feec.vutbr.cz, drno@feec.vutbr.cz, 3 xruzek00@stud.feec.vutbr.cz Abstract. The paper deals wth the EMI flter models for the calculaton of the nserton loss characterstcs. The nserton loss s n fact the basc EMI flter property. Unfortunately t s not easy to precsely defne and measure ths parameter n a wde frequency range due to varablty of termnatng mpedances. The uncertanty of the potental mpedance termnaton really complcates the measurements and also comparson of the performance of flters. A model wth spurous components s ntroduced n ths paper. The procedure model desgn s also added up. The spurous components make together wth the real ones form resonant crcuts. The resonance frequences make breakages n the nserton loss characterstc. Ther resonance frequences were dentfed by the analyss of equvalent crcuts of the flter for dfferent measurng systems. The calculaton of the values of spurous components, based on knowledge of resonance frequences, s mentoned at the end of the paper. Keywords Inserton loss, EMI flter, current compensated nductor, spurous component, MNVM, Modfed Nodal Voltage Method. 1. Introducton The basc property of an EMI flter s usually descrbed by the nserton loss characterstc. That characterstc s typcally frequency dependent and t refers to the attenuaton of the EMI flter. The measurement of nserton loss s complcated by several aspects. The confguraton of the nput and output termnals of an EMI flter s changed through several types of measurement setups and ths fact complcates the measurement tself. Techncal standards dstngush several types of measurement setups accordng to nterferng sgnals, whch penetrate through the power supply network. The symmetrc part of the nserton loss defnes attenuaton of the symmetrcal nterferng sgnals whch are drectly superposed on the useful sgnal. A generator of harmonc sgnal and a measurng recever wth symmetrcal output and nput, respectvely, are necessary for the symmetrcal measurements. It s also possble to use transformers for sgnal transformaton. Measurement setup wth these transformers s depcted n Fg. 1b). The asymmetrc part of the nserton loss defnes the attenuaton of the spurous sgnals whch could be produced by spurous ground capactors of the whole system. Durng the measurement of the asymmetrcal nserton loss, the nput termnals L 1 and N 1 are connected to each other same as the output termnals L and N. Ths stuaton s shown n Fg. 1a). u 1 u 1 G G 1 L1 N L Flter 1 N 1:1 1:1 L1 L Flter N N1 1 SA u SA Fg. 1. Possble nserton loss measurng systems: a) asymmetrcal; b) symmetrcal. L1 L Flter G N N SA u c) Another problem s represented by non-defned mpedance u 1 termnatons at the nput and output sdes of the 1 flter. The mpedance of the power supply network s connected to the nput termnals of the EMI flter. The current mpedance value of the power supply network depends on the type of the power network, current load and also on the operatng frequency of the test sgnal. The output of the flter s generally loaded wth mpedance whch s usually unknown and not steady n the tme doman. Dfferent termnatng mpedances could be used for the measurement of the nserton loss of the flter accordng to the harmonzed techncal standard ČSN CISPR 17 [1]. Ths standard dstngushes several methods: the frst approach wth 50 Ω mpedances at the nput and output termnals of the flter; the approxmate method for the EMI flters wth 0.1 Ω at the nput and 100 Ω at the output and vce versa. Anyway, none of the mentoned methods corresponds to the realty. It s possble to assert, based on the exstng research, that the standard method gves optmstc results compared to the realty and the approxmate method produces pessmstc results []. It s not possble to produce a lot of physcal measurement systems wth a huge number of termnatng u a) b)

2 314 Z. KEJÍK, J. DŘÍNOVSKÝ, V. RŮŽEK, ESTIMATION OF THE EMI FILTER CIRCUITRY FROM THE INSERTION LOSS... mpedances and several test setups for precse testng, due to techncal lmts. Ths s the motvaton for creaton of precse models of EMI flters. These models wll be able to compute nserton loss characterstcs for a lot of dfferent termnatng mpedances and dfferent measurement setups. The proposed model wll be usable for dentfyng the worst case performance of the flter. The worst-case represents dentfcaton of the lowest nserton loss of the flter. It s possble to prefabrcate the worst case test setup and confrm the results by measurements.. Flter Model Based on Real Crcutry The man am of creatng the model s ts usablty n dfferent test systems (asymmetrc, symmetrc, etc.). For that reason the bascs of the model are based on real crcutry of an EMI flter. Other ways for computaton of EMI flter models, for example synthess of nserton loss characterstc, are unusable n dfferent measurement systems and mpedance condtons. The basc crcutry of EMI flter s shown n Fg. a). Ths basc crcutry has to be enlarged by spurous components of the flter [3]. The enlarged EMI flter model s depcted n Fg. b). Ths model can be called the realstc model of the flter. followng equatons [4]: I L1 = Y 11 U L1 + Y 1 U N1 + Y 13 U L + Y 14 U N, (1) I N1 = Y 1 U L1 + Y U N1 + Y 3 U L + Y 4 U N, () I L = Y 31 U L1 + Y 3 U N1 + Y 33 U L + Y 34 U N, (3) I N = Y 41 U L1 + Y 4 U N1 + Y 43 U L + Y 44 U N (4) where Y XY are the components of the admttance matrx Y of the tested EMI flter; the meanng of the currents and voltages s clear from Fg. 3. The set of equatons (1) to (4) can be easly rewrtten nto the followng matrx form: I = Y U (5) where I s the vector of unknown currents; U s the vector of varable voltages and Y s the admttance matrx of the EMI flter. Fg. 3. The EMI flter as a sx-pole. Nearly all EMI flters contan a current compensated nductor, whch complcates a model based on the crcutry of the flter. It s necessary to add up the mutual coeffcent of nducton of the current compensated nductor. The Modfed Nodal Voltage Method (MNVM) could be used to solve the crcutry [5]. Frstly, the admttance matrx has to be made up from the flter crcutry but wthout the current compensated nductor. Secondly, the admttance matrx s extended by two lnes and columns whch refer to the rest of the crcut (about the current compensated nductor) accordng to the followng equatons: U ab = jωl 1 I 1 + jωmi, (6) U cd = jωmi 1 + jωl I. (7) Each of the quantte s descrbed by Fg. 3. The mutual coeffcent of nducton s put together wth both nherent coeffcents of nducton (L 1 and L ) by: M = k L 1 L (8) Fg.. Basc model of the Schurter flter and ts enlarged crcutry. It s possble to descrbe the model of an EMI flter mathematcally as a sx-pole crcut accordng to the knowledge of the admttance parameters Y. The mathematcal descrpton could be made n agreement wth Fg. 3 and the where k represents the couplng coeffcent. The values of the nherent coeffcents of nducton L 1 and L are commonly the same for most of EMI flters (L = L 1 = L ). These mathematcal operatons and formulas can be rewrtten nto matrxes whch are descrbed n detals n [4]. Also the pvot condensaton of fnal matrxes are descrbed there and the formulas for calculaton of the nserton loss n dfferent measurement setups are determned.

3 RADIOENGINEERING, VOL. 19, NO., JUNE Reduced Equvalent Crcutres for EMI flters The real model of an EMI flter wth connecton termnals for the asymmetrc system s depcted n Fg. 4a). Fg. 4b) shows the same crcutry after reducton for the asymmetrc measurng system. The capactor C x wth ts spurous components are shorted out by the nput termnaton. Ths capactor s not taken nto account n the reduced equvalent crcutry, because there s no nfluence of ths component. The parng components for the real model wth ndex 1 or are marked n the reduced model wth no ndex number because they are dentcal, for example L p1 = L p = L p, or C p1 = C p = C p, etc. The current compensated nductor s connected n both longtudnal legs wth ts spurous component, too. Hence, all of components n the longtudnal legs due to the drect connectons L 1 /L and N 1 /N are connected parallelly. It s possble to wrte the converson equatons for the equvalent components for reduced model of the asymmetrc measurng system as C lpn = C lp, (9) R lpn = R lp. (10) The nductors whch make the current compensated nductor are also connected parallelly. Generally, t s possble to consder that both nductors have same nherent coeffcent of nducton. It means that through both nductors flows the same currents n the same drecton. Ths stuaton s depcted n Fg. 6a). The voltage over the current compensated nductors s gven by the followng relaton: U ab = U cd = jωli + jωmi = jωli(1 + k). (11) The current compensated nductor s practcable to replace by the equvalent nductor accordng to next formula: L pn = L p (1 + k). (1) The transverse leg contans the capactor C y and ts own spurous components R ys and L ys whch make two seral resonant crcuts n the asymmetrcal system. These two resonant crcuts are n fact connected parallelly. So, the components n the equvalent crcut should have these values: C yn = C y, (13) L ysn = L ys, (14) R ysn = R ys. (15) Model for the symmetrcal measurng system, whch s depcted n Fg. 5a), has also smlar crcutry. Fg. 5b) shows Fg. 4. Real model of Schurter flter n asymmetrcal system a); reduced equvalent model n asymmetrcal system b). the reduced equvalent model for the symmetrcal measurng system. Ths crcutry s extended by the nput leg compared to the asymmetrcal case. Ths leg conssts of the capactor C x and spurous components R xs and L xs. There are no parng components. These spurous components have to be ncluded n the equvalent model wth no changes and ther values as well. The current compensated nductor L p wth ts spurous components (C lp and R lp ) make the longtudnal leg. Ths leg represents two parallel resonance crcuts whch are connected to each other serally n the symmetrcal system. The values of the equvalent components could be determned by the followng equatons for the symmetrc measurng system: C lpn = C pn (16) R lpn = R lp. (17) The sngle nductors whch both create the current compensated nductor are connected accordng to Fg. 5b). The currents whch flow through them have the same values but opposte drectons. The voltages over current compensated nductor could be calculated by the followng formula: U ab = U cd = jωli + jωm( I) = jωli(1 k) (18) and the current compensated nductor should be replaced by an equvalent nductor wth the value: L pn = L p (1 k). (19) The output transverse leg n the symmetrcal system s composed of the seral combnaton of the followng components: C yn = C y, (0) L ysn = L ys, (1) R ysn = R ys. ()

4 316 Z. KEJÍK, J. DŘÍNOVSKÝ, V. RŮŽEK, ESTIMATION OF THE EMI FILTER CIRCUITRY FROM THE INSERTION LOSS... The four-pole descrpton s used n the reduced equvalent models. The models are dfferent for dfferent measurng systems, therefore t s necessary to produce several dfferent models. The connecton wth real models s not lost because the components of the equvalent crcuts were calculated by precse transformaton formulas. The formula (5) s more elementary than n the sx-pole models, so PC calculatons are faster and also the requrements put on the PC performance are lower. Fg. 5. Real model of Schurter flter n symmetrcal system a), reduced equvalent model n symmetrcal system b). Fg. 6. The connecton of the current compensated nductor n asymmetrcal system a) and n the symmetrcal system b). Now, the EMI flter could be descrbed as a four-pole crcut. Ths s the beneft for the generally formulated models and measurng systems. The usual measurng systems defne flters as four-pole crcuts. Such a flter could be defned by a smple mathematcal apparatus based on the admttance parameters. The basc mathematcal relatonshps are: I 1 = Y 11 U 1 + Y 1 U, (3) 4. Fndng Spurous Components from the Inserton Loss Characterstc The beneft of the reduced equvalent crcuts was not only n the reduced relaton formula for the calculaton of the nserton loss of the flter. Reduced crcutry s now more transparent and t s now possble to see the new relatonshps between the components and the nserton loss characterstc. Fg. 7 shows the mentoned equvalent crcuts for asymmetrc and symmetrc measurng systems. It s obvous that both crcuts contan several resonant crcuts. Each resonant crcut s collected by one component of flter and some spurous components. Each resonant crcut resonates on the resonant frequency whch could be calculated by the Thompson s formula. L and C n the Thompson s formula represent the concrete components of the resonance crcut. The resonance frequences make breakages n the nserton loss characterstc. I = Y 1 U 1 + Y U. (4) These equatons could also be defned n the matrx form (5). The exact formulaton for the nserton loss could be defned as follows [6]: L[dB] = 0 log Y 1 Y 1 Y 1 (Y S +Y L ) (Y 11+Y S ) (Y L +Y ) Y 1 (Y S +Y L ) (5) where Y S s the admttance connected to the nput termnal of the EMI flter (source), Y L s the admttance connected to the output clams (load), Y 11, Y 1, Y 1 and Y are the admttance parameters of the flter. All these parameters make up the admttance by matrx Y. Fg. 7. The reduced equvalent crcuts for the asymmetrc a) and symmetrc b) measurng systems. The result of smulaton of Schurter flter as an example s depcted n Fg. 8. Smulaton was executed wth the value of spurous components, whch was chosen accordng to the expected range of these spurous components [7]. The chosen values of spurous components are gven n Tab. 1. The standard test method wth 50 Ω nput and output mpedances was used n ths case. The components of the flter were set accordng to the data sheet and the spurous components were chosen randomly n the expected range.

5 RADIOENGINEERING, VOL. 19, NO., JUNE Spurous element Chosen value C lp [F] 1.00 e 15 R lp [Ω] 1.00 e 7 L xs [H] 1.00 e 10 R xs [Ω] 5.00 e 3 L ys [H] 1.00 e 10 R ys [Ω] 1.00 e 3 Tab. 1. Chosen value of spurous components used for smulaton. resonant frequency whch s defned by the Thomson s formula wll dffer a lot. The dfference between these two frequences for asymmetrcal and symmetrcal system can be defned exactly. The followng formula defnes the resonant frequency of the L p and C lp crcut n the symmetrcal crcut f the resonance frequency s known n the asymmetrcal system: 1 + k f lps = f lpa 1 k. (6) If the resonant frequency s known n the symmetrc system, t s possble to calculate the resonant frequency for the asymmetrcal system: f lpa = f lps 1 k 1 + k. (7) Fg. 8. Smulaton of the nserton loss of the Schurter flter n asymmetrc and symmetrc measurng systems. Fg. 8 shows the nserton loss characterstcs n the asymmetrc and also symmetrc measurng system. The characterstc for the symmetrc system has three resonance frequences, but the asymmetrc one has only two. The dfferent number of the resonance crcuts s caused by the dfferent connecton of the EMI flter n the measurng setups. Identfcaton of each resonant crcut and ts resonant frequency s necessary for the potental use of the Thompson s formula. The leg wth the capactor C y s n the same poston n both systems. The resonant frequency f cy of the resonant crcut C y, L ys and R ys s same for both measurng modes (asymmetrcal and symmetrcal). By comparson of (13) and (14) for the asymmetrcal system wth (0) and (1) for symmetrcal system, the proof for that asserton s determned. The resonant frequences are not the same n case of the current compensated nductor n dfferent measurng systems. Ths nductor s composed by the L p and spurous components C lp and R lp. The nfluence of the couplng coeffcent s dfferent n these systems and the values of the equvalent nductors are not the same accordng to (1) for the asymmetrc system and (19) for the symmetrc system. The current compensated nductor s composed from two dfferent nductors whch are wnded up usually on the same torod core. One can assume that the coeffcent of nducton reaches the hgher values between 0.9 and 1 whch refers to the tght couplng. The dfference between the equvalent nductons accordng to (1) and (19) s sgnfcant. The The experence mentoned above can be used n the dentfcaton of resonant frequences of ndvdual resonant crcuts wth C y, L p and spurous components. The remanng resonance crcut based on the C x capactor wth spurous L xs and R xs components s dsplayed only n the symmetrcal system. Each resonant frequency was matched to the exact resonant crcut. After that, the Thomson s formula can be used for calculatng the C lp, L ys and L xs components. Fg. 9 compares the results of smulaton of the Schurter nserton loss characterstcs n the symmetrc measurng system. The performance n two dfferent mpedance systems s compared: 50 Ω standard method and approxmaton method when the nput mpedance was set on the 100 Ω and output mpedance was 0.1 Ω. The resonant frequences have the same values n ths case. It s obvous from ths example that the R lp, R ys and R xs components only nhbted the resonance crcuts. The resonant crcuts could be strongly nhbted, so the frequency responses are not vsble. Ths fact really complcates the usage of ths method. The bggest nfluence of the nhbted resstors s easly vsble around the resonant frequency on a concrete resonance crcut. Ths experence could be used n optmzng the values of spurous resstors, e.g. by partcle swarm optmzaton (PSO) [8]. The optmzaton tself could have only one dmenson accordng to the knowledge of resonant frequences of each crcut, where the optmzed component has the man nfluence. It s possble to defne the part of the nserton loss characterstc for that optmzaton n ths case. Ths experence s the precondton for the successful creaton of models of EMI flters. Fgs. 10 and 11 show comparson of the measurement characterstc and the optmzed characterstc of the Schurter flter n both measurng systems. A certan correspondence between the characterstcs s evdent. PSO optmzaton was used. In the measured data, breakages of the nserton loss characterstc were searched. The ponts where the breakages appeared were prvleged. Optmzaton was based on the breakages. Drect dentfcaton of the reactve spurous component was mpossble, because the measured characterstcs had dffcult shapes.

6 318 Z. KEJÍK, J. DŘÍNOVSKÝ, V. RŮŽEK, ESTIMATION OF THE EMI FILTER CIRCUITRY FROM THE INSERTION LOSS... Spurous element Optmzed value C lp [F] 1.00 e 17 R lp [Ω] 3.19 e 3 L xs [H] 8.3 e 9 R xs [Ω] 4.01 L ys [H] 1.00 e 7 R ys [Ω] 1.87 Tab.. Optmzed values of spurous components acqured by PSO. 5. Conclusons Fg. 9. Smulaton of the nserton loss of the Schurter flter n the symmetrcal measurng system for dfferent mpedance condtons. Fg. 10. Comparson of measurement characterstc and optmzed characterstc of the Schurter flter n asymmetrcal measurng system. Fg. 11. Comparson of measurement characterstc and optmzed characterstc of the Schurter flter n symmetrcal measurng system. Some of the breakages were suppressed or not contaned because of the frequency range of measurement. Optmzed values of spurous components acqured by PSO are wrtten n Tab.. The descrpton of the model creaton was mentoned n the begnnng of the paper. The models were based on real crcutry of EMI flters and also ncluded the current compensated nductor. The spurous components of EMI flter, whch degrade the nserton loss n the hgh frequency range, were also added up. The sx-pole mathematc descrpton was used for the model concretzaton and the modfed nodal voltage method was used, too. The basc equatons were extended for the current compensated nductor descrpton. Ths led to requrement of a bgger matrx. Pvot condensaton was used for matrx reducton to the 4 4 dmenson. The equvalent crcuts for the asymmetrcal and symmetrcal measurng systems were used for better orentaton n the nserton loss characterstcs. The equvalent crcuts were based on real crcutry of the tested EMI flter. The nfluence of the nput and termnaton was also taken nto account for both systems under test. Same values of the par components were consdered. The advantage of the equvalent crcuts s n the four-pole confguraton, whch corresponds to the basc measurng setups. The fnal calculaton of the nserton loss characterstcs s easer and faster. The relatonshp between the equvalent crcuts and the nserton loss characterstcs were ntroduced at the end of the artcle. Th the smlartes of both measurng systems were dscussed. The matchng between the resonant crcuts and the exact resonant frequenes were shown n addton. After ths dentfcaton, t s possble to calculate the values of the reactve spurous components accordng to the knowledge of the resonance frequency by the Thompson s formula. The confrontaton wth the measured characterstcs was shown at the end of the paper. Spurous components of EMI flter were acqured by PSO, whch was based on breakages found n measured data. The measured and the optmzed characterstcs are not completely smlar. Ths may be caused by spurous elements of the whole measurement system, especally n hgher frequency range. These components were not nvolved n the used model. The future work wll be focused on creaton of more accurate models of the whole measurement system based on physcal measurement.

7 RADIOENGINEERING, VOL. 19, NO., JUNE Acknowledgements Ths paper has been prepared as a part of the soluton of the grant no. 10/07/0688 Advanced mcrowave structures on non-conventonal substrates of the Czech Scence Foundaton, grant no. 10/09/P15 Advanced EMI flters Inserton Loss Performance Analyses n System wth Uncertan Impedance Termnaton of the Czech Scence Foundaton, grant no. GD10/08/H07 Advanced method, structures and components of electronc wreless communcaton of the Czech Scence Foundaton and wth support of the research plan MSM Advanced Electronc Communcaton Systems and Technologes (ELCOM). References [1] ČSN CISPR 17: Methods of Measurement of the Suppresson Characterstcs of Passve Rado Interference Flters and Suppresson Components. Czech Techncal Standard. Prague: Czech Normalzaton Insttute, pages. (n Czech). [] Schaffner, Swtzerland. Usng 50 Ω Attenuaton Curves to: Compare Flter Performances; Select Second Sources; Do Incomng Inspecton. (applcaton note). [Onlne] Cted Avalable at pdf/ techncal nformatons/. [3] DŘÍNOVSKÝ, J., OLIVA, L. Modelng of performance of EMI flter. In Zvůle 007. Brno (Czech Republc): FEEC BUT, 007, p (n Czech). [4] DŘÍNOVSKÝ, J., SVAČINA, J., RAIDA, Z. Smple models of EMI flters for low frequency range. Radoengneerng, 008, vol. 17, no. 3, p [5] BIOLEK, D. Solvng Electrcal Crcuts. Prague: BEN, 004. (n Czech). [6] DŘÍNOVSKÝ, J., SVAČINA, J. Estmaton of EMI flter performance for the worst-case system. Radoengneerng, 006, vol. 15, no. 4, p [7] TIHANYI, L. Electromagnetc Compatblty n Power Electroncs. The IEEE Press, 004. [8] ROBINSON, J., RAHMAT-SAMII,Y. Partcle swarm optmzaton n electromagnetcs. IEEE Transactons on Antennas and Propagaton, 004, vol. 5, no., p About Authors... Zdeněk KEJÍK was born n Valtce, Czech Republc. He receved hs M.Sc. degree n electroncs and communcaton from the Brno Unversty of Technology, Czech Republc, n 009. Hs research nterests nclude selected topcs of EMI flters, ther desgn and measurement. Currently, he has been workng towards PhD. degree at Department of Rado Electroncs, Brno Unversty of Technology. Jří DŘÍNOVSKÝ was born n Ltomyšl, Czech Republc, n He receved the M.Sc. and Ph.D. degrees n electroncs and communcaton from the Brno Unversty of Technology, Czech Republc, n 003 and 007, respectvely. Hs Ph.D. thess was awarded by Eml Škoda Award n 007. Snce 006 he has been an assstant professor n electroncs and communcaton at the Dept. of Rado Electroncs, Brno Unversty of Technology. Hs research actvtes nclude selected topcs of EMC, EMI measurements, and EMS testng. He s also nterested n specalzed problems of radofrequency and mcrowave measurements. Snce 008, he has been leadng the Radoelectronc measurements course n master degree study program and snce 009 he has been leadng the Electromagnetc compatblty course n bachelor study program at the Faculty of Electrcal Engneerng and Communcaton, Brno Unversty of Technology. He s a member of IEEE. Václav RŮŽEK was born n Tábor, Czech Republc, n He receved hs M.Sc. from the Brno Unversty of Technology, Brno, Czech Republc, n 009. Hs research nterests nclude EMC, pre-complance EMS testng and AVR mcrocontrollers.