Frequency Domain Conductive Electromagnetic Interference Modeling and Prediction with Parasitics Extraction for Inverters

Transcription

1 Frequency Domain Conducive Elecromagneic Inerference odeling and Predicion wih Parasiics Exracion for Inverers Xudong Huang Disseraion submied o he Faculy of he Virginia Polyechnic Insiue and Sae Universiy in parial fulfillmen of he requiremens for he degree of Docor of Philosophy In Elecrical Engineering Jih-Sheng Lai, Chairman J. D. van Wyk Douglas Nelson Yilu Liu Guo-Quan Lu Sepember, 4 Blacksburg, Virginia Keywords: elecromagneic inerference EI, frequency domain, common mode C, differenial mode D Copyrigh 4, Xudong Huang

2 FREQUENCY DOAIN CONDUCTIVE ELECTROAGNETIC INTERFERENCE ODELING AND PREDICTION WITH PARASITICS EXTRACTION FOR INVERTERS By Xudong Huang Jih-Sheng Lai, Chairman Elecrical Engineering ABSTRACT This disseraion is o focus on he developmen of modeling and simulaion mehodology o predic conducive elecromagneic inerference EI for high power converers. Convenionally, he EI predicion relies on he Fas Fourier Transformaion FFT mehod wih he ime-domain simulaion resul ha requires long hours of simulaion and a large amoun of daa. The proposed approach is o use he frequencydomain analysis echnique ha compues he EI specrum direcly by decomposing noise sources and heir propagaion pahs. This mehod no only largely reduces he compuaional effor, bu also provides he insighful informaion abou he criical componens of he EI generaion and disribuion. The sudy was firs applied o a dc/dc chopper circui by deriving he high frequency equivalen circui model for differenial mode D and common mode C EIs. The noise source was modeled as he rapezoidal curren and volage pulses. The noise cu-off frequency was idenified as a funcion of he rise ime and fall ime of he rapezoidal waves. The noise propagaion pah was modeled as lumped parasiic inducors and capaciors, and addiional noise cuoff frequency was idenified as he funcion of parasiic componens.. Using he noise source and pah models, he proposed mehod effecively predics he EI performance, and he resuls were verified wih he hardware experimens. Wih he well-proven EI predicion mehodology wih a dc/dc chopper, he mehod was hen exended o he

3 predicion of D and C EIs of hree-phase inverers under complex pulse widh modulaion PW paerns. The inverer noise source requires he double Fourier inegral echnique because is swiching cycle and he fundamenal cycle are in wo differen ime scales. The noise pah requires parasiic parameer exracion hrough finie elemen analysis for complex-srucured power bus bar and prined circui layou. Afer inverer noise source and pah are idenified, he effecs of differen modulaion schemes on EI specrum are evaluaed hrough he proposed frequency-domain analysis echnique and verified by hardware experimen. The resuls, again, demonsrae ha he proposed frequency-domain analysis echnique is valid and is considered a promising approach o effecively predicing he EI specrum up o ens of Hz range. iii

4 TO Y WIFE QUAN LI AND Y PARENTS SHIZHU FENG AND SHUCHUN HUANG iv

5 ACKNOWLEDGENTS Pursuing Ph. D degree is like going hrough dark jungle. I wouldn have reached he desinaion wihou he illuminaion of many oher people. I would like firs o express my sincere appreciaion o my advisor, Dr. Jih-Sheng Lai for his guidance, paience, encouragemen and coninuous suppor. He eaches me no only power elecronics knowledge, bu also he rigorous aiude owards research. I am graeful o my commiee: Dr. Daan van Wyk, Dr. Guoquan Lu, Dr. Douglas Nelson and Dr. Yilu Liu for heir valuable suggesions on my research. I would hank Elon Pepa, Huijei Yu, Chris Smih, ike Gilliom, Amy Johnson, Changrong Liu, Junhong Zhang, ike Schenck and Joel Gouker for heir valuable suggesion, commens and discussions. I would like o hank my parens, for heir endless love and suppor. I highly appreciae my wife, Quan Li, for her coninuous love and encouragemen. v

6 Table of Conens Chaper Lieraure Research and Presen Challenge..... Background and moivaion of sudy.... Lieraure review on conducive EI modeling and predicion Time domain approach..... Frequency domain approach Ouline of he disseraion... Chaper Frequency Domain EI odeling and Predicion Single phase chopper.... Differenial mode modeling and predicion Convenional mehod of D EI predicion The proposed D model D Noise pah impedance modeling and parasiics characerizaion Gae resisance effec on curren rising ime, Experimenal verificaion of D modeling D Case Sudy-Adding high frequency capacior snubber.... Common mode modeling and predicion Convenional mehod of C EI predicion for single phase chopper Proposed C noise source modeling Parasiic capaciance calculaion C experimenal verificaion C case sudy- Adding high frequency capacior snubber Summary Chaper D EI odeling and Predicion- hree phase inverer Inroducion.... The proposed modeling and predicion mehod Differenial mode noise source modeling Differenial mode pah modeling Validaion hrough simulaion and experimen odulaion scheme effec on D EI specrum... 8 vi

7 ... Noise source modeling under differen odulaion Scheme Experimen verificaion Summary... 9 Chaper 4 C Noise modeling and predicion for hree phase inverer Inroducion Inverer common mode model-based on PW swiching Common mode noise source model Duy cycle effec on common mode source specra Common mode noise source model under differen PW schemes High frequency C mode noise model for inverer-based on parasiic resonance Experimenal verificaion Summary... 7 Chaper 5 Conclusion and Fuure work Conclusion Summary of research conribuions Fuure work Reference Via... 5 vii

8 Lis of Figures Fig.. The general disribuion mechanism of C and D noise... Fig.. Presen approaches of EI modeling and predicion... 5 Fig.. Noise source and propagaion concep... 7 Fig.. Single phase Chopper Circui... 9 Fig.. Convenional D EI odel and noise source represenaion.... Fig.. Specral represenaion of noise source wih differen fall imes... Fig..4 Noise propagaion pah of convenional mehod... Fig..5 Plo of noise propagaion pah ransfer funcion... Fig.. Calculaed resul of D noise specrum based on he convenional mehod a f = ns b f =7 ns... Fig..7 Experimenal resul of D EI specrum... 4 Fig..8 Chopper Circui wih parasiic inducance... 5 Fig..9 DC link curren waveform... Fig.. High frequency equivalen circuis during swiching ransien a during boom device urn off b during op device urn off... Fig.. Proposed D noise model and noise curren source represenaion... 7 Fig.. Typical waveforms of diode reverse recovery... 9 Fig.. Noise curren pah idenificaion.... Fig..4 Propagaion pah ransfer funcion... Fig..5 Gae resisance effec during device swiching... Fig.. Swiching waveform wih differen gae resisance... 4 Fig..7 Calculaed D noise specrum a r =ns b r =7ns... 5 Fig..8 Simulaed and experimenal specrum a specrum from ime domain simulaion followed by FFT of Saber b Experimenal resul... Fig..9 Chopper circui wih he added high frequency capacior... 7 Fig.. Frequency domain circui wih high frequency capacior... 7 Fig.. High frequency capacior ampliude plo... 9 Fig.. Comparison of simulaion and experimenal resuls: a propagaion pah impedance; b calculaed frequency specrum wih differen capaciors; and c experimenal resuls... 4 Fig... Common mode circui configuraion for a par of he inverer Fig..4 Convenional Common mode model... 4 Fig..5 Envelop of he ampliude of specrum of C volage source... 4 Fig.. Plo of noise propagaion pah ransfer funcion Fig..7 Prediced resul based on convenional model Fig..8 Device volage decomposiion waveform... 4 Fig..9 C high frequency equivalen circuis during swiching ransien-curren source a during boom device urn off b during op device urn off... 4 Fig.. C noise equivalen circui in frequency domain Fig.. C high frequency equivalen circuis during swiching ransien-volage source a during op device urn off b during boom device urn off Fig.. The sep volage wih finie rising ime Fig.. The ampliude of erm e sτ Fig..4 C pah formed beween cable and he ground plane viii

9 Fig..5 Calculaed D noise specra a r =ns b r =7ns... 5 Fig.. Experimenal resul of C noise specra obained wih differen gae resisance a R g = b.r g =... 5 Fig..7 Toal noise specra obained wih differen mehods; a frequency-domain approach b experimenal resul Fig..8 Common mode circui configuraion wih he added high frequency capacior 54 Fig..9 C frequency domain equivalen circui wih high frequency capacior Fig..4 C EI specrum wih added capacior a calculaed resul b experimenal resuls... 5 Fig..4 Toal EI Specrum wih added capacior a calculaed resul b experimenal resuls Fig.. Single phase Chopper Circui... Fig.. High frequency equivalen circui and noise curren source represenaion... Fig.. Swiching curren wihin swiching cycle... Fig..4 Inverer circui wih parasiic Inducance... Fig..5 Combinaion of inverer oupu curren disribuion... 4 Fig.. Sub-circuis of inverer operaion... Fig..7 High frequency model of phase leg... Fig..8 High frequency linear circui of sub-circui... 7 Fig..9 A unified circui model for D noise calculaion... 8 Fig.. Unified High Frequency linear model of inverer phase leg... 8 Fig.. Space vecor... 7 Fig.. Duy cycles of he upper swich of each phase under cener aligned SV... 7 Fig.. Specral represenaion of noise source in each phase... 7 Fig..4 DC bus srucure a posiive bus b negaive bus Fig..5. Equivalen circui of exraced inducance marix... 7 Fig.. High frequency model of inverer of D noise predicion Fig..7 The plo of he propagaion pah ransfer funcion Fig..8 Block diagram of EI es seup Fig..9 Frequency domain calculaed resul of D EI specrum... 8 Fig.. Experimenal resul of D EI specrum... 8 Fig.. Duy cycles of he upper swich of each phase under SPW... 8 Fig.. Sum of he noise source models under SPW Fig.. Duy cycles of he upper swich of each phase under SV Fig..4 Sum of he noise source models under SV Fig..5 Duy cycles of he upper swich of each phase under clamped-bus DPW... 8 Fig.. Sum of he noise source models under DPW Fig..7 Calculaed D EI specrum under differen modulaion Schemes a SV b SPW c DPW Fig..8 Experimenal resuls of D EI specrum under differen modulaion Schemes a SV b SPW c DPW... 9 Fig. 4. Inverer moor sysem... 9 Fig. 4. Common mode volage a moor side Fig. 4. Common mode equivalen circui from moor side Fig. 4.4 Inverer Circui wih parasiic capaciance... Fig. 4.5 Simplified C model of inverer... ix

10 Fig. 4. Derived C model of inverer... Fig. 4.7 Duy cycle waveform of he hree phase inverer... Fig. 4.8 The bounds of specra of rapezoidal waveform wih differen duy... 4 Fig. 4.9 Frequency specra of rapezoidal waveform wih differen duy cycles... 5 Fig. 4. C noise source model under SPW wih differen modulaion index... Fig. 4. C noise source model under SV wih differen modulaion index... 7 Fig. 4. C noise source model under DPW wih differen modulaion index... Fig. 4. High frequency model for C EI modeling... Fig. 4.4 Equivalen circui during swiching ransiion of phase A... 4 Fig. 4.5 The volage ransfer funcion of each phase... 5 Fig. 4. Swiching funcion under differen scheme... Fig. 4.7 inverer C EI es seup... 7 Fig. 4.8 Calculaed EI specrum under SPW... 9 Fig. 4.9 Experimenal C EI resuls under SPW... Fig. 4. Calculaed EI specrum under SV... Fig. 4. Experimenal C EI resuls under SV... Fig. 4. Calculaed EI specrum under DPW... Fig. 4. Experimenal EI specrum under DPW... Fig. 4.4 EI Specrum comparison in high frequency range under SV a Calculaed resul b Experimenal resul... 4 Fig. 4.5 EI Specrum comparison in high frequency range under SPW a Calculaed resul b Experimenal resul... 5 Fig. 4. EI Specrum comparison in high frequency range under DPW a Calculaed resul b Experimenal resul... 5 Fig. 4.7 C background noise... Fig. 4.8 Parasiic ringing in he phase volage... Fig. 4.9 Phase volage waveform during swiching ransiion a urn-off b urn-on 7 x

11 Lis of Tables Table. Time consans of differen periods for a moor drive... Table. Exraced dc and Hz ac inducance and resisance... Table. easured high frequency capacior values... 9 Table. Duy cycle funcion of op swich in each space vecor secor... 7 Table. Calculaed resuls of he device parasiic inudcance... 7 Table. Calculaed resuls of he DC bus parasiic inudcance Table.4 Reduced parasiic inducance marix of DC bus... 7 Table 4. v a, v b and v c under each swiching vecor xi

12 Chaper Lieraure Research and Presen Challenge The disseraion sars wih a brief background of EI. I hen provides he moivaion of he research work and a lieraure review of he exising work in relaed areas. Finally, he objecives of he research work are oulined and a brief descripion of he accomplishmens in he subsequen chapers is presened... Background and moivaion of sudy Elecromagneic inerference EI is undesirable elecromagneic noise from a device or sysem ha inerferes wih he normal operaion of he oher devices or sysems. Generally, EI sudy is characerized ino four differen groups: conduced emissions, radiaed emissions, conduced suscepibiliy, and radiaed suscepibiliy [, ]. The firs wo groups arge he undesirable emanaions from a paricular piece of equipmen while he second wo deal wih a piece of equipmen s abiliy o rejec inerference from exernal sources of noise. In his disseraion, we are only concerned wih he conduced EI emissions, which are defined as elecromagneic energy undesirable coupled ou of an emier or ino a recepor via any of is respecive connecing wires or cables [, 4]. The purpose of sudying conduced EI is o undersand wha he causes are and how o preven or suppress hem. Ulimaely he designed objec should comply wih is elecrical environmen or mee elecromagneic compaibiliy EC crieria. Power inverers based moor drives have been radiionally used in indusrial applicaions.

13 Recenly hey were found more and more applicaions in specialy purposes such as he auomoive elecric power seering sysems, elecric calipers and inegraed sarergeneraors ha end o have more sringen EC requiremens [7-9]. Since he inverer based moor drives are known o have he endency of producing large EI, and he impac of inverer swiching o he moor drive EI is relaively unknown, i is necessary o have a sysemaic sudy o beer undersand inverer EI so ha he inverer design can comply wih he environmens ha have more and more sringen EC requiremens. In he convenional design mehodology, EC issues are addressed only afer a prooype is buil. A ha sage, he radiional EC remedies are confined o adding exra componens, meal shields, and meal planes, ec. The wors siuaion is o redesign he enire sysem because he added componens may inerfere wih he original conrol loop bandwidh. In his case, here will be a significan penaly boh on he cos and on he ime-o-marke of he producs. To avoid such band-aid soluions a he posdevelopmen, i is desirable o ake EI ino accoun a he converer design sage. Wih complexiy of circuis and conrol mehods, he EI produced in a hree-phase inverer is even much more difficul o sudy han in a dc/dc converer. uch of pas research was focusing on he EI impac o he moor, ac oupu cable and compaibiliy issue [ 7], bu no on he inverer iself, which is indeed he major source of EI in he enire moor drive sysem. Alhough EI producion mechanism has been regarded as a black magic, especially for complicaed circuis such as a hree-phase inverer, i is necessary o find ways of solving such a black magic so ha he EI prevenion can be

14 aken care of a he early design sage bu no aferward. How o model and predic EI is hus becoming he major subjec in recen power elecronics researches. The conduced EI noise in a PW inverer can be viewed as consising of wo major pars, differenial mode D noise and common mode C noise [5, ]. The general disribuion mechanism for C noise and D noise is illusraed in Fig... The D noise propagaes beween power lines including line and neural wihou going hrough ground. While he C noise propagaes boh power lines and ground, for insance, i goes hrough no only beween line and ground, bu also beween neural and ground. In order o model and predic EI generaed by a hree-phase inverer, i is necessary o analyze and model boh C noise and D noise generaion and propagaion mechanism. Line Power Source Device under Tes Neural Common Ground Fig.. The general disribuion mechanism of C and D noise

15 . Lieraure review on conducive EI modeling and predicion The purpose of EI modeling of power converer is o ge a beer undersanding of EI generaion mechanism, o predic he EI level and o avoid or o alleviae EI problem a he design sage. The goal o be aimed a is o provide insighful analysis on EI generaion and propagaion mechanism, o predic wih reasonable accuracy and o cover a wide frequency range. The basic process of EI modeling and predicion requires wo seps: exracing parasiic parameers of PCB and circui componens o build high frequency circui model and predicing EI emission wih mahemaics mehods. Parasiics exis in all kinds of elemen in power converers such as power device, capaciors, magneic componen, PCB races, wire cables, ec. Several research effors have been repored on mehods of exracing parasiic parameers [8-5]. These mehods can be classified ino wo approaches, measuremen-based mehod and mahemaicsbased mehod. The mahemaics mehod is o solve axwell field equaion based on physical srucure, maerial propery and he geomery informaion. Alhough many differen mahemaics mehods have been proposed, hey can be divided ino hree caegories: finie elemen mehods FE, finie differen mehods FD and mehod of momens o. FE and FD echniques ha solve he axwell s differenial field equaions require exensive compuaion and someimes show poor convergence. The simulaion ools using hese mehods are axwell D, axwell D, ec. o solves he axwell s inegral equaion insead so ha i can grealy reduce he compuaion cos []. There are some simulaion ools using o echnique, such as axwell QD, ec. Some lieraures claim ha axwell QD is based on parial elemen equivalen circui 4

16 PEEC mehod. This is misconcepion because PEEC model is he resul of o or axwell QD, no he echnique being used o solve axwell field equaion. For he measuremen-based mehod, he commercially off-he-shelf impedance analyzer can be used as a convenien ool for relaively large parasiics, bu for small parasiics such as nano-henry nh or sub-nh inducances, he ime domain reflecory TDR mehod was proposed []. Once he parasiic parameers are exraced, he nex sep is o mahemaically model and predic EI emission. Recenly, more and more mahemaical modeling and analysis on elecromagneic inerference EI sources and propagaion had shed a ligh on a beer undersanding of he EI producion mechanism [ ]. These researches can be divided ino wo classes, ime domain approach and frequency domain approach, as shown in Fig... The former mehod is o have ime-domain simulaion followed by fas Fourier ransform FFT analysis. While he frequency domain approach is based on noise source/propagaion pah concep, which can be furher divided ino wo caegories, empirically measuremen mehod and analyical mehod. EI modeling and predicion Time domain simulaion followed by FFT analysis Frequency domain Empirical measuremen Analyical Fig.. Presen approaches of EI modeling and predicion 5

17 .. Time Domain Approach The ime domain mehod was performed by circui simulaor such as PSPICE, Saber. I was proven o be effecive for differenial mode D EI, which dominaes he lowfrequency region including he pulse-widh-modulaion PW frequency and he resonan frequencies caused by he parasiic elemens coupling wih device swiching dynamics in he EI exciaion [45]. However, his mehod is ime consuming and requires a large amoun of daa sorage because he simulaion sep needs o be very fine, ypically in nano seconds. Table. shows he ime consan of differen periods. I is edious for circui simulaion o finish several fundamenal cycles wih simulaion sep of nano seconds because he fundamenal cycle is several orders of magniude larger han he swiching ransiion. Table. Time consans of differen periods for a moor drive On/off Transiion Swiching period Fundamenal period ns us ms For dc/dc converers, he simulaion using he classical approach is possible because he simulaion ime is in he order of swiching period, which is relaively manageable. For moor drive inverers, i is very difficul o reach he seady-sae operaing condiion. The nonlinear characerisic of he semiconducor and many sray parameers make he model very complicaed and someimes lead o convergence problems in simulaion. To include all he parasiic componens for common mode C EI sudy, he imedomain simulaion can be even more roublesome, and he FFT resuls are difficul o

18 mach he experimenal resuls [45-47]. Furhermore, he ime domain mehod canno provide he deep sigh ino converer EI behavior and i lacks he appreciaion of he EI mechanism, such as how he noise is excied and how i is propagaed... Frequency Domain Approach The frequency domain mehod is based on noise source/propagaion pah concep. In conduced EI measuremen, a sandard nework, known as Line Impedance Sabilizaion Nework LISN, is used o provide sandard load impedance o he noise source. The volage across his load is measured as conduced noise emission of he device under es. Seen from he LISN, he whole sysem could be simplified as equivalen noise source, noise pah and noise receiver. Here he LISN serves as he noise receiver. This basic concep is shown in Fig... Noise source Noise propagaion pah Receiver Fig.. Noise source and propagaion concep Noise source is ime varian. Noise pah is also ime-varian and non-linear due o he swiching operaion. The noise measured a LISN is deermined by he exciaion of he 7

19 noise source and he response of he noise ransmission nework. If in frequency domain, he noise source is expressed by is ransfer funcion as Ns, and he noise ransmission nework is expressed by is ransfer funcion as Zs, hen he noise measured a LISN, Fs, can be expressed in frequency domain as he funcion of Ns and Zs. If he source is volage source, hen N s F s = - Z s If he source is curren source hen F s = N s Z s - If he magniude of each iem in he above formula is represened in db, hen we have following equaion: log F s = log N s log Z s - or log F s = log N s log Z s -4 Hence, he problem of EI predicion becomes he problem of EI noise source deerminaion and EI noise propagaion pah deerminaion. There are also wo mehods o deermine he noise source and noise propagaion pah. One is hrough empirical measuremen and he oher is hrough analyical mehod. The empirical mehods eiher measure he noise source hrough probe and noise pah hrough nework analyze direcly, or calculae he Thévnin equivalen circui for he noise source and noise pah based on measuremen resuls [55-57]. This mehod is good for 8

20 EI characerizaion, bu no appropriae for EI predicion. Firs, because he measuremen can only be done afer he circui prooype is buil, i lacks of he essence of predicion which can be done wihou prooype. Second, his mehod belongs o black box in naure because he noise source and noise propagaion pah deermined in his mehod have no physical meaning. Neiher he relaionship beween parasiics of componens and noise propagaion pah is indicaed nor is he relaionship beween swiching paern and noise source esablished. This mehod canno indicae he relaionship beween he performance and he componens in he converer. Furhermore his way canno give he converer designer a concree concep on how o change some key componens parameer o comply wih he EC sandards. In addiion, from measuremen poin of view, hese mehods are only suiable for circui wih a noise source ha is convenienly measured, no for muliple noise source circui like a hreephase inverer. This is due o he fac ha i is exremely difficul o measure several noise sources simulaneously and here are also ineracion beween hese sources. In shor, hese mehods provide lile insigh how EI generae and propagae. I is also crucial ha he noise source and noise propagaion pah have a predefined physical meaning, hence hey can be modified according o EI requiremen a design sage. The analyical mehod which was derived from circui operaion analysis fis he above crieria and is of ineres in he EI predicion of power elecronics circui.. The analyical frequency-domain mehod was proposed in [5, 54] based on he descripion of he sysem opology using ransfer funcion and a direc frequency represenaion of he noise sources. The frequency-domain analysis using ransfer 9

21 funcions of noise pah and direc frequency idenificaion of he noise sources can be used o avoid compuaional convergence problem in ime domain simulaion. The presen saus of analyical frequency domain EI modeling and predicion can be divided ino hree caegories from converer opology perspecive: boos derived power facor correcion PFC converer, buck chopper converer, and hree-phase inverer. In boos derived PFC converer, Crebier proposed in [, ] a volage perurbaion source as EI source for boh common mode noise and differenial mode noise. However, he model derived is suiable for curren-fed converers as boos converers and is associaed PFC circui while no for volage-fed converer. For our purpose, his scope of he research will concenrae on volage source converer such as buck or chopper circui and hree-phase inverer. For modeling of buck converer, Nave proposed a curren source o be used as he differenial mode noise source and he volage source for common mode noise source [5 54]. This mehod is appropriae for PW swiching frequency harmonics analysis, bu far from accuracy a he high frequency range due o simplificaion of he model. No parasiics effec was considered in his paper and he ineracion beween C and D noises was negleced. Roude considered he effec of parasiic componen in [9] and showed he ineracion beween C and D noises. This model is no so accurae because only a curren source is regarded as D noise source; he parasiic capaciance of he device is no considered in D noise model. The oher disadvanage is ha i lacks

22 of a complee model o replace he nonlinear device so ha he model is hardly adoped in muliple device converer circui such as hree phase inverers. Few lieraures can be found aiming a dealing wih he EI modeling of hree phase inverer. Chen proposed a simple model o idenify major EI source. In [5], he D noise source is he dc link curren and he D noise pah is he dc link capacior. There are several reasons ha preven his mehod providing reasonable resuls beyond a few Hz. Neiher C noise source model nor D noise source model is analyically derived based on modulaion scheme, herefore he source model is no accurae enough. In addiion, he noise pah mode is far from compleed because he device parasiics and he power bus parasiics are no included. Ran published wo papers dealing wih conduced elecromagneic emissions in inducion moor drive sysem. Apar from he ime domain analysis in one paper, he oher paper [] mainly focused on frequency domain model. In his paper, he modulaion operaion of inverer was given consideraion. However, he C source only considered he C curren going hrough he moor side, no ha going hrough he inverer side ha are parasiic capaciance beween he device and he hea sink. The D noise source is modeled as a volage source, which is confliced wih he D noise generaion mechanism, where he D noise is supposed o be curren-driven. oreover, he noise pah model is far from compleed because he device parasiics and he power bus parasiics are no included. Finally, he ineracion beween he C and D noise sources was oally negleced as well.

23 In shor, he saus of EI modeling is summarized in he following:. Presen mehods provide lile insigh ino he EI generaion and propagaion in he medium and high frequency ranges.. For hree phase inverer circui, he complexiy of PW paern has no been aken ino accoun during EI modeling. Neiher analyical C source model nor analyical D source model has been presened wih regard o swiching paerns. The lack of knowledge in PW impac o EI producing mechanism could resul in eiher over-design or under-design for he EI filer.. The relaionship beween parasiic value in noise propagaion pah and he peaks in EI specrum needs o be esablished. The dominan parasiics in circui componens need o be idenified. From he above review, i can be seen ha he firs essenial par of EI predicion is o ge a high frequency equivalen circui ha can agree wih he EI propagaion mechanism. The nex sage is o ge more accurae represenaion of noise source and noise propagaion pah in frequency domain.. Ouline of he Disseraion The main emphasis of his disseraion is on he developmen of he mehodology for modeling and predicing conducive EI for a hree-phase inverer in frequency domain. Since each phase in a hree-phase inverer operaes eiher as a buck converer or as a chopper, i is necessary o sar from he single chopper circui analysis o ensure he validiy of he mehodology.

24 In chaper D EI mechanism for a single phase chopper is sudied firs. The limi of he convenional frequency domain model is presened. The convenional model fails o predic D EI up o high frequency range due o he absence of parasiic componens. A new high frequency equivalen model including dc bus parasiic and device lead inducance and oupu capaciance is proposed. The parasiics inducance is obained hrough axwell QD sofware. To verify he proposed D model, ime domain simulaion and experimen were performed. Adding high frequency across dc bus will change he D noise propagaion pah significanly. The proposed frequency domain mehod successfully predics is impac and he resul maches wih he hardware experimen. Afer finishing he sudy on D EI, C EI mechanism for single phase chopper is invesigaed. The convenional model only considers he rapezoidal waveform as he C noise source and neglecs he volage ringing as addiional imporan noise source in he high frequency range. This causes he inaccuracy of he predicion in high frequencies. The proposed C high frequency equivalen model includes his volage ringing as he resul of eiher a curren source exciaion or volage source exciaion. The closed-forms of his noise source expression in frequency domain are presened. The experimenal C EI specrum agrees well wih he prediced resul. Second, a frequency domain approach o predicion of D conduced EI from hree-phase inverer has been presened in chaper. This approach relies on idenificaion of noise source based on inverer operaion and exracion of parasiic parameers of he inverer componens o predic he EI currens produced in an inverer circui. The analyical expression of D noise source model was derived based

25 on double Fourier echnique. ehodologies for exracion of parasiic parameers of he inverer circui are developed using finie elemen analysis. Wih accurae noise source and pah models, he proposed frequency-domain analysis mehod avoids he compuaional problems in he convenional ime-domain analysis and effecively predics he D EI performance in high frequencies for an SV based inverer. Afer he frequency domain analysis of D EI for hree phase inverer is verified, i is feasible o evaluae he effec of differen modulaion schemes on D EI specrum hrough frequency domain mehod analyically. Differen modulaion scheme leads o differen noise sources and he noise sources under differen modulaion scheme are derived analyically in close form respecively. The calculaed resuls are verified hrough experimen es. Compared wih coninuous PW scheme, he disconinuous PW scheme has a significan porion running wih zero duy, and hus he overall produced noise source is lower in frequency domain, including in high frequency regions. Chaper 4 proposes he frequency domain approach o predicion of C conduced EI from hree-phase inverer. The convenional mehod usually derives he C noise source and C noise pah from he AC load side, while his proposed approach focuses on he inverer side o idenify he C noise source and parasiic parameers of he inverer componens in order o predic he C EI currens. A simplified C circui model of C EI in swiching frequency and is harmonics range is proposed firs and he noise source models under differen modulaion schemes are analyically derived hrough double Fourier echnique. The impac of modulaion index on C EI specrum wih differen modulaion schemes also evaluaed analyically hrough frequency domain 4

26 mehods. The impac mainly occurs in he swiching frequency and is harmonics range. To predic he C EI up o ens of ega Hz range, addiional C noise source caused by volage ringing is idenified. A C high frequency equivalen circui model is derived wih exraced parasiic parameers of he inverer circui o predic he noise peak caused by he resonance of parasiic componens. Compared wih experimenal resuls, he proposed frequency-domain analysis mehod effecively predics he C EI performance no only in swiching frequency and is harmonics range bu also in high frequency range. The EI performance, however, is highly affeced by he modulaion scheme boh in he swiching frequency relaed harmonic frequencies and in he noise pah relaed resonan frequencies. In high frequency range, disconinuous PW gives lowes noise envelop due o less swiching acion. Finally, Chaper 5 summarizes he enire disseraion and proposes some ideas for fuure work. 5

27 Chaper Frequency Domain EI odeling and Predicion Single phase chopper To avoid ime-consuming compuing process, he frequency-domain simulaion approach was suggesed in [5]. The frequency-domain approach requires knowledge on noise source and propagaion pah bu significanly reduces compuaional effor, and hus is recommended as he preferred approach for EI modeling and simulaion. The basic idea is o model he swiching noise source as a rapezoidal wave, which has a known frequency-domain characerisic, and hen apply his source o he parasiic nework wih frequency-domain analysis. To make his approach effecive, however, i is necessary o model he differenial mode D and common mode C parasiic nework separaely and compue hem independenly. Single phase chopper, a parial inverer phase leg, is used in his chaper as an example o show how o apply frequency-domain approach. Since i is he basic circui for hree phase inverer, i is necessary o sudy single phase chopper firs before he invesigaion of hree phase inverer. Alhough he circui is simple, he resul can be exended o more complex circuis and phenomena ha will be discussed in he sequen chapers. D noise curren, unlike C noise curren, propagaes beween power lines wihou going ino ground. However, i has impac on C noise propagaion in high frequency range as invesigaed in he sequen chapers. Hence, he firs sep of EI modeling is o

28 derive an accurae D EI model for single phase chopper. In his chaper, we sar wih he convenional model for D EI modeling and predicion of single phase chopper. The limi of his convenional mehod, which lacks he accuracy for noise source and noise pah deerminaion, is idenified. A high frequency equivalen circui for D EI predicion and modeling is proposed, which focuses on more accurae noise source and parasiic pah idenificaion. The acive device in he circui is regarded as noise source which is replaced wih a curren source in parallel wih device oupu capaciance. The parasiic componens are idenified using parasiics exracion ool axwell QD T. The noise source and noise propagaion pah are represened in frequency domain by close form. I can be seen ha he resonan poin in he noise propagaion pah deermines he noise peak occurring in he D noise specrum. This indicaes ha he EI specrum a high frequency range is mainly deermined by he resonance of parasiic componens. C noise, which is conduced hrough parasiic capaciance beween componen and ground plane, is anoher imporan aspec of EI sudy. Under mos cases, he C noise could be more severe han D noise. oreover, C model noise and differenial noise are even relaed. The limi of he convenional mehod, which lacks he accuracy for C noise source and noise pah deerminaion, is idenified. We propose a high frequency equivalen circui for C EI predicion and modeling, which focuses on more accurae noise source and parasiic pah idenificaion. The C noise source and noise propagaion pah are represened in frequency domain by close form. I can be seen ha he resonan poin in he C noise propagaion pah deermines he noise peak occurring 7

29 in he C noise specrum. This indicaes ha he C EI specrum a high frequency range is mainly deermined by he resonance of parasiic componens. To verify he proposed frequency domain mehod, Time domain simulaions followed by FFT analysis and hardware experimens were performed. The resuls of hese mehods are successfully mached for he sudied circui. Furher verificaion are hen direced o he EI improvemen wih manipulaion of he dc bus capacior, which is a high frequency polypropylene capacior and serves as he snubber o suppress he device urn-off volage spike. This capacior changes he EI specrum envelope drasically due o he resonance beween his dc snubber capacior and he parasiic inducance of he PCB rack. The C EI and D EI wih he snubber capacior are sudied wih he proposed frequency domain mehods. The resuls indicae ha he frequency domain analysis wih accurae noise source and parasiic modeling is an effecive ool for EI predicion. Wih is simpliciy and numerical sabiliy, his mehod is hus recommended for he sudy of a much more complicaed converer sysem.. Differenial mode modeling and predicion Topologically, he hree-phase PW inverer can be configured wih a oal of eigh differen sub-circuis [75]. In order o verify he proposed approach, i is necessary o simplify he analysis, and hus only a par of he inverer phase-leg wih lower swich and 8

30 upper diode as he acive componen is considered in he following discussions. This circui can also be regarded as volage-fed single phase chopper circui... Convenional mehod of D EI predicion Iniially, he convenional mehod of D EI predicion for volage-fed circui should be reviewed. Fig.. shows he simple chopper circui ha consiss an acive device, and a freewheeling diode, and an elecrolyic capacior wih an equivalen series resisor ESR, R dc and inducor ESL, L dc. The LISN is insered beween he dc source and he elecrolyic capacior o preven he noise curren from flowing o he source and o collec he noise volage. LISN 5u DC Cap. L ou 5.5 u u 5k.k 5 R dc D C ou R ou V dc L dc u 5k.k 5 C dc S 5.5 u 5u Fig.. Single phase Chopper Circui 9

31 . Nave proposed ha he D noise source can be deermined as a curren source which is seen by dc link and he noise pah can be deermined as he parasiics of he decoupling capaciors across he dc bus. Fig.. shows he equivalen circui based on he convenional model and is noise source represenaion. I dm 5Ω R dc I τ 5Ω L dc V noise I n T C dc r f Fig.. Convenional D EI odel and noise source represenaion. The swiching noise source can be considered as a rapezoidal pulse rain. Alhough he acual waveform will have differen curren rise and fall imes r and f, o simplify analysis, i is reasonable o assume ha r = f. The frequency domain represenaion of he D noise curren can hen be expressed in -. n f n τ f sin nd sin j I T T n = Id l - nd n f T In he above expressions, d is he duy cycle, T is he inverer swiching period, I is he curren ampliude, τ is he on ime of he swich and n is he harmonic order.

32 AmpliudedBA 4 8 db/dec f = 7 ns f = ns 4dB/dec.. f Hz f f Fig.. Specral represenaion of noise source wih differen fall imes Fig.. shows he specral represenaion of a curren source wih and 7 ns fall ime, respecively. The noise source plo shows an iniial db/dec drop, and an addiional db/dec drop in he high frequency region, which is aribued o he swiching period and fall ime. A slower swiching speed means larger f, which subsequenly yields a lower cu-off frequency or less noise in high frequency range. Differen fall imes can be obained by varying he gae resisance. A larger gae resisance would resul in a lower noise source specral envelope. Fig..4 shows he noise propagaion pah of convenional mehod which is he parasiic inducance and resisance of he decoupling capacior. Neiher iner-connec parasiics nor device parasiics are included in he noise propagaion pah. Fig..5 shows derived propagaion pah ransfer funcion ploed by he ahcad. The fla par up o Hz is dominaed by parasiic resisance and beyond ha he parasiic inducance becomes dominan.

33 5Ω 5Ω R dc L dc Zs Rdc sldc Vnoise s scdc Z s = = I s Rdc sldc sc dc C dc Fig..4 noise propagaion pah of convenional mehod Pah Ampliude fhz Fig..5 Plo of noise propagaion pah ransfer funcion The D noise volage observed a LISN can be calculaed by - V noise f = I f Z f - Fig.. shows he calculaed resul of D noise specrum wih differen swiching speed. Compared o he experimenal resul shown in Fig..7, he calculaed resul maches wih he experimenal resul from low frequency range hundreds of khz up o Hz, bu fails o predic he noise peak beyond Hz.

34 9 Ampliude dbuv f =ns fhz 9 a Ampliude dbuv f =7ns fhz b Fig.. Calculaed resul of D noise specrum based on he convenional mehod a f = ns b f =7 ns

35 Ampliude dbuv Rg= Rg= fhz Fig..7 Experimenal resul of D EI specrum The discrepancy beween he calculaed resul and experimenal resul presens ha he convenional mehod is no complee for high frequency EI predicion. Inerconnec parasiics and device parasiics should be included and he cause of he dominan noise high frequency peak should be idenified... The proposed D model Since he parasiic inducance plays an imporan role on he EI performance, all he parasiic inducance values have o be known in order o predic EI performance accuraely. Fig..8 shows he single phase chopper circui wih parasiic inducance. Here, he parasiic inducance includes he PCB rack inducances L dc, L mid and L dc-, op device lead inducance L and oupu capaciance C, boom device lead inducance L b and oupu capaciance C b and ESL of elecrolyic capacior. These parasiic inducance can be obained hrough parasiics exracion ools or measuremen wih impedance analyzer. 4

36 LISN DC Cap. 5u L dc L ou 5.5 u L u 5k.k 5 R dc D C C ou R ou V dc L dc L mid u 5k.k 5 C dc S C b 5.5 u L b 5u L dc- Fig..8 Chopper Circui wih parasiic inducance The concep of frequency domain EI predicion is o ge he frequency domain represenaion of he noise source and noise pah respecively, hen muliply hem ogeher, herefore he frequency domain equivalen circui wih parasiics mus be derived firs. In convenion model, only he PW swiching curren can be seen by he decoupling capacior. In fac he decoupling capacior absorbs no only he PW swiching curren, bu also he parasiic ringing curren caused by he oscillaion beween he parasiic inducance and device oupu capaciance. Fig..9 shows he waveform of he dc link curren which is he sum of PW swiching curren and parasiic ringing curren. This explains why he convenional model can predic he D EI successfully in low frequency range bu fail in high frequency range. 5

37 I Parasiic Ringing Fig..9 DC link curren waveform A new high frequency equivalen circui of he chopper circui is necessary for D EI modeling a high frequency range. Such an equivalen circui has o be derived based on he circui operaion analysis. I can be seen from Fig..9 ha he parasiic ringings occur during swiching ransien. For he chopper circui, here are wo swiching ransien, one is boom acive swich urn-off, he oher is boom acive swich urn-on, which is equivalen o op swich urn-off. Two high frequency equivalen circuis can be derived for hese wo swiching ransiens respecively. Fig.. shows hese circuis. L dc L L dc L 5Ω R dc R on 5Ω R dc I s C L dc V noise L mid L dc V noise L mid 5Ω C dc I s C b 5Ω C dc R on L b L b a L dc- b L dc- Fig.. High frequency equivalen circuis during swiching ransien a during boom device urn off b during op device urn off

38 I is indicaed from he above circuis ha he parasiic ringing is caused by he resonaion beween loop parasiic inducance and device oupu capaciance. For insance, during boom device urn off, he oupu capaciance of he boom device resonaes wih loop parasiic inducance; while during op urn device urn-off, which is he same of boom device urn-on, he oupu capaciance of he op device resonaes wih he loop inducance. If he op device parasiic capaciance is he same as he boom device oupu capaciance, which is he case for wo devices in a phase leg of inverer, hese wo equivalen circuis can be synhesized o a unified circui. Fig.. illusraes he proposed D mode for EI predicion ha is generalized from he wo equivalen circuis shown in Fig... C oss represens he device oupu capaciance. The proposed D model should be he model in which he real dc link can be represened. In his model, he curren source represenaion is sill he same of ha in convenional model, however, he parasiic ringing curren has been aken ino accoun by adding all he inerconnec parasiics and device parasiics. No only he PW swiching curren can be seen by he decoupling capacior, bu he parasiic ringing curren as well. 5Ω R dc L dc L R on I s I τ L dc V noise L mid T 5Ω C dc I s C b L b r f L dc- Fig.. Proposed D noise model and noise curren source represenaion 7

39 From anoher perspecive, he nonlinear swich should be replaced by a volage or curren source o predic he EI specrum in frequency domain. The swich is commonly represened as a curren source for D mode modeling. Hence his proposed model can be viewed ha he acive swich is replaced wih a curren source in parallel wih device capaciance while he free-wheeling diode is shored. I is noed ha he diode reverse recovery is approximaed as parasiic ringing in his frequency domain approach during diode urn-off. This is no he same as he swiching characerisic of diode reverse recovery. However, he approximaion leads o he convenience for he modeling process wihou oo much sacrifice a resul accuracy. The ypical waveform of diode reverse recovery is shown in Fig... The firs peak of device curren is caused by he recovered charge Q rr while he res of he peaks are caused by parasiic ringing of he circui. The modeling mehod assumes he firs peak is also deermined by parasiic ringing insead of reverse recovery charge, which could resul in he sligh difference in he ampliude of he firs peak. Since his only happens abou one period of parasiic resonance and he EI resul is shown in log scale, he assumpion will no have significan effec on he prediced resul. 8

40 I D I o I S Q rr Parasiic ringing I o Fig.. Typical waveforms of diode reverse recovery.. D Noise Pah Impedance odeling and Parasiics Characerizaion The noise propagaion pah impedance ransfer funcion can be obained by solving he equivalen circui shown in Fig.. and can be expressed in -. Rdc sldc V noise s sc Z s = = dc I s s s Rdc sldc Q scdc - The frequency of resonan peak is given in The damping facor is given by -4 = L loop C oss Q R Lloop Coss = -5 9

41 The loop inducance and loop resisance are given by R Rdc Rdcplus Rdc us Rmiddle Ron = min - Lloop = Ldc Ldc Lmid L Lb Ldc L L L -7 For he muual inducances, L is beween dc and dc races, L is beween dc and middle races, and L is beween dc and middle races. I can be seen from - ha he frequency of resonan poin in he noise prorogaion pah is deermined by he loop parasiic inducance and he device oupu capaciance. The damping facor is deermined by loop inducance, loop AC resisance and device oupu capaciance. Larger AC resisance in he circui can be helpful o reduce he resonan peak. The parasiic inducance of he PCB rack is obained hrough axwell QD exracor. Fig.. shows he PCB layou for noise pah idenificaion. To ge he appropriae inducance value, i is imporan o deermine he curren source and curren sink when seing up he source condiion for axwell QD exracor. In he chopper circui, he high frequency curren disribuion deermines he EI propagaion pah, no he DC curren disribuion. Hence, he connecion poins of he oupu filer don have an effec on he EI pah. For example, if he connecing poin of he filer inducor changes from A o G or from B o H, he EI pah doesn change because he high frequency curren flows from C A B D E F. Therefore, he source seup in axwell QD exracor is ha C is source, A is sink, B is source, D is sink, E is source and F is sink. Table. liss he exraced inducance and resisance under dc and Hz ac condiions. I can be seen ha he parasiic inducance changes very

42 slighly from dc o Hz, herefore, he dc inducance can be used for he high frequency model. H middle DCminus F C D B E A G DCplus Fig.. Noise curren pah idenificaion. Table. Exraced dc and Hz ac inducance and resisance Inducance H Dc ac a Hz dc-plus ground m-race dc-plus ground m-race dc-plus.9e-8.98e-9.e-9.5e-8 4.5E-9.79E-9 ground.98e E-8.9E-9 4.5E E-8.E-9 m-race.e-9.9e-9.4e-9.79e-9.e-9.99e-9 Resisance Ω Dc ac a Hz dc-plus ground m-race dc-plus ground m-race dc-plus ground m-race The dc bus capacior was measured wih L dc = nh, R dc = mω, C dc = mf. The device oupu capaciance is C ds =.9 nf. The lead inducance of deice and diode can be obained using axwellqd as well, L b =L =4 nh. Since all he parasiic componens are known, we can calculae he loop inducance using -7, which is abou 58 nh. The derived propagaion pah ransfer funcion is ploed by he ahcad, as shown in Fig.

43 .4. I can be seen ha here is resonan poin occurring a Hz, which is deermined by he loop inducance and he parasiic oupu capaciance of he device. Pah Ampliude fhz Fig..4 Propagaion pah ransfer funcion..4 Gae resisance effec on curren rising ime, The curren rising ime and falling ime can be calculaed according o he gae drive circui and operaing condiion. An equivalen circui including parasiic inducance and he parasiic capaciance was presened in [7] o calculae he curren rising speed of volage-driven device during urn-on. Fig..5 shows he equivalen circui.

44 L a D I L R g S L d V g L s Fig..5 Gae resisance effec during device swiching The curren rising speed can be calculaed by di Vg Vgs Vg Vh gm gm -8 d on CissRgon gmls CissRgon gmls I shows ha he curren rising speed is deermined by gae-source volage, hreshold volage, device inpu capaciance, ransconducance, lead inducance and gae resisance. If all he values are fixed excep he gae resisance, he curren rising speed will be deermined by gae resisance. The smaller he gae resisance is, he faser he curren rising speed. The curren rising ime is deermined by load curren and he curren rising speed as given in -9. I di d L τ r = -9 on

45 ..5 Experimenal verificaion of D modeling To verify he proposed modeling mehod, he hardware es and ime domain simulaion are performed. The chopper specificaions are: Inpu volage: 4V Oupu volage: 4V Oupu power: W Swiching frequency: khz ajor devices and componens are OSFET: HUFA745P, Freewheeling diode: CTQ45, Inpu capacior C dc : uf, 4 oupu capacior: 47uF, and 5 oupu inducor: 4 uh. Fig.. shows he experimenal swiching waveform wih he differen gae resisance and i indicaes he urn-off ringing is abou 4 Hz ha is caused by he oscillaion beween he loop inducance and parasiic capaciance of he OSFET. The swiching speed reduces as he increase of he gae resisance, for insance, curren fall ime increase from ns wih Ω gae resisance o 7ns wih Ω gae resisance. Rg=Ω VV/div I5A/div VV/div I5A/div 4ns/div Rg= Ω 8ns/div Fig.. Swiching waveform wih differen gae resisance 4

46 The D noise specrum can hen be calculaed by muliplying - and -, and Fig..7 shows he calculaed resul of D noise specrum wih differen swiching speed. The above frequency domain EI predicion resuls can be verified wih he experimenal resul and he convenional ime domain simulaion resul. Ampliude dbuv fhz Ampliude dbuv fhz a b Fig..7 Calculaed D noise specrum a r =ns b r =7ns The D noise specrum from ime domain simulaion followed by FFT analysis and he experimenal resuls are given in Fig..8. Boh resuls well mach wih he frequency-domain predicion. They also indicae ha wih he larger gae resisance he peak of he noise specrum will be smaller. ff meg, meg,.848 ff Rg=Ω Rg= Ω...k meg meg meg meg fhz a 5

47 Rg= Rg= Fig..8 Simulaed and experimenal specrum a specrum from ime domain simulaion followed by FFT of Saber b Experimenal resul. D Case Sudy-Adding high frequency capacior snubber To furher sudy he D frequency domain modeling and predicion of he chopper circui, anoher case was considered. I is a common pracice o pu high frequency capacior across he dc bus as snubber o suppress he volage spike across he device during OSFET urn-off. In addiion, he capacior is required o pu as near he swiching device as possible as shown in Fig..9. However, he addiion of such snubber will have an effec on he D noise specrum because i changes he noise propagaion pah, which can be demonsraed by he frequency domain modeling and predicion mehod.

48 5u L dc L ou 5.5 u L u 5k.k 5 R dc R h D C C ou R ou V dc L dc L h L mid u 5k.k 5 C dc C h S C b 5.5 u L b 5u L dc- Fig..9 Chopper circui wih he added high frequency capacior The frequency domain equivalen circui of chopper is shown in Fig.. wih he addiion of he high frequency capacior. Alhough he noise source is sill a curren source wih he same expression as -, he noise pah changes significanly by adding he capacior. Therefore he noise specrum will change because of he resonance beween he dc bus parasiic inducances and added capacior. L dc L R dc R h R on 5Ω V noise I l I L mid L dc L h 5Ω C dc Loop Loop I C oss C h L b L dc- Fig.. Frequency domain circui wih high frequency capacior 7

49 as By solving he wo curren loop equaions, he relaion beween I and I can obained F s I s zz z = -9 s s I s The relaion beween V noise and I can be derived as s Q Q s Rdc sldc Vnoise s scdc Z s = = - I s Rdc sldc sc Therefore, he noise propagaion pah ransfer funcion is Vnoise s Z s = = F s Z I s s s s Rdc sldc Qz z z scdc - s s Rdc sldc Q sc dc dc where: =, L C h z =, L Q z z =, L C Rh Ch dc z h R = R R R, L dcplus Q L =, R Rh C h dc minus Ldcplus Ldc min us Ldc Lh L =, Lz = Lh L L. - indicaes ha here is a pair of resonan poles caused by he high frequency capacior and he parasiic inducance of dc-plus rack and dc-minus rack in he noise propagaion pah. The qualiy facor Q is mainly deermined by he capacior value provided ha he ESR and ESL value vary slighly. There is also a pair of high frequency zeros mainly caused by he self-resonaion of he high frequency capacior. To furher explain his, hree high frequency capaciors wih differen values are seleced and he 8

50 impedances of hese capaciors are ploed in Fig... Their capaciance value and measured ESR and ESL are shown in Table.. Table. easured high frequency capacior values Ch.7nF 4nF nf Lh 8.4nH 9.5nH 5nH Rh 7.47mΩ mω 4mΩ Ampliude db ohm C C C.. f Hz Fig.. High frequency capacior ampliude plo Fig.. compares he frequency-domain predicion and experimenal resuls. Fig..9a gives he plo of noise propagaion pah wih differen capaciors. I can be seen ha he resonan pole moves o a higher frequency as he capaciance decreases, and he resonan peaks also increase. The D noise specrum can be calculaed by muliplying - and -. Fig. 9b shows he calculaed resul of D noise specrum wih differen capacior. The resuls illusrae ha he resonan poins of he noise propagaion pah deermine he locaion of he peak of he EI specrum. Fig. 9c shows he experimenal specrum wih differen capaciors. The firs resonan peak poins well mach wih he frequency-domain predicion. 9

51 nf 8nF nf Zs Ampliude 4 Ampliude dbuv Ampliude dbuv fhz a nf 8nF nf. f Hz b wihnf wih 8nF wihnf. f Hz c Fig.. Comparison of simulaion and experimenal resuls: a propagaion pah impedance; b calculaed frequency specrum wih differen capaciors; and c experimenal resuls 4

52 . Common mode modeling and predicion C mode noise is mainly conduced hrough parasiic capaciance beween componen and ground plane. I is excied by he common mode volage, which is source volage of he op device or drain volage of he boom device in a phase leg. The single phase chopper is sill used as an example o illusrae how o apply frequency domain approach o modeling and simulae common mode noise. Fig.. shows he chopper circui configuraion wih hree parasiic capaciors C Lgnd, C Lgnd, and C mgnd, circled o represen he major C noise pah. The volage ampliude variaion on hese capaciances is larger han hose on oher capaciance such as, dc bus o ground plane capaciance. The sum of hese hree parasiic capaciances is defined as Cp, which is he dominan elemen in he noise propagaion pah. Noe ha he oupu capacior C can be regarded as shor circui a high frequency. The common mode volage is he drain volage of he boom device S 4. LISN DC Cap. 5u L dc L ou u L 5 R dc D C C ou R ou C Lgnd V dc L dc L mid C Lgnd 5 C dc S C b u L b C mgnd 5u L dc- Fig... Common mode circui configuraion for a par of he inverer. 4

53 .. Convenional mehod of C EI predicion for single phase chopper Fig.4 shows he convenional common mode proposed by Nave. In his convenional model C noise flows hrough boh posiive and negaive buses symmerically, swiching dv/d is he major source of C noise, and parasiic capaciance Cp is he major propagaion pah, boh reaed as consan. 5Ω 5Ω I cm I cm R dc L dc C dc v - C p V V bus τ T r f Fig..4 Convenional Common mode model The swiching noise source can be considered as a rapezoidal pulse rain. To simplify analysis, i is assumed ha r = f. The frequency domain represenaion of he C volage source can hen be expressed in -. n f n τ f sin n d sin j V T T n = Vdc d l - n d n f T In he above expressions, d is he duy cycle of he boom device, T is he inverer swiching period, V dc is he dc bus volage,τ is he off ime of he swich and n is he harmonic order. 4

54 V n V dc -D /τ / f Fig..5 Envelop of he ampliude of specrum of C volage source Fig..5 shows envelop of he ampliude specrum of C source volage. I can be seen ha envelop of he specra follows hree asympoes and wo corner frequency. The firs asympoe has a slope of db/decade and he second asympoe has a slope of - db/decade. The firs corner frequency is a /τ. The hird asympoe has a slope of -4 db/decade in he high frequency region and he second corner frequency is a / f., which is aribued o he swiching period and fall ime. A slower swiching speed means larger f, which subsequenly yields a lower cu-off frequency or less noise in high frequency range. The ransfer funcion of noise propagaion pah of convenional model is given in - and is plo is shown in Fig... V s Z s noise 5 = = - Vn 5 scp 4

55 Ampliude db ohm fhz Fig.. Plo of noise propagaion pah ransfer funcion uliplying - and -, he C noise volage observed a LISN can be calculaed by -4 V cmnoise f = V f Z f -4 Fig..7 shows ha he predicion resul based on he convenional mode. I can be seen ha he C specra envelop is a fla pedesal up o Hz range. This is due o ha he -db/decade slope of noise source is offse by he db/decade slope of noise pah. In addiion, he C EI specrums are almos he same up o abou Hz under differen swiching speed. 44

56 AmpliudedBuV f =ns f =7ns fhz Fig..7 Prediced resul based on convenional model.. Proposed C Noise Source odeling The limiaion of he convenional model is ha he volage source descripion is so simple ha i doesn include volage overshoo and undershoo. Boh of hem are he C noise source a high frequency and relaed o circui parasiics because i is deermined he resonance beween he loop inducance and device parasiic capaciance. Fig..8 shows decomposiion waveform of he swiching volage. The swiching volage can be divided ino wo pars, one par is he same of he convenional model ha is rapezoidal from, he oher par is parasiic ringing deermined by he resonaion beween he parasiic inducance and device oupu capaciance. 45

57 V DS r f V ds I s Fig..8 Device volage decomposiion waveform Using he decomposiion waveform, he proposed C model includes wo noise sources, one is rapezoidal volage swiching waveform, and he oher is parasiic ringing on he volage waveform. The rapezoidal waveform is he same as he convenional model. The parasiic ringing on he volage waveform is excied during swiching acion. Because boh device volage and curren changes during swiching ransien, hey all could be he exciaion source. Fig..9 shows he C high frequency equivalen circui during swiching ransien if he exciaion source is he device swiching curren. The frequency domain expression of he parasiic ringing volage across C p can be calculaed based on hese equivalen circuis. u L dc L L dc L 5 R dc R on 5Ω R dc I s C oss L dc V noise L mid L dc V noise L mid C p 5 C dc I s C oss C p 5Ω C dc R on u L b L b L dc- L dc- Fig..9 C high frequency equivalen circuis during swiching ransien-curren source a during boom device urn off b during op device urn off 4