Optimization Methods for Equivalent Source Identification and Electromagnetic Model Creation based on Near-Field Measurements

Transcription

1 Optimization Methods fo Equivalent Souce dentification and Electomagnetic Model Ceation based on Nea-Field Measuements D. Rinas, S. Niedzwiedz, J. Jia, S. Fei Dotmund Univesity of Technology Dotmund, Gemany Abstact The field emission fom pinted cicuit boads (PCB) plays an impotant ole in the electomagnetic compatibility of electonic systems. The established field measuement methods accoding to CSPR suffe fom the need to use lage anechoic chambes. Futhemoe the measuement data cannot be used fo modeling concening the calculation of the oveall fields adiated fom e.g. a ca. Othe methods which ty to identify an equivalent souce distibution by nea-field measuements do not equie lage anechoic chambes, but instead an electomagnetic invese poblem has to be solved. This often leads to an ill-posed equation system due to unavoidable eos in measuement data, long computation times, and finally inaccuate esults. n this pape an appoach to optimize the chaacteization method of pinted cicuit boads by nea-field measuements is poposed. The adiation of a PCB is modeled with a set of elementay souces, esulting in the same field like the electonic system itself. The electomagnetic fields in a plane above the PCB ae measued. Optimized time domain methods ae applied in ode to educe measuement time, to eceive phase infomation, and to coelate diffeent measuement data sets. As the cuent distibution on a PCB mainly depends on the conducto paths, the distibution of chaacteizing equivalent souces can be chosen with espect to the tace outing. Amplitude and phase coelation of the equivalent souces along each cuent path ae taken into account. The outing infomation can be extacted fom mechanical CAD-data o is based on high-esolution nea field scans. The appoaches ae integated in the equivalent souce identification pocess. The advantages of the new method ae pesented and discussed.. NTRODUCTON Electomagnetic Compatibility plays an impotant ole in the development of electonic systems. Beside the adiating cable bundles PCBs can be significant souces fo electomagnetic emissions. Standadized component field measuement methods, like the ALSE antenna method povided e.g. in CSPR 5 [1] fo evaluation of electo-magnetic emissions fom automotive systems, suffe fom the need of lage and expensive anechoic chambes. Also a single field stength value is often not sufficient to chaacteize the EM behavio of a complex system. Futhemoe it is not possible to use the measuement data fo behavioal simulation model ceation. f accuate simulation models would be used, a statement about the adiating electomagnetic fields could be made in ealy development phases. Basically the electo-magnetic emission can be distinguished in the emission of pinted cicuit boads with housing and the emission of the connecting cable bundles. Whee in lowe fequency ange adiation fom the bundles is dominant the impotance of emission fom PCBs gows with ising fequency. To be able to detemine the adiated fa fields it is necessay to tansfe the adiating PCB stuctue into an equivalent behavioal model with educed complexity. Knowing the fields in an indefinitely extended plane above an object means, all infomation is available to calculate any field vecto above this plane []. Fom theoetical point of view this would be sufficient to calculate the fa fields. But thee ae seveal poblems with such a diect appoach. E.g. accuacy of measuements is limited and accuacy of fa field calculation can be low. t is bette to solve the invese poblem and thus to identify impotant popeties of the test object by the measued field. This appoach is discussed e.g. in [3], [4], [5] o [6]. Solution methods fo the invese poblem, whee equivalent elementay adiation souces ae placed equally distibuted and e.g. exciting dipole moments can be calculated by solving a linea equation system, ae ill-posed due to the pesence of measuement data eos. The measuements must have eliable amplitude and phase infomation in ode to poduce pope esults. Because eos mainly occu in phase measuement [6] it is possible to etieve the full complex field distibution data only fom the knowledge of nea-field amplitude data. This leads to an invese poblem, which is often tied to be solved using phase etieval algoithms [7], [8]. Othe appoaches use optimization methods, in which spatial position, oientation, and magnitude of the souces is modified, until the field chaacteistics of the cicuit boad and its model agee in the efeence plane [9]. These methods involve the poblem of conveging to local minima o lead vey long computation

2 times fo each model. One eason fo the poblems is the missing coelation of the appoximating souces. Methods to intoduce physical coelations in the souces distibution can educe the numbe of fee souce paametes and computation time. Additional possibilities of eo coection ae given. As the cuent distibution on pinted cicuit boads is mainly bounded to the tace geomety the spatial distibution of the souces can be limited. Futhemoe amplitudes and phases of equivalent souces must be coelated to each othe. Techniques fo localization of cuent distibution ae pesented in [1]. Anothe appoach investigated hee is it to locate the taces by means of CADdata of the boad. This pape pesents a special method fo estimating emissions fom plana stuctues like pinted cicuit boads without vetical expansion in a fequency ange up to 5 MHz. Theefoe the electomagnetic nea-field in a plane close to the test object is measued. Fo an equivalent model geneation the appoximating souces ae distibuted only along the taces. The paametes of the appoximating souces ae detemined based on the field measuement data. Consideing the coelation between the elementay souces the invese poblem is solved with optimization algoithms. The geneated model enables diffeent types of post-pocessing, e.g. fa field estimations. The method can be combined with scan data of cable bundles, in ode to detemine the full system behavio and to ceate behavioal models fo lage system simulations. To get fast the amplitude and phase infomation fo the complete fequency ange measuements ae done in time domain, using a standad 4-channel digital oscilloscope, and subsequent FFT. The implemented data pocessing chain is pesented in the following chapte.. TME DOMAN MEASUREMENTS WTH ADDTONAL PHASE DETERMNATON FOR ACQURNG COMPLETE NEAR FELD NFORMATON The measuing system shown in figue 1 can be subdivided into 3 functional pats a pepocessing fontend including analog-to-digital-convesion to obtain data, the cental digital signal-pocessing pat including fequency domain tansfomation, and a post-pocessing algoithm fo data coection and analysis as the data pocessing backend. Fontend Pepaation ADC / Oscilloscope DSP FFT Figue 1. Time-domain measuing system Backend Coection Analysis A. Pepocessing techniques fo inceasing measuing dynamics n ode to obtain data of highe pecision it is impotant to incease fist the quality of the undelying measuement aw data. This can be achieved by combining technological and methodical measues to a pocess chain as pesented below (figue ). LP TP Oscilloscope ADC 1 ADC ADC 3 Figue. Pepocessing chain AVG & NT The fist and fundamental step in the pocess chain is the use of an analog low-noise low-pass filte, mainly to pevent alias effects. Additionally, this filte can also be used to mask uppe fequency anges that ae not of inteest o whee known measuement system distubances ae pesent. Additionally to the masking in the uppe fequency ange a masking of the lowe fequencies fom DC up to a theshold fequency can be implemented using a high-pass filte. This is done, fo example, to analyze only cetain hamonics instead of the fundamental with high amplitude. Howeve, besides this fequency band selection, a moe impotant aspect is the incease of the amplitude dynamic ange. The easiest way to lowe the minimum level of detection is the use of an optional low-noise amplifie. But as the physical esolution of an oscilloscope s analog-to-digitalconvetes is fixed, i.e. less than 8-bit, the uppe detection limit is simultaneously loweed leading to the dilemma to decide whethe the lage o smalle signal pats ae moe impotant. To ovecome this dilemma one can use moe than one oscilloscope channel hee 3 to simultaneously measue the same signal with diffeent vetical esolutions and late ecombine the diffeent channels data to one signal with a than much highe esolution. Hee the quantization chaacteistic of this multichannel-measuing that is not linea anymoe, has to be taken into account. A fouth channel on the oscilloscope can be used as efeence and tigge channel fo example to ecod the oiginal stimulus signal of a device unde test. n ode to benefit fom the inceased dynamic ange it is additionally impotant to suppess white noise and to limit influences of non-stationay pocesses by aveaging the esults of epeated single measuements. This aveaging can also be used to incease mathematically the dynamic ange when using a data epesentation fomat having moe bits than the oiginal quantization i.e. 3-bit instead of 16-bit allowing a much fine quantization of the data values. Using intepolation techniques it is theeby possible to lineaize o smooth the quantization chaacteistic of the multichannel-measuing. At the end of this pe-pocessing chain a clealy enhanced time domain data base optionally including the efeence signal is povided fo the following Fouie-tansfomation, which will not be discussed hee, and the post-pocessing. PC

3 B. Post pocessing data coection methods The esult of the Fouie-tansfomation is the complete complex nea-field spectum data, containing magnitude and phase infomation. As these data still contain the influences caused by the pepocessing chain it is necessay to apply post pocessing in ode to coect and enhance the esulting data. Fo emoving those influences it is necessay to detemine the complex tansfe function of any equipment used within the measuement chain. These ae used ight afte the domaintansfomation to coect the esulting complex fequency domain data. Theeby the coect magnitude and phase infomation of the measued nea-field data is estoed. t is necessay to detemine the tansfe function of each used measuement device fist sepaately, and then calculate the tansfe function of the whole chain aftewads o apply the single tansfe functions successively. This appoach allows a moe detailed knowledge of the chain s influences and pevents that neutalizing effects within the chain ae oveseen. Futhemoe it makes the stuctue of the chain easie adaptable to diffeent use cases. At the end the complete nea-field infomation, including the coect magnitude and phase data, is available. t has to be taken into account that the phase data efes to a mathematically implicit cosine signal. f an optional efeence signal is available, the diffeence between the two signals phase data can be used. C. Advantages of time domain measuement system fo souce identification pocess A time domain measuement system as pesented above has the advantage of obtaining the desied infomation in a consideable shote time than a fequency domain measuing system. This allows nea-field scans of lage device with a vey good spatial esolution in a vey time- and theeby costefficient way. Combined with the techniques of the multichannel measuement and the aveaging of multiple sweeps a vey high dynamic ange can be achieved. So this povides a vey efficient basis fo ceating maps of a PCB without having any CAD-data, especially when fequency selective maps fo electomagnetic field components ae of inteest.. SOURCE DENTFCATON Fo an electic cuent the magnetic vecto potential A at obsevation point = ( x, y, z) is given by jk µ e A.( ) = ( x, y, z ) 4π C dl' whee is the distance to obsevation point, C is the path along the souce and = ( x, y, z ) the souce position. With (1) the magnetic field H u can be calculated as (1) 1 H = ot A. µ To appoximate the electomagnetic emission of a given plana stuctue a set of equally distibuted electic dipoles can be used. As shown in figue 3 e.g. thee othogonal aanged dipoles each adiating a magnetic field given by k z z 1 1 = 4π k k z z 1 1 = 4π k k y y 1 1 = 4π k y y 1 k jk 1 H jk x y x x + 1 k jk 1 H jk y x x x 1 k jk 1 H jk z x () z z (3) y whee x, y and z ae the dipole moments and H x, H y and H z the magnetic field values in x, y and z diection [11]. R i U Figue 3. Simple plana stuctue (above) and appoximating model with equally distibuted souces (below) Since the model is built with M dipole sets, the magnetic field is calculated as the sum of thei contibutions. To detemine the dipole moments, a system of equations is set up to 1 =ψ H. Whee ψ contains the wave vecto k and the emaining fixed geometic paametes fo each dipole. H is the magnetic field, measued at N nea field points in a plane above the plana stuctue. To get an accuate solution of the invese poblem the measuements must have eliable amplitude and phase infomation. As the eos incease with ising fequency, mainly in phase measuement, the electomagnetic model can be ceated with amplitude data only, using the minimization functional F conducto Elementay souces = H B(H ). R L gound Simple plana stuctue gound Appoximating Model (4) (5)

4 Whee the B is a quadatic opeato, with espect to eal and imaginay pats of the magnetic field of the appoximating souces H and H ae the measued field amplitudes [7]. Function (5) can be teated with the use of optimization algoithms. As descibed befoe, this appoach often leads to long computation time and inaccuate solution [7][8]. V. METHODS FOR SOURCE DENTFCATON OPTMZATON n this chapte methods to optimize the souce identification pocess ae intoduced. Thei benefit is the decease of the numbe of fee souce paametes and the eduction of computation time. Futhemoe they allow the use of eo coection methods and incease accuacy of the esults. A. Souce distibution with compliance to the conducting paths geometies To impove the accuacy of a solution, mechanical CADdata of the pinted cicuit boad o location of the adiating conductos on the boad fom scan data can be integated in the model ceation pocess. This way the possible cuent paths ae defined. With knowledge of the cuent paths the appoximating dipoles no longe need to be equally distibuted on the plana stuctue, but the souce distibution can be pecisely adapted to the physical boad chaacteistics (figue 4). Elementay souces φ Figue 4. Dawingof the appoximating model with souces along the cuent path This leads to a consideable eduction of the numbe of elementay souces, the esulting eduction of computational cost and ise of model accuacy. B. Phase coelation of souces taking into account the conducting paths geometies Distibution dependences of the elementay souces adapted to the outing of the conducto ae used to coelate phases of the dipoles. Fo a spatial distibution d the phase shift between two adjacent dipoles is set to π ϕ = d λ gound Appoximating Model as shown in figue 4. With adheence to (6) phase jumps between two souces geate and diffeent fom φ ae pevented and the model becomes moe physically. (6) C. ntegation in souce identification pocess n a fist step, befoe calculation of fee souce paametes, the electic dipoles ae aanged along the cuent paths. With that the geometic paametes fo each dipole ae specified. n a next step optimization methods ae used to solve the invese poblem. Theefoe the weighted minimization poblem { H, H } ( ) P F = w1, w A{ H, H } (7) is consideed. Whee P{} is the phase eo and A{} the amplitude eo between H and H. w 1 and w ae the weights of phase and amplitude eos. This enables the algoithm to solve a complex o amplitude-only poblem o to decease elevance of phase in case of measuement eos. Fo each step in evaluation of the minimization function the phase of only one souce element φ k,1 of each cuent path k is vaied. With espect to (6) the othe phases φ k,m ae coelated with φ k,1. The pocess of souce identification is shown in figue 5. Souce distibution CAD-data Figue 5. Pocess of souce identification V. RESULTS n the following section esults ae pesented. Model ceation pocess was tested with diffeent configuations (figue 6) on the basis of measuements and Method of Moments (MoM) simulation data. C 1 C 1 teation step Amplitudes, phases φ k,1 Minimization function Calculation of phases φ k,m Check minimum Optimization algoithm C C 3 conf. 1 conf. conf. 3 Model Figue 6. Test configuations; conf. 1 (left), conf. (middle) and conf. 3 (ight) To show the impovement of the optimizations the weight of phase elevance w 1 in algoithm with espect to (7) is set to zeo. Thus the souce paametes ae computed with amplitudedata only. Simulated Annealing is used as optimization method fo finding the minimum of evaluation function. The

5 computation time fo each discete fequency is limited to 3 minutes. A. nceased measuement dynamic by multichannel measuement n figue 7 a compaison between a single-channel measuement and a multichannel measuement of 1 MHz ectangula pulse signal is shown. Clealy ecognizable is the inceased dynamic ange in the multichannel measuement, thus poviding a much bette data base fo souce identification o the ceation of fequency dependent field distibutions of electonic devices. Magnitude [dbµv] Magnitude [dbµv] Fequency [Hz] Fequency [Hz] Figue 7. Compaison of single-channel measuement (above) and multichannel measuement (below) B. Souce identification esults 1) Configuation 1 Simulation based esults To show benefit of souce location identification a simple plana stuctue (conf. 1), shown in figue 6 is analyzed. t consists of a.8 x.1 m plane and a conducto C 1 with length of.45 m. The souce voltage is 1 Volt, with an intenal esistance of 5 Ohm; temination is a 5 Ohm esisto. The magnetic field data is collected fom MoM simulation in a height of. m ove gound at 56 nea field points. n table nea field calculations of the electomagnetic model with equally distibuted souces without phase coelation and the optimized model ae shown and compaed with a full field simulation (MoM). The fequency is set to MHz. Figue 8 pesents the magnetic fields of both models at a distance of 3 m in compaison with the full field simulation in a fequency ange fom 1 MHz to 1 MHz. As shown, the field appoximation is much bette when the distibution of souces is matched with the conducto path and the coelation of phases is consideed. TABLE. Full field simulation Appoximating models Magnetic Field [dbua/m] MAGNETC NEAR FELDS OF BOTH MODELS N COMPARSON WTH FULL FELD SMULATON AT MHZ Equally distibuted souces Full Field Simulation Equally Distibuted Souces Souces along cuent path and phase coelation Souces along cuent path with phase coelation Fequency [MHz] Figue 8. Magnetic field at distance of = 3 m fo both models in compaison with full field simulation ) Configuation Simulation based esults The second example (conf., figue 6) consists of a.16 x.1 m plane and two conductos. Conducto C 1 has a length of.45 m and C has a length of.1 m. The souce voltage is 1 Volt, with an intenal esistance of 5 Ohm; temination of C 1 is a 5 Ohm esistance and a 1 µh inductance; temination of C is a 1 Ohm esistance. The magnetic field is collected fom MoM simulation in a height of. m ove gound at 56 nea field points. n table nea field calculations of the optimized model ae shown and compaed to a full wave simulation. The fequency is set to MHz. Figue 9 pesents the magnetic field of the model at a distance of 3 m in compaison with the full field simulation in a fequency ange fom 1 MHz to 1 MHz. TABLE. MAGNETC NEAR FELD OF MODEL N COMPARSON TO FULL FELD SMULATON AT MHZ Full Field Simulation Souces along cuent path and phases coelation

6 Magnetic Field [dbua/m] Full Field Simulationen Souces along cuent paths and phase coelation Fequency [MHz] Figue 9. Magnetic field at distance of = 3 m of the model in compaison with full field simulation 3) Configuation 3 Measuement based esults The analyses of the thid plana stuctue (conf. 3, figue 6) is based on measuement data taken fom the time domain measuing system pesented in the pevious chaptes. The configuation consists of a.16 x.1 m gound plane and a conducto C 3 with total length of.19 m. The intenal esistance of the souce is 5 Ohm; temination is 5 Ohm. The input is a pulsed signal, with a fundamental fequency of 4 MHz, ise and fall time of 1 ns, pulse/pause atio of 1, and amplitude of 5 Volts (figue 1). The magnetic nea field is measued in a plane.1 m ove gound at 187 points. Figue 11 shows the envelope of the magnetic field of the appoximating model in compaison with the full field simulation of plana stuctue. The field is calculated at a distance of 3 m in a fequency ange fom 1 MHz to MHz. Voltage [dbv] Magnetic Field [dbua/m] Fequency [MHz] Figue 1. Pulsed input signal in fequency domain Full Field Simulation Souces along cuent path and phase coelation Fequency [MHz] Figue 11. Magnetic field at distance of = 3 m of the model in compaison with full field simulation The esults agee in a fequency ange between 8 MHz and MHz with a maximum eo of 3 db. The diffeence in lowe fequencies might be due to measuement eos. Anothe eason could be the poblem of finding a unique solution with the optimization algoithm, when the height of the scanning aea deceases consideably in compaison to the wavelength. V. CONCLUSON n this pape methods to optimize the pocess of equivalent souces identification ae intoduced. The souces distibution is chosen with espect to the outing on the cicuit boad. Coelations between phase data of souces along each conducto ae consideed and integated in the computation pocess. The advantages of the appoaches wee shown on basis of magnetic nea field data collected with a time domain measuing system and data based on Method of Moments simulations. Futhe investigations in choice of height and esolution of the scanning aea as well as the choice of the most suitable optimization algoithm fo souce paamete identification have to be done. REFERENCES [1] CSPR 5 Ed.3: Vehicles, boats and intenal combustion engines Radio distubance chaacteistics Limits and methods of measuement fo the potection of on-boad eceives. [] Constantine A. Balanis, Antenna Theoy Analysis & Design, Wiley, [3] Yolanda Vives Gilabet, Modélisation des emissions ayonées de composants électoniques, Univesité de Rouen, 7. [4] D. Baudy, M. Kadi, Z. Riah, C. Acambal, Y. Vives-Gilabet, A. Louis, B. Mazai, Plane wave spectum theoy applied to nea-field measuements fo electomagnetic compatibility investigations, ET Science, Measuement and Technology, 15. June 8. [5] Tommaso senia, Giovanni Leone, Rocco Piei, Radiation Patten Evaluation fom Nea-Field ntensities on Planes, EEE Tansaction on Antennas and Popagation, Vol. 44, No. 5, May [6] Xin Tong, D.W.P. Thomas, A. Nothofe, P. Sewell, C. Chistopoulos, A Genetic Algoithm Based Method fo Modeling Equivalent Emission Souces of Pinted Cicuits fom Nea-Field Measuements, APEMC Beijing, 1. [7] T. senia, G. Leone, R. Piei, Radiation patten evaluation fom neafield intensities on planes, EEE Tans. Antennas Popogat., vol. 44, pp , May [8] R. Piei, G. D Elia, F. Soldoviei, A two pobes scanning phaseless nea-field fa-field tansfomation technique, EEE Tans. Antennas Popogat., vol. 47, pp. 79 8, May [9] Joan-Ramon Regué, Miquel Ribó, Josep-Maia Gaell, Antonio Matin, A Genetic Algoithm Based Method fo Souce dentification and Fa- Field Radiated Emissions Pediction Fom Nea-Field Measuements fo PCB Chaacteization, EEE Tans. On Electomagnetic Compatibility, vol. 43, No. 4, Novembe 1 [1] Qiang Chen, Jedvisanop Chakaothai, Kunio Sawaya, Estimation of Cuent Distibution by Nea-Field Measuement, CEEM, China, 9 [11] P. Wilson, On Coelating TEM Cell and OATS Emission Measuements, EEE Tansactions on Electomagnetic Compatibility, 37, Febuay 1995