Electromagnetic Noise Source Approximation for Finite- Difference Time-Domain Modeling Using Near-Field Scanning and Particle Swarm Optimization

Transcription

1 Eletomagneti Noise Soue Appoximation fo Finite- Diffeene Time-Domain Modeling Using Nea-Field Sanning and Patile Swam Optimization Autho Siven, Ian, Lu, Junwei, Lewis, Andew Published 2010 Jounal Title IEEE Tansations on Eletomagneti Compatibility DOI Copyight Statement 2010 IEEE. Pesonal use of this mateial is pemitted. Pemission fom IEEE must be obtained fo all othe uses, in any uent o futue media, inluding epinting/epublishing this mateial fo advetising o pomotional puposes, eating new olletive woks, fo esale o edistibution to seves o lists, o euse of any opyighted omponent of this wok in othe woks. Downloaded fom Giffith Reseah Online

2 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY Eletomagneti Noise Soue Appoximation fo Finite-Diffeene Time-Domain Modeling Using Nea-Field Sanning and Patile Swam Optimization Ian Siven, Membe, IEEE, Junwei Lu, Senio Membe, IEEE, and Andew Lewis Abstat This pape pesents an eletomagneti noise soue appoximation method based on a 2-D aay of eleti dipoles fo use in finite-diffeene time-domain simulations. The uents (both magnitude and phase) of these dipoles ae optimized via a patile swam algoithm so as to minimize the diffeene between the magneti nea-field podued by the dipole aay and the magneti nea-field podued by the devie unde test. The method pesented equies only the magnitude of the magneti field to be measued, simplifying the measuement poess. The new noise soue modeling method has been applied to a tansmission-line test ase, demonstating the pefomane and auay of the method. Index Tems Finite-diffeene time-domain (FDTD) method, nea-field sanning, noise soue modeling, patile swam optimization (PSO). I. INTRODUCTION MEETING eletomagneti emissions standads fo new eletoni poduts an be an expensive exeise when following the taditional oute of physial pototyping and testing, espeially if a lage numbe of tests and design evisions ae equied to ahieve ompliane. Computational eletomagnetis (CEMs) simulation ould theefoe pove to be a valuable eletomagneti (EM) ompatibility (EMC) design tool if it an be utilized duing the design poess to ensue fist-pass ompliane with emissions standads. In ode to ealize suh gains in design-poess effiieny, howeve, auate appoximate models fo EM noise soues ae equied, as it is often vey diffiult o impossible to dietly model sophistiated eletoni omponents in CEM simulations. Thee ae a numbe of possible methods fo modeling the soues of EM emissions fom eletoni devies. Simplified soues suh as a single eleti and magneti dipole antenna, path antennas, o multiple andomly plaed dipoles, uently dominate the field [1] [5], due to the appaent diffiulty in obtaining moe auate (and omplex) models. Altenatively, a speially onfigued aay of magneti o eleti dipole Manusipt eeived Febuay 18, 2009; evised May 28, Fist published Januay 22, 2010; uent vesion published Febuay 18, This wok was suppoted in pat by the Austalian Reseah Counil unde Pojet A Vitual Eletomagneti Compatibility (EMC) Lab Based on Advaned Compute Modelling and Simulation Tehniques. I. Siven and J. Lu ae with the Shool of Engineeing, Giffith Univesity, Bisbane, Qld. 4111, Austalia ( ian.siven@student.giffith.edu.au; j.lu@giffith.edu.au). A. Lewis is with the Institute fo Integated and Intelligent Systems, Giffith Univesity, Bisbane, Qld. 4111, Austalia ( a.lewis@giffith. edu.au). Digital Objet Identifie /TEMC antennas an be used to moe auately epesent EM noise soues [6], [7]. This method involves taking nea-field measuements of the fields aound a physial ealization of the devie in question, then epliating that nea-field as auately as possible using a olletion of dipoles. This an be done using eithe a diet solution of the equations govening adiation fom eleti o magneti dipoles [6], o though omputational optimization [7], although the latte poess tends to take signifiantly longe to ahieve the equied auay. The finite-diffeene time-domain (FDTD) method is a poedue fo solving the diffeential time-dependent fom of Maxwell s equations by appoximating the ontinuous patial deivatives at finite intevals. It is a poweful tool fo EMC analysis as it allows a wide ange of fequenies to be investigated in a single simulation. One dawbak, howeve, is that the model being simulated must be disetized onto a lattie of ubi o etangula Yee ells [8], meaning that if an aay of dipoles is used to appoximate the adiated fields fom a given devie, those dipoles an only be oiented along the x-, y- oz-axes. This is an issue fo the method desibed in [6], whih dietly alulates the equied dipole uents, as it equies flexible dipole oientation. This pape attempts to oveome this obstale by fixing the oientation of eah dipole in the aay along eithe the x- o y-axis. Modifying the existing method in this manne is demonstated to enable the x- and y-omponents of the magneti neafield to be modeled vey auately, while intoduing signifiant eo in the z-omponent. A patile swam optimization (PSO) algoithm is then applied to this initial solution in ode to edue this eo. II. APPROXIMATE SOURCE MODEL Any soue model used in an FDTD simulation must meet a numbe of equiements. Obviously, it must be a time-domain soue, and it must adequately ove the ange of fequenies that ae to be examined. When simulating EM emissions fom a devie, the fequeny ange to be examined is typially between 30 MHz and 1 GHz, the ange speified in the FCC standad fo adiated emissions. In the time domain, this ange an be ahieved using a Fouie seies of sinusoids, whose fequenies ae seleted in ode to adequately ove the equied spetum. In this pape, a 2-D aay of eleti dipoles is used to appoximate the emissions fom any abitay devie. A gid of eleti dipoles is used as it is muh simple to model than the omplex eletonis in moden devies, while being able to /$ IEEE

3 90 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 Fig. 2. Poposed magneti field measuement appaatus. Fig. 1. Magneti fields podued by an eleti dipole in Catesian oodinates. epodue a measued nea field with good auay, povided enough dipoles ae used. This dipole aay is oiented in the x y plane of a 3-D Catesian gid. In FDTD simulations, the oientation of these dipoles is estited by this gid, meaning that eah dipole must be oiented in eithe the x-dietion o the y-dietion. The magneti nea-field adiation of these dipoles an be obtained fo a given fequeny by alulating the ul of the magneti veto potential. In Catesian oodinates, the x-, y- and z-omponents of the adiated magneti field at point (x p,y p,z p ) fom an eleti dipole of length λ at (x d,y d,z d ) aying uent I at fequeny ω ae given in (1), (2), and (3), espetively [6]. The uent I is a omplex phaso epesenting both the magnitude and phase of the uent, and angle θ epesents the angle subtended with the x-axis, as shown in Fig. 1. Using this method, the dipole uents (magnitude and phase) must be alulated at a lage numbe of fequenies in ode to build up an auate, boad-band time-domain model of the EM noise soue H x = I λe jk ( zp z d ( zp z d H y = I λe jk H z = I λe jk [ + jω(z ) p z d ) sin θ (1) + jω(z p z d ) ( xp x d + jω(x p x d ) ( yp y d + + jω(y p y d ) ) os θ (2) ) sin θ ) ] os θ. Altenatively, the appoximate dipole uents an be obtained in the time domain using the Biot Savat law, whih states that the ontibution to the total magneti field at a point fom a segment of wie aying uent I is B = µ 0 I λ ˆ (4) (3) whee ˆ is a unit veto dieted fom the wie segment towad the measuement point. The Biot Savat law applies to stati fields; howeve, it povides an auate appoximate to timevaying fields when λ. As time-domain measuement of magneti fields is vey diffiult at high fequenies, it is muh moe onvenient to use fequeny-domain measuements when alulating the dipole uents equied to math the tue nea-field of the devie unde test. Howeve, given the elative simpliity of alulating the magneti field podued by an aay of dipoles aying known uents in the time domain, optimization algoithms an be applied to seah fo the most suitable dipole uents. In ode to solve this so-alled invese poblem, the auay of eah potential solution must be alulated ompaed to the fequeny-domain data obtained fom testing of the devie to be modeled. As suh, a Fouie tansfom is equied, so the magneti fields podued by the dipole model must be alulated ove a lage numbe of time steps. This method was found to be signifiantly slowe than the peviously disussed fequenydomain method, even though suh a method must be evaluated ove a lage numbe of fequenies to adequately ove the equied spetum. III. CALCULATION OF DIPOLE CURRENTS A. Aquiing Nea-Field Data Befoe an appoximate soue model an be onstuted, magneti field measuements must be pefomed ove a gid of points in the nea-field of the devie to be modeled. The height above the devie at whih the measuements ae pefomed is not ovely impotant, as long as all measuement points ae loated well within the nea-field egion. The poposed measuement onfiguation an be seen in Fig. 2. The magneti field pobe is positioned ove the devie to be modeled at eah measuement point, oiented in suh a way to pik up only a single omponent of the magneti field. The Magneti Sienes EMC-100 seies magneti field pobes espond only to fields othogonal to the pikup loop, and ae eletostatially shielded to povide isolation fom ommon-mode signals. The position and oientation of the pobe an be ontolled eithe manually o with the assistane of a oboti am [6]. The uent indued in the pobe is amplified and measued on a spetum analyze, and the measued magneti field is alulated using the pobes alibation data.

4 SCRIVEN et al.: EM NOISE SOURCE APPROXIMATION FOR FDTD MODELING 91 B. Seeding the Optimize This seond step in soue-modeling poess pesented in this pape is to alulate a seed solution. It is so named as it identifies the egion in the solution spae aound whih auate appoximate models ae likely to be found. The tem solution spae is used hee to mean the many-dimensional hypevolume ontaining all possible ombinations of uent phasos used in the dipole aay appoximate model. The seed solution is omputed using a diet solution of (1) (3). As mentioned peviously, all dipoles ae onstained to be oiented dietly along eithe the x-oy-axis. Theefoe, fo the x-dietion dipoles (i.e., the dipoles that an be defined as a line between two endpoints (x 1, ŷ, ẑ) and (x 2, ŷ, ẑ), whee ŷ and ẑ ae onstants), (1) (3) an be ewitten as follows: H x =0 (5) H y = I x λe jk ( zp z d + jω(z ) p z d ) = I x α x (6) H z = I x λe jk ( yp y d + jω(y ) p y d ). (7) Likewise, fo all the y-dietion dipoles, the same magneti field equations an be ewitten as follows: ( ) zp z d H x = I y λe jk + jω(z p z d ) = I y α y (8) H y =0 (9) H z = I y λe jk ( xp x d + jω(x ) p x d ). (10) Fom this, it an be seen that the y-omponent of the magneti field aound the appoximate model is only dependent on the uents in the x-dietion dipoles, and the x-omponent of the magneti field is similaly dependent on only the uents in the y-dietion dipoles. Using these equations in onjuntion with measued data fom the devie to be modeled, it is tivial to develop an aay of suh dipoles that will vey auately model the x- and y-omponents of the devie s magneti nea field, using the following equations: [I x ]=[α y ] 1 [H y ] (11) [I y ]=[α x ] 1 [H x ]. (12) If z-dietion dipoles wee used, the x-omponent of the magneti field would no longe be dependent on only the y-dietion dipoles, and would instead be elated to the z-dietion dipole uents as well. Similaly, the y-omponent of the magneti field would also be dependant on the z-dietion dipoles as well as those oiented along the x-axis, and a diet solution of (1) (3) would no longe be possible due to this ovelap. Suh a model will be signifiantly less auate in tems of the z-omponent of the magneti field, as this omponent was not utilized in its geneation. It is possible, howeve, to inease the auay of the geneated model in this espet, by slightly alteing the uent phasos that exite the dipoles. To put it in tems of omputational optimization, by seahing the peviously defined solution spae in the egion of this seed solution, appoximate models that ae moe auate oveall may be found. In this pape, a patile swam algoithm is used to pefom this seah. C. PSO Algoithm The PSO algoithm is based on swam intelligene, an atifiial intelligene tehnique that studies olletive behavio in deentalized, self-oganized goups [9]. It utilizes a population of potential solutions, o patiles, whih move aound the design spae with evey iteation. The movement of these patiles is govened by following two equations [10]: v ij (t +1)=wv ij (t)+ 1 1j (t)[y ij (t) x ij (t)] + 2 2j (t)[ŷ ij (t) x ij (t)] (13) x ij (t +1)=x ij (t)+v ij (t +1). (14) Hee, v ij (t) is the veloity of patile i in dimension j at time t and x ij (t) is the position of patile i in dimension j at time t. The veloity of a patile depends on both the best position that patile has found to time t, y ij (t) (the loal best solution), and the best solution the entie swam has found to time t, ŷ ij (t) (the global best solution). An inetial omponent is saled by onstant w, and 1 and 2 ae onstants used to ontol the impat of the loal and global omponents in veloity equation (13). Fo the puposes of this wok, w was set to 0.3, and 1 and 2 wee set to 1.4. The veto is a veto of andom numbes evenly distibuted between zeo and one geneated fo eah patile at eah time step t. The PSO algoithm is an iteative one. Fo the wok pesented in this pape, the initial position of eah patile is andomized aound the peviously disussed seed solution. Though the use of this pio knowledge of the solution spae, faste onvegene an be attained [11], [12]. At evey iteation, the patile positions ae evaluated, the loal and global best solutions ae updated and new veloities ae alulated using (13). Using these new patile veloities, the position of eah patile is updated as in (14). The algoithm is teminated when the impovement in the best solution found ove a numbe of iteations dops below a given theshold, in this ase 0.1% ove ten iteations. D. Evaluation of Potential Solutions Patile positions ae evaluated using a fitness funtion, whih quantifies the eo pesent in the appoximate soue model geneated by that dipole aay onfiguation. To measue the eo, the aveage (absolute) diffeene between the measued value and the appoximated value of eah omponent of the magneti field at eah measuement point was alulated. Equation (15) shows the fitness funtion used by this soue modeling method: f(i) = 1 3 ( ) g x (I)+g y (I)+g z (I) (15)

5 92 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 whee g x (I) = 1 N g y (I) = 1 N g z (I) = 1 N N ) ( (H ix eal Hi x appox) 2 i=1 N ) ( (H iy eal Hi y appox) 2 i=1 N i=1 ( (H iz eal Hi z appox) 2 ). In this equation, I is the veto of uent phasos being evaluated. Vetos H x eal, H y eal, and H z eal ontain the values of the measued magneti field at all N measuement points, while H x appox, H y appox, and H z appox ontain the values of the appoximated magneti field at the same loations. E. Conveting to the Time Domain As the final goal of this method is to podue a time-domain appoximation to a given eletomagneti noise soue, it is impeative that the numeous optimized fequeny-domain esults podued ove the equied spetum be ombined into a single time-domain soue. This time-domain soue is obtained using a Fouie seies of the individual fequeny-domain solutions, as shown in following equation: I i (t) = n I i (ω) sin(2πft + I i (ω)). (16) ω =1 Hee, I i (t) is the uent in dipole i at time t, and I i (ω) is the omplex uent phaso fo the same dipole at fequeny numbe ω. The total numbe of fequenies used, n, is poblem dependant. If using a linea ange of fequenies, the gap between fequenies should be low enough so that all majo omponents of the measued magneti fields ae aounted fo. Typially, the gap between adjaent fequenies would be set between 1 and 10 MHz, o the minimum esolution of the spetum analyze used. Altenatively, a pedefined set of fequenies an be used based on an initial investigation of the devie unde test. IV. CASE STUDY: MODELING EMISSIONS FROM A TRANSMISSION LINE In ode to demonstate the soue modeling method poposed in this pape, a simple tansmission-line model is used. The model, shown in Fig. 3, onsists of a tansmission line with a ight-angle bend. The shote setion of tansmission line to the ight is teminated to a 100-mm squae gound plane on the bottom laye of the pinted iuit boad (PCB) with a 1-kΩ esistive load. The PCB itself is 2 mm thik and has a elative pemitivitty of 4.4. This tansmission line is exited with a 50-MHz squae-wave signal having ise and fall times of 1 ns, as shown in Fig. 4. A. Geneating the Appoximate Model To geneate the appoximate model, the x-, y- and z- omponents of the magneti field geneated by the tansmission line wee measued at 10 mm intevals in both the x- and Fig. 3. Layout of the tansmission-line ase study. Note the gound plane on the unde side is not shown. Fig. 4. soue. Two peiods of the tansmission line model s squae-wave exitation y-dietions stating fom the oigin (0,0) in Fig. 3. These measuements wee pefomed at a fixed height of 20 mm above the PCB. A total of 242 dipoles wee used, positioned, as shown in Fig. 5. Using the measuement data, an initial model was alulated ove the fequeny ange 30 MHz 1 GHz at 10-MHz intevals using (11) fo the x-dietion dipoles, and (12) fo the y-dietion dipoles. On a moden Intel poesso unning at 2.7 GHz, these alulations equied less than a minute of omputation time. This initial seed solution will henefoth be efeed to as the unoptimized appoximate model. The final appoximate model fo this tansmission-line test ase was obtained by optimizing the seed solution at eah fequeny in the afoementioned ange using the patile swam algoithm desibed in Setion III-C. This optimized model, whih equied about 30 min of omputational time to deive, was then finally onveted to a set of time-domain uent soues.

6 SCRIVEN et al.: EM NOISE SOURCE APPROXIMATION FOR FDTD MODELING 93 Fig. 5. Layout of dipoles in tansmission-line appoximate soue model. Fig. 7. Measued H z field stength (f =100 MHz) at eah measuement point ompaed to the equivalent optimized appoximate field. Fig. 6. Measued H z field stength (f =100 MHz) at eah measuement point ompaed to the equivalent unoptimized appoximate field. B. Veifiation of the Model In ode to veify that the poedue pesented in this pape podues an optimized appoximate model that is both an impovement ove the oiginal seed solution and an auate epesentation of the noise soue it is designed to model, two stages of veifiation and testing wee pefomed. Fist, the magneti fields podued by both the optimized and unoptimized appoximate models at the measuement points wee ompaed to the data obtained fom measuement of the tansmission-line devie at the same points, 20 mm above the tansmission-line PCB. Seond, moe physial measuements wee made at a height of 40 mm above the tansmission-line PCB, and these measuements ompaed to the esults podued by the optimized appoximate model at the same height. Fig. 6 shows the z-omponent of the magneti field at eah measuement point podued by the unoptimized appoximate model at a single seleted fequeny, 100 MHz, along with the measued data fom the physial devie. This fequeny was seleted as the aveage impovement at 100 MHz was appoximately 22%, whih is oughly the mean of the gaph in Fig. 12, and theefoe, this fequeny point epesents a typial ase. The poo auay of the initial appoximate model fo this field omponent was expeted, as the z-omponent of the measued field data was not used in the geneation of this model. Fig. 8. Measued H x field stength (f =100 MHz) at eah measuement point ompaed to the equivalent optimized appoximate field. When ompaed to the z-omponent of the magneti field podued by the optimized appoximate model at the same fequeny and measuement points shown in Fig. 7, it an be seen that the optimization algoithm has signifiantly impoved the auay of the appoximate model in egads to z-omponent of the field. Thee is still some eo pesent in the z-omponent of the optimized esult aound points , as the optimization algoithm foused on impoving the auay of the appoximate model in egions whee the field stength is highest. Regions of high field stength ae moe impotant when assessing devies fo ompliane with EMC standads that ae based on maximum allowable emissions. Signifiant impovement an be seen in these egions. The oiginal unoptimized appoximate model was geneated by ignoing the z-omponent of the magneti field, and teating the x- and y-omponents independently, whih is possible due to the peviously disussed estitions plaed on the oientation of the dipoles. Although Fig. 6 shows that this leads to signifiant eo in the z-omponent of the magneti field, it does allow this model to exatly epliate the fields podued by the devie in question in the x- and y-omponents of the magneti field, at least at the points used to geneate the model. As suh, the x- and y-omponents of the magneti field podued by the optimized appoximate model wee examined, as shown in Figs. 8 and 9 espetively, to ensue that this auay has not

7 94 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 Fig. 9. Measued H y field stength (f =100 MHz) at eah measuement point ompaed to the equivalent optimized appoximate field. Fig. 11. Eo in the z-omponent of the magneti field geneated by the optimized appoximate model (f =100 MHz). Fig. 10. Eo in the z-omponent of the magneti field geneated by the unoptimized appoximate model (f =100 MHz). Fig. 12. Aveage impovement gained by optimization of the dipole uents. been diminished as a esults of impoving the auay in tems of the z-omponent of the magneti field. Fom these esults, it an be seen that the optimization algoithm esults in vey little eo being intodued into the y-omponent of the magneti field, although some eo is intodued to the x-omponent, patiulaly aound measuement point 50. Howeve, both the maximum and aveage eo in this data ae signifiantly less than the eo pesent in the z-omponent of the magneti field podued by the unoptimized model, due to the geate magnitude of the z-omponent of the field. To ompae the optimized appoximate model with the oiginal unoptimized one, the eos between the magneti fields podued by the appoximate models and the measued data fom the tansmission-line devie wee alulated. Fig. 10 shows the aveage eo in the z-omponent of the magneti fields geneated by the oiginal unoptimized appoximate model, and Fig. 11 shows the eo measuements fo the optimized appoximate model. Lage eos an be seen at measuement points 52, 63, and 74 fo the unoptimized appoximate model. These points ae loated at (x, y) points (40 mm, 70 mm), (50 mm, 70 mm), and (60 mm, 70 mm), espetively (at the measuement height of 20 mm). In elation to the tansmission line shown in Fig. 3, these points ae loated in an aea whee the x-oiented and y-oiented segments of tansmission line will both be poduing elatively stong H z fields. This is to be expeted in this initial model, as it is podued by ignoing the z-omponent of the measued field. As suh, it will plae high uents on the y-dietion dipoles nea the y-oiented segment of tansmission line (as this aea will ontain the highest H x fields), and high uents on the x- dietion dipoles nea the x-oiented segment (as this aea will ontain the highest H y fields), without onsideing the oupling in the z-omponent of the magneti field. The optimization algoithm is able to emedy this shotfall, as seen in Fig. 11, as it does aount fo z-omponent of the magneti field podued by the dipole aay. The aveage impovement obtained though the use of the optimization poedue an be defined as aveage impovement = 1 N N ( ) Eu E o i=1 E u (17) whee E u is the aveage eo pesent ove all spatial omponents in the unoptimized appoximate model, E o is the aveage eo in the optimized model, and, as in pevious equations, N is the numbe of measuement points, in this ase 121. As shown in Fig. 12, the optimized appoximate model epesents a signifiant impovement in auay ove to the unoptimized

8 SCRIVEN et al.: EM NOISE SOURCE APPROXIMATION FOR FDTD MODELING 95 Fig. 13. Measued H x field stength ompaed to the equivalent H x field stength geneated by the appoximate model, 40 mm above the tansmissionline PCB. Fig. 15. Measued H z field stength ompaed to the equivalent H z field stength geneated by the appoximate model, 40 mm above the tansmissionline PCB. Fig. 14. Measued H y field stength ompaed to the equivalent H y field stength geneated by the appoximate model, 40 mm above the tansmissionline PCB. Fig. 16. Fa-field adiation geneated by the tansmission-line PCB devie. model, aoss the entie fequeny ange. It should be noted that while Figs. 10 and 11 demonstate a 30% impovement in H z at 100 MHz, the eos intodued in the H x and H y deeased the oveall aveage impovement shown in Fig. 12 to appoximately 22%. To veify that the appoximate model geneated is auate at all heights above the devie being modeled (in this ase the tansmission line), the magneti fields podued by the devie wee again measued using the same gid of measuement points, this time at a height of 40 mm above the PCB. Figs show the H x,h y, and H z omponents (espetively) of the measued magneti field as well as the magneti fields podued by the optimized appoximate model at the same measuement points. Fom these figues, it an be seen that the optimized appoximate model geneated using the poedue pesented in this pape podues auate magneti fields at multiple heights above the devie being modeled, veifying the auay and usefulness of the model fo modeling nea-field adiated emissions fom an abitay devie. In ode to demonstate the auay of the method in the fa-field, fa-field adiation pattens at a fequeny of 100 MHz wee alulated though FDTD modeling of both Fig. 17. Fa-field adiation geneated by the appoximate model. the atual tansmission-line model and the appoximate dipole aay, as shown in Figs. 16 and 17. In these figues, the φ and θ axes epesent the azimuth and elevation of the fa-field measuement point, as shown in Fig. 18. The adiation patten podued by the tansmission-line devie esembles that podued by an eleti dipole antenna oiented

9 96 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 esults. Using 121 x-dietion dipoles and 121 y-dietion dipoles, the method was able to podue an appoximate model that losely mathed the nea-field adiated fields fom the tansmission-line PCB not only at the positions used to geneate the model, but also at a distane twie as fa again fom the PCB. Futhemoe, the appoximate model geneated using the poposed method was able to epliate the fa-field adiation podued by the tansmission-line devie to a high degee of auay. Fig. 18. Spheial oodinate system used fo the fa-field adiation pattens. Fig. 19. Diffeene between fa-field adiation pattens podued by the tansmission-line devie and the appoximate model. along the x-axis due to the longe tansmission-line segment, with a slight otation aused by the shote segment. It an be seen that the appoximate soue model podues a highly auate epesentation of the tansmission line s fa-field adiation patten, with the 0.4-dB eo at peak of the adiation patten not disenable fom the figues. The lage eos seen in Fig. 19 ae aused by a slight diffeene in otation between the two adiation pattens. REFERENCES [1] A. Dolente, U. Reggiani, and L. Sandolini, Compaison of adiated emissions fom diffeent heatsink onfiguations, in Po. IEEE 6th Int. Symp. Eletomagn. Compat. Eletomagn. Eol., 2005, pp [2] J. Lu and X. Duan, EMC ompute modelling tehniques fo CPU heat sink simulation, in Po. 3d Int. Conf. Comput. Eletomagn. Appl., 2004, pp [3] J. Lu and F. Dawson, EMC ompute modelling tehniques fo CPU heat sink simulation, IEEE Tans. Magn., vol. 42, no. 10, pp , Ot [4] C. Wang, J. L. Dewniak, J. L. Knighten, D. Wang, R. Alexande, and D. M. Hokanson, Gounding of heatpipe/heatspeade and heatsink stutues fo EMI mitigation, in Po. IEEE Symp. Eletomagn. Compat., 2001, vol. 2, pp [5] L. Covet and J. Lin, Simulation and measuement of a heatsink antenna: A dual-funtion stutue, IEEE Tans. Antennas Popag.,vol.54,no.4, pp , Ap [6] Y. Vives-Gilabet, C. Aambal, A. Louis, F. de Daan, P. Eudeline, and B. Mazai, Modelling magneti adiations of eletoni iuits using nea-field sanning method, IEEE Tans. Eletomagn. Compat.,vol.49, no. 2, pp , May [7] J-R. Regué, M. Ribó, J.-M. Gaell, and A. Matín, A geneti algoithm based method fo soue identifiation and fa-field adiated emissions pedition fom nea-field measuements fo PCB haateization, IEEE Tans. Eletomagn. Compat., vol. 43, no. 4, pp , Nov [8] K. Yee, Numeial solution of initial bounday value poblems involving Maxwell s equations in isotopi media, IEEE Tans. Antennas Popag., vol. AP-14, no. 3, pp , May [9] J. Kennedy and R. Ebehat, Patile swam optimization, in Po. IEEE Int. Conf. Neual Netw., 1995, pp [10] A. P. Engelbeht, Fundamentals of Computational Swam Intelligene. Chiheste, U.K.: Wiley, [11] C.-H. Chou and J.-N. Chen, Geneti algoithms: Initialization shemes and genes extation, in Po. 9th IEEE Int. Conf. Fuzzy Syst., 2000, vol. 2, pp [12] S. Rahnamayan, H. R. Tizhoosh, and M. M. A. Salama, A novel population initialization method fo aeleating evolutionay algoithms, Comput. Math. Appl., vol. 53, no. 10, pp , V. CONCLUSION The EM noise soue appoximation method pesented in this pape has been shown to be apable of poduing vey auate appoximate models fo use in FDTD simulations. The method uses an aay of eleti dipoles whih ae estited to eithe the x- o y-oientation by the FDTD gid. An initial model based on a diet solution of the equations govening adiation fom eleti dipole antennas and measued H x and H y data wee not suffiiently auate in egad to the z-omponent of the magneti field being modeled. Though the use of a PSO algoithm, the uent phasos exiting the dipoles ae optimized to minimize the oveall eo pesent in the appoximation. This soue modeling method was applied to a tansmissionline devie in ode to veify its ability to podue auate Ian Siven (S 07 M 09) was bon in Ipswih, Qld., Austalia, in He eeived the eletial engineeing and ompute siene degees in 2006 fom Giffith Univesity, Bisbane, Qld., whee he is uently woking towad the Ph.D. degee in the same aeas. His uent eseah inteests inlude omputational eletomagnetis, EMC, and deentalized patile swam optimization algoithms.

10 SCRIVEN et al.: EM NOISE SOURCE APPROXIMATION FOR FDTD MODELING 97 Junwei Lu (M 92 SM 05) eeived the B.Eng. degee in eletial engineeing fom Xian Jiaotong Univesity, Xian, China, in 1976, the M.Eng. degee in eletoni and ompute engineeing fom the National Toyama Univesity, Toyama, Japan, in 1988, and the Ph.D. degee in eletial and ompute engineeing fom the National Kanazawa Univesity, Kanazawa, Japan, in Fom 1976 to 1984, he was with the Institute of Qinhai Eleti Powe Testing and Reseah, China, whee he was involved in the vaious national eseah pojets fo the eletial powe industy. Duing 1985, he was with the Laboatoy of Eletial Communiations, Toyama Univesity, Japan, whee he was involved in the aea of omputational eletomagnetis. Duing 1988, he was with the Laboatoy of Eletial Enegy Convesion, Kanazawa Univesity, whee he was involved in the applied omputational eletomagnetis and was involved in the development of magnetis devies. In 1992, he joined the Shool of Mioeletoni Engineeing, Giffith Univesity, Bisbane, Qld., Austalia, whee he is uently an Assoiate Pofesso. His eseah inteests inlude omputational and visual eletomagnetis, EMC ompute modeling and simulation, smat mobile teminal antennas and RF/MW devies and iuits, and high-fequeny magnetis and powe eletonis. Andew Lewis eeived the B.Eng. degee in ompute engineeing fom the Univesity of Newastle, Tyne and Wea, U.K., in 1984 and the Ph.D. degee in ompute siene fom Giffith Univesity, Qld., Austalia, in He is a Senio Reseah Speialist in Reseah Computing Sevies, Giffith Univesity, Bisbane, Qld., Austalia, whee he is an Adjunt Senio Letue with ICT. He was with BHP Billiton, whee he was engaged in industial applied eseah. His uent eseah inteests inlude paallel optimization algoithms fo lage numeial simulations, inluding gadient desent, diet seah methods, evolutionay pogamming, patile swam and ant olony systems, multiobjetive optimization tehniques fo engineeing design, and paallel, distibuted, and gid omputing methods. He has authoed o oauthoed in the aea of optimization algoithms and appliations.