Distributive Radiation Characterization Based on the PEEC Method

Transcription

1 Title Distibutive Radiation haacteization Based on the PEE Method Autho(s) ao, Y; Jiang, L; Ruehli, AE itation The IEEE Intenational Symposium on Electomagnetic ompatibility (EM), Raleigh, Noth aolina, USA, 48 August 4. In the Intenational Symposium on Electomagnetic ompatibility Poceedings, 4, p. 8 Issued Date 4 URL Rights Intenational Symposium on Electomagnetic ompatibility Poceedings. opyight I E E E.

2 Distibutive Radiation haacteization Based on the PEE Method Ying S. ao Depatment of Electical and Electonic Engineeing The Univesity of Hong Kong Pokfulam Road, Hong Kong Li Jun Jiang Depatment of Electical and Electonic Engineeing The Univesity of Hong Kong Pokfulam Road, Hong Kong A. E. Ruehli UMRI/MST EM Laboatoy Missoui Univesity of Science and Technology Rolla, MO 6549, USA Abstact The intentional and unintentional adiations ae of geat impotance to electomagnetic coupling and adiation poblems in both high and low fequency egimes. Howeve, conventional computational methods emphasize the pottopot pefomance instead of the detailed adiation mechanism that is citical to designs and optimizations. In this pape, we employ the PEE method to quantitively analyze, model, and illustate how the enegy is coupled and adiated. We also ty to point out, based on calculations, which pat is a geate contibuto to the wanted o unwanted adiation. Employing the dynamic Geen s function, the powe tems associated with the inductive and capacitive components in the PEE model can be explicitly extacted and categoized. Then the powe elationship between multiadiatos and subsegmentations of a single adiato can be analyzed clealy. How the patial elements contibute to adiation and tansmission powes is also demonstated at the end of the pape. I. INTRODUTION Novel electonic devices and new atificial mateials have been suging in the past decade []. With the inceasing density of devices and bandwidth of the signal channel, the complexity of Is and elated inteconnects ae becoming bottlenecks fo many high pefomance systems. Electonic design automation (EDA) is indispensable fo successful designs. Howeve, modeling of high speed signals in a complex envionment is not a tivial task. To make a tadeoff between speed and accuacy, many empiical o theoetical appoximations have been used at diffeent stages of designs. Meanwhile, with the inceasing speed, the adiation becomes moe and moe significant. It comes fom all distibutive stuctues and thei combinations. Modeling the adiation of I inteconnects is mostly ignoed by signal integity (SI) and powe integity (PI) pactices. Its analysis is also aely available in moden EDA tools. Howeve, conventional computational electomagnetic methods seem not to be good enough to answe these questions, eithe. So fa, vaious methods of modeling adiation EM methods have been developed based on computational electomagnetics, such as method of moments (MOM), finite element method (FEM), and finite diffeence method (FD). Recently a fullwave solve has been developed by using the augmented electic field integal equation (AEFIE) [] fo the low fequency egime. Howeve, they mostly focus on chaacteizing potbased popeties such as matching conditions, insetion losses, o they give geneal efficiency desciptions and adiation pattens. Howeve, it is unclea how the enegy is adiated and coupled fom diffeent pats of the adiato. Although computational electomagnetics basedalgoithms ae mighty enough to analyze vey complex poblems, they lack the flexibility to do the adiation popety extaction. The patial element equivalent cicuit (PEE) method, which was poposed by Ruehli in the 97s [] [5], is based on electic field integal equation (EFIE) and povides an equivalent cicuit model fo electomagnetic poblems. Afte nealy foty yeas of development, PEE is now widely used in vaious modeling applications. A vast categoy of PEE applications ae fo static o quasistatic poblems. Unde those conditions, patial elements in PEE ae all eal numbes by ignoing the etadation. In the full wave egime, the patial elements utilize the dynamic Geen s function that can coectly count the adiation effects. In pinciple, PEE is capable of handling fullband poblems. Because it popely bidges cicuit theoies and electomagnetic analysis togethe, and can help us in claifying the adiation pocess modeling. A study in [6] has poposed a new way of using the PEE method to decompose the adiation pocess and evaluate the contibutions fom diffeent adiatos. It consides the etadation and theeby extacts all the eal powes fom the phase powe epesentation. The selfadiation and powe tansfe ae sepaated by using selfpatial elements and by coupling patial elements. It popely splits the powe composition within adiatos. Anothe ecent wok calculated the adiated powe fo PB [7] based on the pot netwok paametes. It assumes that the adiated powe can be calculated using incident pot voltages and Spaametes. Howeve, the cuent distibution on the geomety and electic field cannot be quantitively obtained fom this pot based method. In [8], a new adiation calculation method was poposed using the etadation and the eoganization of the patial components. It pedicts the Hetian dipole vey well. Howeve, it is difficult to be used fo lage geneal stuctues. In this wok, we extend the patial element equivalent cicuit (PEE) method to distibutive adiation analysis in a method /4/$. 4 IEEE

3 simila to [6] so that the adiation and coupling contibutions fom each segment of the whole adiato can be singled out. The distinct diffeences between this wok and [6] ae that we deive moe geneal powe fomulations with dynamic self tems. And we analyze not only the coupling between adiation objects, but also the coupling and adiation of diffeent pats of the same adiato. This wok is valuable to electomagnetic intefeence (EMI) optimization, noise coupling eduction, and othe I and PB applications. The oganization of the est of the pape is shown as follows: Section II will intoduce adiated powe analysis of PEE method; Section III demonstates the eal and complex mutual impedances accoding to static and dynamic Geen s function; Section IV combines cicuit analysis with coupled adiatos togethe, to epesent adiatos in a new way; and Section V investigates seveal benchmaks to veify the poposed idea. onclusions and discussions ae pesented at the end of this pape. V s Fig.. II. RADIATED POWER ANALYSIS Lp kk Lp mm R k Ik φ P kk P k,k k φ k R m Im φ P mm P m,m m φ m k V k Vk m Vm Vm An equivalent cicuit model with a souce. Fig. depicts a epesentative PEE cicuit model of cell k and cell m. Thee ae contolled voltage souce on each of the two inductive coupled banches k, m. They can be appoximated to be [6]. k = jωl km I m e jkd km, Vm L = jωl kmi k e jkd km. (a) (b) whee d km is the cental distance between two inductive cells k and m. And fo two capacitive banches k, m the contolled voltage souces ae V k = p km jω I me jkd km, V m = p km jω I k e jkd km. (a) (b) whee d km is the cental distance between two capacitive cells k and m. Im and I k means cuent though the mth and k th capacitive banch, espectively. The detailed demonstation can be found in [6]. Howeve, this method has a dawback. It does not take the selftem adiation into account. It is accuate when two cells ae well sepaated. But fo close and selftems, it does not wok well. Meanwhile, the selftem is coesponding to a Hetzian dipole [8]. Its dynamic popety shall be pesented to model the etadation accuately. Using the dynamic Geen s function, diectly inside the integation kenal, the above mentioned issue could be solved. Patial inductances and patial coefficients of potential will all become complex. Let L km epesent the complex inductance, and p ki epesent the complex potential. The banch cuents I m and I k ae also complex cuents in cicuit m and k. Then µ L km = 4πa k a m p ki = 4πS i S k ε a k a m l k l m S k S i e jk da k da m dl kdl m, e jk ds k ds i. (a) (b) whee K hee is the wave numbe. Then () can be ewitten to k = jω L km I m, m = jω L km I k. (4a) (4b) Fo selftems, which has the adiation equivalent to a Hetian dipole, we can set k = m in above equations to get the needed self complex patial inductances and patial potential coefficients. The powe can be calculated fom the complex node voltages and the complex banch cuents. The total complex powe of a pai of inductive banches k and m is S km =(R k jωl k )I k (R m jωl m )I m k I k mi m whee Vk L epesents induced voltage souces on banch k, and we have Vk L I k = jω L km I m Ik. (6) Real pat of the coupling powe is what we want to be concened about. If the supescipt L means inductive, Pkm L epesents the adiated powe tansfeed to cell k fom the inductive coupling with m. It is composed of two pats, P L, km fo adiation and P L,t km fo tansmission. So does PL mk. Hence, P L km = P L, km PL,t km, (5) PL mk = P L, mk PL,t mk (7) Accoding to enegy consevation law, powe tansmitted fom cell m to cell k should be the same to the powe tansmitted fom k to m. If we assume the powe leaving the conducto is positive, they will have opposite signs. Hence, P L,t km = PL,t mk. Similaly, fo capacitive banch k and capacitive banch m, we have P km = P, km P,t km, P mk = P, mk P,t mk (8) 4

4 Also P,t km = P,t mk. The supescipt hee means capacitive. The total adiated powe fom two inductive cells m and k, due to thei mutual couplings, can be deived to be P L, km,total =Re(V ki k V m I m) =Re(I m I k) Re(jω L km ). Unde cetain cicumstances, especially when the segmentation cells ae simila to each othe, it is found [6] that kth element s adiated powe due to the coupling fom m is (9) P L, km = Re(I ki m) Re(jω L km ). () onsequently, the tansmitted powe between two cells caused by inductive effect can be deived to be P L,t km = Im(I ki m ) Re(ω L km ). () The active adiated and tansmitted powes due to coupled capacitive banches can be deived to be P, km = Re(I ki m ) Re( p km jω ). P,t km = Im(I ki m) Re( p km ω ). (a) (b) whee P, km and P,t km coespond to the adiated and tansmitted powes between capacitive cells k and m, espectively. I k and I m in Eq. ae cuents though capacitive banches k and m. III. NUMERIAL EXPERIMENTS In ode to evaluate the pefomance of the poposed method, two epesentative cases have been benchmaked. A. Two Dipoles Two lossless, zeothickness dipoles ae both metes long and. mm wide. They ae placed to be paallel to each othe. The cental distance between them is also metes. The eceive is loaded with a Ohm esisto and the tansmitte is excited by a lumped sinusoidal voltage souce with the amplitude V S = Volt. The geomety is illustated in Fig.. Using the complex patial inductance and patial potential fomula in (), the adiated and coupled powes can be popely modeled based on the poposed method. Equation 9 to have to be employed to extact diffeent composition of the powe. Thee ae seveal key elements in the powe. Hee we define Pab t as the tansfeed powe fom antenna a to antenna b because of inductive, capacitive and adiative couplings: Pab t = Pkm, t () k M a m M b whee M a and M b ae PEE cells that belong to antenna a and antenna b, espectively. Pkm t is the powe tansfeed fom cell k to cell j. Futhe decompose Pkm t into pats fom inductive coupling and capacitive coupling, we have P t km = P L,t km 4 (P,t km P,t k,m P,t k,m P,t k,m ) (4) The powe adiated due to antenna a, b themselves and thei couplings ae Paa = Pkm, (5a) k M a m M a P = (5b) P ab = Pkm, k M b m M b Pkm. k M a m M b whee the powe adiated by two PEE cells is (5c) Fig.. Geomety of two dipoles, and thei powe composition. P km = P L, km 4 (P, km P, k,m P, k,m P, k,m ) (6) To veify the accuacy of the poposed calculation pocess, we need to compae thei esults with those obtained fom othe methods, such as the powe computed based on the Ponying vecto. By PEE, cuents of each segment can be obtained fist. Then using the dynamic Geen s Function and Poynting vecto, the adiated powe is calculated by the fa field integation equation. Fig. (a) shows a compaison fo P. Vey good ageement between the poposed method and the field equation based method can be achieved. In Fig. (b), we can see that the total adiated powe P is composed of two pats, PL, which is positive and P, which is negative. onsequently, the adiated powe demonstates cetain esonance popeties of the stuctue due to combined contibutions fom both inductance and potential tems. 5

5 Powe, mw P by cuent P by PEE Fequency, MHz. (a) P B. A Pai of oupled Loops ) Two Loops ase: The geomety of two lossless loops with zeo thickness is shown in Fig. 4. The length of each loop is. m and the width is. m. The vetical distance between two loops is. m with V sinusoidal voltage souce in the middle of one side. Fig. 5 and 6 show the compaison fo P of loop a and loop b calculated fom the field integal equation and the poposed method based on (9) to (). It is seen that by taking advantage of the PEE method, we can easily calculate the adiated powe and thei compaison fom loop a and b sepaately P of loop a by uent P of loop a by PEE Powe, mw P P L, P, Powe, mw Fequency, MHz Fig.. (b) Powe of P, PL, and P, Radiated powe fom the second dipole. Powe, mw Fequency, GHz 5 5 (a) P of Loop a P of loop a P of loop a L P of loop a Fequency, GHz (b) Powe of Paa, PL, aa and Paa, Fig. 5. Radiated powe of Loop a. Fig. 4. Geomety of two squae loops. The length of each loop is. m and the width is. m. The vetical distance between two loops is. m with V sinusoidal voltage souce in the middle of one side. Fom Fig. 5 and Fig. 6 we can see that P is composed of two pats: P L, which is positive; and P, which is negative. The total summation of these inductive and capacitive effects fom the total adiation powe. Fig. 7 shows the total adiated powe fom Loop. Each inductive cell and capacitive cell has its own adiation effect. It is inteesting to compae thei contibutions, which is the sensitivity analysis of the powe contibution fom diffeent pats. As shown in Fig. 8, the inductive selfpowe is all positive while the capacitive adiated powe is all negative. 6

6 x 4 5 Powe, mw P of loop b by uent P of loop b by PEE Powe, W Self P L.5 Powe, mw Fequency, GHz (a) P of Loop b P of loop b P of loop b L P of loop b Powe, W Numbe of Inductive ell x 4 (a) SelfP L, Self P Fequency, GHz (b) Powe of P, PL, and P, Numbe of apacitive ell Fig. 8. (b) SelfP, Self inductive and capacitive powe. Powe, mw Fig. 7. Fig. 6. Radiated powe of Loop b. P of loop b by cuent P of loop b by PEE Distance, m Radiated powe at Loop b with diffeent distances. By analyzing Fig. 8, the highest cuent coesponds to the highest inductive adiation powe. The highest node voltage coesponds to the highest capacitive adiation powe. This means that the inductive cell that has highe cuent can adiate while the capacitive cell that has highe voltage can adiate moe. And the total self and mutual adiation effects of a complete cell ae the adiation combinations fom both inductive cells and coesponding capacitive cells. The esult is shown in Fig. 9. The fist 6 cells ae fo loop a and the emaining6 cells ae fo loopb. By doing this, adiated effect of each inductive and capacitive cell could be calculated. We can see that the selfadiated powe in Fig. 9 and the adiated powe due to mutual couplings in Fig. can sometimes be negative. This is due to powe oscillation between these cells. By eliminating abitay inductive o capacitive cell, the total adiated powe would change due to loss of contibutions fom those deleted cells. Fom Fig., powe contibution distibution could be quantitively modeled. It shows the powe sensitivity of the system due to diffeent distibutive pats. Hence, by using the poposed method, the powe sensitivity of a model can be conveniently computed and plotted. 7

7 Powe, W Powe, W x 4 4 x 4 Self P Numbe of ell Fig. 9. SelfP fo cells in loop a and loop b. eviewes, editos, and fo the constuctive suggestions fom Pof. W.. hew. REFERENES [] A. Kus, A. Kaalis, R. Moffatt, J. D. Joannopoulos, P. Fishe, and M. Soljacic, Wieless powe tansfe via stongly coupled magnetic esonances., Science, vol. 7, no. 584, pp. 86, Jul. 7. [] Z.G. Qian and W.. hew, Fast fullwave suface integal equation solve fo multiscale stuctue modeling, IEEE Tans. Antennas Popag., vol. 57, no., pp. 687, Nov. 9. [] A. E. Ruehli, Equivalent cicuit models fo thee dimensional multiconducto systems, IEEE Tans. Micow. Theoy Tech., vol. MTT, no., pp. 6, Ma [4] A. E. Ruehli, Inductance calculations in a complex integated cicuit envionment, IBM J. Res. Develop., vol. 6, no. 5, pp. 4748, Sep. 97. [5] A. E. Ruehli and P. A. Bennan, Efficient capacitance calculations fo theedimensional multiconducto systems, IEEE Tans. Micow. Theoy Tech., vol., no., pp. 768, Feb. 97. [6] G. Wollenbeg and S. V. Kochetov, Fast computation of adiated powe distibution in coupled wie systems by the PEE method, in IEEE Intenational Symposium on Electomagnetic ompatibility,. EM.,, pp. 555 Vol.. [7] B. Achambeault, S. onne, M. S. Halligan, J. L. Dewniak and A. E. Ruehli, Electomagnetic adiation esulting fom PB/High Density onnecto Intefaces, IEEE Tans. Electomagn. ompat., vol. 55, n. 4, pp. 64 6, Aug.. [8] L. K. Yeung, and K. Wu, Genealized Patial Element Equivalent icuit (PEE) Modeling with Radiation Effect, IEEE Tans. Mico. Theoy Tech., vol. 59, no., pp. 7784,. Numbe of ell 5 5 Numbe of ell Fig.. P fo self and mutual cells in loop a and loop b. IV. ONLUSION In this pape, a geneal fomulation fo calculating and decomposing the adiated and tansmitted powe based on the etaded PEE method is poposed. By applying this method to the coupled o adiated objects, the powe adiated and tansmitted can be easily calculated. The method can be conveniently implemented since it is well connected to both cicuit theoy and electomagnetic theoy. Benchmaks have demonstated vey good accuacy. This method is quite useful in pedicting the noise coupling of I inteconnect systems, the electomagnetic intefeence diagnosis, antenna optimizations, etc. AKNOWLEDGMENT This wok was suppoted in pat by Hong Kong RG GRF 76, GRF 75, NSF 6758, US AR8 contacted though UTAR, and Hong Kong UG AoE/P4/8. The authos ae also gateful fo the helpful comments fom 8