TECHNICAL REPORT: CVEL-13-053 Maximum Radiated Emission Calculato: Powe Bus EMI Algoithm Chentian Zhu and D. Todd Hubing Clemson Univesity Octobe 12, 2013
Abstact The Maximum Radiated Electomagnetic Emissions Calculato (MREMC) is a softwae tool that allows the use to calculate the maximum possible adiated emissions that could occu due to specific souce geometies on a pinted cicuit boad. This epot descibes the Powe Bus EMI algoithm, which detemines the maximum possible adiated emissions that could occu fom a ectangula powe bus stuctue. The methods used, calculations made, and implementation details ae descibed. 1. Intoduction High fequency noise on the powe bus can esult in significant adiated emissions. The Powe Bus EMI calculato was developed to calculate the maximum possible adiated emissions fom pinted cicuit boad powe plane stuctues. The calculato utilizes simple closed-fom expessions developed by Leone [1], Shim [2] and Zeng [3]. Fig. 1. Powe plane stuctue. The powe bus stuctue is illustated in Fig. 1. The powe planes have a length, L, a width, W, and a conductivity,. The dielectic laye has a thickness, t, a elative dielectic constant,, and a loss tangent, tan. The noise souce can be expessed as the maximum cuent dawn fom the planes by the active devices, I i, o the maximum voltage fluctuation at the boad edge, V max. Fo the cuent souce, paametes of the components on the boad ae needed to estimate the voltage fluctuations that will appea on the planes. These paametes include the numbe of active and passive component connections to the powe bus, N c, the equivalent seies esistance of these components, R c, and the connection inductance of these components, L c [2]. The calculato calculates the maximum adiated electic field at a distance of 3 metes fom the boad and plots the esults in db V / m fom a specified minimum fequency, f 1, to a specified maximum fequency, f 2, as shown in Fig. 2. Page 2
2. Desciption of Algoithm Fig. 2. Example of output fom Powe Bus EMI calculato. The calculato uses one of two sepaate algoithms depending on the type of noise souce specified. The Components on Boad algoithm detemines the maximum adiated emissions based on the maximum noise cuent dawn fom the powe planes and infomation about the components on the boad. The Maximum Voltage at Boad Edge algoithm detemines the maximum adiated emissions based the maximum voltage fluctuation at the boad edge. 2.1 Components on Boad Algoithm The deivation of the closed-fom expession used by the algoithm is well documented in [2]. Fo elatively high-q esonances, the maximum adiated field fom a populated ectangula boad can be expessed as, 120I t N R E tan i s c c 2 2 2 min( W, L) t C0 Rc Lc whee is the distance fom the boad, s is the skin depth of the plane conductos, and C 0 is the capacitance between the powe planes. is set to thee metes in the calculato, s and C 0 can be found by, 1 (1) s 2 (2) 0 W L C0 0. (3) t Page 3
The calculato etuns an eo if the input value of the boad width, W, is geate than the input value fo the boad length, L. As a esult, the tem, min (W, L), in (1) is equivalent to W. 2.2 Maximum Voltage at Boad Edge Algoithm The noise cuent dawn fom the powe planes causes voltage fluctuations. Fo boads that have aleady been built, it is usually easie and moe accuate to measue the powe bus voltage instead of estimating it based on the cuent dawn by the active components. The Maximum Voltage at Boad Edge algoithm is based on the closed-fom equation in [3], which calculates the maximum adiated emissions fom a ectangula powe bus with a given maximum voltage along the boad edge. The maximum adiated electic field stength is expessed as, f 0VmaxW f f f V L E f f f 2 2 f 0Vmax L W f f 0 max max t1 c2 t1 c2 (4) whee f t1 is a tansition fequency that occus midway between adjacent esonances just below the cutoff fequency of the TM 01 mode and f c2 is the cutoff fequency of the TM 11 mode. They can be found by [3], f t1 1 1 1 1 2 2 W 0 2 0 m L (5) f c2 2 0 2 2 1 1 1 L W. (6) The tem 1 2 0 m L in (5) is the cutoff fequency of the TM m0 mode that occus at the mode fequency closest to, but lowe than, the TM 01 mode. 2.3 Assumptions Made in this Deivation The closed-fom equations in both algoithms ae developed based on a esonant cavity model that assumes the spacing between the two planes is electically small and much smalle than the length and width of the boad. Also, the shape of the planes must be ectangula (o nealy ectangula). The Components on Boad algoithm makes additional assumptions in ode to estimate the voltage fluctuations caused by the active components on the boad. This algoithm assumes that the active and passive components ae distibuted faily unifomly ove the boad. It also assumes that a wost-case equivalent seies esistance and connection inductance can be defined that adequately epesents the majoity of the boad components. Fo boads with lage numbes of decoupling capacitos, the ESR and connection inductance of these capacitos should be used. The decoupling capacito capacitances ae not elevant, since the inductance will typically dominate at boad esonance fequencies. Page 4
3. Conclusion This calculato detemines the maximum possible adiated emissions fom a ectangula powe bus stuctue based on equations deived and validated in [1], [2] and [3]. It can be applied to powe buses consisting of two nealy ectangula planes with a small spacing elative to the length and width of the planes. It calculates the maximum adiated fields fo a boad in fee space and does not model neafield inteactions with cables o enclosues that might also contibute to a adiated emissions poblem. Refeences [1] M. Leone, The adiation of a ectangula powe-bus stuctue at multiple cavity-mode esonances, IEEE Tans. Electomagn. Compat., vol. 45, no. 3, pp. 486 492, Aug. 2003. [2] H. Shim, Y. Fu, and T. Hubing, Radiated emissions fom populated pinted cicuit boads due to powe bus noise, 2004 Intenational Symposium on Electomagnetic Compatibility (IEEE Cat. No.04CH37559), 2004, vol. 2, pp. 396 400. [3] H. Zeng, H. Ke, G. Loenzo Giuliattini Bubui, and T. Hubing, Detemining the maximum allowable powe bus voltage to ensue compliance with a given adiated emissions specification, IEEE Tans. Electomagn. Compat., vol. 51, no. 3, pp. 868 872, Aug. 2009. Page 5
Appendix (Java code) Components on Boad Algoithm in Suboutine calcem() va c0=eps0*eps*l*w/t; va qd=losstan; va ymin,ymax; fo (i=0;i<maxpoints;i++){ va tans=1/math.sqt(pi*mu0*x[i]*1e6*cond); va qc=tans/t; va qcomp=nc*c/(2*pi*x[i]*1e6*c0*(pasefloat(c*c)+pasefloat(2*pi*x[i]*1e6*2*pi*x[i]*1e6*lc*lc))); va q=pasefloat(qd)+pasefloat(qc)+pasefloat(qcomp); y[i]=signumbe(20*math.log(120*ic/eps/math.min(l,w)*t//q*1e6)*math.log10e); if (i==0){ ymin=y[0]; ymax=y[0]; else{ if (y[i]<ymin){ ymin=y[i]; pos[0]=i; if (y[i]>ymax){ ymax=y[i]; pos[1]=i; Maximum Voltage at Boad Edge Algoithm va m=math.floo(l/w); va ft1=math.ound(1/4/math.sqt(mu0*eps*eps0)*(1/w+m/l)); va fc2=math.ound(1/2/math.sqt(mu0*eps*eps0)*math.sqt((1/l)*(1/l)+(1/w)*(1/w))); fo (i=0;i<maxpoints;i++){ if (x[i]*1e6<ft1) y[i]=x[i]*1e6*math.sqt(mu0*eps0)*vmax*w/; else{ if (x[i]*1e6<fc2) y[i]=x[i]*1e6*math.sqt(mu0*eps0)*vmax*l/; else y[i]=fc2*math.sqt(mu0*eps0)*vmax*math.sqt(l*l+w*w)/; y[i]=signumbe(20*math.log(y[i]*1e6)*math.log10e); ymin=y[0]; ymax=y[maxpoints-1]; pos[0]=0; pos[1]=maxpoints-1; Page 6