Lumped-element Sections for Modeling Coupling Between High-Speed Digital and I/O Lines W. Cui, H. Shi, X. Luo, F. Sha*, J.L. Drewniak, T.P. Van Doren and T. Anderson** ElectromagneticCompatibility Laboratory University of Missouri-Rolla Rolla, MCI 65401 * Northern Jiao Tong University EMC ResearchSection Beijing 100044,P.R.China * * HP-EEsof Division Hewlett-PackardCo. SantaRosa, CA 95403 Abstract: Lumped-elementsections are used for modeling designstage to estimateEM1 and minimize the noise coupling coupling betweenhigh-speed digital and I/O lines on printed to I/O lines on the PCB. As digital designs become more circuit boards (PCBs) in this paper. Radiatedelectromagnetic dense, flexibility in trace routing is reduced. Adherence to interference(EMI) is investigatedwhen the I/O line going off simple design maxims for avoiding adjacent segmentsof an the board is driven as an unintentional, but effective antenna. I/O line and a high-speeddigital line becomesmore difficult. Simulated results are compared with measurementsfor A meansfor estimatingEM1 at the design stageis desirableto coupled lines. A suitable number of lumped-elementsections maintainrouting flexibility while minimizing EM1 risk. for modeling is chosen based on the line length and the highestfrequency of interest. The three essentialcomponents for estimating EM1 resulting from coupling to I/O lines are suitable sourceand load models, a coupled transmission-line model, and an EM1 antenna I. INTR~DUC~~N model. Of particular interest at this stage are models for the coupled transmission lines, and the EM1 antenna. Two As the speed of digital designs continues to increase, approaches have been previously pursued for modeling unintentionalradiation from cablesattached to PCBs becomes coupled transmission-lines.One technique is to decouple the problematic.For clock speedsless than 50 MHz, a typical 1 m lines in the frequency domain by modal decomposition [l]. cable attachedto a PCB is an electrically short antennafor all Transientanalysis of a lossy line has also beenreported [2]. A but very high harmonics. Since the magnitude of the input secondmethod is to divide the coupled line into a number of impedanceof an electrically short antennaexceeds 500 0 and lumped-elementsections [3]. Although the lumped-element is almost entirely reactive, an electrically short cable driven section approach is an approximation to the distributed againsta PCB or conductingenclosure is not easily driven by a transmissionline with someartifacts, this modeling is easierto noise source of moderate impedance. However, as clock implement, and compatible with general-purpose circuit frequencies exceed several hundred megahertz, nearly all simulation tools such as SPICE. Moreover, the frequency- cables attachedto a PCB will be of resonantdimensions for dependentline loss can be easily incorporatedinto a lumped- low-order harmonics. Resonant dipole-type EM1 antennas element model,, and IBIS device models, terminations, and typically have an input impedanceon the order of 100 !& and filtering can also be easily integrated. can be effectively driven by low-impedancenoise sourcesto result in an EM1 problem. Coupling between a high-speed An approach for modeling the coupling using cascaded digital line and an adjacent I/O line can provide an lumped-elementsections is presentedherein together with a unintentional source to drive this antenna. Even a few simple antenna model for determining a worst-case EM1 centimeters of common length for two closely spaced lines estimate. This modeling method can be used to provide an can cause strong coupling and a potential EM1 problem. estimate of EM1 due to coupling to I/O lines in high-speed Quantifying and modeling the coupling between two designs. transmission lines or multiconductor transmission lines is essentialto analyze and evaluatethis class of EM1 problems. Simple and reliable modeling techniquesare required at the 0-7803-4140-6/97/$10.00 260 II. LUMPED-ELEMENTMODELING OF COUPLED example, the criteria based on characteristic impedance TRANSMISSIONLINES requiresa numberof sectionsN such that N 114.14; , (2) A lumped-element circuit model is typically used to approximatea transmission line when the line is electrically where d is the length of the modeled line, and h is the short. As the frequency becomes higher, a lumped-element wavelengthof the highest frequency of interest, to achieve an model can still provide adequateresults for coupling if a error of 2.5% or less. The published error criteria for single sufficient number of lumped sections are employed. A line sectionscan also be applied to coupled lines using modal commonly used broad maxim is five lumped-elementsections decompositionand applying the criteria to eachmode. per wavelength at the highest frequency of interest [3]. The lumped-elementsections can be in the form of ?r, T, F or Useful insight can be gainedby defining a simple error based backwardF models [3][4]. The parametersof eachsection are on IS211between the driven line, and the coupled I/O line the per-unit-length quantities times the section length. A going off the boardas coupledrc-section, shown in Figure 1, with elementparameters I IS21NI - IS21tx1i”el I &= x 100% ) R’, G’, L’, C’, L,’ and C,’ was usedin this study. 1~2 1 txline I (3) tx’inel is from the solution for coupling betweentwo transmissionlines using the transmission-line equations and modal decomposition.A disadvantageof this error definition a function of the terminationson both the driven lines. The error defined in Equation (3) is plotted in Figure 2 for the case of two coupled losslesstransmission lines with the driven line and far-end of the coupled line terminated in open circuits. Although the error increases abruptly at certain frequencies,these frequencies correspond to resonancesin the coupled lines at which the coupling is a minimum. For example,the first minimum in IS211 in Figure 6(a) occurs at approximately180 MHz (3LFn4= 80 cm) and the ratio of the coupling length d=17.8 cm to the wavelengthis Figure l.< coupled lumped-element z-siction for approximately0.22. modeling coupled transmission lines. The valuesof elementsfor the i’ sectionare 80 R’ =$ (l-a), .+=b$ (1-b), Li & (l-c), ci =!$ U-4, N Lm’ =Imd (l-e), Cm’=y U-E), N wherer, g, 1and c are the self per-unit-lengthparameters of the transmission line, Z, and c, are the per-unit-lengthmutual parameters, d is the line length, and N is the total numberof sectionsused for modeling the line. 10 The choice of the number of cascaded lumped-element sections is a key factor in the accuracy of this approachfor 0.5 1.0 modeling transmission lines. In general, each section of the Line length/wavelength (in FR-4) lumped-elementmodel must be electrically short at the highest frequency of interest. However, in order to achieve higher Figure 2. Relative error on IS211for N= 8,16,32 and 64. accuracy, other criteria for the number of sectionshave been suggested[3]. Previously publishederror criteria are basedon The error shown in Figure 2 convergesto its final value, i.e., lumped-element sections for modeling a single line, and no further changes with additional sections, with include errors in the characteristic impedance, natural approximately64 sectionsin the frequency range shown (O< resonancefrequencies, and [ABCD] matrix coefficients. For d/J, < 1.25). The convergenceis similar for other loading conditions of the driven and coupled lines. An approximate 261 number of sections per normalized length of coupled inductive coupling dominatesfor an open or short termination, transmissionlines is then respectively,of the driven line [4]. In either case,the coupling is proportional to the mutual parameters, and the mutual N>X$. (4) capacitance and inductance can be determined from S21 Although this is a factor of ten greater than typically suggested measurements.An equivalent circuit for this measurementis for single lines [3], and three times that of Equation (2), good shown in Figure 3. comparison of the simulated and experimental results (shown in the next section) requires a finer discretization than five sectionsper wavelength over the coupled segments. III. DETERMINATIONOF LINE PARAMETERS There are several approaches for determining the per-unit- length parametersof a transmissionline. For certain conductor configurations in a homogeneousmedium, the per-unit-length parameters can be calculated in closed-form from cross- Figure 3. Two coupled transmission lines. sectional dimensions [S]. However, for microstrip lines, striplines and other PCB traces, in which closed-form solutions If the load of the driven line is shorted (ZL’O), mutual are not available, empirical expressionsare often used [6][7]. inductive coupling is dominant at low frequencies.If the near- For more complex configurations characteristic of PCB end load of the coupled line is also shorted (Zm=O), then geometries,such as asymmetric microstrip or stripline where , s41 ,,5!- IVFEI _ I.MLmIlI- 2WLm , (7) the coupled lines do not lie on the same layer, the per-unit- IVJ IV,/21 II1 zsv2 zs length parameters can be determined by numerical cross- section analysis commonly employed in signal integrity tools. where Z, is the 50 SL source impedance of the network Here, an experimentalmethod is used to determinethe self and analyzer.From Equation (7), IS411 is proportional to mutual mutual capacitanceand inductance of a transmissionline. The inductance, and increaseswith frequency by 20 dB/decade. self capacitance and inductance are also calculated with a Likewise, the mutual capacitancecan be determined with S41 cross-sectionanalysis tool LineSim Pro for comparison. measurementsby open circuiting the load of the driven line and the near-endload of the coupled line. In this case, mutual The self capacitanceand inductanceper-unit-length are related zcapacitive =z = coupling is dominant at low frequencies. For to the characteristicimpedance of the transmissionline, as well L NE OoT as the speedof the signal traveling down the line. The per-unit- I s41 I= ---Iv;1 _ IVFEI length parameters can be determined by measuring the Iv:1 IVs/21 characteristicimpedance, and the time of flight (or delay time) 21ZFEI of a step signal.