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 suitablesource and 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 spacedlines 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 capacitivez =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. The wavespeed v, and characteristic = 20 ZFECm, (8) impedanceZ, are related to I and c as =I&+ZFE+l/j~CmI where Zrn is the 50 Q impedance of Port 2 of the network ++=;, (5) analyzer. Again, IS411 increases with frequency by 20 f-7 dB/decade. zo= “, d C where d is line length, td is the time of flight, and &r is the IV. SIMIJLATEDANDEXPERIMENTALRESULTS relative dielectric constant of the PCB. The values of I and c can be calculated from the measuredvalues of d, Zo and td, Simulations and measurementsof coupling to I/O lines were while Z, and td can be measured with a time-domain made to test the lumped-elementsection modeling for coupled reflectometer (TDR), and d can be obtained from layout microstrip lines. A special lo-layer test board with a FR-4 diagrams or a simple length measurement.Equation (5) also dielectric substratewas used for this study. The layer stackup gives a good estimate of &r for measuredvalues of td and d. from top to bottom was SIGl-GND-SIG2-GND-SIG3-SIG4- This value is the relative dielectric constantfor a measurement GND-SIGS-GND-SIG6, where SIG is a signal conductor with a stripline configuration, or effective relative dielectric plane. The trace cross-sectional geometry is shown for the constantfor a microstrip line. coupled microstrip in Figure 4.

Mutual capacitance and inductance can be determined The dielectric constant of the FR-4 substrate,and the line self experimentally as well. In the low-frequency range where the parameterswere determined experimentally through time of transmission lines are electrically short, either capacitive or flight and impedancemeasurements with a Tektronix 11801B

262 @--8nlils- *--8 mils* p, Cu - 183mm- p-5 mik.+ I 15-01 @oJ i, ,.. 178mm -b 6mm dielectric. .j. cr f:4,33’,‘:, :: .: jj. :+J:~ls 31 substrate 5 mils separation(edge to edge) :: 6 -ij Lo-4 Figure 4. Cross-section geometry of the coupled lines /4- 201mm ~4 studied. 0 3 TDR. Since the 17.8 cm lines used in this investigation were relatively long given the 10 ps rise-time of the source,time-of- Z,, I,= 6 mm flight measurementsgave a reasonably good measurementof z,, zz=178 mm Z,, I,= 6 mm line characteristic impedance and Ed. The measured and o D 0 simulated results for the line self parametersare compared in J%vCIn Table 1. The simulated results were computed with LineSim 3 Pro, a signal integrity and circuit analysis CAD tool that o includes line cross-sectionalanalysis for self parameters.The Z,, Z3=11.5 mm Z,, Z2=178 mm z,, z,= 11.5 mm line thicknesswas included in the LineSim Pro calculation.

Table 1. The per-unit-length parameters for two coupled 0 a Figure 5. Coupled line dimensions and transmission line microstrip lines modeling. Per-unit-length Experimental Simulated parameters Data Result might impact the effective electrical length. Neglecting the self inductance 1 conductor loss may also contribute to the difference in WW 280 263.4 amplitude, particularly at the higher frequencies,which would self capacitance c affect the shorted cases.The discrepancy for the short-circuit (P/m) 135 133 loading cases below 2 MHz may be a result of the finite mutual inductance conductorresistance as well. 1, (nH/m) 70.79 N/A mutual capacitance It is interesting to note for this particular geometry that the cm(pF/m) 33.71 N/A coupling at low frequenciesis approximately the same for the capacitive and inductive cases.Using Equations (7) and (8), Simulated near-end and far-end coupling with different I S211‘,, LItI -=- (9) impedancesat the loads in the driven line and the coupled line 5o*cm * were compared with measurements for the microstrip 1S%,, geometry. The IS211 was measured between the driven and For the values of Z, and c, in Table 1, the ratio is coupled lines using an HP8753C network analyzer. SMA- approximately - 1.5 dB. connectors were used on the board, and the network analyzer calibration did not include the test connectors. The coupled lines were modeled with losslessIt-sections. The segmentsof V. AN EM1 ESTIMATEFOR COUPLING TO I/O LINES the coupled line 12shown in Figure 5 were modeled with N=64 n-sections, while I1 and Z3 are modeled as ideal lossless A cable attachedto an I/O line and going off the board can be transmissionlines. driven against the PCB ground or chassis as a dipole-type antenna.Noise coupled to the I/O line from a clock or high- The measured and modeled results for near-end and far-end speeddata line results in a common-modecurrent on this EM1 coupling with the driven line short and open circuited are antenna,and radiation is emitted. The cable in the present case compared in Figure 6. In general, the agreementis reasonably is driven against the PCB ground that comprises the other good for the frequency range studied to 1 GHz, in particular portion of the dipole-type antenna.At higher order harmonics, for the open-circuit load casesin Figures 6 (a) and (b). There this EM1 antenna has a low impedance that can result in are some discrepanciesfor the short circuit loading cases,in significant common-mode current and an EM1 problem. For particular in the resonant frequencies and amplitudes. The the purpose of determining the common-mode current and discrepancies could result in part from the additional estimatingEMI, the dipole-type antennais consideredas a inductancein the shortedloads due to the connectorsthat

263 /S21/ at Neeor end I=280 Lwm cd35 pl’lm Lm=70.79 nIllm _ 0~33.71 pl’lm

lp= 42 cm 1 10 100 1000 Figure 7. The geometry of the dipole-type EM1 antenna. /S21/ az liar end I= 280 nlllm A test geometrywas constructedusing the 38 cm x 42 cm PCB E= 135 pl’/m Lm=7#.79 nlllm used in the previous coupling experiments. The test Cm=33.7J pl’lm configuration (shown in Figure 8) was designedto place the effective antennaterminals at the edge of the PCB. A 0.085” coaxial semi-rigid cable was layed across the middle of the PCB with an WA-connector on one side. The outer shield was terminatedon the oppositeside of the PCB, and the center 1 10 100 conductorextended 30 cm beyondthe board edge. The semi- Frequency(MHz) rigid cable outer shield was solderedto a PCB ground (Layer 2) throughvias distributedat locationsalong the cableshield.

/S21/ at Near end 6280 nlltm _ c= 135 pIVm SMA 0.085”semi-rigid Lm=?O.79 nllfm connector - Cm=33.71 pl’lm coaxialcable

sblder&nnections to PCBground plane throughvias Figure 8. Test configuration for the dipole-type antenna impedancemeasurement.

The impedancewas measuredwith an HP4291A impedance analyzer.In addition to measurements,the impedanceof the describedEMI antennawas also computedusing the Finite- Difference Time-Domain (FDTD) method. A comparisonof the measuredand simulated results is shown in Figure 9. Although there is a discrepancyin particular in the resonance frequenciesbetween the simulatedand measuredresults, both Figure 6. Experimental and simulated result of coupling results show that the impedanceof the dipole-type antennais between microstrip lines with around 70-90 Q at odd-integer half wavelength resonance (a) ZL=ZFE=03,Zs=Z~~=50L2; frequencies. (b) ZL=ZNE=-, Z,=ZFE=SOQ (c) zL,=zm=o, z,=zm=50 i-2; The common-modecurrent on a cable and EM1 can be (d) ZL=ZNE=O,Z,=Z,=SO $2. estimatedfor coupling from a high-speeddigital signal to an I/O traceby modelingthe coupling betweenthe digital and I/O load on the coupled I/O line. The geometry of the EMI lines using the lumped-elementsections, and using the antenna antennais shown in Figure 7, with the sourcerepresentation impedanceto terminatethe I/O line at the connector.A worst- being schematiconly. A worst-caseestimate of the antenna caseestimate is to assumethe cable is driven as a resonanthalf input impedancewas neededfor EM1 calculations. wavelengthantenna and ignorethe signalload. The common-

264 Further work is necessaryin improving and experimentally corroboratingthe estimate.

VI. CONCLUSION

A lumped-elementsection model for coupling betweenPCB traceshas been demonstrated experimentally for two extremes of loading conditions.This model was used togetherwith an antennamodel of a cable driven againsta PCB ground plane for a worst-caseEM1 estimate.The resultsindicated that even very shortparallel segmentsof a high-speeddigital line tightly 2 o- coupledto an I/O line can result in significant common-mode 8s -200 - currentand EMI. x -400 -

i! -600 - REFERENCES -600 ’ 1’ ’ ’ 1 1000 Frequency (MHz) [l] C. R. Paul, “Decoupling the multiconductor transmission lines equations,” IEEE Trans. on Microwave Theory and Figure 9. Experimental and simulated results of the input Tech., vol. 44, no. 8, pp. 1429- 1440,August 1996. impedancefor the antenna in Figure 8. [2] J. S. Roychowdhury and. D. 0. Perderson, “Efficient mode current and radiation due to the coupling betweentwo transient simulation of lossy interconnect,”28th ACM/IEEE microstrip lines were estimated for the previously studied Design Automation Conference, pp. 740-745, 1991. geometryshown in Figure 5. The line was driven with a 5 V, 100 MHz, 1 ns rise-time trapezoidal signal with 50% duty- [3] T. Dhaeneand D. D. Zutter, “Selectionof lumpedelement cycle. The sourceimpedance was 50 Q. The I/O line (far-end) modelsfor coupledlossy transmissionlines, ” IEEE Trans. on was terminatedin 70 &2for a worst-caseEM1 estimateof the Computer-Aided Design, vol. 11, no. 7, pp. 805-815, July antennainput impedance.The coupledlength of the two lines 1992. was 3 cm, and both the load of the driven line and near-end load of the coupledline were terminatedin 50 Q. The radiated [4] C. R. Paul, Introduction to Electromagnetic Compatibility, field at 3 m (FCC ClassB) was estimatedsimply with the field New York: JohnWiley & Sons,Inc., 1992. maximumfor a half-wavelengthdipole as [4] 60 iICMi [5] C. R. Paul, Analysis of Multiconductor Transmission 161max=-. (10) r Lines, New York: JohnWiley & Sons,Inc., 1994. While this is a far-field approximation,it is a reasonableEM1 approximationat 100 MHz, since the field is dominatedby [6] K. C. Guptaet. al., Computer-Aided Design of Microwave this term, even for kr-1 [8]. The estimatedcommon-mode Circuits, Dedham,MA: Artech House,1981. currentand the electric field at 3m are (68.3@, 63 dBpV/m), (63.6 PA, 62 dBpV/m), and (12.2 pA, 48 dBpV/m) at 100, [7] K. C. Guptaet. al., Microstrip Lines and Slotlines, Boston, 500 and 1100MHz, respectively.Although the coupledlength MA: Artech House,1996. is only 3 cm, the calculatedradiation from the driven cable [8] C.A. Balanis,Antenna Theory: Analysis and Design, New was as high as 63 dBl.tV/m at 100MHz. The calculatedworst- York: JohnWiley, 1997. caseestimate exceeds FCC Class B limits by 20 dB at 100 MHz. While the 100 MHz trapezoidalsignal is 5 V, andthe 8 mil. wide traces are separatedby only 5 mils., the estimate appearssevere in the absenceof supporting radiated EM1 measurements.Among the shortcomingsof the model, which may contributeto an over-estimateof the radiation,is that the signalreturn path, which is effectively in parallel with the EM1 antenna,is not modeled.Also, a 70 Szinput impedanceof the antennabeing driven by the I/O line was assumed.While this is a worst-casescenario, the likelihood of it happeningat every harmonic is not high. In addition, no filtering was added.

265