IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 421
Differential Extrapolation Method for SeparatingDielectric and Rough Conductor Losses
in Printed Circuit BoardsAmendra Koul, Student Member, IEEE, Marina Y. Koledintseva, Senior Member, IEEE,
Scott Hinaga, and James L. Drewniak, Fellow, IEEE
Abstract—Copper foil in printed circuit board (PCB) trans-mission lines/interconnects is roughened to promote adhesion todielectric substrates. It is important to characterize PCB substratedielectrics and correctly separate dielectric and conductor losses,especially as data rates in high-speed digital designs increase.Herein, a differential method is proposed for separating conductorand dielectric losses in PCBs with rough conductors. Thisapproach requires at least three transmission lines with identical,or at least as close as technologically possible, basic geometryparameters of signal trace, distance-to-ground planes, anddielectric properties, while the average peak-to-valley amplitudeof surface roughness of the conductor would be different. Thepeak-to-valley amplitude of conductor roughness is determinedfrom scanning electron microscopy images.
Index Terms—Conductor surface roughness, dielectric constant(Dk), dissipation factor (Df), loss tangent, printed circuit board(PCB), S-parameters.
I. INTRODUCTION
VALUES of dielectric constant Dk, or real part of relativepermittivity, and dissipation factor Df, or loss tangent,
over a wide frequency range of various printed circuit board(PCB) dielectric substrate materials are important informationfor high-speed digital design engineers and researchers [1]. Inthe majority of practical cases, designers are provided with con-stant values of Dk and Df over very wide frequency bands forPCB dielectrics at their disposal. However, the loss tangent formany of the currently used fiber-glass epoxy-resin-type dielec-tric composites, employed in PCBs, cannot be considered asindependent of frequency over the wide frequency range fromtens of megahertz to 20 GHz or higher, or for data rates above10 Gb/s [1]–[5]. From the signal integrity (SI) point of view, di-electric dispersion, and frequency-dependent loss are reflectedin the closing of an eye diagram as wideband signals containinghigh-frequency components propagate in longer interconnects,
Manuscript received March 17, 2010; revised August 28, 2010; acceptedSeptember 22, 2010. Date of publication March 24, 2011; date of current ver-sion April 18, 2012.
M. Y. Koledintseva and J. Drewniak are with the EMC Laboratory, Elec-trical and Computer Engineering Department, Missouri University of Scienceand Technology (Missouri S&T), Rolla, MO 65401 USA (e-mail: [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEMC.2010.2087341
such as the copper traces of a PCB. Therefore, in order to chooseappropriate PCB materials and improve functional properties oftheir designs at the stage of research and development, engineersneed accurate data on PCB dielectric and conductor parameters.There are known different techniques for PCB dielectric sub-strate characterization over a frequency range of interest. Thesetechniques can be classified as resonator (cavity) methods, “free-space” techniques, and transmission-line methods [2], [3]. Cav-ity methods are comparatively narrowband, and they are basedon the variation in the quality factor of a resonator and resonancefrequency shift when a cavity is loaded with a sample of the ma-terial under test. For wideband material characterization, eithera set of specially designed cavities of different center frequen-cies, or a tunable cavity may be needed. “Free-space” techniquesare based on reflection and transmission of plane waves, inci-dent upon a large, as compared to the longest wavelength, layerof a dielectric under test. Traveling-wave techniques for wide-band material characterization can be realized using TEM cells,coaxial lines, or waveguides with samples under test completelyfilling the cross section of a test line [2], [3]. One difficulty withthis kind of technique is that the sample under test may be inho-mogeneous and anisotropic, so measurement data will dependon how the electric field is applied. Thus, measurements mightbe conducted with the E-field in-plane with the sample, whereasin practical applications, the E-field is in an out-of-plane direc-tion, and the dielectric properties for these two directions maydiffer significantly.
Measurements “in situ,” i.e., just on the PCB transmissionline of interest, are preferable. Then, the measured data foranisotropic substrates is in the same direction as used in designsin practice. For this reason, wideband TEM (or quasi-TEM)traveling-wave S-parameter measurements on PCB striplinesor microstrip lines are attractive. S-parameters of a section of atransmission line may be directly measured in the frequency do-main using vector network analyzers (VNAs), or measurementscan be done using time-domain reflectometers (TDR), and time-domain results then converted to frequency domain [4]. Then,the effective dielectric properties of the substrate under test areextracted from S-parameters using corresponding analytical ornumerical models of the line. Another traveling-wave methodis propagation of a short pulse on a line [5].
The PCB material characterization technique used for theexperimental studies in this paper has been detailed earlierin [6]–[8]. This is a wideband traveling-wave method employinga single-ended stripline structure, comprised of laminate layers
422 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
Fig. 1. Flowchart of the procedure for extracting effective dielectric parameters from S-parameter measurements on a PCB test vehicle [7], [8].
of the PCB. Test vehicles have independent auxiliary “thru-reflect-line” (TRL) calibration traces on each board to de-embedport effects [8]. S-parameters are measured using a VNA orTDR, and then the complex propagation constant γ = α + jβis calculated. The extraction procedure for dielectric parametersDk and Df over a frequency range of interest is schematicallyshown in Fig. 1. According to this extraction procedure, thereal ε′ and the imaginary ε′′ parts of permittivity are interre-lated through causality relations, and they depend on both phaseconstant β and loss constant α.
The procedure as in Fig. 1 takes into account asymmetryof the two-port network, and imposes Debye-like behavior ofthe extracted real and imaginary parts of permittivity [7] atleast over the frequency range of interest, 10 MHz–20 GHz.Over the microwave region, fiber-glass-filled epoxy resins (e.g.FR-4 type) are assumed to behave as the initial parts of theDebye-like frequency dependencies typical for dielectrics witha pure dipole polarization loss mechanism. The nature of thepermittivity dependence for PCB dielectrics has not been wellstudied to date, and dielectric parameters of different PCBlaminates vary in a wide range depending on constituents, mor-phology, in which direction parameters are measured, and onhow the trace crosses the fiber-glass weave. As a result, theactual frequency behavior of fiber-glass-filled epoxy resin com-posites may be much more complex than a pure Debye de-pendence [9]. Complex permittivity of such materials is often
modeled as a sum of Debye-like terms [10], or as a widebandDebye dependence, also called logarithmic Djordjevic–Sarkarmodel [11].
The total attenuation constant for any transmission line isαT = αC + αD , where αC is the conductor loss, and αD isthe dielectric loss. For accurate extraction of dielectric parame-ters, processing of measurement results obtained by any of thetraveling-wave methods requires adequate separation of con-ductor and dielectric losses. If a conductor is perfectly smooth,this is comparatively straightforward, since αC behaves as
√ω,
a square root of frequency, according to the classical skin-depthmodel [12]. Koul et al. [7] proposed to curve-fit the total dielec-tric loss αT by three terms—proportional to
√ω, ω, and ω2 . It
was assumed that the conductor loss behaves as√
ω term, whilethe dielectric loss behaves as a sum of ω and ω2 terms. Thismethod has been extensively used to extract dielectric proper-ties of PCB laminates, but the roughness of conductors was nottaken into account. So far, this curve-fitting technique, whichcan be called the “smooth
√ω-fit,” is the only way to sepa-
rate conductor loss from dielectric loss, if no information of thestripline geometry and type of the foil is available.
As operating frequencies or data rates increase, the skin depthin copper becomes comparable or even less than levels of rough-ness of copper foils in PCBs. Thus, in a copper conductor,the skin depth at 5 GHz is approximately 1 μm, while rough-ness on copper foils currently used in PCBs is on the order of
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 423
1–10 μm [6]. Then, the frequency dependence of conductor lossfor a rough conductor deviates from the classical proportionalityto
√ω [13], [14], and will contain higher-order frequency com-
ponents in a power-series representation. Since a PCB dielectricsubstrate is also dispersive, and its frequency response may bequite complex, separation of dielectric and conductor loss is anessential problem. It is important to know, which part of lossis caused by the dielectric, and which by the conductor. Thisknowledge is needed not only for using correct data in the de-sign cycle, but also in choosing appropriate laminate dielectricsand foils from a cost-to-performance perspective when gettingthem from PCB manufacturers and vendors.
Surface roughness on transmission-line conductors can beeither calculated through an adequate analytical or numericalmethod, or retrieved experimentally. Then, the dielectric losscan be obtained by subtraction of evaluated conductor loss fromthe total measured loss, even if the dielectric is not followingpure Debye dependence, or its frequency response is unknown.
Currently existing analytical or numerical models are inade-quate for separating dielectric loss from conductor loss in thecase of a rough conductor. The simplest empirically based mod-els for signal attenuation on a transmission line with rough con-ductor surfaces are the Hammerstad–Bekkadal [15] and Groissmodels [16]. However, both models are inapplicable for signifi-cantly rough PCB conductors with r.m.s. amplitude of conductorroughness exceeding approximately 1 μm, since correspondingroughness correction factors asymptotically approach a constantvalue at roughness amplitudes higher than approximately 1 μm.Another problem with these models is that they address onlyr.m.s. roughness amplitude, without consideration of distancesbetween neighboring peaks or valleys on roughness profiles.However, the information on spatial distribution of peaks andvalleys in the plane of the foil is important at frequencies, whereskin depth is comparable to or less than the roughness level.
Another group of surface-roughness models is based on asmall perturbation theory (SPT). In Sanderson’s SPT formula-tion [17], the roughness profile is considered as 1-D periodicroughness function along the direction of propagation. To cal-culate attenuation of waves traveling along a periodic corru-gated surface of a metal of finite conductivity, Sanderson ap-plied concepts of surface impedance and surface displacement.Sundstroem specified this approach for a number of particularperiodic function profiles, including a saw-tooth function [18],which was applied to extract dielectric parameters [6].
Modeling of a conductor roughness profile as a 1-D quasi-periodic roughness function is an approximation. Actually, thesurface-roughness profile in a typical copper foil is a 2-D randomfunction. The papers [19], [20] also use SPT and describe sur-face roughness in terms of 2-D power spectral densities (PSD)or, equivalently, in terms of correlation functions of random con-ductor surface profiles. However, accurate knowledge of the sta-tistical distribution function, spectral power density, and spatialperiodicity range for roughness are needed and can be obtainedonly through detailed surface-roughness images, for example,using profilometers and suitable image processing.
The SPT approach utilizing the 2-D PSD data for randomroughness profiles, obtained using atomic force microscopy,
is presented in [19] and [20]. This approach was applied tocomparatively low-level (submicron) roughness profiles on in-terconnect surfaces in microelectronic packaging, and hence theresults agree well with the Hammerstad–Bekkadal formula [15].The advantage of using PSD data is that it does not solely de-pend on the average roughness height (r.m.s.), but indirectlytakes into account spatial distribution of roughness on the sur-face; so in principle, can be applied to substantially higher levelsof roughness than [15] or [16] allow.
There are several other papers that mathematically analyzeconductor surface roughness. The numerical simulation method-ology called “scale wave modeling” (SWM) is considered in[21] and [22]. The spectral stochastic collocation to constructa statistical model of roughness is presented in [23]. However,these papers, as well as [24], provide analytical or numerical re-sults of potential effective conductivity degradation, without anycomparison with measurement results on physical samples. Amethod for modeling conductor loss on a rough surface throughscattering on multiple hemispheres was proposed in [25]. Thismethod, denoted as hemispherical boss modeling (HBM), mod-els surface irregularities as the size-controlled hemisphericalbosses distributed regularly or randomly on the plane. BothHBM and SWM methods require detailed microscopic analy-sis for characterization of surface-roughness profiles. A tech-nique based on a numerical finite-element method with Trefftzelements and local impedance adjustment is described in [26].However, this technique is difficult to implement due to the com-plexity of solving integral equations in this method, and needvery specialized numerical codes. Furthermore, knowledge ofsurface-roughness rms amplitude and period is needed for thistechnique as well.
The aforementioned analytical and numerical models are pro-posed to characterize rough conductor loss in the cases, whereempirical formulas [15], [16], or Sanderson’s 1-D SPT modelwith periodic roughness [17] are no longer applicable. However,all currently existing theories are either insufficient for substan-tially rough conductors surfaces as in present-day PCBs, or aretoo complex and costly for implementation, demanding high lev-els of computational resources for numerical analysis, roughnessevaluation, and image processing. All known models requireknowing a priori accurate information on the transmission-linegeometry and surface-roughness profiles. This data is typicallyobtained through destructive microscopic analysis of rough sur-faces. In practice, information on the surface-roughness profileon each conductor surface may be unavailable to designers, andany analytical or numerical model will be unreliable withoutthis data. Moreover, all existing models deal with translation-ally invariant cross-sectional parameters of transmission lines,while in practice, the geometry of the line along the directionof propagation might vary randomly within some limits. Fill-ing factor and position of fiber-glass bundles with respect tothe line conductors are also statistical rather than deterministicparameters, and none of the known theories takes this into ac-count. Indeed, any PCB laminate dielectric adjacent to a roughconductor is an inhomogeneous and multilayered compositemedia, and this yields additional complexity of the problem[27].
424 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
These current models, even the most advanced and sophisti-cated, are sensitive to geometrical and surface-roughness param-eters, and inaccurate input data may result in incorrect evaluationof conductor loss, and, hence, incorrect extracted Df of thedielectric. As a result, a conductor model applied to a set of testboards with identical geometries and dielectrics, but differentconductor surface-roughness profiles, will result in ambiguityof the extracted Df curve as a function of frequency, whilethis curve should be unique in characterizing the very samedielectric.
Herein, a straight-forward experiment-based differentialmethod to separate dielectric and conductor losses is pro-posed. Geometrically identical (within the limits of PCBmanufacturing capability) transmission lines on identicaldielectric substrates are needed, while the surface roughnesson the conductors must be different. This method still requiresdestructive analysis of at least one sample of a test line witheach type of conductor foil. A review of the roughness profilecharacterization on the test samples is given in Section II.The principle of the differential extrapolation method and itsapplication to extract dielectric properties on the multiple PCBtest vehicles with identical dielectric, but different copper foilsis described in Section III. This method for identical dielectricsubstrates on all the three test board groups with differingconductor surface roughness has a single Df curve.
II. ROUGHNESS PROFILE CHARACTERIZATION
An approach to separate conductor loss from dielectric loss,either analytical, numerical, or experimental, needs adequatedata on the conductor roughness profile. Herein, basic parame-ters to characterize roughness profiles and the main approachesof getting this information are described.
An accurate way of characterizing conductor surface-roughness topology is to apply a destructive microscopic anal-ysis. Samples of the rough conductor surface, the same as inthe actual test transmission line, can be prepared specificallyfor an instrument that is used for roughness characterization.Instruments for getting images of foil topology include me-chanical (stylus) profilometers [28], optical profilometers [29],scanning electron microscopy (SEM) [30], or high-resolutionatomic force scanning probe microscopy [31].
Typically, the output roughness parameters of a profilometerare Ra , Rq , Rz , and Rt [29], [32]. Ra is the arithmetic mean ofdeparture of roughness from the mean level. Rq is the rms valuecorresponding to Ra . Rz is defined as the mean peak-to-valleyamplitude. The parameter Rt is the maximum peak-to-valleyamplitude over the entire profile. An example of an opticalprofilometer image for one of the copper foils used in this studyis shown in Fig. 2.
According to the IPC test method [33], foil profiles can becharacterized using an Rz parameter, which is calculated byadding the averaged N highest peaks and N deepest valleys on asample (typically N = 5). Rz numbers for PCB foils are substan-tially greater than r.m.s. Rq values, and may reach 20 μm in somecases of standard foils. Typically, peak-to-valley amplitudesmeasured with mechanical profilometers are approximately two
Fig. 2. Roughness image obtained with an optical profilometer (manufac-turer’s data).
times less than those measured with an optical method. Mechan-ical profilometers have lower resolution than their optical coun-terparts, since the tip of a stylus is not able to reach all the depres-sions on the metal surface as the light beam does, and is, there-fore, “blind” to concave features whose size is smaller than thediameter of the tip of the profilometer. Though peak-to-valleyvalues in the mechanical case are underestimated, many PCBlaminate material manufacturers provide Rz values obtained us-ing mechanical profilometry, which they have at their disposal.
Different conductor loss models or extraction procedures maydeal with different roughness parameters. This could be an r.m.s.roughness parameter Rq , as in [15]–[18], or an average peak-to-valley amplitude (Rz), as in the present study, or 1- or 2-D PSDdata and the correlation length, as in [18]–[20], or other deter-ministic [25] or statistical distribution data for a rough conductorsurface, e.g., [21]–[23]. The problem is that even when measur-ing the same parameter, e.g., average peak-to-valley amplitude,different techniques and instruments may result in significantdiscrepancies in the output data due to different resolution, as ismentioned earlier.
There are some other problems with profilometry from thepoint of view of its use in conductor loss models. All fourroughness parameters that a profilometer provides (Ra , Rq , Rz ,and Rt) are amplitude parameters. However, information on thedistances between peaks and/or valleys, or the average spatialperiod in the plane of the conductor surface is necessary forcharacterizing and modeling the surface-roughness loss in aPCB signal trace. It is known that the calculated conductor lossin some models, for example, Sanderson’s SPT, is very sensitiveto the value of the chosen period of the roughness function [18],or corresponding correlation length [19], [20]. An example isshown in Appendix A.
Also, it is known that peeling a foil off a PCB laminate cancause mechanical deformation of the roughness profile, and theprofilometry data may be not accurate and repeatable. All thesefactors may require looking for alternative ways of roughnesscharacterization.
Currently in industry, there are three typical groups offoils used by PCB manufacturers. The first group is denotedSTD (standard) foils, with the highest roughness of Rz ∼10–20 μm. The second group is the VLP (very low profile)and RTF (reverse-treated foil) foils with medium roughness of
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 425
Fig. 3. Cross-sectional SEM of the three different types of copper foils usedin this study.
Rz ∼ 5–10 μm. The third group includes the smoothestSVLP/HVLP (super/hyper very low profile) foils with lowestroughness Rz ∼ 1–5 μm. These three classes of foils are rep-resentative of most currently existing foils on the market usedin PCBs from the point of view of the surface roughness. As ismentioned earlier, roughness on at least one side of the signaltrace is required for adhesion to the dielectric substrate. Thecross-sectional pictures of PCB stripline traces made of threedifferent types of copper foil are shown in Fig. 3. These pictureswere obtained using a Hitachi 4700 SEM.
Surface-roughness parameters may be extracted from theSEM images of line cross-sections. An advantage of SEMcross-sectional analysis over profilometry is that it does notneed peeling the foil off from the dielectric. However, SEMrequires special preparation of test samples, which includes cut-ting out cross-sections of the PCB stack-ups, placing them inepoxy holders, polishing, and coating with an ultrathin film ofelectrically conducting material, commonly gold or platinum,deposited on the sample either by low-vacuum sputter coating,or by high-vacuum evaporation.
Though an SEM picture is a 2-D image in the line cross-section, making a number of cross-sections, analogous to thosein Fig. 3, along the same line would provide more statisticaldata on roughness along the direction of signal propagation. Afoil roughness statistics along the line and in the cross-sectionshould be the same. Also, it is possible to study foil roughnessnot on the trace, but on the ground plane. This would allow forgetting the longer samples for statistical study.
High-magnification detailed SEM images should be taken ona number of consecutive sections of the sample under study, forexample, signal trace. These images should be stitched togetherwithout gaps or overlapping to form the picture of the entireoriginal trace. Surface-roughness parameters can be obtainedby applying image-processing software to the entire profile ofinterest. The extracted parameters are an average peak-to-valley
amplitude Ar and a spatial quasi-period Λ, which further will becalled “a spatial period” or just “a period.” Ar is extracted fromthe image profile analogously to Rz , as is mentioned earlier, butit may differ from the Rz values obtained using either optical ormechanical profilometry. The period Λ can be calculated as themost probable period on the entire length of the sample understudy, and it can be determined as the correlation length, bycalculating the correlation integral of the sample function withitself, but shifted.
III. EXPERIMENTAL APPROACH FOR SEPARATING DIELECTRIC
AND ROUGH CONDUCTOR LOSSES
An experimentally based method for separating rough con-ductor loss from dielectric loss is proposed herein. The exper-imental study was carried out on three groups of PCBs fromthe same manufacturer, with each group having a different con-ductor roughness profile of the trace. There were nine test ve-hicles in each group. All the boards had identical dielectricof the same resin content and fiber-glass morphology, and thesame single-ended stripline geometry. The laminate material inthis study was low-loss, non-FR4-type fiber-glass-filled resinpolymer. All the striplines under test had the same geome-try specifications with the width of the trace w = 13.27 mils(0.34 mm), the thickness of the trace t = 0.55 mils (0.014 mm),and the total height, or the distance between reference planesof the symmetric stripline h = 24.40 mils (0.62 mm). The tracelength in all the test vehicles was also the same at l = 15.41inches (391.41 mm). The conductors on all the three groupswere made of electrodeposited copper with conductivity closeto the International Annealed Copper Standard (IACS) value ofσ= 5.818 × 107 S/m, but they differed only by the type of cop-per foil roughness as STD, VLP, or HVLP. The SEM analysis ofcross-section of one board from each group resulted in averagepeak-to-valley roughness amplitudes Ar ≈ 7 μm for STD foil,3 μm for VLP, and 1.5 μm for HVLP. The values for averagepeak-to-valley amplitude of roughness were estimated by apply-ing image-processing software to the high-magnification SEMimages of the entire signal-trace cross-sections. The sections ofthe profiles on the roughest sides of the traces for three differenttypes of foils converted to MATLAB plots are shown in Fig. 4.The “detrend” function in MATLAB was then used to removethe linear trend associated with sample tilt.
The S-parameters of test vehicles within each group weremeasured with a VNA, and corresponding port effects werede-embedded applying a TRL calibration. To reduce the ran-dom errors associated with possible tolerance ranges of geome-try deviations and material inhomogeneity, the S-parameters ofthe nine PCB samples in each group were measured and thenaveraged. The averaged S-parameters of each group were usedin the material extraction procedure outlined in Fig. 1. Fig. 5(a)shows the measured frequency dependencies of |S21 |, andFig. 5(b) the extracted total loss curves for these three typesof boards. Fig. 6(a) and (b) shows the phase of the measuredS21 in two frequency segments: from 50 MHz to 5 GHz, andfrom 5 to 10 GHz, respectively. A phase difference betweenthe three types of samples is solely due to different roughness
426 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
Fig. 4. Roughness profile sections obtained from SEM for samples of threedifferent copper foil types.
Fig. 5. Characteristics of three test boards with different conductor foils.(a) Measured insertion loss. (b) Total loss on the line.
Fig. 6. Characteristics of three test boards with different conductor foils.(a) Measured phase of S21 for 50 MHz–5 GHz. (b) Measured phase of S21 for5–10 GHz. (c) Phase constant β on the line.
profiles on the lines, and it increases with frequency. The resul-tant calculated phase constants β have slightly different slopeswith respect to frequency, and this is noticeable at higher fre-quencies in Fig. 6(c). If surface roughness is not taken intoaccount, this will lead to a slight discrepancy of the extractedDk values, especially at frequencies above 10 GHz.
In the present extraction procedure as described in [6]–[8],a Debye dependence for a PCB dielectric behavior is adopted.For the frequency range of interest, from 10 MHz to 20 GHz,Dk is almost constant, slightly decreasing with frequency, whileDf almost linearly increases [34]. For the case of a single-termDebye behavior, the corresponding dielectric loss αD can beapproximated as approximately ∼Qω + Rω2 , as is shown inAppendix B. Even if the multiterm Debye dependence isassumed, the behavior of αD would still be approximately∼Qω + Rω2 , not adding any
√ω term. The total loss αT on
the transmission line can be curve-fitted as P√
ω + Qω + Rω2 .If the conductor is smooth, the corresponding conductor loss isac = P
√ω. However, this is not true for a rough conductor.
The total loss data in Fig. 5(b) is for three PCB groups with dif-ferent conductor surface-roughness levels, but having the samegeometry and dielectric specifications. Subtraction of the totalloss curves in pairs results in a frequency behavior of differ-ences between the corresponding surface-roughness terms, asshown in Fig. 7. Since dielectric loss is the same, the differenceis solely due to surface roughness. The small “kinks” in themeasured curves in Fig. 7 are due to the periodic structure ofvias on the TVs, connecting the ground planes of the striplineson the PCB, and they can be neglected.
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 427
Fig. 7. Differences in total loss for pairs of test boards with different conductorroughness.
The difference curves in Fig. 7 can be curve-fitted by theterms proportional to different powers of frequency with
The frequency-dependent terms associated with roughness arewell fit with
√ω, ω, and ω2 terms. This means that the ω and
ω2 terms in the roughness response will get lumped into the ωand ω2 terms of the dielectric loss, if not explicitly separated inthe extraction of the Df value.
Let the total loss in the measured test vehicles be representedas a sum of frequency-dependent components
αT = a√
ω + b√
ω + cω + dω2 + eω + fω2 , (4)
where the total conductor loss is comprised of the first fourterms as
αC = a√
ω + b√
ω + cω + dω2 (5)
with the smooth conductor loss αC 0 = a√
ω, the roughness lossαr = b
√ω + cω + dω2 , and the dielectric loss is
αD = eω + fω2 . (6)
If the surface roughness is neglected, both√
ω terms in (4)will be assigned to the conductor loss, whereas the remain-ing terms cω + dω2 + eω + fω2 will included in the dielectricloss. This may result in incorrect loss tangent extraction, sinceconductor loss will be underestimated, while dielectric loss isoverestimated.
The measured total loss in Fig. 5(b) can be curve-fitted withthree terms
√ω, ω, and ω2 , in the same way as the difference
curves shown in Fig. 7. The results of the curve-fitting identifythree sets of equalities for STD, VLP, and HVLP foils, respec-tively, as
The coefficients K1 , K2 , and K3 in (7) are plotted as functionsof average peak-to-valley roughness amplitude Ar in Fig. 8(a)–(c), respectively. The Ar values in these plots correspond toroughness profiles indicated in Fig. 4. If these curves are ex-trapolated to zero roughness Ar = 0, the resultant coefficientsK1(0), K2(0), and K3(0) would correspond to the perfectlysmooth conductor case. Using this extrapolation, the dielectricloss contributions and the surface roughness can be separated.
The conductor and dielectric losses in the case of the perfectlysmooth conductor for all three groups of test vehicles are
αC 0 + αD = a√
ω + eω + fω2 (8)
when the coefficients in (4) are set as b = c = d = 0, and themain assumption is identical geometry and dielectrics on alltest vehicles. In this case, the coefficients a = 2.338 × 10−6 ,e = 1.496 × 10−11 , and f = 4.014 × 10−23 are obtained by ex-trapolating the graphs for K1 , K2 , and K3 to zero roughness, asshown in Fig. 8(a)–(c). Then, the total loss for the three cases ofdifferent roughness profiles can be represented in the form (4)with the coefficients summarized in Table I.
It is important that the differences between the correspond-ing coefficients in Table I, associated with roughness, are self-consistent with the coefficients in (3), and result in the samecurve-fitted lines as in Fig. 7.
The sums of the coefficients corresponding to√
ω, ω, and ω2
terms in Table I equal to the total loss coefficients in (8) as
a + b = K1 c + e = K2 d + f = K3 . (9)
Note that in Table I, the part proportional to√
ω is higher fora smooth conductor (8). Also, Fig. 8(a) shows that the coeffi-cient K1 decreases as the roughness parameter Ar increases.This means that the field penetration into the conductor dueto roughness decreases, and is noticeable at comparatively lowfrequencies, where
√ω loss part is dominating. The higher the
roughness, the more this effect is pronounced. This effect couldbe due to partial scattering of the field on the roughness, pre-venting it from penetrating inside the metal. This scattering willgive rise to the ω term in roughness loss at the expense of the√
ω part. At higher frequencies this scattering will dominate ascompared to the decrease of the
√ω term; therefore, this effect
will be masked. A similar effect was noted by Sanderson [17].The coefficient K2 monotonically increases with the increase
of roughness amplitude, as shown in Fig. 8(b). This means thatthe ω-term due to roughness will add to the dielectric loss ω-term. Also, according to Fig. 8(c), the ω2-term decreases asroughness increases, and may be negative at some roughness
428 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
Fig. 8. Curve-fitting coefficients as functions of average peak-to-valley am-plitude. (a) K1 . (b) K2 . (c) K3 .
amplitude. This indicates that at higher frequencies, the increasein the loss due to the dielectric may be slowed down due to theconductor roughness effect.
If roughness is substantial and not taken into account properly,the slope of the extracted Df curve as a function of frequencymight appear to be negative instead of positive, leading to anincorrect result from a physics point of view. This has beenexperimentally encountered when extracting the Df of PCB ma-
TABLE ICURVE-FITTING COEFFICIENTS FOR DIFFERENT FOILS
terials with STD types of foil having roughness amplitude Argreater than approximately 8 μm. This effect may be related toexcitation of surface waves in a layered dielectric structure [26],and it was also noted by Goubau in lossy conductors [35].
A comparison of the proposed differential extrapolationmethod and the simplest Sanderson’s SPT with 1-D saw-toothroughness is shown in Fig. 9. In these calculations, the periodof the saw-tooth function is assumed to be twice the roughnessamplitude, Λ = 2 Ar . According to SEM tests of different foilson PCBs, the roughness period Λ is approximately twice as theroughness amplitude Ar , as is seen in Fig. 4. Calculations aredone for three types of foils with Ar = 7 μm (STD), 3 μm(VLP), and 1.5 μm (HVLP), respectively. The total loss curvesare obtained directly from the measurements, and the smoothconductor loss is extracted using the proposed extrapolationmethod with a
√w as in Table I.
As seen from the curves in Fig. 9(a)–(c), for STD foil resultscompare well, over the frequency range of interest, while for theVLP and HVLP foils, there are significant discrepancies. Thismay be related to the fact that in the calculations Λ/Ar = 2 isused for all three cases of foils, while for the foils with lowerroughness, VLP and HVLP, this ratio may be different. As ismentioned earlier, it is difficult to correctly assign the roughnessperiod Λ in the SPT to the random surface-roughness profile ofactual conductor foils, while the SPT results are sensitive to thechoice of Λ. Also, the SPT model does not take into accountthe layered dielectric structure and scattering of waves on arough metal surface embedded in an inhomogeneous dielectricmedium.
The loss extracted using the SPT for low- and high-roughnessboards are shown in Fig. 10. It is seen that the SPT model ofconductor roughness applied to the measurements on the testvehicles with identical dielectric, but different roughness, resultsin the different DF curves. This is not correct. If roughnessparameters are not known accurately, any model, even the mostsophisticated, will result in ambiguity of the extracted Df.
The proposed differential extrapolation method results in asingle curve of Df for boards having the same dielectric and ge-ometry, but various roughness profiles. This is the inherent con-sequence of (7). The extracted curves for Df and Dk are shownin Fig. 11. The loss tangent for the dielectric composite behaves
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 429
Fig. 9. Comparison of rough conductor loss modeled using proposed methodand SPT. (a) STD. (b) VLP. (c) HVLP.
as expected, nearly linearly increasing with frequency. This isobtained from (6) and the extraction procedure as in Fig. 1.
The results extracted using the proposed differential extrapo-lation approach have been compared also with the curve-fittingtechnique described in [7]. This smooth
√ω-fit method [7],
curve-fits the total loss αT with three terms proportional to√
ω,ω, and ω2 , and neglects the surface roughness. Fig. 12 shows thecomparison between the dielectric parameters extracted throughcurve-fitting and through the proposed differential extrapolationmethod. Fig. 12(a) shows the Dk as a function of frequency. Dif-ference in the extracted Dk values using the smooth
√ω-fit for
Fig. 10. Applying SPT with saw-tooth function leads to two different dielectricloss curves for the same material.
boards with identical dielectric, but different foil types, is a con-sequence of the different phase behavior and different β shownin Fig. 6. This is a result of neglecting roughness (see the leftpart in Fig. 1). The actual Dk value, extracted using the methodproposed herein, is very close to the one for the HVLP board.This is because the HVLP foil is the closest to the smooth con-ductor case. Fig. 12(b) shows the extracted conductor loss αc .Since the smooth
√ω-fit takes the total conductor loss as
√ω,
neglecting its ω and ω2 parts, the extracted αc are underesti-mated. The HVLP loss is closer to the actual, while the STDloss is significantly lower than the extracted using the methodproposed herein. This leads to an overestimated dielectric lossαd compared to the actual, as Fig. 12(c) demonstrates. The Dfextracted using the smooth
√ω-fit is also overestimated. Among
all the studied boards with identical dielectric and different foils,the board with HVLP foil has the Df curve which is the closestto that obtained by the differential extrapolation method.
Fig. 13 shows the measured total loss for the three groups oftest vehicles with different foils, and the results of extractionusing the proposed differential extrapolation procedure with thesingle curve for dielectric loss in all test vehicles, and the threecurves for conductor loss in STD, VLP, and HVLP foils.
IV. CONCLUSION
A new experiment-based traveling-wave method to sepa-rate conductor from dielectric losses when measuring dielectricproperties of PCB substrates “in situ” is proposed. This methoddoes not require solving a complex electromagnetic problemwith a detailed analysis of scattering phenomena on conduc-tor roughness and other underlying physics. In this method,the S-parameters of a transmission line with the dielectric un-der study as a substrate are measured. Total loss on the lineis curve-fitted to frequency terms behaving as
√ω, ω, and
ω2 . Conductor and dielectric losses are separated by buildingauxiliary dependencies of curve-fitting coefficients as functionsof surface roughness, and extrapolating these curves to zero
430 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
Fig. 11. Dielectric properties of PCB laminate material extracted using theproposed method. (a) Df. (b) Dk.
roughness. The resultant values at zero roughness would corre-spond to an ideally smooth conductor and pure dielectric loss.
This method can be realized only when test boards with iden-tical geometries and dielectrics, but different conductor surface-roughness profiles, are available. An example of such separationis shown for three groups of boards with three different typesof available foils—standard (STD), very low profile (VLP), andhyper very low profile (HVLP) foil. The results of calculat-ing Df, or loss tangent, are obtained for the frequency rangefrom 50 MHz to 20 GHz, with potential practical extension tohigher frequencies. Though the presented results are obtainedfor stripline geometries of specific width of signal traces andheight of dielectric layer (resulting in 50-Ω wave impedance),the approach can be extended for PCBs with different widths oftraces, making this approach more general.
The advantage of the proposed differential extrapolationmethod is that it does not require the detailed information on themicrostructure of surface roughness. If roughness for all threetypes of boards is described in the same terms R = (Rq , Rz ,Rt , Ar , or Λ), obtained either through SEM, or profilometry, itis possible to build the corresponding K1 , K2 , and K3 curves as
Fig. 12. Dielectric parameters extracted through smooth√
ω-fit and throughthe proposed differential extrapolation method. (a) Dielectric constant Dk.(b) Conductor loss αc . (c) Dielectric loss αd . (d) Dissipation factor Df.
the functions of one of those R-parameters from the measuredαT frequency dependencies. Then extrapolation of these curvesto the zero roughness will result in the same coefficients for anychosen type of roughness parameters R = (Rq , Rz , Rt , Ar , orΛ) due to the proportionality between those R-parameters. For
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 431
Fig. 13. Measured total loss and loss parameters extracted using the proposeddifferential extrapolation approach: dielectric loss and conductor loss for PCBswith three types of foil.
example, the same results of Dk and Df extraction are obtainedif K1 , K2 , and K3 curves are built as functions of Rz .
The proposed method separates terms that behave differentlywith frequency (∼√
ω, ω, or ω2), in the total loss on the line.Hence, there is no need to determine whether roughness termsare caused by a signal trace or ground planes. There is no need toanalyze, which side of the trace is rougher, whether roughness ishomogeneous or not, and what its correlation length or effectivespatial period is.
APPENDIX A
SENSITIVITY OF A SPT TO CHOICE OF QUASI-PERIOD
OF ROUGHNESS FUNCTION
An example presented herein shows that the conductor lossαc , calculated, using Sanderson’s SPT with a 1-D periodic saw-tooth roughness model [17], [18], is sensitive to the value ofthe spatial period Λ. The calculations are obtained for VLPfoil with peak-to-valley roughness amplitude Ar = 3 μm andvarious periods Λ. Fig. 14 demonstrates that the uncertainty inestimation of Λ can result in significant variation of the modeledconductor loss. However, it is difficult to assign one value ofspatial period (or quasi-period) Λ to a roughness profile, sinceit is random rather than periodic.
APPENDIX B
FREQUENCY-DEPENDENT DIELECTRIC PROPERTIES
(DEBYE MODEL)
Low-loss PCB substrate dielectrics (tanδ < 0.01) are oftenmodeled with Dk and Df parameters constant over the limitedfrequency range. Then, dielectric attenuation constant αD =βtanδ/2 for TEM waves is directly proportional to frequency[12]. However, assigning a constant nonzero Df to a dielectric
Fig. 14. Conductor loss as a function of frequency calculated through Sander-son’s SPT with saw-tooth profile: Ar = 3 μm, and Λ is variable.
would contradict causality, since according to Kramers–Kronigrelations, frequency-independent Dk must correspond to zeroloss. Besides, from experiments on many PCB dielectrics in awide frequency range (up to 40 GHz), it is known that Df is notconstant, but increases almost linearly with frequency. Assumethat a PCB substrate behaves as a Debye dielectric with a d.c.conductivity term
εr = ε∞ +εS − ε∞1 + jωτe
− jσe
ωε0. (B1)
At frequencies well below the relaxation frequency (ω �ω0 = 1/τe), the Dk
ε′r = ε∞ +εS − ε∞
1 + (ω τe)2 (B2)
would slightly decrease with frequency as
ε′r = εS − k1ω2 (B3)
with the coefficient k1 = (εs − ε∞)/ω20 , where k1ω
2 � εs.The first term in the imaginary part of the permittivity (B4)
is associated with polarization loss, and the d.c. conductivityterm is due to impurities and existence of free electrons in thedielectric
ε′′r =(εs − ε∞)ω τe
1 + (ω τe)2 +σe
ω ε0. (B4)
The first term in (B4) behaves linearly with frequency in thesame region of frequencies below relaxation ω � ω0 = 1/τe
(ε′′r )1 = k2ω, where k2 =εs − ε∞
ω0. (B5)
The second term in (B4) associated with d.c. (ohmic) conduc-tivity is
(ε′′r )2 =σe
ωε0. (B6)
Then, the total loss tangent is
tanδ =(ε′′r )1
ε′r+
(ε′′r )2
ε′r=
k2ω
εs − k1ω2 +σe
(εs − k1ω2)ωε0.
(B7)
432 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012
Fig. 15. Loss constant calculated from the Debye dielectric dependence andapproximation with linear and squared frequency terms
Since the coefficients are related as k1 � k2 , the real part ofpermittivity decreases with frequency much slower than the firstterm of the imaginary part of permittivity(ε′′r )1 = k2ω increaseswith frequency. The loss tangent at frequencies much lower thanthe relaxation frequency can be approximated as
tanδ ≈(
1 − ε∞εs
)ω
ω0+
σe
εsω ε0= (tanδ)1 + (tanδ)2 .
(B8)Then, the first term in the dielectric loss αD associated with
polarization processes in the Debye dielectric, even for low-lossdielectric, would be proportional to the square of frequency
(αD )1 =β(tanδ)1
2∼ ω2 , (B9)
since the propagation constant β = (ω/c)√
εs − k1ω2 at fre-quencies, where the polarization loss dominates, is proportionalto ω. At lower frequencies, where d.c. dielectric loss dominatesover polarization (Debye) loss, β is proportional to
√ω, and the
d.c. conductivity loss term is
(αD )2 =β(tanδ)2
2∼ 1√
ω. (B10)
The term (B10) becomes negligibly small at frequen-cies above approximately 10 MHz for the present-day di-electrics. Loss tangent at frequencies much lower thanthe relaxation frequency (ω � ω0) may produce almostfrequency-independent behavior, which can be understoodas a nonzero “offset” causing almost linear frequency be-havior of (αD ). Hence, it is reasonable to approximate di-electric loss behavior in the frequency range of interest(50 MHz–20 GHz) as
αD ≈ eω + fω2 (B11)
where e and f are constants. Fig. 15 shows the agreement be-tween dielectric loss αD calculated through the Debye depen-dence and approximated using (B11). The Debye parametersfor the curve “Debye 1” are εs = 4.4; ε∞ = 4.1; τ = 1.592 ×10−12 s; and σe = 0. Df varies almost linearly from 0.00034at 50 MHz to 0.013 at 20 GHz. The approximation coefficientsfor this “Debye 1” curve in the frequency range from 50 MHzto 20 GHz are e = 2.06 × 10−12 and f = 3.91 × 10−22 . TheDebye parameters for the curve “Debye 2” are εs = 4.4;ε∞ = 4.0; τ = 1.592 × 10−12 s; and σe = 10−4 S/m. The dis-crepancy between the αD curves in both cases over the fre-quency range of interest does not exceed 0.2%. Note that in thefirst case (“Debye 1”), the d.c. conductivity term is zero, andin the second case (“Debye 2”) it is nonzero, but this does notaffect the approximation with a linear and squared frequencyterms over the frequency range of interest. The extracted αD inthis study is plotted together with αD obtained from “Debye 1”and “Debye 2” curves.
ACKNOWLEDGMENT
This work was supported in part by a National ScienceFoundation (NSF), grant no. 0855878, through the I/UCRC re-search program. The authors would like to thank C. Wisner,Dr. S. Reis, Dr. E. Kulp, and Prof. M. O’Keefe (colleagues fromMaterials Research Center of Missouri University of Scienceand Technology), and F. Zhou (former graduate student of theEMC Laboratory of the same University) for their assistancewith preparing samples, running scanning electron microscopy,and image processing of roughness profiles.
REFERENCES
[1] E. Bogatin, S. Begley, and M. Resso, “The role of dielectric constantand dissipation factor measurements in multi-gigabit systems,” Design-Con, 2007 [Online]. Available: http://www.designcon.com/newsletter/chapter19.pdf
[2] Agilent Basics of Measuring the Dielectric Properties of Materials. Ap-plication Note, Agilent, 5989–2589 EN, June 26, 2006.
[3] J. Baker-Jarvis, M. Janezic, B. Riddle, C. L. Holloway, N. G. Paulter,and J. E. Blendell, “Dielectric and conductor-loss characterization andmeasurements on electronic packing materials,” Tech. Note 1520, NIST,Boulder, CO, 2001.
[4] M. Engl, K. Shiller, W. Eurskens, and R. Weigel, “High resolution timedomain and frequency domain package characterization up to 65 GHz,”in Proc. IEEE Electron. Compon. Tech. Conf., 2006, pp. 1274–1280.
[5] A. Deutsch, T. Winkel, G. V. Kopcsay, C. W. Surovic, B. J. Rubin, G.A. Katopis, B. J. Chamberlin, and R. S. Krabbenhoft, “Extraction of εr (f)and tanδ(f) for printed circuit board insulators up to 30 GHz using theshort-pulse propagation technique,” IEEE Trans. Adv. Packag., vol. 28,no. 1, pp. 4–12, Feb. 2005.
[6] S. Hinaga, M. Koledintseva, P. Anmula, and J. Drewniak, “Effect of con-ductor surface roughness upon measured loss and extracted values of PCBlaminate material dissipation factor,” in Proc. Tech. Conf. IPC Expo/APEX2009, Las Vegas, USA, Mar. 31–Apr. 2,2009, pp. S20–2.
[7] A. Koul, P. K. R. Anmula, M. Y. Koledintseva, J. L. Drewniak, andS. Hinaga, “Improved technique for extracting parameters of low-lossdielectrics on printed circuit boards,” in Proc. IEEE Symp. Electromag.Compat., Austin, TX, Aug. 17–21, 2009, pp. 191–196.
[8] A. Rajagopal, B. Achkir, M. Koledintseva, A. Koul, and J. Drewniak,“Material parameter extraction using time-domain TRL (t-TRL) mea-surements,” in Proc. IEEE Symp. Electromag. Compat., Austin, TX, Aug.17–21, 2009, pp. 280–285.
[9] K. Hinckley, D. Winterberg, M. Ballou, G. Blando, J. Miller, R. Dame,A. Nosovitski, G. Truhlar, S. Begley, and I. Novak, “Introduction and
KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 433
comparison of an alternate methodology for measuring loss tangent forPCB laminates,” DesignCon 2010, San Jose, CA, Feb. 1–4, 2010, Paper5-TP2.
[10] A. Deutsch, C. W. Surovic, R. S. Krabbenhoft, and G. V. Kopcsay, “Pre-diction of losses caused by roughness of metallization in printed circuitboards,” IEEE Trans. Adv. Packag., vol. 30, no. 2, pp. 279–287, May2007.
[11] A. R. Djordjevic, R. M. Biljic, V. D. Likar-Smiljanic, and T. K. Sarkar,“Wideband frequency-domain characterization of FR-4 and time-domaincausality,” IEEE Trans. Electromag. Compat., vol. 43, no. 4, pp. 662–667,Nov. 2001.
[13] G. Brist, S. Hall, S. Clouser, and T. Liang, “Non-classical conductor lossesdue to copper foil roughness and treatment,” in Proc. Electron. CircuitsWorld Conv. 10, Anaheim, CA, Feb. 22–24, 2005, paper S19–2–1.
[14] S. P. Morgan, Jr., “Effects of surface roughness on eddy current losses atmicrowave frequencies,” J. Appl. Phys., vol. 20, pp. 352–362, Apr. 1949.
[15] E. O. Hammerstad and F. Bekkadal, Microstrip Handbook, ELAB report,the Electron. Res. Lab., Univ. Trondheim, Norway, STF44 A74169, Feb.1975.
[16] S. Groiss, I. Bardi, O. Biro, K. Preis, and K. Richter, “Parameters of lossycavity resonators calculated by the finite element method,” IEEE Trans.Magn., vol. 32, no. 3, pp. 894–897, May 1996.
[17] A.E. Sanderson, “Effect of surface roughness on propagation of the TEMmode,” in Advances in Microwaves, vol. 7, Cambridge, MA: AcademicPress, 1971, pp. 1–57.
[18] S. Sundstroem, “Stripline models with conductor surface roughness,” M.S.thesis, Helsinki Univ. Tech., Finland, Feb. 2004.
[19] H. Braunisch, X. Gu, A. Camacho-Bragado, and L. Tsang, “Off-chiprough-metal-surface propagation loss modeling and correlation with mea-surements,” in Proc. IEEE Electron. Compon. Tech. Conf., 2007, pp. 785–791.
[20] X. Gu, L. Tsang, and H. Braunisch, “Modeling effects of random roughinterface on power absorption between dielectric and conductive mediumin 3D problem,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 3,pp. 511–517, Mar. 2007.
[21] Q. Chen and N. Wong, “New simulation methodology of 3D surfaceroughness loss for interconnects modeling,” in Proc. Des., Autom. TestEur. (DATE), Apr. 2009, pp. 1184–1189.
[22] Q. Chen, H. W. Choi, and N. I. Wong, “Robust simulation methodologyfor surface-roughness loss in interconnect and package modelings,” IEEETrans. Comput.-Aid. Des. Integr. Circuits Syst., vol. 28, no. 11, pp. 1654–1665, Nov. 2009.
[23] Q. Chen and N. Wong, “An efficient stochastic integral equation methodfor modeling the influence of conductor surface roughness on interconnectohmic loss,” in Proc. Midwest Symp. Circuits Syst. (MWSCAS), Aug. 2007,pp. 1417–1420.
[24] L. Proekt and A. C. Cangellaris, “Investigation of the impact of conductorsurface roughness on interconnect frequency-dependent ohmic loss,” inProc. Electron. Compon. Technol. Conf., New Orleans, LA, May 27–30,2003, pp. 1004–1010.
[25] S. Hall, S. G. Pytel, P. G. Huray, D. Hua, A. Moonshiram, G. A. Brist, andE. Sijercic, “Multigigahertz causal transmission line modeling methodol-ogy using a 3-D hemispherical surface roughness approach,” IEEE Trans.Microw. Theory Tech., vol. 55, no. 12, pp. 2614–2624, Dec. 2007.
[26] Y. Shlepnev, A. Neves, T. Dagostino, and S. McMorrow,“Measurement-assisted electromagnetic extraction of interconnect pa-rameters on low-cost FR-4 boards for 6–20 Gb/sec applications,”in Proc. DesignCon 2009, Santa Clara, CA, Feb. 2009. Available:http://simberian.com/TradeShow.php.
[27] M. Y. Koledintseva, A. Koul, F. Zhou, and J. Drewniak, “Surfaceimpedance approach to calculate loss in rough conductor coated withdielectric layer,” in Proc. IEEE Symp. Electromag. Compat., Fort Laud-erdale, FL, Jul. 25–30, 2010, pp. 790–795.
[28] K. J. Stout and L. Blunt, Three-Dimensional Surface Topograhy, 2nd ed.New York: Penton Press, 2002.
[29] T. Chi, T. Ballinger, and R. Olds, “Surface texture analy-sis using stylus profilers,” VEECO, 2010. Available: http://www.veeco.com/pdfs/appnotes/AN38_SurfTexture_17.pdf
[30] G. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, C. Fiori, and E. Lif-shin, Scanning Electron Microscopy and X-ray Microanalysis. NewYork: Plenum Press, 1981.
[31] F. J. Giessibl, “Advances in atomic force microscopy,” APS Rev. ModernPhys., vol. 75, no. 3, pp. 949–986, 2003.
[32] E. P. Degarmo, J. T. Black, and R. A. Kohser, Materials and Processes inManufacturing, 9th ed. Hoboken, NJ: Wiley, 2003, pp. 223–224.
[33] IPC-TM-650 Test Methods Manual 2.2.17 a, IPC Associ-ation. (2001, Feb.). [Online]. Available: http://www.ipc.org/4.0_Knowledge/4.1_Standards/test/2–2_2–2-17a.pdf
[34] J. Zhang, M. Y. Koledintseva, G. Antonini, J. L. Drewniak, A. Orlandi,and K. N. Rozanov, “Planar transmission line method for characterizationof printed circuit board dielectrics,” Progr. Electromagn. Res. (PIERS),vol. 102, pp. 267–286, Mar. 2010.
[35] G. Goubau, “Surface waves and their application to transmission line,” J.Appl. Phys., vol. 21, no. 11, pp. 1119–1128, 1950.
Amendra Koul (S’04) received the B.Tech. degree inelectronics and communication from Vellore Instituteof Technology, Tamil Nadu, India, in 2006 and theM.S. degree in electrical engineering from MissouriUniversity of Science and Technology, Rolla, in May2010.
He was with the EMC Laboratory, EcoleSuperieure d’Ingenieurs, Rouen, France, during hislast semester of undergraduate studies. During 2006–2007, he was a system engineer at Tata ConsultancyServices. He is currently a Hardware Engineer in En-
terprise Switching Technology Group (ESTG) in Cisco Systems, Inc., San Jose,CA. His work is related to signal and power integrity of printed circuit boards,application specific integrated-circuits (ASICs), integrated-circuit (IC) pack-ages, connectors and cables.
Marina Y. Koledintseva (M’96–SM’03) receivedM.S. and Ph.D. degrees in radio physics and elec-tronics from Moscow Power Engineering Insti-tute (Technical University)—MPEI(TU), Moscow,Russia.
Since 2000, she has been a research professor withthe EMC Laboratory of the Missouri University ofScience and Technology (Missouri S&T). Her scien-tific interests are microwave engineering, interactionof electromagnetic field with ferrites and compositemedia, their modeling, and application for electro-
magnetic compatibility.Dr. Koledintseva is a member of TC-9 (Computational Electromagnetics)
and TC-10 (Signal Integrity), and the Secretary of TC-11 (Nanotechnology)Committees of the IEEE EMC Society.
Scott Hinaga received the B.S. degree in chemistryfrom Stanford University, Stanford, CA, in 1985.
He has vast printed circuit board (PCB) manufac-turing and engineering management experience. Hejoined Cisco Systems, Inc. in 2004, where he is cur-rently a Technical Leader in PCB Technology Group,and is responsible for investigation and characteriza-tion of new laminate materials.
James L. Drewniak (S’85–M’90–SM’01–F’06) re-ceived B.S., M.S., and Ph.D. degrees in electricalengineering from the University of Illinois at Urbana-Champaign.
He is with Electromagnetic Compatibility Lab-oratory in the Electrical Engineering Department atMissouri University of Science and Technology. Hisresearch and teaching interests include electromag-netic compatibility in high-speed digital and mixed-signal designs, signal and power integrity, electronicpackaging, electromagnetic compatibility in power
electronic based systems, electronics, and antenna design. He is an AssociateEditor for the IEEE Transactions on EMC.
