VALUES of dielectric constant Dk, or real part of relative

Transcription

1 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL Differential Extrapolation Method for Separating Dielectric and Rough Conductor Losses in Printed Circuit Boards Amendra 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) transmission lines/interconnects is roughened to promote adhesion to dielectric substrates. It is important to characterize PCB substrate dielectrics 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 conductor and dielectric losses in PCBs with rough conductors. This approach requires at least three transmission lines with identical, or at least as close as technologically possible, basic geometry parameters of signal trace, distance-to-ground planes, and dielectric properties, while the average peak-to-valley amplitude of surface roughness of the conductor would be different. The peak-to-valley amplitude of conductor roughness is determined from 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 relative permittivity, and dissipation factor Df, or loss tangent, over a wide frequency range of various printed circuit board (PCB) dielectric substrate materials are important information for high-speed digital design engineers and researchers [1]. In the majority of practical cases, designers are provided with constant values of Dk and Df over very wide frequency bands for PCB dielectrics at their disposal. However, the loss tangent for many of the currently used fiber-glass epoxy-resin-type dielectric composites, employed in PCBs, cannot be considered as independent of frequency over the wide frequency range from tens of megahertz to 20 GHz or higher, or for data rates above 10 Gb/s [1] [5]. From the signal integrity (SI) point of view, dielectric dispersion, and frequency-dependent loss are reflected in the closing of an eye diagram as wideband signals containing high-frequency components propagate in longer interconnects, Manuscript received March 17, 2010; revised August 28, 2010; accepted September 22, Date of publication March 24, 2011; date of current version April 18, A. Koul and S. Hinaga are with Cisco Systems, Inc., San Jose, CA ( amekoul@cisco.com; shinaga@cisco.com). M. Y. Koledintseva and J. Drewniak are with the EMC Laboratory, Electrical and Computer Engineering Department, Missouri University of Science and Technology (Missouri S&T), Rolla, MO USA ( marinak@ mst.edu; drewniak@mst.edu). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TEMC such as the copper traces of a PCB. Therefore, in order to choose appropriate PCB materials and improve functional properties of their designs at the stage of research and development, engineers need accurate data on PCB dielectric and conductor parameters. There are known different techniques for PCB dielectric substrate characterization over a frequency range of interest. These techniques can be classified as resonator (cavity) methods, freespace techniques, and transmission-line methods [2], [3]. Cavity methods are comparatively narrowband, and they are based on the variation in the quality factor of a resonator and resonance frequency shift when a cavity is loaded with a sample of the material under test. For wideband material characterization, either a set of specially designed cavities of different center frequencies, or a tunable cavity may be needed. Free-space techniques are based on reflection and transmission of plane waves, incident upon a large, as compared to the longest wavelength, layer of a dielectric under test. Traveling-wave techniques for wideband material characterization can be realized using TEM cells, coaxial lines, or waveguides with samples under test completely filling the cross section of a test line [2], [3]. One difficulty with this kind of technique is that the sample under test may be inhomogeneous and anisotropic, so measurement data will depend on how the electric field is applied. Thus, measurements might be conducted with the E-field in-plane with the sample, whereas in practical applications, the E-field is in an out-of-plane direction, and the dielectric properties for these two directions may differ significantly. Measurements in situ, i.e., just on the PCB transmission line of interest, are preferable. Then, the measured data for anisotropic substrates is in the same direction as used in designs in practice. For this reason, wideband TEM (or quasi-tem) traveling-wave S-parameter measurements on PCB striplines or microstrip lines are attractive. S-parameters of a section of a transmission line may be directly measured in the frequency domain using vector network analyzers (VNAs), or measurements can be done using time-domain reflectometers (TDR), and timedomain results then converted to frequency domain [4]. Then, the effective dielectric properties of the substrate under test are extracted from S-parameters using corresponding analytical or numerical models of the line. Another traveling-wave method is propagation of a short pulse on a line [5]. The PCB material characterization technique used for the experimental studies in this paper has been detailed earlier in [6] [8]. This is a wideband traveling-wave method employing a single-ended stripline structure, comprised of laminate layers /$ IEEE

2 422 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 thrureflect-line (TRL) calibration traces on each board to de-embed port effects [8]. S-parameters are measured using a VNA or TDR, and then the complex propagation constant γ = α + jβ is calculated. The extraction procedure for dielectric parameters Dk and Df over a frequency range of interest is schematically shown in Fig. 1. According to this extraction procedure, the real ε and the imaginary ε parts of permittivity are interrelated through causality relations, and they depend on both phase constant β and loss constant α. The procedure as in Fig. 1 takes into account asymmetry of the two-port network, and imposes Debye-like behavior of the extracted real and imaginary parts of permittivity [7] at least 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 the Debye-like frequency dependencies typical for dielectrics with a pure dipole polarization loss mechanism. The nature of the permittivity dependence for PCB dielectrics has not been well studied to date, and dielectric parameters of different PCB laminates vary in a wide range depending on constituents, morphology, in which direction parameters are measured, and on how the trace crosses the fiber-glass weave. As a result, the actual frequency behavior of fiber-glass-filled epoxy resin composites may be much more complex than a pure Debye dependence [9]. Complex permittivity of such materials is often modeled as a sum of Debye-like terms [10], or as a wideband Debye dependence, also called logarithmic Djordjevic Sarkar model [11]. The total attenuation constant for any transmission line is α T = α C + α D, where α C is the conductor loss, and α D is the dielectric loss. For accurate extraction of dielectric parameters, processing of measurement results obtained by any of the traveling-wave methods requires adequate separation of conductor and dielectric losses. If a conductor is perfectly smooth, this is comparatively straightforward, since α C behaves as ω, a square root of frequency, according to the classical skin-depth model [12]. Koul et al. [7] proposed to curve-fit the total dielectric loss α T by three terms proportional to ω, ω, and ω 2.It was assumed that the conductor loss behaves as ω term, while the dielectric loss behaves as a sum of ω and ω 2 terms. This method has been extensively used to extract dielectric properties of PCB laminates, but the roughness of conductors was not taken into account. So far, this curve-fitting technique, which can be called the smooth ω-fit, is the only way to separate conductor loss from dielectric loss, if no information of the stripline geometry and type of the foil is available. As operating frequencies or data rates increase, the skin depth in copper becomes comparable or even less than levels of roughness of copper foils in PCBs. Thus, in a copper conductor, the skin depth at 5 GHz is approximately 1 μm, while roughness on copper foils currently used in PCBs is on the order of

3 KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB μm [6]. Then, the frequency dependence of conductor loss for a rough conductor deviates from the classical proportionality to ω [13], [14], and will contain higher-order frequency components in a power-series representation. Since a PCB dielectric substrate is also dispersive, and its frequency response may be quite complex, separation of dielectric and conductor loss is an essential problem. It is important to know, which part of loss is caused by the dielectric, and which by the conductor. This knowledge is needed not only for using correct data in the design cycle, but also in choosing appropriate laminate dielectrics and foils from a cost-to-performance perspective when getting them from PCB manufacturers and vendors. Surface roughness on transmission-line conductors can be either calculated through an adequate analytical or numerical method, or retrieved experimentally. Then, the dielectric loss can be obtained by subtraction of evaluated conductor loss from the total measured loss, even if the dielectric is not following pure Debye dependence, or its frequency response is unknown. Currently existing analytical or numerical models are inadequate for separating dielectric loss from conductor loss in the case of a rough conductor. The simplest empirically based models for signal attenuation on a transmission line with rough conductor surfaces are the Hammerstad Bekkadal [15] and Groiss models [16]. However, both models are inapplicable for significantly rough PCB conductors with r.m.s. amplitude of conductor roughness exceeding approximately 1 μm, since corresponding roughness correction factors asymptotically approach a constant value at roughness amplitudes higher than approximately 1 μm. Another problem with these models is that they address only r.m.s. roughness amplitude, without consideration of distances between neighboring peaks or valleys on roughness profiles. However, the information on spatial distribution of peaks and valleys in the plane of the foil is important at frequencies, where skin depth is comparable to or less than the roughness level. Another group of surface-roughness models is based on a small perturbation theory (SPT). In Sanderson s SPT formulation [17], the roughness profile is considered as 1-D periodic roughness function along the direction of propagation. To calculate attenuation of waves traveling along a periodic corrugated surface of a metal of finite conductivity, Sanderson applied concepts of surface impedance and surface displacement. Sundstroem specified this approach for a number of particular periodic 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 quasiperiodic roughness function is an approximation. Actually, the surface-roughness profile in a typical copper foil is a 2-D random function. The papers [19], [20] also use SPT and describe surface roughness in terms of 2-D power spectral densities (PSD) or, equivalently, in terms of correlation functions of random conductor surface profiles. However, accurate knowledge of the statistical distribution function, spectral power density, and spatial periodicity range for roughness are needed and can be obtained only through detailed surface-roughness images, for example, using profilometers and suitable image processing. The SPT approach utilizing the 2-D PSD data for random roughness profiles, obtained using atomic force microscopy, is presented in [19] and [20]. This approach was applied to comparatively low-level (submicron) roughness profiles on interconnect surfaces in microelectronic packaging, and hence the results agree well with the Hammerstad Bekkadal formula [15]. The advantage of using PSD data is that it does not solely depend on the average roughness height (r.m.s.), but indirectly takes into account spatial distribution of roughness on the surface; so in principle, can be applied to substantially higher levels of roughness than [15] or [16] allow. There are several other papers that mathematically analyze conductor surface roughness. The numerical simulation methodology called scale wave modeling (SWM) is considered in [21] and [22]. The spectral stochastic collocation to construct a statistical model of roughness is presented in [23]. However, these papers, as well as [24], provide analytical or numerical results of potential effective conductivity degradation, without any comparison with measurement results on physical samples. A method for modeling conductor loss on a rough surface through scattering on multiple hemispheres was proposed in [25]. This method, denoted as hemispherical boss modeling (HBM), models surface irregularities as the size-controlled hemispherical bosses distributed regularly or randomly on the plane. Both HBM and SWM methods require detailed microscopic analysis for characterization of surface-roughness profiles. A technique based on a numerical finite-element method with Trefftz elements and local impedance adjustment is described in [26]. However, this technique is difficult to implement due to the complexity of solving integral equations in this method, and need very specialized numerical codes. Furthermore, knowledge of surface-roughness rms amplitude and period is needed for this technique as well. The aforementioned analytical and numerical models are proposed to characterize rough conductor loss in the cases, where empirical formulas [15], [16], or Sanderson s 1-D SPT model with periodic roughness [17] are no longer applicable. However, all currently existing theories are either insufficient for substantially rough conductors surfaces as in present-day PCBs, or are too complex and costly for implementation, demanding high levels of computational resources for numerical analysis, roughness evaluation, and image processing. All known models require knowing aprioriaccurate information on the transmission-line geometry and surface-roughness profiles. This data is typically obtained through destructive microscopic analysis of rough surfaces. In practice, information on the surface-roughness profile on each conductor surface may be unavailable to designers, and any analytical or numerical model will be unreliable without this data. Moreover, all existing models deal with translationally invariant cross-sectional parameters of transmission lines, while in practice, the geometry of the line along the direction of propagation might vary randomly within some limits. Filling factor and position of fiber-glass bundles with respect to the line conductors are also statistical rather than deterministic parameters, and none of the known theories takes this into account. Indeed, any PCB laminate dielectric adjacent to a rough conductor is an inhomogeneous and multilayered composite media, and this yields additional complexity of the problem [27].

4 424 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 These current models, even the most advanced and sophisticated, are sensitive to geometrical and surface-roughness parameters, and inaccurate input data may result in incorrect evaluation of conductor loss, and, hence, incorrect extracted Df of the dielectric. As a result, a conductor model applied to a set of test boards with identical geometries and dielectrics, but different conductor surface-roughness profiles, will result in ambiguity of the extracted Df curve as a function of frequency, while this curve should be unique in characterizing the very same dielectric. Herein, a straight-forward experiment-based differential method to separate dielectric and conductor losses is proposed. Geometrically identical (within the limits of PCB manufacturing capability) transmission lines on identical dielectric substrates are needed, while the surface roughness on the conductors must be different. This method still requires destructive analysis of at least one sample of a test line with each type of conductor foil. A review of the roughness profile characterization on the test samples is given in Section II. The principle of the differential extrapolation method and its application to extract dielectric properties on the multiple PCB test vehicles with identical dielectric, but different copper foils is described in Section III. This method for identical dielectric substrates on all the three test board groups with differing conductor 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 adequate data on the conductor roughness profile. Herein, basic parameters to characterize roughness profiles and the main approaches of getting this information are described. An accurate way of characterizing conductor surfaceroughness topology is to apply a destructive microscopic analysis. Samples of the rough conductor surface, the same as in the actual test transmission line, can be prepared specifically for an instrument that is used for roughness characterization. Instruments for getting images of foil topology include mechanical (stylus) profilometers [28], optical profilometers [29], scanning electron microscopy (SEM) [30], or high-resolution atomic force scanning probe microscopy [31]. Typically, the output roughness parameters of a profilometer are R a, R q, R z, and R t [29], [32]. R a is the arithmetic mean of departure of roughness from the mean level. R q is the rms value corresponding to R a. R z is defined as the mean peak-to-valley amplitude. The parameter R t is the maximum peak-to-valley amplitude over the entire profile. An example of an optical profilometer image for one of the copper foils used in this study is shown in Fig. 2. According to the IPC test method [33], foil profiles can be characterized using an R z parameter, which is calculated by adding the averaged N highest peaks and N deepest valleys on a sample (typically N=5). R z numbers for PCB foils are substantially greater than r.m.s. R q values, and may reach 20 μminsome cases of standard foils. Typically, peak-to-valley amplitudes measured with mechanical profilometers are approximately two Fig. 2. Roughness image obtained with an optical profilometer (manufacturer s data). times less than those measured with an optical method. Mechanical profilometers have lower resolution than their optical counterparts, since the tip of a stylus is not able to reach all the depressions on the metal surface as the light beam does, and is, therefore, blind to concave features whose size is smaller than the diameter of the tip of the profilometer. Though peak-to-valley values in the mechanical case are underestimated, many PCB laminate material manufacturers provide R z values obtained using mechanical profilometry, which they have at their disposal. Different conductor loss models or extraction procedures may deal with different roughness parameters. This could be an r.m.s. roughness parameter R q, as in [15] [18], or an average peak-tovalley amplitude (R z ), as in the present study, or 1- or 2-D PSD data and the correlation length, as in [18] [20], or other deterministic [25] or statistical distribution data for a rough conductor surface, e.g., [21] [23]. The problem is that even when measuring the same parameter, e.g., average peak-to-valley amplitude, different techniques and instruments may result in significant discrepancies in the output data due to different resolution, as is mentioned earlier. There are some other problems with profilometry from the point of view of its use in conductor loss models. All four roughness parameters that a profilometer provides (R a, R q, R z, and R t )areamplitude parameters. However, information on the distances between peaks and/or valleys, or the average spatial period in the plane of the conductor surface is necessary for characterizing and modeling the surface-roughness loss in a PCB signal trace. It is known that the calculated conductor loss in some models, for example, Sanderson s SPT, is very sensitive to the value of the chosen period of the roughness function [18], or corresponding correlation length [19], [20]. An example is shown in Appendix A. Also, it is known that peeling a foil off a PCB laminate can cause mechanical deformation of the roughness profile, and the profilometry data may be not accurate and repeatable. All these factors may require looking for alternative ways of roughness characterization. Currently in industry, there are three typical groups of foils used by PCB manufacturers. The first group is denoted STD (standard) foils, with the highest roughness of R z μm. The second group is the VLP (very low profile) and RTF (reverse-treated foil) foils with medium roughness of

5 KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 425 amplitude A r and a spatial quasi-period Λ, which further will be called a spatial period or just a period. A r is extracted from the image profile analogously to R z, as is mentioned earlier, but it may differ from the R z values obtained using either optical or mechanical profilometry. The period Λ can be calculated as the most probable period on the entire length of the sample under study, and it can be determined as the correlation length, by calculating the correlation integral of the sample function with itself, but shifted. Fig. 3. Cross-sectional SEM of the three different types of copper foils used in this study. R z 5 10 μm. The third group includes the smoothest SVLP/HVLP (super/hyper very low profile) foils with lowest roughness R z 1 5 μm. These three classes of foils are representative of most currently existing foils on the market used in PCBs from the point of view of the surface roughness. As is mentioned earlier, roughness on at least one side of the signal trace is required for adhesion to the dielectric substrate. The cross-sectional pictures of PCB stripline traces made of three different types of copper foil are shown in Fig. 3. These pictures were obtained using a Hitachi 4700 SEM. Surface-roughness parameters may be extracted from the SEM images of line cross-sections. An advantage of SEM cross-sectional analysis over profilometry is that it does not need peeling the foil off from the dielectric. However, SEM requires special preparation of test samples, which includes cutting out cross-sections of the PCB stack-ups, placing them in epoxy holders, polishing, and coating with an ultrathin film of electrically 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 crosssection, making a number of cross-sections, analogous to those in Fig. 3, along the same line would provide more statistical data on roughness along the direction of signal propagation. A foil roughness statistics along the line and in the cross-section should be the same. Also, it is possible to study foil roughness not on the trace, but on the ground plane. This would allow for getting the longer samples for statistical study. High-magnification detailed SEM images should be taken on a number of consecutive sections of the sample under study, for example, signal trace. These images should be stitched together without gaps or overlapping to form the picture of the entire original trace. Surface-roughness parameters can be obtained by applying image-processing software to the entire profile of interest. The extracted parameters are an average peak-to-valley III. EXPERIMENTAL APPROACH FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES An experimentally based method for separating rough conductor loss from dielectric loss is proposed herein. The experimental study was carried out on three groups of PCBs from the same manufacturer, with each group having a different conductor roughness profile of the trace. There were nine test vehicles in each group. All the boards had identical dielectric of the same resin content and fiber-glass morphology, and the same single-ended stripline geometry. The laminate material in this study was low-loss, non-fr4-type fiber-glass-filled resin polymer. All the striplines under test had the same geometry specifications with the width of the trace w = 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 planes of the symmetric stripline h = mils (0.62 mm). The trace length in all the test vehicles was also the same at l = inches ( mm). The conductors on all the three groups were made of electrodeposited copper with conductivity close to the International Annealed Copper Standard (IACS) value of σ= S/m, but they differed only by the type of copper foil roughness as STD, VLP, or HVLP. The SEM analysis of cross-section of one board from each group resulted in average peak-to-valley roughness amplitudes A r 7 μm for STD foil, 3 μm for VLP, and 1.5 μm for HVLP. The values for average peak-to-valley amplitude of roughness were estimated by applying image-processing software to the high-magnification SEM images of the entire signal-trace cross-sections. The sections of the profiles on the roughest sides of the traces for three different types of foils converted to MATLAB plots are shown in Fig. 4. The detrend function in MATLAB was then used to remove the linear trend associated with sample tilt. The S-parameters of test vehicles within each group were measured with a VNA, and corresponding port effects were de-embedded applying a TRL calibration. To reduce the random errors associated with possible tolerance ranges of geometry deviations and material inhomogeneity, the S-parameters of the nine PCB samples in each group were measured and then averaged. The averaged S-parameters of each group were used in the material extraction procedure outlined in Fig. 1. Fig. 5(a) shows the measured frequency dependencies of S 21, and Fig. 5(b) the extracted total loss curves for these three types of boards. Fig. 6(a) and (b) shows the phase of the measured S 21 in two frequency segments: from 50 MHz to 5 GHz, and from 5 to 10 GHz, respectively. A phase difference between the three types of samples is solely due to different roughness

6 426 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 Fig. 4. Roughness profile sections obtained from SEM for samples of three different copper foil types. Fig. 6. Characteristics of three test boards with different conductor foils. (a) Measured phase of S 21 for 50 MHz 5 GHz. (b) Measured phase of S 21 for 5 10 GHz. (c) Phase constant β on the line. Fig. 5. Characteristics of three test boards with different conductor foils. (a) Measured insertion loss. (b) Total loss on the line. profiles on the lines, and it increases with frequency. The resultant calculated phase constants β have slightly different slopes with respect to frequency, and this is noticeable at higher frequencies in Fig. 6(c). If surface roughness is not taken into account, this will lead to a slight discrepancy of the extracted Dk 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, while Df almost linearly increases [34]. For the case of a single-term Debye behavior, the corresponding dielectric loss α D can be approximated as approximately Qω + Rω 2,asisshownin Appendix B. Even if the multiterm Debye dependence is assumed, the behavior of α D would still be approximately Qω + Rω 2, not adding any ω term. The total loss α T on the transmission line can be curve-fitted as P ω + Qω + Rω 2. If the conductor is smooth, the corresponding conductor loss is a c = 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 different conductor surface-roughness levels, but having the same geometry and dielectric specifications. Subtraction of the total loss curves in pairs results in a frequency behavior of differences between the corresponding surface-roughness terms, as shown in Fig. 7. Since dielectric loss is the same, the difference is solely due to surface roughness. The small kinks in the measured curves in Fig. 7 are due to the periodic structure of vias on the TVs, connecting the ground planes of the striplines on the PCB, and they can be neglected.

7 KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 427 The measured total loss in Fig. 5(b) can be curve-fitted with three terms ω, ω, and ω 2, in the same way as the difference curves shown in Fig. 7. The results of the curve-fitting identify three sets of equalities for STD, VLP, and HVLP foils, respectively, as αt STD = ω ω ω 2 ; αt VLP = ω ω ω 2 ; αhv LP T = ω ω ω 2 Fig. 7. Differences in total loss for pairs of test boards with different conductor roughness. The difference curves in Fig. 7 can be curve-fitted by the terms proportional to different powers of frequency with ω, ω, and ω 2 as STD V LP ΔαT = ω ω ω 2 ; STD HV LP ΔαT = ω ω ω 2 ; VLP HV LP ΔαT = ω ω ω 2. (3) The frequency-dependent terms associated with roughness are well fit with ω, ω, and ω 2 terms. This means that the ω and ω 2 terms in the roughness response will get lumped into the ω and ω 2 terms of the dielectric loss, if not explicitly separated in the extraction of the Df value. Let the total loss in the measured test vehicles be represented as a sum of frequency-dependent components α T = a ω + b ω + cω + dω 2 + eω + fω 2, (4) where the total conductor loss is comprised of the first four terms as α C = a ω + b ω + cω + dω 2 (5) with the smooth conductor loss α C 0 = a ω, the roughness loss α r = b ω + cω + dω 2, and the dielectric loss is α D = eω + fω 2. (6) If the surface roughness is neglected, both ω terms in (4) will be assigned to the conductor loss, whereas the remaining terms cω + dω 2 + eω + fω 2 will included in the dielectric loss. This may result in incorrect loss tangent extraction, since conductor loss will be underestimated, while dielectric loss is overestimated. Set of K 1 Set of K 2 Set of K 3 (7) The coefficients K 1, K 2, and K 3 in (7) are plotted as functions of average peak-to-valley roughness amplitude A r in Fig. 8(a) (c), respectively. The A r values in these plots correspond to roughness profiles indicated in Fig. 4. If these curves are extrapolated to zero roughness A r = 0, the resultant coefficients K 1 (0), K 2 (0), and K 3 (0) would correspond to the perfectly smooth conductor case. Using this extrapolation, the dielectric loss contributions and the surface roughness can be separated. The conductor and dielectric losses in the case of the perfectly smooth conductor for all three groups of test vehicles are α C 0 + α D = a ω + eω + fω 2 (8) when the coefficients in (4) are set as b = c = d =0, and the main assumption is identical geometry and dielectrics on all test vehicles. In this case, the coefficients a = , e = , and f = are obtained by extrapolating the graphs for K 1, K 2, and K 3 to zero roughness, as shown in Fig. 8(a) (c). Then, the total loss for the three cases of different roughness profiles can be represented in the form (4) with the coefficients summarized in Table I. It is important that the differences between the corresponding coefficients in Table I, associated with roughness, are selfconsistent with the coefficients in (3), and result in the same curve-fitted lines as in Fig. 7. The sums of the coefficients corresponding to ω, ω, and ω 2 terms in Table I equal to the total loss coefficients in (8) as a + b = K 1 c + e = K 2 d + f = K 3. (9) Note that in Table I, the part proportional to ω is higher for a smooth conductor (8). Also, Fig. 8(a) shows that the coefficient K 1 decreases as the roughness parameter A r increases. This means that the field penetration into the conductor due to roughness decreases, and is noticeable at comparatively low frequencies, where ω loss part is dominating. The higher the roughness, the more this effect is pronounced. This effect could be due to partial scattering of the field on the roughness, preventing it from penetrating inside the metal. This scattering will give rise to the ω term in roughness loss at the expense of the ω part. At higher frequencies this scattering will dominate as compared to the decrease of the ω term; therefore, this effect will be masked. A similar effect was noted by Sanderson [17]. The coefficient K 2 monotonically increases with the increase of roughness amplitude, as shown in Fig. 8(b). This means that the ω-term due to roughness will add to the dielectric loss ω- term. Also, according to Fig. 8(c), the ω 2 -term decreases as roughness increases, and may be negative at some roughness

8 428 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 TABLE I CURVE-FITTING COEFFICIENTS FOR DIFFERENT FOILS Fig. 8. Curve-fitting coefficients as functions of average peak-to-valley amplitude. (a) K 1.(b)K 2.(c)K 3. amplitude. This indicates that at higher frequencies, the increase in the loss due to the dielectric may be slowed down due to the conductor roughness effect. If roughness is substantial and not taken into account properly, the slope of the extracted Df curve as a function of frequency might appear to be negative instead of positive, leading to an incorrect result from a physics point of view. This has been experimentally encountered when extracting the Df of PCB ma- terials with STD types of foil having roughness amplitude A r greater than approximately 8 μm. This effect may be related to excitation 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 extrapolation method and the simplest Sanderson s SPT with 1-D saw-tooth roughness is shown in Fig. 9. In these calculations, the period of the saw-tooth function is assumed to be twice the roughness amplitude, Λ=2A r. According to SEM tests of different foils on PCBs, the roughness period Λ is approximately twice as the roughness amplitude A r, as is seen in Fig. 4. Calculations are done for three types of foils with A r = 7 μm (STD),3μm (VLP), and 1.5 μm (HVLP), respectively. The total loss curves are obtained directly from the measurements, and the smooth conductor loss is extracted using the proposed extrapolation method with a w as in Table I. As seen from the curves in Fig. 9(a) (c), for STD foil results compare well, over the frequency range of interest, while for the VLP and HVLP foils, there are significant discrepancies. This may be related to the fact that in the calculations Λ/A r =2is used for all three cases of foils, while for the foils with lower roughness, VLP and HVLP, this ratio may be different. As is mentioned earlier, it is difficult to correctly assign the roughness period Λ in the SPT to the random surface-roughness profile of actual conductor foils, while the SPT results are sensitive to the choice of Λ. Also, the SPT model does not take into account the layered dielectric structure and scattering of waves on a rough metal surface embedded in an inhomogeneous dielectric medium. The loss extracted using the SPT for low- and high-roughness boards are shown in Fig. 10. It is seen that the SPT model of conductor roughness applied to the measurements on the test vehicles with identical dielectric, but different roughness, results in the different DF curves. This is not correct. If roughness parameters are not known accurately, any model, even the most sophisticated, will result in ambiguity of the extracted Df. The proposed differential extrapolation method results in a single curve of Df for boards having the same dielectric and geometry, but various roughness profiles. This is the inherent consequence of (7). The extracted curves for Df and Dk are shown in Fig. 11. The loss tangent for the dielectric composite behaves

9 KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 429 Fig. 10. Applying SPT with saw-tooth function leads to two different dielectric loss curves for the same material. boards with identical dielectric, but different foil types, is a consequence of the different phase behavior and different β shown in Fig. 6. This is a result of neglecting roughness (see the left part in Fig. 1). The actual Dk value, extracted using the method proposed herein, is very close to the one for the HVLP board. This is because the HVLP foil is the closest to the smooth conductor case. Fig. 12(b) shows the extracted conductor loss α c. Since the smooth ω-fit takes the total conductor loss as ω, neglecting its ω and ω 2 parts, the extracted α c are underestimated. The HVLP loss is closer to the actual, while the STD loss is significantly lower than the extracted using the method proposed herein. This leads to an overestimated dielectric loss α d compared to the actual, as Fig. 12(c) demonstrates. The Df extracted 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 closest to that obtained by the differential extrapolation method. Fig. 13 shows the measured total loss for the three groups of test vehicles with different foils, and the results of extraction using the proposed differential extrapolation procedure with the single curve for dielectric loss in all test vehicles, and the three curves for conductor loss in STD, VLP, and HVLP foils. Fig. 9. Comparison of rough conductor loss modeled using proposed method and SPT. (a) STD. (b) VLP. (c) HVLP. as expected, nearly linearly increasing with frequency. This is obtained from (6) and the extraction procedure as in Fig. 1. The results extracted using the proposed differential extrapolation approach have been compared also with the curve-fitting technique described in [7]. This smooth ω-fit method [7], curve-fits the total loss α T with three terms proportional to ω, ω, and ω 2, and neglects the surface roughness. Fig. 12 shows the comparison between the dielectric parameters extracted through curve-fitting and through the proposed differential extrapolation method. Fig. 12(a) shows the Dk as a function of frequency. Difference in the extracted Dk values using the smooth ω-fit for IV. CONCLUSION A new experiment-based traveling-wave method to separate conductor from dielectric losses when measuring dielectric properties of PCB substrates in situ is proposed. This method does not require solving a complex electromagnetic problem with a detailed analysis of scattering phenomena on conductor roughness and other underlying physics. In this method, the S-parameters of a transmission line with the dielectric under study as a substrate are measured. Total loss on the line is curve-fitted to frequency terms behaving as ω, ω, and ω 2. Conductor and dielectric losses are separated by building auxiliary dependencies of curve-fitting coefficients as functions of surface roughness, and extrapolating these curves to zero

10 430 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 Fig. 11. Dielectric properties of PCB laminate material extracted using the proposed method. (a) Df. (b) Dk. roughness. The resultant values at zero roughness would correspond to an ideally smooth conductor and pure dielectric loss. This method can be realized only when test boards with identical geometries and dielectrics, but different conductor surfaceroughness profiles, are available. An example of such separation is shown for three groups of boards with three different types of available foils standard (STD), very low profile (VLP), and hyper very low profile (HVLP) foil. The results of calculating Df, or loss tangent, are obtained for the frequency range from 50 MHz to 20 GHz, with potential practical extension to higher frequencies. Though the presented results are obtained for stripline geometries of specific width of signal traces and height of dielectric layer (resulting in 50-Ω wave impedance), the approach can be extended for PCBs with different widths of traces, making this approach more general. The advantage of the proposed differential extrapolation method is that it does not require the detailed information on the microstructure of surface roughness. If roughness for all three types of boards is described in the same terms R=(R q, R z, R t, A r,orλ), obtained either through SEM, or profilometry, it is possible to build the corresponding K 1, K 2, and K 3 curves as Fig. 12. Dielectric parameters extracted through smooth ω-fit and through the proposed differential extrapolation method. (a) Dielectric constant Dk. (b) Conductor loss α c. (c) Dielectric loss α d. (d) Dissipation factor Df. the functions of one of those R-parameters from the measured α T frequency dependencies. Then extrapolation of these curves to the zero roughness will result in the same coefficients for any chosen type of roughness parameters R=(R q, R z, R t, A r,or Λ) due to the proportionality between those R-parameters. For

11 KOUL et al.: DIFFERENTIAL EXTRAPOLATION METHOD FOR SEPARATING DIELECTRIC AND ROUGH CONDUCTOR LOSSES IN PCB 431 Fig. 14. Conductor loss as a function of frequency calculated through Sanderson s SPT with saw-tooth profile: A r = 3 μm, and Λ is variable. Fig. 13. Measured total loss and loss parameters extracted using the proposed differential extrapolation approach: dielectric loss and conductor loss for PCBs with three types of foil. example, the same results of Dk and Df extraction are obtained if K 1, K 2, and K 3 curves are built as functions of R z. The proposed method separates terms that behave differently with frequency ( ω, ω, or ω 2 ), in the total loss on the line. Hence, there is no need to determine whether roughness terms are caused by a signal trace or ground planes. There is no need to analyze, which side of the trace is rougher, whether roughness is homogeneous or not, and what its correlation length or effective spatial period is. APPENDIX A SENSITIVITY OF A SPT TO CHOICE OF QUASI-PERIOD OF ROUGHNESS FUNCTION An example presented herein shows that the conductor loss α c, calculated, using Sanderson s SPT with a 1-D periodic sawtooth roughness model [17], [18], is sensitive to the value of the spatial period Λ. The calculations are obtained for VLP foil with peak-to-valley roughness amplitude A r = 3 μm and various periods Λ. Fig. 14 demonstrates that the uncertainty in estimation of Λ can result in significant variation of the modeled conductor loss. However, it is difficult to assign one value of spatial period (or quasi-period) Λ to a roughness profile, since it is random rather than periodic. APPENDIX B FREQUENCY-DEPENDENT DIELECTRIC PROPERTIES (DEBYE MODEL) Low-loss PCB substrate dielectrics (tanδ <0.01) are often modeled with Dk and Df parameters constant over the limited frequency range. Then, dielectric attenuation constant α D = βtanδ/2 for TEM waves is directly proportional to frequency [12]. However, assigning a constant nonzero Df to a dielectric would contradict causality, since according to Kramers Krönig relations, frequency-independent Dk must correspond to zero loss. Besides, from experiments on many PCB dielectrics in a wide frequency range (up to 40 GHz), it is known that Df is not constant, but increases almost linearly with frequency. Assume that a PCB substrate behaves as a Debye dielectric with a d.c. conductivity term ε r = ε + ε S ε j σ e. (B1) 1+jωτ e ωε 0 At frequencies well below the relaxation frequency (ω ω 0 =1/τ e ), the Dk ε r = ε + ε S ε 1+(ωτ e ) 2 would slightly decrease with frequency as ε r = ε S k 1 ω 2 (B2) (B3) with the coefficient k 1 =(ε s ε )/ω 2 0, where k 1 ω 2 ε s. The first term in the imaginary part of the permittivity (B4) is associated with polarization loss, and the d.c. conductivity term is due to impurities and existence of free electrons in the dielectric ε r = (ε s ε )ωτ e 1+(ωτ e ) 2 + σ e. (B4) ωε 0 The first term in (B4) behaves linearly with frequency in the same region of frequencies below relaxation ω ω 0 =1/τ e (ε r ) 1 = k 2 ω, where k 2 = ε s ε ω 0. (B5) The second term in (B4) associated with d.c. (ohmic) conductivity is (ε r ) 2 = σ e. ωε 0 Then, the total loss tangent is tanδ = (ε r ) 1 ε r + (ε r ) 2 ε r = (B6) k 2 ω ε s k 1 ω 2 + σ e (ε s k 1 ω 2. )ωε 0 (B7)

12 432 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 54, NO. 2, APRIL 2012 where e and f are constants. Fig. 15 shows the agreement between dielectric loss α D calculated through the Debye dependence and approximated using (B11). The Debye parameters for the curve Debye 1 are ε s =4.4; ε =4.1; τ = s; and σ e =0. Df varies almost linearly from at 50 MHz to at 20 GHz. The approximation coefficients for this Debye 1 curve in the frequency range from 50 MHz to 20 GHz are e = and f = The Debye parameters for the curve Debye 2 are ε s =4.4; ε =4.0; τ = s; and σ e =10 4 S/m. The discrepancy between the α D curves in both cases over the frequency range of interest does not exceed 0.2%. Note that in the first case ( Debye 1 ), the d.c. conductivity term is zero, and in the second case ( Debye 2 ) it is nonzero, but this does not affect the approximation with a linear and squared frequency terms over the frequency range of interest. The extracted α D in this study is plotted together with α D obtained from Debye 1 and Debye 2 curves. Fig. 15. Loss constant calculated from the Debye dielectric dependence and approximation with linear and squared frequency terms Since the coefficients are related as k 1 k 2, the real part of permittivity decreases with frequency much slower than the first term of the imaginary part of permittivity(ε r ) 1 = k 2 ω increases with frequency. The loss tangent at frequencies much lower than the relaxation frequency can be approximated as ( tanδ 1 ε ) ω + σ e = (tanδ) 1 + (tanδ) 2. ε s ω 0 ε s ωε 0 (B8) Then, the first term in the dielectric loss α D associated with polarization processes in the Debye dielectric, even for low-loss dielectric, would be proportional to the square of frequency (α D ) 1 = β(tanδ) 1 ω 2, (B9) 2 since the propagation constant β =(ω/c) ε s k 1 ω 2 at frequencies, where the polarization loss dominates, is proportional to ω. At lower frequencies, where d.c. dielectric loss dominates over polarization (Debye) loss, β is proportional to ω, and the d.c. conductivity loss term is (α D ) 2 = β(tanδ) ω. (B10) The term (B10) becomes negligibly small at frequencies above approximately 10 MHz for the present-day dielectrics. Loss tangent at frequencies much lower than the relaxation frequency (ω ω 0 ) may produce almost frequency-independent behavior, which can be understood as a nonzero offset causing almost linear frequency behavior of (α D ). Hence, it is reasonable to approximate dielectric loss behavior in the frequency range of interest (50 MHz 20 GHz) as α D eω + fω 2 (B11) ACKNOWLEDGMENT This work was supported in part by a National Science Foundation (NSF), grant no , through the I/UCRC research program. The authors would like to thank C. Wisner, Dr. S. Reis, Dr. E. Kulp, and Prof. M. O Keefe (colleagues from Materials Research Center of Missouri University of Science and Technology), and F. 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Phys., vol. 21, no. 11, pp , Amendra Koul (S 04) received the B.Tech. degree in electronics and communication from Vellore Institute of Technology, Tamil Nadu, India, in 2006 and the M.S. degree in electrical engineering from Missouri University of Science and Technology, Rolla, in May He was with the EMC Laboratory, Ecole Supérieure d Ingénieurs, Rouen, France, during his last semester of undergraduate studies. During , he was a system engineer at Tata Consultancy Services. He is currently a Hardware Engineer in Enterprise 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) packages, connectors and cables. Marina Y. Koledintseva (M 96 SM 03) received M.S. and Ph.D. degrees in radio physics and electronics from Moscow Power Engineering Institute (Technical University) MPEI(TU), Moscow, Russia. Since 2000, she has been a research professor with the EMC Laboratory of the Missouri University of Science and Technology (Missouri S&T). Her scientific interests are microwave engineering, interaction of electromagnetic field with ferrites and composite media, their modeling, and application for electromagnetic 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 chemistry from Stanford University, Stanford, CA, in He has vast printed circuit board (PCB) manufacturing and engineering management experience. He joined Cisco Systems, Inc. in 2004, where he is currently a Technical Leader in PCB Technology Group, and is responsible for investigation and characterization of new laminate materials. James L. Drewniak (S 85 M 90 SM 01 F 06) received B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana- Champaign. He is with Electromagnetic Compatibility Laboratory in the Electrical Engineering Department at Missouri University of Science and Technology. His research and teaching interests include electromagnetic compatibility in high-speed digital and mixedsignal designs, signal and power integrity, electronic packaging, electromagnetic compatibility in power electronic based systems, electronics, and antenna design. He is an Associate Editor for the IEEE Transactions on EMC.