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Cross-sectional geometry and characteristic dimensions of (a) the stripline cross section and (b) signal trace in a PCB stripline.
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![Fig. 4. Components in [φ 21 ]: √ ω (a); ω (b); and ω 2 (c) for test...](profile/Aleksei-Rakov/publication/272928497/figure/fig3/AS:614010953154572@1523403027741/Components-in-ph-21-o-a-o-b-and-o-2-c-for-test-boards-with-different-surface_Q320.jpg)
Recently, an experiment-based traveling-wave technique to separate conductor loss from dielectric loss on printed circuit board (PCB) striplines, called the differential extrapolation roughness measurement (DERM), has been proposed. The further development of this procedure is presented in this paper. The new procedure is applied to both loss const...
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... extracted components of loss are α c0 = 2.35 × 10 −6 √ ω and α d = 1.44 × 10 −11 ω + 4.22 × 10 −23 ω 2 . This is close to the data extracted using the DERM technique [12] for almost the same set of test vehicles, as is published in [12]: α c0 = 2.338 × 10 −6 √ ω and α d = 1.496 × 10 −11 ω + 4.014 × 10 −23 ω 2 . If the auxiliary axis is taken as A r , then the extracted α c0 = 2.37 × 10 −6 √ ω and α d = 1.48 × 10 −11 ω + 3.98 × 10 −23 ω 2 . Though Set III geometrically and dielectrically is almost the same as that described in [12], the data extracted using DERM [12] and using the improved procedure slightly differs (compare Fig. 12 and [12, Fig. 11]). Now there are no low-frequency "tails," and the overall extracted dielectric constant is slightly lower than in [12], which results in the slightly higher loss tangent. Also, it is seen that using the QR axis instead of A r in extrapolation to zero roughness slightly changes the extracted dielectric ...
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... 4: Solving the system of (3) and (4), one can obtain the refined dielectric parameters: DK and DF, as is shown on the flowchart in [12, Fig. 1] ...
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... the consistency check is done for both loss and the phase constant differences, similar to the check done in [12] for loss. The differences of the total loss curves taken in pairs (STD-VLP, STD-HVLP, and VLP-HVLP) and the differences of the corresponding roughness parts of the losses, obtained from the proposed procedure were compared. Note that the subtraction gives only the rough part, since the dielectric is same in all the boards. Fig. 11 shows an excellent agreement between the corresponding differences. Consistency only shows that the curve fitting is proper. Fig. 12. Extracted dielectric data for Set III applying DERM [12] and the new procedure with A r and QR axis for building auxiliary ...
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... the consistency check is done for both loss and the phase constant differences, similar to the check done in [12] for loss. The differences of the total loss curves taken in pairs (STD-VLP, STD-HVLP, and VLP-HVLP) and the differences of the corresponding roughness parts of the losses, obtained from the proposed procedure were compared. Note that the subtraction gives only the rough part, since the dielectric is same in all the boards. Fig. 11 shows an excellent agreement between the corresponding differences. Consistency only shows that the curve fitting is proper. Fig. 12. Extracted dielectric data for Set III applying DERM [12] and the new procedure with A r and QR axis for building auxiliary ...
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... frequency dependences of the pure dielectric loss α d , smooth conductor loss α c0 , and rough conductor loss calculated as α rough = α T − (α d + α c0 ) for all the test vehicles are shown in Fig. 10. There is a good agreement for the dielectric loss between Set I and Set II, for smooth conductor loss between Set I and Set II, and the rough conductor losses for all test vehicles are different, because foils are ...
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... example of an SEM picture and the basic dimensions of a test vehicle cross section are shown in Fig. 1. Note that P in Table I is the trapezoidal perimeter of the trace. Table I. Table I. Fig. 2 shows cross sections of signal traces for test vehicles of Sets I and II. The geometrical parameters of all test vehicles of Sets I and II are almost identical within the manufacturing tolerance. But the geometry of Set III is significantly different. Signal traces in Set III are wider and thinner than those in Sets I and ...
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... To firstly determine ′ , it is necessary to consider that the experimental β = Im(γdd) can be represented as the sum of two components, βc and βd, which account for the delay introduced by the conductor and dielectric effects, respectively. In this regard, βc is due to the internal inductance of the trace and ground planes (Lint), and the corresponding effect on β is only significant at relatively low frequencies even when the lines are fabricated with copper foils with roughness as high as that associated to STD profiles [21]. In this case, βc can be approximately determined from the structure and properties of the conductor material [22]. ...
... In this case, βc can be approximately determined from the structure and properties of the conductor material [22]. In fact, ≈ 0 √ can be considered without significantly penalizing accuracy, where b0 is determined through a fitting involving experimental β versus frequency data at frequencies below around 1 GHz [21]. Now, βd = ββc is calculated, which enables determining the relative permittivity as a function of frequency (f) without the influence of the internal inductance of the conductor materials. ...
A temperature-dependent modeling approach for interconnects is presented from 23 °C to 139 °C. To develop the proposal, the contribution of the conductor and the dielectric effects to the signal attenuation and delay is quantified from
$S$
-parameters measured to edge-coupled transmission lines configured for differential signaling. Moreover, by obtaining the frequency and temperature-dependent complex permittivity of the dielectric and the characteristic impedance of the lines, a model and parameter extraction strategy for the
RLGC
parameters is proposed. This allows for a representation as a function of temperature and up to 12 GHz, which falls within the operation conditions of practical printed circuit boards based on glass fiber reinforced epoxy laminate materials.
... To avoid this situation, we can first define the form of the solution. In this method, we use a third-order polynomial expression to approximate the insertion loss [6], which is written as ...
In this paper, we investigate data-driven parameterized modeling of insertion loss for transmission lines with respect to design parameters. We first show that direct application of neural networks can lead to non-physics models with negative insertion loss. To mitigate this problem, we propose two deep learning solutions. One solution is to add a regulation term, which represents the passive condition, to the final loss function to enforce the negative quantity of insertion loss. In the second method, a third-order polynomial expression is defined first, which ensures positiveness, to approximate the insertion loss, then DeepONet neural network structure, which was proposed recently for function and system modeling, was employed to model the coefficients of polynomials. The resulting neural network is applied to predict the coefficients of the polynomial expression. The experimental results on an open-sourced SI/PI database of a PCB design show that both methods can ensure the positiveness for the insertion loss. Furthermore, both methods can achieve similar prediction results, while the polynomial-based DeepONet method is faster than DeepONet based method in training time.
... Regarding dielectric characterization approaches, several test fixtures are used to collect the data that allows for the determination of the dielectric constant (Dk) and the dissipation factor (Df) or loss tangent: capacitors (either coaxial or parallel plate), resonators, horn antennas (e.g., for freespace measurements), Bereskin arrays, etc. [3]. Nevertheless, the transmission line based method is the most popular choice since it allows for a broadband quasi-continuous parameter determination [4]. Particularly, stripline structures are preferred since the measurements include the effects to be considered in a practical planar interconnect embedded within the laminate of interest. ...
... where c is the speed of light, whereas A is a fitting constant that allows accounting for the effect of the internal inductance on β at low frequencies [4]. In this case, A can be obtained by using low frequency characteristic impedance (Zc) data as explained in [9]. ...
... In this case, A can be obtained by using low frequency characteristic impedance (Zc) data as explained in [9]. At this point, it is necessary to remark the fact that simplifying (8) to the popular equation Dk ≈ (cβ/2πf ) 2 implies neglecting the impact of the effect of the metal line on β, which is noticeable up to several hundreds of megahertz [4]. Hence, it is preferable to use (8) to avoid overestimation of Dk at low frequencies. ...
Whereas determining Dk of a PCB laminate is simple from transmission-line measurements using either TRL-like or Delta-L extractions, obtaining Df is cumbersome since S-parameters include the combined effect of dielectric and metal losses. This becomes accentuated in advanced processes due to the extremely low Df achieved in today's laminates. Nonetheless, Df is a key figure-of-merit for assessing PCBs intended for multigigabit-per-second data transmission. Hence, we take advantage of the accuracy achieved in obtaining Dk to systematically implement, through simple linear regressions, a multi-pole Debye model that allows reproducing Df for an advanced laminate up to at least 50 GHz. 3 Authors Biographies Eduardo Moctezuma-Pascual was born in Veracruz, Mexico. He received the B.S. degree in Electronics from the Tecnológico de La Piedad, Michoacán, Mexico in 2016 and the M.Sc. from INAOE Research Center, Puebla, Mexico, in 2018. He is currently working toward the Ph.D. degree in Electronics at INAOE. His areas of interest include high-frequency measurement, characterization, and modeling of dielectric materials intended for high-frequency applications. Svetlana C. Sejas-García is a Research Engineer with SV-Probe, AZ. She received the B.S. degree in Electronics from the University of Puebla, Mexico, in 2005 and the Ph.D. degree in Electronics from INAOE, in 2014. In 2008, she was an Intern with Intel, and from 2015 to 2019 she worked for Isola Co. in developing experiment and simulation based methodologies for assessing the performance of high-speed interconnects on packaging technology. Currently, she works for SV-Probe, AZ working in a R&D team dedicated to power integrity oriented projects. Doug Trobough is the Corporate Director of Application Engineering at Isola Corp. Doug has worked introducing new materials and PCB processing enhancement with Isola for several years. Prior to Isola, Doug had almost 30 years of experience building a wide variety of PCB types and interconnection systems, for Tektronix and Merix Corp., in a variety of technical positions, including CTO for Merix Corp. Reydezel Torres-Torres is with INAOE Research Center, Mexico. He possesses 20 years of experience in developing models and parameter extraction methodologies for materials, interconnects, and devices used for RF electronics. For several years he has been a Speaker at Designcon and, among the technology companies where former graduate students of his have worked with include: Intel, Visteon, SV-Probe, Isola, imec, and Corning. 4
... Coaxial airfilled line that is shown in Fig. 3c is applicable for measurements of popping compounds using differential phase method [3] or solid dielectrics and magnetic materials using Nicolson-Ross-Weir (NRW) technique [4]. A specially designed test vehicle "General Board" that includes 6 types of the transmission lines for measurements by Stripline Sweep S-parameters (S3) method [5] and ring resonator method is shown in Fig. 3d. Measuring cell for ceramic substrate materials is shown in Fig. 3e. ...
Designed and manufactured set of measuring test fixtures for printed circuit board (PCB) materials research and characterization is described in this article. Attention is paid to special designed test vehicle “General board” which includes six types of transmission lines that are used for PCB materials characterization by two measurement methods. Measurements of the frequency dependencies of the dielectric constant and dielectric loss for a number of the most widely used PCB substrates are presented. The comparison of the measurement results made by two measurement methods is also shown. The influence of the inhomogeneities of the PCB dielectric and some differences in the extracted material parameters data correlated with electro-magnetic fields structure in different transmission lines is demonstrated. In addition it is shown that measurements performed using “General board” can be used for characterization of the losses due to PCB surface plating.
... The profiles can be obtained by scanning electron microscope (SEM). As shown in Fig. 6 [16], they are standard (STD), very-low-profile (VLP), and hyper-VLP (HVLP) foils, respectively. The geometrical dimensions and roughness data of them are listed in [16]. ...
... As shown in Fig. 6 [16], they are standard (STD), very-low-profile (VLP), and hyper-VLP (HVLP) foils, respectively. The geometrical dimensions and roughness data of them are listed in [16]. ...
... From Fig. 10, it is seen that the simulated attenuation due to the conductor loss agrees well with the measured one for all three structures. Furthermore, combined with the impact of Dk and Df in dielectric layers [16], the total attenuation constants of (19) Fig. 11. ...
In this paper, a novel semianalytical gradient model (SAGM) for characterizing conductors with surface roughness is presented. Based on the linear function of conductivity, the governing equation of the magnetic field is reduced to the modified Bessel equation, which has an analytical solution. With the piecewise linear approximation technique, the SAGM is derived to deal with arbitrary functions of conductivity. Three typical distributions, including the uniform, normal, and Rayleigh distributions, are investigated. The proposed SAGM is employed to evaluate the propagation properties of typical transmission line structures with different surface roughness profiles. The simulation results agree well with those from measurements, which confirm the validity and accuracy of the proposed method.
... The properties of the ambient laminate dielectric (Megtron 6) are also taken the same as in [6]. These dielectric and roughness parameters were extracted using the experiment-based differental extrapolation roughness method (DERM) applied to the complex propagation constant as is described in [4], [7]. Since these dielectric and ERD data have been well validated by numerous measurements and numerical simulations, they can be reliably used herein to predict mixed-mode Sparameters based on the full-wave numerical simulations. ...
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... A proper metric is required to quantify roughness profile effects upon loss and phase constant (or delay time). A roughness factor QR introduced in [14] is defined as ...
... In [14], it is proposed that the total roughness factor on the trace QR consists of two terms, corresponding to the roughness on the "foil" and "oxide" sides of the conductor ...
... A few examples of the extracted roughness profile data using the proposed herein technique, correlating these data with effective roughness dielectric parameters, and validation through the agreement between the measured and 3-D full-wave numerical modeling are provided in [14], [15], and [17]. ...
Conductor (copper) foil surface roughness in printed circuit boards (PCBs) is inevitable due to adhesion with laminate dielectrics. Surface roughness limits data rates and frequency range of application of copper interconnects and affects signal integrity (SI) in high-speed electronic designs. In measurements of dielectric properties of laminate dielectrics using traveling-wave techniques, conductor surface roughness may significantly affect accuracy of measuring dielectric constant (DK) and dissipation factor (DF), especially at frequencies above a few gigahertz, when copper roughness is comparable to skin depth of copper. This paper proposes an algorithm for characterization of copper foil surface roughness. This is done by analyzing the microsection images of copper foils obtained using optical or scanning electron microscopes. The statistics obtained from numerous copper foil roughness profiles allows for introducing a new metric for roughness characterization of PCB interconnects and developing “design curves,” which could be used by SI engineers in their designs.
... As opposed to the DERM technique, in the new improved technique, which we have called DERM2 [6], both real and imaginary parts of the complex propagation constant (loss constant ; ...
A new improved traveling-wave technique to characterize material properties of printed circuit boards over a broad frequency range is proposed. This experiment-based technique is the further development of the differential extrapolation roughness measurement (DERM) technique, which separates conductor loss from dielectric loss on PCB striplines. The new improved technique is called DERM2. It is applied to both loss constant and phase constant, as opposed to the DERM procedure, which deals with the loss constant only. The DERM2 technique allows for more accurate extraction of DK and DF values, as well as losses due to smooth conductor and rough conductor-dielectric interface. The application of the DERM2 procedure to a set of five test vehicles with the same dielectric and geometry, but different copper foil roughness, is demonstrated. A new metric called "roughness factor" QR to quantify roughness profiles has been introduced. The correlation between additional slope in insertion loss due to roughness and the QR factor has been established, and it leads to the development of the "design curves", which could be used by SI engineers in their designs.
The conductor surface roughness effect on microstrip lines is physically represented by proposing a step-by-step methodology that uses experimental
$S$
-parameters supported by electromagnetic (EM) simulations assuming smooth conductor surfaces. This avoids implementing the microstrip line model by arbitrarily fitting simulations with experimental data that include multiple-frequency-dependent effects. Furthermore, a priori knowledge of the roughness profile is not required in this proposal. From the analysis, the peak-to-valley feature of the surface roughness that allows for the representation of the corresponding effect on the electrical response of the lines is obtained. The implemented models show a correlation with experimental data up to 35 GHz.
