Jan B. Preibisch

An Efficient Analysis of Power/Ground Planes With Inhomogeneous Substrates Using the Contour Integral Method

An efficient analysis using the contour integral method (CIM) for the modeling of inhomogeneous substrates with circular or arbitrarily shaped dielectric inclusions in planar structures is presented. It is shown how the segmentation method is applied to obtain circuit parameters as well as field values and how different boundary conditions can be implemented. Such an analysis is especially useful for the modeling of photonic crystals power/ground layers (PCPLs) in power delivery networks (PDNs) on printed circuit boards (PCBs). For circular inclusions, an analytical solution is presented, which improves efficiency and accuracy of the proposed method. An equivalent circuit model for cylindrical inclusions is derived, in order to obtain an effective capacitance for low frequencies and an estimate for parasitic effect at higher frequencies. It is shown how circular inclusions can be compared to decoupling capacitors on a basis of impedances. The method is validated with full-wave simulations showing a reduction in simulation time of about one order of magnitude.

Efficient Total Crosstalk Analysis of Large Via Arrays in Silicon Interposers

In this paper, we present for the first time a rigorous crosstalk analysis of through silicon via (TSV) arrays consisting of several hundreds of TSVs in interposers with metallized surfaces, using the physics-based via (PBV) modeling approach for applications up to 500 GHz. The PBV modeling approach is valid for complete and almost complete metallizations of the substrate where radial wave propagation in the parallel-plate structure dominates the electromagnetic properties and is utilized with models of good accuracy for localized and propagating fields in the inhomogeneous dielectrics. The approach shows very good to good agreement of crosstalk results for frequencies up to 500 GHz in comparison to full-wave simulations and attains a speedup of at least two orders of magnitude in comparison to general-purpose simulators. The definition of a weighted power sum for total uncorrelated crosstalk is applied for all channels in the TSV array. These power sum results give more meaningful insights into the global effects of the parameter variations than single crosstalk contributions. Based on variations of several technology and design parameters of TSVs, we derive quantitative estimations of the impact of these parameters on the total crosstalk.

Efficient stochastic transmission line modeling using polynomial chaos expansion with multiple variables

The polynomial chaos expansion (PCE) is widely used in computational electromagnetics to model stochastic parameters and uncertainty. The major drawback of PCE is that the computational costs grow exponentially with the number of stochastic variables. This work presents a systematic and numerically efficient approach for the application of PCE to cascaded transmission lines where the characteristic impedances are stochastically given and independent from each other. As an example, a stepped impedance filter is analyzed containing up to 31 transmission line segments. The modeling approach is validated with Monte-Carlo (MC) and shows a very good agreement and a significant speedup. The presented method is valid for concatenation of any passive linear circuit.

Physics-Based Via and Waveguide Models for Efficient SIW Simulations in Multilayer Substrates

In this paper, the conventional physics-based via (PBV) model is extended to multilayer substrate integrated waveguide (SIW) structures with via feeds. Furthermore, a novel PBV model for a more efficient modeling of multilayer SIW is proposed. This novel method allows to describe SIWs as transmission lines and to model the coupling between the layers with an equivalent circuit near-field model. Both PBV models are compatible and can be combined within a framework for modeling complex multilayer SIWs in an efficient manner. Results obtained by both methods are compared with full-wave solver results and show very good agreement from below cutoff frequency to about three times the cutoff frequency as well as a speed up of several orders of magnitude.

Sensitivity analysis and empirical optimization of cross-domain coupling on RFICs using polynomial chaos expansion

This work aims at investigating the variability of internal coupling mechanisms between different domains of a Radio Frequency Integrated Circuit (RFIC). In doing so, an Equivalent Circuit Model (ECM) is used in order to model the various coupling paths. First, the elements of the ECM are assumed to be uniformly distributed and their exact values therefore not fully known. Afterwards, the impact of theses uncertainties on the cross-domain transfer function, i.e. the coupling from the digital domain – the aggressor – into the other more sensitive domains – the victims – is analyzed using Polynomial Chaos Expansion (PCE) in combination with a sampling-based technique known as Stochastic Testing (ST). This approach intends to account for not accurately known configurations of the RFIC and package. In addition, the PCE representation allows for conducting sensitivity analysis through the derivation of conditional variances, i.e. Sobol indices, and sensitivities. PCE in combination with ST offers an efficient way to analyze the coupling effects. Finally, an improved version of the original design is proposed using an empirical optimization approach based on the techniques described above.

Variability analysis of via crosstalk using polynomial chaos expansion

In this work we use the method of polynomial chaos expansion (PCE) for statistical analysis of a via interconnect in a printed circuit board (PCB) in presence of geometrical uncertainties. A physics-based via (PBV) model is applied to the case of two signal vias surrounded by ground vias. This model consist of a near-field part and a far-field part. Here, the focus is on the far-field part modeled by the contour integral method (CIM). In order to account for variability in the geometry, namely a variation of the pitch, PCE is applied to the CIM in an intrusive manner. The system matrix of the deterministic case is replaced by an augmented version. The method is validated with Monte Carlo Sampling (MC) and shows excellent agreement for a simple geometry. We observe the same agreement in more complicated geometric configurations - at least for frequencies below the first resonance.

Efficient Prediction of Equalization Effort and Channel Performance for PCB-Based Data Links

High-speed data links that utilize multilayer printed circuit boards suffer from loss, dispersion, and intersymbol interference. Often, equalization and error correction are required to make these channels functional at gigabit data rates and demand costly analyses. The characterization of loss-dominated links can be generalized and simplified by means of a normalized link length as presented herein. Based on a correlation of this normalized length and observed eye opening, a novel assessment of wired digital links for frequencies up to 50GHz and data rates up to 30 Gb/s is proposed. It allows for an efficient prediction of the amount and type of required equalization for a given link as well as determining maximum tolerable loss for a given equalizer configuration. The proposed method and its applicability are demonstrated by means of practical examples.

Design space exploration for printed circuit board vias using polynomial chaos expansion

This work discusses how the Williamson equivalent circuit for the modeling of via transitions is augmented using the polynomial chaos expansion (PCE) method to take into account stochastic variations of model parameters. In addition, it is shown how the PCE can be applied in combination with Monte-Carlo (MC) sampling to conduct an efficient design space analysis. The physics-based via (PBV) model is used to efficiently model multilayer via interconnects by concatenating equivalent circuit models representing certain geometric sections of the interconnect. These equivalent circuits are expanded with respect to the stochastic model parameters by means of PCE and concatenated to derive an augmented model of the whole interconnect. From this representation, stochastic scattering parameters are extracted. Numerical examples verify the method and the computational advantages over MC sampling. The method provides a fast and comprehensive approach to design space exploration and variability assessment in the design stage of via interconnects. The presented approach is not limited to via models and can be applied to various microwave structures in a similar way.

Modeling of mutual coupling between coaxial probes in flat metallic casings using the contour integral method

This paper investigates electromagnetic interference mechanisms in flat metallic casings using the contour integral method (CIM). Coaxial monopole probes are used to represent potential radiators, and a local field model is developed and combined with the CIM for evaluation of mutual admittance between the probes. Limitations of the method are discussed.