Showing papers by "Fred Barlow published in 2015"

Spectrally Accurate Causality Enforcement Using SVD-Based Fourier Continuations for High-Speed Digital Interconnects

Abstract: We introduce an accurate and robust technique for accessing the causality of network transfer functions given in the form of band-limited discrete frequency responses. These transfer functions are commonly used to represent the electrical response of high-speed digital interconnects used on chip and in electronic package assemblies. In some cases, small errors in the model development lead to noncausal behavior that does not accurately represent the electrical response and may lead to a lack of convergence in simulations that utilize these models. The approach is based on Hilbert transform relations or Kramers–Kronig dispersion relations and a construction of causal Fourier continuations using a regularized singular value decomposition method. Given a transfer function, nonperiodic in general, this procedure constructs highly accurate Fourier series approximations on the given frequency interval by allowing the function to be periodic in an extended domain. The causality dispersion relations are enforced spectrally and exactly. This eliminates the necessity of approximating the transfer function behavior at infinity and explicit computation of the Hilbert transform. We perform the error analysis of the method and take into account a possible presence of a noise or approximation errors in data. The developed error estimates can be used in verifying the causality of the given data. The performance of the method is tested on several analytic and simulated examples that demonstrate an excellent accuracy and reliability of the proposed technique in agreement with the obtained error estimates. The method is capable of detecting very small localized causality violations with amplitudes close to the machine precision.

A Study of Differential Signaling: Stable and Accurate Mixed-Mode Conversion and Extraction of Differential S-Parameters

Abstract: Low voltage differential signaling (LVDS) in high-speed digital systems is utilized to effectively reduce EMI and improve signal quality. Mixed-mode S-parameters are a more general way to characterize a differential network. Therefore, an accurate extraction of mixed-mode S-parameters from single-ended S- parameters is critical for Signal and Power Integrity co-simulation where SSN is generated mainly by high-frequency interconnects. The standard conversion between mixed-mode and single-ended S-parameters involves inversion of a transformation matrix. If there is no coupling, this transformation matrix is orthogonal and numerical inversion can be done accurately. In the presence of coupling, the transformation matrix depends on S-parameters and may become ill-conditioned, i.e. has high condition number, for some values of physical parameters resulting in unstable inversion of the transformation matrix and leading to highly inaccurate converted mixed-mode S-parameters. To analyze the possibility of ill-conditioning, we consider two cases: broadside coupled striplines and coupled microstrip pairs. We find that in both cases when two transmission lines are strongly coupled, the condition number becomes very large. In this case, regularized methods from the theory of ill-posed problems should be used, for example, the truncated SVD method, to obtain accurate mixed-mode S- parameters.

Time Delay Extraction from Frequency Domain Data Using Causal Fourier Continuations for High-Speed Interconnects

Abstract: We present a new method for time delay estimation using band limited frequency domain data representing the port responses of interconnect structures. The approach is based on the recently developed by the authors spectrally accurate method for causality characterization that employs SVD-based causal Fourier continuations. The time delay extraction is constructed by incorporating a linearly varying phase factor to the system of equations that determines Fourier coefficients. The method is capable of determining time delay using data affected by noise or approximation errors that come from measurements or numerical simulations. It can also be employed when only a limited number of frequency responses is available. The technique can be extended to multi-port and mixed mode networks. Several analytical and simulated examples are used to demonstrate the accuracy and strength of the proposed technique.

Delay estimation using SVD-based causal fourier continuations for high speed interconnects

Abstract: We propose a new method for time delay extraction in the frequency domain. It is based on the spectrally accurate method for causality characterization that employs singular value decomposition (SVD) based Fourier continuations, which was recently developed by the authors. The time delay estimation approach is constructed by incorporating a linearly varying phase factor. Several analytic and simulated examples are used to demonstrate performance of the proposed technique.

Time Delay Extraction from Frequency Domain Data Using Causal Fourier Continuations for High-Speed Interconnects

Abstract: We present a new method for time delay estimation using band limited frequency domain data representing the port responses of interconnect structures. The approach is based on the spectrally accurate method for causality characterization that employs SVD-based causal Fourier continuations, which was recently developed by the authors. The time delay extraction is constructed by incorporating a linearly varying phase factor to the system of equations that determines the Fourier coefficients. The method is capable of determining the time delay using data affected by noise or approximation errors that come from measurements or numerical simulations. It can also be employed when only a limited number of frequency responses is available. The technique can be extended to multi-port and mixed-mode networks. Several analytical and simulated examples are used to demonstrate the accuracy and strength of the proposed technique.

Causality enforcement for electrical interconnects through periodic continuations

Abstract: Causality evaluation for transfer functions representing the behavior of electrical interconnects of a system is provided herein. An initial transfer function can be received that represents the behavior of electrical interconnects of a system over an initial frequency range. A causal, periodic continuation can then be constructed based on the initial transfer function and one or more causality conditions. The continuation is periodic over an extended frequency range that is larger than the initial frequency range. At a plurality of frequencies, values for the initial transfer function and values for the continuation can be compared. The causality of the initial transfer function can be assessed based on the comparing.