Causal Transient Simulation of Systems Characterized by Frequency-Domain Data in a Modified Nodal Analysis Framework

Lalgudi, S.N.; Srinivasan, Krishna; Casinovi, G.; Mandrekar, R.; Engin, Ege; Swaminathan, Madhavan; Kretchmer, Yaron

doi:10.1109/epep.2006.321207

Cited by 6 publications

(4 citation statements)

References 3 publications

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“…The relatively large reconstruction error at the boundary comes from low smoothness order of the transfer function and the polynomial continuation, as well as from low resolution. To show this, we investigate the error E F of the approximation of a function g that has k continuous derivatives with a first 2M-mode Fourier series, given in (21). We note that…”

Section: Finite Element Model Of a Dynamic Random Access Memory Pamentioning

confidence: 99%

“…The dispersion relations are extremely important in many areas of physics, science and engineering. In particular, in electronics, they are used in reconstruction [12] and correction [13,14] of measured data; delay extraction [15][16][17]; timedomain conversion [18]; estimation of optimal bandwidth and data density [19]; and various causality verification and enforcement techniques that are based on minimum phase and all-pass decomposition [16,17,[20][21][22], generalized dispersion relations with subtractions [23][24][25], causality characterization via analytic continuation for L 2 integrable functions [26], and causality enforcement using periodic continuations [27,28], which is the subject of the current study.…”

Section: Introductionmentioning

confidence: 99%

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Causality Verification Using Polynomial Periodic Continuations for Electrical Interconnects

Barannyk¹,

Aboutaleb²,

Elshabini³

et al. 2014

Journal of Microelectronics and Electronic Packaging

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We present a method for checking causality of band-limited tabulated frequency responses. The approach is based on Kramers-Krönig relations and construction of periodic polynomial continuations. Kramers-Krönig relations, also known as dispersion relations, represent the fact that real and imaginary parts of a causal function form a Hilbert transform pair. The Hilbert transform is defined on an infinite domain, while, in practice, discrete values of transfer functions that represent high-speed interconnects are available only on a finite frequency interval. Truncating the computational domain or approximating the behavior of the transfer function at infinity causes significant errors at the boundary of the given frequency band. The proposed approach constructs a periodic polynomial continuation of the transfer function that is defined by raw frequency responses on the original frequency interval and by a polynomial in the extended domain, and requires the continuation to be periodic on a wider domain of a finite length and smooth at the boundary. The dispersion relations are computed spectrally using fast Fourier transform and inverse fast Fourier transform routines applied to periodic continuations. The technique does not require the knowledge or approximation of the transfer function behavior at infinity. The method significantly reduces the boundary artifacts that are due to the lack of out-of-band frequency responses, and is capable of detecting small, smooth causality violations. We perform the error analysis of the method and show that its accuracy and sensitivity depend on the smoothness and accuracy of data and a polynomial continuation. The method can be used to verify and enforce causality before the frequency responses are employed for macromodeling. The performance of the method is tested on several analytic and simulated examples.

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Section: Finite Element Model Of a Dynamic Random Access Memory Pamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Causality Verification Using Polynomial Periodic Continuations for Electrical Interconnects

Barannyk¹,

Aboutaleb²,

Elshabini³

et al. 2014

Journal of Microelectronics and Electronic Packaging

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show abstract

“…In some applications, models are directly utilized; for example, self-impedance Zn of power delivery planes are analyzed and optimized to push resonant frequencies beyond load operating frequencies and below target impedance [1]. In other applications where time domain SPICE based simulation is necessary, the frequency domain models are processed further [2]; for example, performance of package interconnects [3] can be assessed only in time domain by running a long sequence of Is and Os to evaluate the actual degradation caused to eye diagrams [4]. In such cases, the frequency domain model needs to be converted to a pole/residue representation before being synthesized [5] as lumped element network.…”

Section: Introductionmentioning

confidence: 99%

Pole residue equivalent system solver (PRESS)

Avula

Zadehgol

2016

2016 IEEE 20th Workshop on Signal and Power Integrity (SPI)

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“…The Hilbert transform may be expressed in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, remote sensing and image reconstruction [16], [6]. Applications in electronics include reconstruction [17] and correction [18] of measured data, delay extraction [19], interpolation/extrapolation of frequency responses [20], time-domain conversion [21], estimation of optimal bandwidth and data density using causality checking [22] and causality enforcement techniques using generalized dispersion relations [23], [24], [25], causality enforcement using minimum phase and all-pass decomposition and delay extraction [26], [27], [28], [29], causality verification using minimum phase and all-pass decomposition that avoids Gibbs errors [30], causality characterization through analytic continuation for L 2 integrable functions [31], causality enforcement using periodic polynomial continuations [32], [33], [34] and the subject of the current paper.…”

Section: Introductionmentioning

confidence: 99%

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

Barannyk

Aboutaleb²,

Elshabini

et al. 2015

IEEE Trans. Compon., Packag. Manufact. Technol.

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Abstract-We introduce an accurate and robust technique for accessing causality of network transfer functions given in the form of bandlimited 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 non-causal 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 KramersKrönig dispersion relations and a construction of causal Fourier continuations using a regularized singular value decomposition (SVD) method. Given a transfer function, non-periodic 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 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.

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Causal Transient Simulation of Systems Characterized by Frequency-Domain Data in a Modified Nodal Analysis Framework

Cited by 6 publications

References 3 publications

Causality Verification Using Polynomial Periodic Continuations for Electrical Interconnects

Causality Verification Using Polynomial Periodic Continuations for Electrical Interconnects

Pole residue equivalent system solver (PRESS)

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

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