16,996 research outputs found
A Parameterization Scheme for Lossy Transmission Line Macromodels with Application to High Speed Interconnects in Mobile Devices
We introduce a novel parameterization scheme based on the generalized method of characteristics (MoC) formacromodels of transmission-line structures having a cross section depending on several free geometrical and material parameters. This situation is common in early design stages, when the physical structures still have to be finalized and optimized under signal integrity and electromagnetic compatibility constraints. The topology of the adopted line macromodels has been demonstrated to guarantee excellent accuracy and efficiency. The key factors are propagation delay extraction and rational approximations, which intrinsically lead to a SPICE-compatible macromodel stamp. We introduce a scheme that parameterizes this stamp as a function of geometrical and material parameters such as conductor-width and separation, dielectric thickness, and permettivity. The parameterization is performed via multidimensional interpolation of the residue matrices in the rational approximation of characteristic admittance and propagation operators. A significant advantage of this approach consists of the possibility of efficiently utilizing the MoC methodology in an optimization scheme and eventually helping the design of interconnects.We apply the proposed scheme to flexible printed interconnects that are typically found in portable devices having moving parts. Several validations demonstrate the effectiveness of the approac
Passivity Enforcement via Perturbation of Hamiltonian Matrices
This paper presents a new technique for the passivity enforcement of linear time-invariant multiport systems in statespace form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system input-output transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on first-order perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that first-order perturbation is applicable. Several examples illustrate and validate the procedure
Rational minimax approximation via adaptive barycentric representations
Computing rational minimax approximations can be very challenging when there
are singularities on or near the interval of approximation - precisely the case
where rational functions outperform polynomials by a landslide. We show that
far more robust algorithms than previously available can be developed by making
use of rational barycentric representations whose support points are chosen in
an adaptive fashion as the approximant is computed. Three variants of this
barycentric strategy are all shown to be powerful: (1) a classical Remez
algorithm, (2) a "AAA-Lawson" method of iteratively reweighted least-squares,
and (3) a differential correction algorithm. Our preferred combination,
implemented in the Chebfun MINIMAX code, is to use (2) in an initial phase and
then switch to (1) for generically quadratic convergence. By such methods we
can calculate approximations up to type (80, 80) of on in
standard 16-digit floating point arithmetic, a problem for which Varga, Ruttan,
and Carpenter required 200-digit extended precision.Comment: 29 pages, 11 figure
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Rational quadratic spline interpolation to monotonic data.
In an earlier paper by Gregory & Delbourgo (1982), a piecewise rational quadratic function is developed which produces a monotonic interpolant to monotonic data. This interpolant gives visually pleasing curves and is of continuity class C1 . In the present paper, the data is restricted to be strictly monotonic and it is shown that it is possible to obtain a
monotonic rational quadratic spline interpolant which is of continuity class .C2 An ○(h4) convergence analysis is included
Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
We present a novel analytic extraction of high-order post-Newtonian (pN)
parameters that govern quasi-circular binary systems. Coefficients in the pN
expansion of the energy of a binary system can be found from corresponding
coefficients in an extreme-mass-ratio inspiral (EMRI) computation of the change
in the redshift factor of a circular orbit at fixed angular
velocity. Remarkably, by computing this essentially gauge-invariant quantity to
accuracy greater than one part in , and by assuming that a subset of
pN coefficients are rational numbers or products of and a rational, we
obtain the exact analytic coefficients. We find the previously unexpected
result that the post-Newtonian expansion of (and of the change
in the angular velocity at fixed redshift factor) have
conservative terms at half-integral pN order beginning with a 5.5 pN term. This
implies the existence of a corresponding 5.5 pN term in the expansion of the
energy of a binary system.
Coefficients in the pN series that do not belong to the subset just described
are obtained to accuracy better than 1 part in at th pN
order. We work in a radiation gauge, finding the radiative part of the metric
perturbation from the gauge-invariant Weyl scalar via a Hertz
potential. We use mode-sum renormalization, and find high-order renormalization
coefficients by matching a series in to the large- behavior of
the expression for . The non-radiative parts of the perturbed metric
associated with changes in mass and angular momentum are calculated in the
Schwarzschild gauge
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