Macro-modeling of non-linear I/O drivers using spline functions and finite time difference approximation

Abstract

In this paper a modeling methodology using spline functions with finite time difference is proposed for modeling digital U 0 drivers. Digital driver circuits can be accurately modeled using their static characteristics for normal excitations, but for faster excitations static characteristic models tend to lose their accuracy as the dynamic characteristics start to dominate the static characteristics. Spline function with finite time difference modeling includes previous time instances to capture dynamic characteristics for accurate modeling of digital drivers. In this paper the speed and accuracy of the proposed method is analyzed and compared with Radial Basis Function (RBF) modeling for different test cases.

Power distribution networks for system-on-package: status and challenges

“…Model reduction [35] and macromodeling methods [36], [40]- [42] have been developed and applied to power distribution structures for reducing the problem size and for black-box representations. The frequency response from linear time invariant networks have been interpolated using vector fitting in [36] and broad-band macromodeling in [41], which enables the representation of the network as a reduced spice netlist to which other circuit elements can be connected.…”

Modeling and design for beyond-the-die power integrity

“…To accommodate the situations where the dynamic characteristics are important (especially in high-speed I/O), several works have been proposed to use the radial basis function (RBF) to represent the I/O buffer's dynamic behavior [24]- [26]. While such models can be quite accurate, their complexities soon become intractable for complex driver circuits with multiple ports [27]. To improve this, modeling technique using spline functions with a finite time difference approximation has been proposed to model moderately nonlinear I/O buffers [28].…”

Automated nonlinear Macromodelling of output buffers for high-speed digital applications

“…Black-box methods refer to a broad set of modelling approaches, such as artificial neural networks (ANN) (e.g., [23]), radial basis functions (RBF) (e.g., [12,19]), lookup tables (e.g., [22]), etc.. They treat the system being modelled as a black box and reverseengineer input-output behavior using data sampled from simulation or measurement.…”

“…Finally, the generated macromodel is represented as an equivalent sub-circuit, which is implemented in SPICE and simulated with load interconnects. It has been shown (e.g., [12,19,20]) that these methods are capable of representing the driver circuit well and capturing the effects like crosstalk, SSO, etc.. However, the efficacy of black-box methods relies heavily on the choice of model representations, data sets generation and interpretation.…”

“…Recently, a newer class of black-box methods (e.g., [12,19,20]) was proposed with the goal of better capturing I/O driver dynamics. In additional to the static I-V characteristics used in IBIS models, this class of methods uses Radial Basis Functions (RBFs) or splines in order to obtain "higher-order" accuracy in capturing the output behavior of driver circuits.…”