Nana Dikhaminjia

PAM4 signaling considerations for high-speed serial links

The paper discusses current challenges and advantages of multi-level signaling for high-speed serial links, showing the differences and similarities in link-path analysis between binary and multi-level signaling. Comparison of two signaling methodologies is given from the general theory viewpoint, as well as on the basis of various tests regarding crosstalk, jitter, equalizations and different channel characteristics, such as material, impedance and overall manufacturing design sensitivity.

Front delay based causality for network parameters

In the present work different methods for delay causality checking and/or enforcing are described. Group delay, phase delay and front delay concepts are discussed and front delay usage for causality checking is suggested. Front delay is approximated as a minimum of a phase delay in the given frequency range for band-limited transfer function. Since measured data usually misses DC values, simple and accurate method for DC extrapolation is offered.

Discrete Hilbert Transform based delay causality enforcement for network parameters

Causality is one of the important properties for quality check of network parameters. Discrete Hilbert Transform (DHT) based delay causality checking and/or enforcing method is discussed in the present paper. DHT based causality checking/enforcing algorithm is known but is not widely used in applications. Comparison analysis between DHT based delay causality and other causality checking algorithms is given and advantage of the DHT based algorithm is discussed. Front delay is used for delay causality definition. Several methods for front delay estimation are suggested. Delay causality is checked and enforced for different test cases using the proposed methodology.

Stable recursive convolution for channel response calculation with causality enforcement

Checking and enforcing causality of simulated or measured system data is a crucial step for obtaining valid results. Previously, several methods for both frequency and time domain have been proposed. This paper explores the time domain causality enforcement method, its effect on the frequency domain transfer function, and proposes modification of the recursive convolution algorithm for impulse responses with time domain enforced causality to ensure calculation stability.

Fast Approximation of Sine and Cosine Hyperbolic Functions for the Calculation of the Transmission Matrix of a Multiconductor Transmission Line

A fast and stable algorithm for approximation of sine and cosine hyperbolic functions is presented in this paper. The algorithm can be used for S-parameter calculation from RLGC parameters. The idea is to construct the recurrent relation for the approximate solution of sine and cosine hyperbolic complex value matrix functions. The stability of the proposed algorithm is shown and convergence theorem is proved. In the last section, different numerical simulations are made and compared with the already existing algorithm in terms of calculation time given.

Construction and numerical resolution of high-order accuracy decomposition scheme for a quasi-linear evolution equation

Abstract In the present work the Cauchy problem for an abstract evolution equation with a Lipschitz-continuous operator is considered, where the main operator represents the sum of positive definite self-adjoint operators. The fourth-order accuracy decomposition scheme is constructed for an approximate solution of the problem. The theorem on the error estimate of an approximate solution is proved. Numerical calculations for different model problems are carried out using the constructed scheme. The obtained numerical results confirm the theoretical conclusions.

Improved MMSE algorithm for DFE optimization

The signal in channels with high-speed designs is attenuated by channel loss, inter-symbol interference, jitter, noise and crosstalk. The main way to recover the signal is by using equalizations, such as Feed-Forward Equalizer, Continuous Time-Linear Equalizer and Decision Feedback Equalizer (DFE). One of the important problems with high-speed design and channel simulations is developing fast optimization algorithms for each equalizer, as each additional tap increases the cost of the chip. The paper proposes a new efficient optimization of DFE for high-speed links. Mathematical formulation of the optimization is discussed. Different test results are given for comparison purposes.

S-parameters quality estimation in physical units

S-Parameters are the most common way to describe electrical behavior of linear electric networks. However, any available S-Parameters that is available for describing a physical system is not perfectly accurate and does not describe it comprehensively. It becomes important to be able to estimate the quality of existing data in order to achieve reliability of the results and conclusions developed based on it. A metric is created in the present work to estimate a physical system based on passivity, reciprocity and causality properties in physical units. First, based on the original S-Parameters, will be created passive, causal and reciprocal S-Parameters; then similarity metric will be defined in time domain to get estimation in physical units; finally similarity metric in time domain will be applied between original and passive, causal and reciprocal matrices to get correspondingly passivity, causality and reciprocity estimations in physical units.

A novel z-directed embedded component for the reduction of voltage ripple on the power distribution network for PCBs

A new capacitor package and PCB embedding technique is introduced to significantly reduce the system power distribution network impedance at the pads of surface mounted integrated circuits. The capacitor is multi-layer ceramic capacitor (MLCC) that is a right cylindrical shape with via channels in the outer wall along the axis of the part. The capacitor called a Z-Directed component (ZDC) is then pressed into a hole in the PCB. The connections to the component are then made by the copper plating process similar to via hole construction. This new configuration dramatically improves the PDN performance of PCBs with fewer components than the conventional solution with SMD decoupling capacitors.

Equalization Enhancement Approaches for PAM4 Signaling for Next Generation Speeds

Four-level pulse-amplitude modulation signal (PAM4) is gaining more attention as an alternate coding scheme to binary modulation NRZ (Non Return to Zero) in high speed systems as the signal rate is reduced by half. Transmitter and receiver equalizations continue to play an important role with PAM4 encoding. Even though de-emphasis is a well standardized approach for equalization in NRZ, two enhancement approaches for PAM4 de-emphasis are proposed in the paper. The first enhancement approach is to compensate voltage levels in the de-emphasis process and the second one is to equalize the signal by bit rather than by symbol. Several test cases are presented to show the improvement in eye opening compared to the old approach. The limitations of these two enhancement approaches are also discussed.