Mikheil Tsiklauri

Causality and delay and physics in real systems

In the present work causality property and physics behind it is analyzed for physical systems. Different methodologies for checking or enforcing causality in both time and frequency domain are discussed. Causality metric for measuring causality violation is introduced. Physical anomaly of a system with perfectly linear phase is discussed and shown that small perturbation of non-linear portion of the phase can fix the non-causal anomaly.

Analytical and numerical sensitivity analyses of fixtures de-embedding

De-embedding procedures are sensitive to manufacturing variations in test fixtures, as well as inaccuracies associated with the calibration and measurement process. Such sensitivities can propagate through de-embedding procedures, resulting in amplified errors. In this paper, analytical and numerical techniques are used to perform sensitivity studies on both simulation and measurement data, with respect to de-embedding.

Design criteria of automatic fixture removal (AFR) for asymmetric fixture de-embedding

Automatic fixture removal (AFR) for asymmetric fixture de-embedding is introduced. Two design criteria for fixture design in AFR, passivity and discontinuity, are proposed. Three different 2x-fixtures are investigated for the verification of proposed two design criteria.

Design Criteria and Error Sensitivity of Time-Domain Channel Characterization (TCC) for Asymmetry Fixture De-Embedding

Time-domain channel characterization (TCC) for de-embedding of an asymmetric fixture is introduced. Two design criteria for the design of a 2x-thru are proposed. Error sensitivity regarding a small error in the S-parameters of the 1x-fixture is analyzed with an insertion loss error-coefficient and a return loss error-coefficient. The TCC procedure, including proposed design criteria and error sensitivity, is also introduced to reduce the error in the TCC application. Three different 2x-thru structures are investigated for the verification of the two proposed design criteria and analyzed for error sensitivity. Test fixtures on a printed circuit boards are fabricated for the experimental verification.

THE FOURTH ORDER OF ACCURACY DECOMPOSITION SCHEME FOR ABSTRACT HYPERBOLIC EQUATION

Abstract Using the rational splitting of a cosine operator-function, the fourth order accuracy decomposition scheme is constructed for hyperbolic equation when the principal operator is self-adjoint positively defined and is represented as a sum of two summands. Stability of the constructed scheme is shown and the error of an approximate solution is estimated.

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.