Takashi Hisakado

Characterization of a simple communication network using Legendre transform

We describe an application of the Legendre transform to communication networks. The Legendre transform applied to max-plus algebra linear systems corresponds to the Fourier transform applied to conventional linear systems. Hence, it is a powerful tool that can be applied to max-plus linear systems and their identification. Linear max-plus algebra has been already used to describe simple data communication networks. We first extend the Legendre transform as the slope transform to non-concave/non-convex functions. We then use it to analyze a simple communication network. We also propose an identification method for its transfer characteristic, and we confirm the results using the ns-2 network simulator.

Live line measurement of untransposed three phase transmission line parameters for relay settings

The purpose of this study is to develop a method to measure untransposed transmission line parameters for protection relay setting. For relaying schemes such as distance relays, current differential relays and fault locators, it is very useful to ascertain the precise setting values in service, without the need for setting calculations prior to installation, and also for the relays to be able to adaptively change their settings as the system configuration changes. This paper describes a method of live line measurement of the parameters of an untransposed three phase one circuit transmission line and untransposed two parallel transmission lines and necessary conditions to measure line parameters. We propose a mathematical approach using synchronous voltages and line currents at both ends of the line in different states, where two models, the equivalent PI circuit and distributed constant line, are employed. For two parallel transmission lines, applying a mode decomposition, we show that two parallel transmission lines can be transformed into double independent three phase circuits. The efficiency and issues are shown using several simulation examples in MATLAB.

Logically reversible arithmetic circuit using pass-transistor

This paper proposes novel reversible logic circuits, i.e., a reversible ExOR gate and a two-way AND gate. The gates operate in both directions and the input and output are indistinguishable. We design the circuits using dual-line pass-transistor logic. Applying the method to arithmetic circuits, we realize logically reversible arithmetic circuits. Because proposed circuits have no garbage output, the adder and multiplier operate as the subtracter and divider respectively by replacing the input with the output. We confirm the behavior of the circuits by both real experiments and SPICE simulations.

An improvement of convergence of FFT-based numerical inversion of Laplace transforms

This paper presents an improvement on the FFT-based numerical inversion of Laplace transforms. Since the inversion obtained by the FFT-based method contains large errors for the latter half of the result, only the former half is acceptable. We analyze the truncation error which is the largest part of the error, and propose the acceleration method, taking notice of the property of the complex frequency s as the differential operator in the time domain. The errors are markedly reduced by this method, and the entire result becomes acceptable.

Algebraic representation of error bounds for describing function using Groebner base [nonlinear circuit analysis example]

This paper presents an algebraic approach to find the region where the true periodic solution of a nonlinear system or circuit lies when a describing function solution is given. Because algebraic representations of the error bounds are obtained by the Groebner base, the dependence of the bounds on parameter values becomes clear. Further, we propose an efficient method to improve the estimation. The Groebner base is shown to be applicable to the describing function method. The estimation is modified considerably.

Analytical calculation of the point-to-point partial inductance of a perfect ground plane

The point-to-point partial self inductance of an infinite and perfectly conducting ground plane has been analytically calculated in closed form. The point-to-point mutual coupling between ground plane and a trace parallel to the ground plane has been expressed in terms of an integral, which should be solved numerically. The calculations are based on a new scalar potential directly related to the concept of partial inductances. Formulas for the conversion of partial inductances between the Lorenzs and Coulombs gauges are also obtained. The definition of partial inductance in terms of the vector potential (e.g. in [1]) implicitly introduces equivalent circuits, where the voltage represents a difference of a scalar potential defined by the electric field and by the magnetic vector potential at the same time. Therefore, it should not surprise the possibility of having a partial inductance also on perfect ground planes. A part from the definition of the magnetic vector potential, the definition of ground plane partial inductance depends on the application, in particular on the considered current distribution on the ground plane. For example, in [2] the ground plane inductance is defined in terms of the induced current on the ground plane by a micro-strip conductor. In the present work, we will consider the current injected in one point and extracted from a second point on the ground plane, similarly to [3]. This type of partial inductance appears when there are connections to a ground plane, such as cables or micro-strip terminations. In a less proper way, it can be used for approximately representing the inductance related to the displacement current, when a micro-strip is decomposed in short segments carrying constant current. The numerical calculation of the point-to-point ground partial inductance is already considered in software of widespread use, such as FASTHENRY [4]. However, the segmentation of the ground plane can become a problem for configurations with high density of conductors [5]. The calculation time increases for larger ground planes, also because the image theory cannot be directly applied to the calculation of partial inductances.

An implementation of numerical inversion of Laplace transforms on FPGA

This paper presents an implementation of numerical inversion of Laplace transforms on FPGAs. To make real-time transient analysis possible using Laplace transforms, it is desirable to implement the hardware of numerical inversion of Laplace transforms. However, the implementation of the FFT-based numerical inversion method with fixed-point numbers results in severely large errors due to the exponential function which appears in the inversion formula. In order to overcome this difficulty, we propose the use of a block floating-point FFT in the implementation. As a result, the errors are much reduced.

Quasi-static lumped element stand-alone package model for quad flat package

A new type of package model is introduced, which allows to take into account the effect of external structures, such as PCB traces and ground plane, by limiting at the same time the disclosure of internal details of the package. The model is verified with a scaled quad flat package (QFP) and two different printed circuit board (PCB) patterns, but the general procedure should be applicable to other types of package.

Indirect extension of the image theory to partial inductance calculations

Within the limitations implicit in the magneto-quasi-static approximation, partial inductances are a valuable tool for modeling IC package and interconnect inductances. In the calculation of partial inductances it is not possible to directly apply the image theory due to the absence of charges on the ground plane. In the present paper a correction term is obtained, which allows to calculate partial inductances with the image theory, avoiding in this way the problem of the ground plane segmentation. The formula is valid for conductors parallel to the ground plane. The accuracy of the formula is verified and discussed.

Interval arithmetic using Gray code

The Gray code arithmetic is characterized by the bit serial arithmetic from the most significant bit and the uniqueness of the representation. This paper describes that the properties of the Gray code are very effective for interval arithmetics. First, we represent the interval using the Gray code and propose an effective representation of the Gray code interval. Next, we show an algorithm for the derivation of the representation. Last, we suggest that the computational cost of the Gray code interval is decreased by the proposed representation.