Inductance Matrix Research Articles

Modeling complex via hole structures

Derives a physics-based circuit model for complex via hole structures in printed circuit boards. The via hole is modeled as a cascade of capacitance and inductance matrices. Capacitance values are computed using a three-dimensional electrostatic solver and inductance values are computed from a two-dimensional quasi-TEM solver. This model is valid at frequencies up to a few gigahertz for typical via hole geometries, where the return current follows a well defined path.

Inductance extraction for packages with adaptive non-orthogonal ground plane meshing

A method is presented in which a geometry and frequency dependent precalculation of large pin count flat package ground plane currents is performed. We use this precalculation to construct an adaptive nonorthogonal partial element equivalent circuit (PEEC) grid for the correct modeling of the inductance matrix of packages with minimal ground plane discretizations needed. The method is illustrated for a 40-pin flat package. Special attention is given to the convergence and accuracy of the results as a function of the number of PEEC filaments, demonstrating the superiority of the adaptive meshing.

Impedances for the Calculation of Electromagnetic Transients within Transformers

In this paper, a deep analysis of the behavior of transformer winding impedances for high frequencies is performed. The properties of inductance matrices are analyzed, as well as the possibility of making assumptions and their range of validity. The properties of resistance matrices are also analyzed, which has not been made in the past. The discussion on the influence of the iron core on inductance and resistance matrices is undertaken. The analysis is based on impedance measurements carried out on experimental transformer windings. Finally, recommendations are made about which are the most suitable impedance models for modeling transformers impedances during transient and resonance calculations.

Mathematical approach to current sharing problem of superconducting triple strands

Current sharing between insulated strands in a superconducting cable is one of the important problems for its utilization. From the view points of the inverse problem, the sensitivity of current sharing between the insulated strands is determined by the condition number of the inductance matrix. For triple strands with self similar structure, we derive the analytic form of the inductance matrix which only includes two parameters; the self inductance of a unit wire and the ratio of mutual to self inductance for unit wires. Since the matrix elements also have self similar structure, we can analytically obtain the eigenvalues, eigenvectors and condition number, which is the ratio of maximum and minimum eigenvalues. Next, we derive the formula to estimate the sensitivity of the current distribution against the displacement of inductance from the ideal case by use of the condition number. This formula shows that the sensitivity is inversely proportional to the difference of self and mutual inductances of unit wires. Moreover, we estimate the condition number of very thin wire to check our formula. Finally, we verify our analytic form by numerical calculations.

Estimation of electrical parameters of large-scale superconducting coil system for fusion plasma experimental facility

The Large Helical Device (LHD) in the National Institute for Fusion Science (NIFS) has six sets of large scale superconducting coils and six dc power supplies to charge them. For the current controllers of these power supplies, high accuracy of current control, good response and robustness of system are required. In the design of the controller, it was pointed out that the correct inductance matrix of the coil system and some electrical parameters that describe metal structures such as a supporting shell are necessary. This paper introduces a method based on a frequency response of impedance to estimate these parameters. First, the measured inductances of the LHD superconducting coils, which are measured from coil terminals, are presented and discussed. Next, an estimation method for circuit parameters is described. Finally, an experimental result of coil excitation using these parameters is presented. The experimental result show that the coil current controller using the estimated model satisfies previous requirements and it is confirmed that this parameter estimation method is valid for the large scale coil system.

Quasi-Static Variational Analysis of Planar Spiral Conductors

The analysis of a multilayered structure consisting of several planar spiral conductors with a common vertical axis is reduced to a treatment of certain rotationally symmetric electro- and magnetostatic field problems. These problems are solved using the variational method and the Rayleigh-Ritz procedure. The unknown charge and current distributions on the surfaces of the conductors are estimated by compact sets of basis functions. Due to the inhomogeneity of the medium the treatment is carried out in the Hankel-transformed domain. The elements of the resulting capacitance and inductance matrices are used to create a network model for the original structure. Finally, the method is verified against FEM simulations in a case of a simple spiral inductor, and a good agreement is found.

Analysis of Circulant Symmetric Coupled Strip Lines

In this paper a new kind of coupled transmission lines called circulant symmetric coupled microstrip structure and its application as an interconnect in high speed integrated circuits will be introduced. Also a simple method for frequency domain and transient analysis of this kind of coupled microstrip transmission lines is presented. First the capacitance ([C]) and inductance ([L]) matrices of the structure are derived. An special matrix is then defined to decompose the differential equations of the lines and diagonalize the [L] and [C] matrices (modal decomposition method). Finally the frequency domain solution is obtained and FFT algorithm is used to find the time domain response of the line.

Analysis of isolated self-excited induction generator feeding a rectifier load

Both transient and steady-state performances of an isolated self-excited induction generator (SEIG) supplying a rectifier load are presented. A hybrid model based on abc and q–d induction machine models is employed to describe the dynamic equations of the studied system to improve simulation results. The stator voltage equations of the SEIG studied are described by a three-phase abc model which can be directly interfaced to the rectifier circuit. The rotor variables are properly transformed into q–d co-ordinates and the elements in the rotor inductance matrix are time-invariant. The controlled rectifiers, including both semi and full converters, are modelled by using three switching functions, which are designated to be tristate switches for each converter leg. Combining the SEIG model proposed with the rectifier model, the transient characteristics of the SEIG under various loading conditions are simulated and evaluated. The FFT algorithm is used to analyse the voltage and current harmonic content under steady-state conditions. Experimental results obtained from a laboratory 1.1 kW induction machine driven by a DC motor are also performed to confirm the effectiveness of the proposed approach.

Required accuracy of inductance measurement for current imbalance phenomena

Current imbalance can be estimated by the solution of the circuit equation, which depends on the result of the measurement of the self- and mutual inductances. Strand circuit is coupled with each other strongly, and therefore the matrix calculation is stiff. This situation leads to enhance the error of the measurement. In order to study this problem, we made a magnet, in which the cable was composed of the nine insulated strands, and measured the inductance matrix of the strand circuits by the LCR-meter. The inductance of the magnet is 11 mH, and the error of the measurement is the order of micro Henry to 10 mH. The average coupling factor of the magnet is 0.9956, and therefore this inductance matrix is almost singular. Finally, we calculated the currents of the strand. The accuracy of the inductance measurement is the order of 5–6 digits. We used ™ Mathematica to solve the circuit equation, and we tested the accuracy of the calculation precision. Random number method is introduced to estimate the required accuracy of the inductance measurement. The required accuracy of the inductance measurement is the order of micro Henry in this magnet to obtain the accuracy of 5% for the strand currents.

Some properties of Eck-like steps in 2D underdamped Josephson junctions arrays

Two-dimensional (2D) Josephson Junctions arrays have been studied largely in the overdamped case. Only recently some experimental, numerical and theoretical results have been obtained in the underdamped case. The nature of dynamical states of an array when placed in a magnetic field is again not fully explained and only approximate (linear) models have been proposed. On the other hand, the comprehension of such dynamics is of great importance for understanding the behavior of such arrays. In this work, we study numerically some of the dynamical states in 2D arrays using a full inductance matrix in the array equations. The results show that the response of the array to the magnetic field is governed at large by the parameter /spl beta//sub L/. Moreover we study the underlying dynamics which is dominated by so-called checkerboard solutions. The properties of such arrays are investigated in view of applications.

Equipotential shells for efficient inductance extraction

To make three-dimensional (3-D) on-chip interconnect inductance extraction tractable, it is necessary to ignore parasitic couplings without compromising critical properties of the interconnect system. It is demonstrated that simply discarding faraway mutual inductance couplings can lead to an unstable approximate inductance matrix. In this paper, we describe an equipotential shell methodology, which generates a partial inductance matrix that is sparse yet stable and symmetric. We prove the positive definiteness of the resulting approximate inductance matrix when the equipotential shells are properly defined. Importantly, the equipotential shell approach also provably preserves the inductance of loops if they are enclosed entirely within the shells of their segments. Methods for sizing the shells to control the accuracy are presented. To demonstrate the overall efficacy for on-chip extraction, ellipsoid shells, which are a special case of the general equipotential shell approach, are presented and demonstrated for both on-chip and system-level extraction examples.

Analysis of very fast transients in transformers

Very fast transient overvoltages generated in gas-insulated switchgear could cause a voltage oscillation inside the connected transformer. A practical method to calculate the high-frequency transients in the transformer winding is developed based on multiconductor transmission-line theory. Resonance characteristics of a transformer are assessed using the inductance matrix obtainable from its winding geometry. Applicability to transients of frequencies up to several megahertz is checked in a model transformer and an actual 500 kV transformer. The calculated interturn voltage waveforms are in particularly good agreement with experiment.

A Novel Approach of Inductance Matrix Inversion in Induction Motor Digital Simulation

Owing to the fact that the inductance matrix of a three-shape induction motor is a cycle matrix and the characteristics of this cycle matrix combinations are valid, it is preferable to derive correlative expressions between the inductance matrix and its inverse to obtain the result in a straightforward manner by assignment instead of calling subroutines for saving much computation time. The computation time required by this approach is compared with that required by the coordinate transformation method. A new approach different from the conventional method is proposed. On the basis of the fact that the inductance matrix in a three-shape induction motor is a cycle matrix, an expression for the inductance inverse matrix is acquired. Thus repetitive inverse operations are replaced with straightforward assignment. It is proved via practical examples that this method not only avoids complex conversion of coordinates but also decreases calculation time.

A position-sensorless IPM motor drive system using a position estimation based on magnetic saliency

This paper describes position-sensorless control of an interior permanent magnet synchronous motor (IPM motor), which is characterized by real-time position estimation based on magnetic saliency. The real-time estimation algorithm proposed in this paper determines the inductance matrix including rotor position information from current harmonics produced by switching operations of an inverter driving the IPM motor, and then estimates the rotor position every period of pulse-width modulation (PWM). Position estimation without any special signal injection is achieved with a satisfactory response and accuracy even at a standstill and at low speed. An experimental system consisting of an IPM motor and a voltage-source PWM inverter has been implemented and tested to confirm the effectiveness and versatility of the approach. Some experimental results show that the experimental system has the function of electrically locking the loaded motor, along with a position response of 20 rad/s and a settling time of 300 ms. © 2000 Scripta Technica, Electr Eng Jpn, 131(2): 68–79, 2000

Modeling of universal motor performance and brush commutation using finite element computed inductance and resistance matrices

This paper presents a computer aided model for the simulation of universal motor performance and brush commutation. The model consists of a set of flux linkage based differential equations. Time stepping integration method and 2D finite element field solutions are used for solving the system. An arcing model is introduced into the system to predict brush arcing and the arcing related energy. Computed results and test data are compared in the paper for a one armature coil per slot motor.

Experimental and finite-element analysis of an electronic pole-change drive

The theory and modeling of an electronic pole-change drive for the purpose of extending the constant power speed range of a four-pole induction machine have been previously reported. This paper presents verification of the power capability characteristics of the proposed drive through experimental implementation. An indirect field-oriented controller is developed for the pole-change drive with the estimated rotor open-circuit time constant and d-axis-current commands dependent on the mode of operation. It is demonstrated that, for a constant power load, the drive can operate at 6340 r/min in two-pole mode without exceeding either the voltage or current limits at 3600 r/min in four-pole mode. A finite-element method is also utilized to examine the influence of magnetic saturation on the pole-change drive performance. The nature of the magnetic flux distribution and saturation progression is investigated in both four-pole and two-pole modes. The saturation-induced inductance variation is also studied and its influence on the dq inductance matrix is quantified.

Single flux quantum comparators for HTS AD converters

We have investigated different comparators for Flash and Σ–Δ high temperature superconducting ADCs designed using three-layer HTS tri-crystal junction integrated circuit technology with spread of the junction critical currents less than 10% and features size 0.6 μm. Using the theoretical estimations for the bit error rate in RSFQ circuit under the restrictions of the given technology, we have estimated working temperature as T=62 K. At this temperature, the circuits were optimized in order to achieve maximum performance of the related ADCs in terms of input bandwidth, resolution and operating margins. For design purposes, a novel method was developed for inductance calculation with 3D magnetic field distribution in multilayer superconducting technology and extraction of the inductance matrix of the equivalent circuit.

New matrix algorithm for calculating diagonally matched impedance of packaging interconnecting lines

A novel numerical algorithm is developed for computation of diagonally matched impedance matrix of multiple coupled interconnecting lines in high-speed digital circuits. The algorithm is based on the properties of capacitance and inductance matrices of transmission lines and has unconditional monotonic convergence. The mathematical development is based on the theory of M matrices. The algorithm was applied to various metal lines with different dimensions, showing very good accuracy in comparison to other methods.

Extraction of multiple coupled line parameters using FDTD simulation

A general characterisation procedure based on the extraction of a 2n-port admittance matrix corresponding to n uniform coupled lines using the Finite Difference Time Domain (FDTD) technique is presented. The frequency-dependent normal mode parameters are obtained from the 2n-port admittance matrix, which in turn provide the frequency-dependent distributed inductance and capacitance matrices. To illustrate the technique, several practical coupled line structures, including a three-line structure, have been simulated. It is shown that the FDTD-based time domain characterisation procedure is an excellent broadband simulation tool for modelling and characterisation of multiconductor coupled transmission lines.

Ramp rate limitation in AC multi-strand superconducting cable due to statistical scattering in inductive coupling between strands

Theoretical investigation results of the current-carrying capacity of a superconducting cable with insulated strands depending on the inductive coupling between the strands are presented. The superconducting state stability was analyzed by a non-isothermal model. On this model, permissible rise in temperature of each strand is bounded by the conditions of magnetic flux diffusion within this strand. It is shown that if the matrix of inductances between the cables strands has asymmetric elements then the degradation of maximum possible current (quench current) can be quite considerable over the whole range of current rates. The degradation becomes stronger with increase of both the number of strands and scattering in their mutual inductance.