Nonlinear Inductance Research Articles

Logic devices based on inductive Josephson logics

Inductive Josephson logic (IJL) is realized by using Josephson junctions as a kind of nonlinear inductance. The operational principle of inductive Josephson logic is studied from a very simple example and generalized to multiple Josephson inductive logic devices. Concepts offorward andbackward are introduced to describe the states of the operations. IJLs operate in terms of current or flux; they are suitable to be used in connection with other flux-control Josephson circuit devices such as DC SQUID or DCFP. Some circuit devices based on the principle of inductive Josephson logic are given as examples of IJL logic functions.

Three dimensional finite element calculation of saturable magnetic fluxes and torques of an actuator

A rotary magnetic actuator of highly three-dimensional geometry is analyzed by the finite-element method. A one-quarter model composed of three-dimensional finite elements is developed for analysis by the vector potential Newton-Raphson approach. The nonlinear saturable magnetic fields, fluxes, inductances, energies, and torques are calculated at three armature positions. The calculated torques compare reasonably well with measurements. >

Coupled mode theory in a lossy, nonlinear transmission line system

A method of analysis that uses the coupled mode formulation has been developed to study the coupling phenomenon in a system of two lossy, identical transmission lines. These lines are uniformly coupled and also have uniformly distributed, nonlinear shunt capacitance and series inductance. The transmission lines are excited at one end with two voltage sources of the same frequency but of different amplitude and phase, and are terminated with proper load impedances at the other end. The coupled mode theory has been developed with the aid of quasiharmonic analysis of the codirectional, nonlinear coupled lines. The analytical expressions for the power carried by each mode in the transmission lines can be obtained for a special case of the low loss system in which the phase difference of two coupled modes is assumed to vary slowly with the position along the line. The derived analytical expressions are also used to study the effect of changing input conditions and circuit parameters on the location where relative minima and maxima occur.

General Relations among Voltages and Currents in Nonlinear Elements. I

In nonlinear capacitors, inductors and resistors, general equations holding among the voltages and currents at different frequencies are derived. These are obtained only on the assumption that the characteristics for the nonlinear elements are single-valued. The well-known Manley-Rowe relation is the lowest order and simplest ones among these equations. But, even then, the relations are more extensive, in the sense that the number of the voltage generators may be arbitrary.

Unified Modeling of Rectifier-Controlled DC-Power Supplies

The known analysis of dc-dc converters in discontinuous operation mode and with voltage commutation based on a piecewise-linear description is extended to the analysis of line-commutated converters. With the latter as system-dependent pulsewidths the overlap angles appear, which can be computed in a manner analogous to the current-flow duration and the reloading time, respectively. This leads to a unified state-space modeling of dc-dc and ac-dc converters by which the steady-state and the dynamic small-signal behavior can be evaluated directly. If the piecewise-defined system equations are integrated numerically, a rather generalized analysis of power converters is found if the structure of switched systems is taken into account. As an illustrative example, a voltage-commutated dc-dc converter with a nonlinear dc inductance is studied.

Harmonics from Transformer Saturation

Saturation effects in transformers and shunt reactors can produce harmonics in power systems. Their magnitude can sometimes be found with an electromagnetic transients program, by going from an approximate linear ac steady-state solution directly into a transient simulation in which the nonlinear effects are included. In lightly damped systems, such simulations can take a long time, however, before the distorted steady state is reached. Therefore, another method was developed which uses superposition of steady-state phasor solutions at the fundamental frequency and at the most important harmonic frequencies, with nonlinear inductances represented as harmonic current sources. This method can either be used by itself, or as an improved initialization procedure for electromagnetic transients programs.

Solution of a set of nonlinear algebraic equations for general-purpose CAD programs

A method is described for solving sets of nonlinear algebraic equations that arise in computer-aided circuit (CAD) programs in the steady-state mode of analysis. The method discriminates among different circuit elements in their contribution to the circuit equations. A logarithmic mapping is used on a subset of the correction vector involved in updating nonlinear current and voltage elements and their partial derivative contribution to the circuit equations. The values of nonlinear resistors, conductors, inductors, and capacitors are updated at every iterative step and then treated as though they were linear elements. However, in the steady-state mode, the values of capacitors and inductors are transformed into conductors and resistors, respectively. The values of these elements are made functions of the Newton iteration. The functional relation depends on the convergence behavior of the solution vector.

Turn-on delay analysis of current-injection Josephson logic circuits

A turn-on delay, during which the output voltage of a Josephson logic circuit is very small, is of prime interest for the design of high-speed Josephson digital integrated circuits. We have derived an analytical formula for the turn-on delay of the current-injection logic circuits, which is in good agreement with computer simulations. Analysis of the circuit equations shows that the nonlinear inductance of a current-summing Josephson junction plays an important role for the turn-on delay. Dependences of the turn-on delay on circuit parameters and operating conditions are calculated. For parameter values typical of 5-μm current-injection circuits, the turn-on delay is on the order of 10 ps. The turn-on delay and operating margin are compared in various types of current-injection logic circuits. The higher sensitivity of the threshold gate current to the input current is found to be desirable not only to reduce the turn-on delay but to operate in a wide margin.

Digital simulation of parallel inverters

Abstract Previously, a model of a nonlinear inductor exhibiting hysteresis loops was proposed, and successfully applied to typical nonlinear electric circuits [1]. This model is now generalized to include the nonlinear transformer, and applied to the digital simulation of parallel inverters. Comparison of experimental results with simulated results shows that the model taking into account the hysteresis loops behaves just like a physical inverter including the unstable operations.

Transient response of a ferroresonant circuit

The transient response of a partical ferroresonant circuit with quintic nonlinearity has been obtained. A suitable closed loop block digram for this circuit is used to allow an iterative approximation technique to be used for the determination of the transient response due to the sudden application of a sinusoidal voltage. The effect of the variation of the amplitude and the angle of the applied voltage and of the various circuit parameters on the voltage across and the current through the nonlinear inductor of the circuit has been investigated.

Predetermination of lateral length to prevent overvoltage problems due to open conductors in three-phase systems

The opening of one or two conductors in three-phase circuits supplying an ungrounded transformer produces a steady-state overvoltage due to ferroresonance between the lateral capacitance and the transformer nonlinear inductance. Available methods of determining the conditions under which such an overvoltage may occur are mostly based on experimental studies, and hence are limited in application to systems whose design parameters are similar to those used in the tests. A simple and elegant approach, presented here, reveals that an incorrect choice of overvoltage limit leads to the selection of an unsafe lateral length, resulting in a potentially dangerous high voltage across the connected apparatus and protective equipment. Generalised mathematical equations are developed to determine the safe lateral length as a function of transformer size for the prevention of the overvoltage problem due to open conductors in three-phase systems. The computed results are in good agreement with experimental observations.

Nonlinear resonance and parametric phenomena in a complicated oscillating circuit

Nonlinear resonance and parametric phenomena in an oscillating circuit with two nonlinear opposite reactive elements and negative resistance are presented. The examination has been performed on the basis of a nonlinear oscillating circuit represented by a two-transistor model of a pnpn-type device with nonlinear inductance and negative resistance and a self bias pn junction with nonlinear capacitance and a nonlinear conductance.

A comparison of lumped and distributed solutions to nonlinear, transient, magnetic field problems

The transient magnetization of highly nonlinear materials is investigated using finite-element techniques and a multimode equivalent circuit approach. The use of constant eddy inductances in the equivalent circuit is shown to be correct only for linear materials or for small field perturbations in nonlinear materials. During large perturbations, the nonuniform permeability of nonlinear materials causes standard equivalent circuit techniques to be grossly inaccurate. Using numerical results, a field-dependent nonlinear eddy inductance has been defined that substantially increases the accuracy of nonlinear lumped analyses and is applicable to arbitrary forcing functions. This nonlinear inductance is a function of the differential permeability of the material surface and of a bulk differential permeability calculated from the average flux density in the material. To verify the accuracy of this approach, the transient total flux predicted by an equivalent circuit analysis incorporating nonlinear inductances is compared to the total flux from a transient finite-element analysis. Comparisons are given for the total flux versus time following the step application and the step removal of a surface field to an infinite flat plate and a long solid cylinder. The response of a toroidal coil with a saturable core to an instantaneous voltage change is also investigated using lumped and distributed techniques.

Modelling of nonlinear inductor exhibiting hysteresis loops and its application to the single phase parallel inverters

A modelling of magnetodynamic fields taking into account dynamic hysteresis loops was previously proposed for predicting three-dimensional magnetodynamic fields in electromagnetic devices [1]. This method is now applied to construct the lumped circuit model for nonlinear inductor exhibiting dynamic hysteresis loops. The lumped circuit model of nonlinear inductor is introduced into the simulation model of single phase paralell inverter, whose various characteristics are calculated and compared with experimental measurements. Good agreement is obtained.

A lumped circuit model for a nonlinear inductor exhibiting dynamic hysteresis loops and its application to the electric circuits

Previously, modeling magnetodynamic fields, taking into account dynamic hysteresis loops, was proposed for predicting three-dimensional magnetodynamic fields in electromagnetic devices. This method is now applied to work out the lumped circuit model for a nonlinear inductor exhibiting dynamic hysteresis loops. This lumped circuit model for a nonlinear inductor is introduced into the simulation models for typical nonlinear circuits, whose dynamic hysteresis loops as well as current responses are calculated and compared with experimental measurements. Good agreement is obtained.

Theory of the stationary macroscopic quantum behavior of inductively coupled superconducting weak links

A theory of the stationary response of a flux-controlled superconducting weak link is presented in the framework of reversible thermodynamics. The superconducting loop containing the weak link (SQUID)—considered as a “black box”—can be characterized by a nonlinear inductance ℒ s which uniquely describes the constitutive properties of the macroscopic quantum system. The influence of the temperature-dependent (nonsinusoidal) current-phase relation (CPR) on − s and on the stability of the SQUID when operated in the nonhysteretic mode is analyzed taking into account the full nonlinearity of the CPR. The model presented enables a rigorous circuit analysis, even in the case of a nonlinear flux transformer.

Port properties of nonlinear reciprocal networks

Time-invariantn-port networks are considered which are constructed from linear resistors and transformers, and nonlinear inductors and capacitors. A port property is sought which is analogous to the symmetry of the impedance matrix obtained in the linear case. Such a property is found using a stochastic characterization: with all resistors assumed to be at the one temperature and modelled to include the usual thermal noise, a fluctuating noise voltage will be observed at the ports of the networks. With some reasonable restrictions on the nature of the nonlinearities in the reactive elements, the vector of such noise voltages is shown to constitute what is known as a reversible stochastic process; in the linear case, reversibility holds if and only if the impedance matrix is symmetric.

Magnetizing Current Harmonics Caused by Pulse Burst Modulated Loads

Pulse Burst Modulated (PBM) circuits inject dc currents into power networks. Non-linear inductances, especially transformers supplying or connected in parallel with PBM loads will be exposed to dc voltages which will cause the operation of the magnetic core to be on an asymmetrical B/H hysteresis loop. This work presents a theoretical model which enables the prediction of magnetizing current harmonics and dc biasing flux caused by a PBM load connected in a circuit with known parameters.

Failure of Electromagnetic Voltage Transformer Due to Sustained Over-Voltage on Switching - an Indepth Field Investigation and Analytical Study

An electromagnetic voltage transformer (EMVT) was damaged when the 220KV bus bar was being de-energised by a circuit breaker fitted with grading capacitors across its contacts. This paper describes the field investigations and analyses the phenomenon using the principle of harmonic balance. It is established that the failure occurred due to fero-resonance between CB grading capacitors and non-linear EMVT inductance causing sustained over-voltage and consequently much higher than usual current. It could be a thermal or insulation failure or both. The analytical results obtained are shown to be similar to those determined by actual field. tests.

On the absolute stability criterion

A feedback system comprising a single nondynamic non-linear link is described by the same relations as a passive circuit consisting of a linear two pole and nonlinear resistor and inductor connected in series, if the current dependences of the voltage on the resistor and of the magnetic flux produced by the inductor are inverse functions compared to the operator of the nonlinear link. This demonstrates the validity of the Popov absolute stability criterion.