Distributed Parameter Circuit Research Articles

Performance Prediction of Carbon Nanotube Bundle Dipole Antennas

A theoretical investigation is carried out for predicting radiation characteristics of single-walled carbon nanotube (SWCNT) bundle dipole antennas based on the distributed circuit parameters and the model of an SWCNT, where the cross section of bundles can be in a circular and a rectangular geometry, respectively. The current distributions in such novel antennas are predicted to investigate the effects of bundle cross-sectional size, tube diameter, tube length, and operating frequency. Furthermore, comparative studies are performed to show the geometry- and frequency-dependent radiation resistance, far-field pattern, and radiation efficiency of some typical bundle dipole antennas, which are numerically confirmed to outperform an SWCNT antenna by 30-40 dB in radiation efficiency.

Study on the Applicability of Extracted Distributed Circuit Parameters of Non-Uniform Transmission Lines by Equivalent Circuit Method

Distributed circuit parameter extraction from field result of non-uniform transmission line provides circuit designers an efficient way to predict the effect of non-uniform structures. The motivation of this paper is to study the efficiency and applicability of the extracted distributed circuit parameters. These parameters are extracted from the FDTD results in this paper and are used to construct an equivalent circuit. Exciting the circuit with Gaussian pulse and using the equivalent circuit method, the transmitted and reflected pulse waveforms on the circuit can be obtained. By comparing these waveforms and the corresponding frequency domain S parameters with those obtained directly from FDTD, the applicable scope of the extracted circuit parameters can be studied.

Novel distributed circuit model for transition between coplanar waveguide and microstrip by using the generalized telegrapher equation method

AbstractIn this article, a novel distributed circuit model of coplanar waveguide to microstrip (CPW‐M) transition is presented by using generalized telegrapher equation. In comparison with conventional nonuniform transmission line equation, the generalized telegrapher equation has two additional terms, dependent series voltage and shunt current sources, which represent local radiation effect from discontinuities of the nonuniform transmission line itself. Based on the full‐wave numerical results, the distributed circuit parameters can be extracted by using the generalized telegrapher equation. Since the generalized telegrapher equation coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the equation is dynamical rather TEM. The numerical experiments show that the novel distributed circuit model for this CPW‐M transition can have broadband characteristics. As a preparatory experiment, an improved CAD method using this model is utilized to model different structures of CPW‐M transition. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1323–1328, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22461

Study on the Applicability of the Static Distributed Circuit Parameters of Non-uniform Microstrip Lines

The Generalized Transmission Line Equations are employed to analyze the circuit parameters of the microstrip lines. The static distributed capacitances and inductances of non-uniform microstrip lines are extracted. By comparing the differences between the port’s S-parameters respectively obtained by the extracted static circuit parameters using circuit method and by the Method of Moment directly, the applicable frequency range of the extracted static distributed circuit parameters can be found. The results show that the extracted static circuit parameters can be used in a frequency band from DC up to millimeter wave.

Measurement of interstrand conductance in multistrand superconducting cables

Multistrand superconducting cables are widely used in large scale applications to obtain large current carrying capacity. Stability is one of the key issues that ensure continuous and reliable operation of superconducting cables. Knowledge of interstrand conductance is essential for analysis of current distribution and redistribution processes that substantially influence the stability of multistrand superconducting cables. In this paper, an approach to measure interstrand conductance is developed using parametric estimation method as used in control theory. First, a distributed parameter circuit model is adopted to calculate the current and voltage distribution in superconducting cables. Then, strand voltage differences at cable ends are measured by experiment. Finally, least squares method is applied to estimate the interstrand conductance which gives the minimum error of the voltage difference at cable ends between calculated and measured data. The interstrand conductance between the subcables in different cabling stages in a cable-in-conduit conductor (CICC) has been studied under different conditions (different temperatures and different cable lengths). The results are consistent, accurate, and fit the distributed parameters circuit model well. This method provides a convenient approach to evaluate electrical coupling parameters in multistrand superconducting cables under different conditions. The estimated parameters can be used to improve the accuracy of analysis of current distribution and cable stability.

Electrical Coupling Parameter Reconstruction From System Model in Multistrand Superconducting Cables

Current distribution in multistrand superconducting cables has substantial influence on stability. Any analysis of current distribution requires knowledge of the electrical coupling parameters, (e.g., self and mutual inductances, and the interstrand contact conductance). In this paper, a new approach that reconstructs the parameters from distributed parameter circuit model of multistrand superconducting cable is proposed. The strand currents are measured by experiment and treated as known conditions. The unknown parameters are then extracted from the partial differential equations that describe the current distribution. The desired results are found to be the minimum norm least squares solution that best fit the system equations and minimize errors. A code is developed to implement this reverse identification process. The results are validated by substituting the reconstructed parameters to the system equations for simulation and then comparing with current distribution experiments. The parameters are also compared with those from conventional experimental methods, (e.g., DC four-point method to measure interstrand conductance). This method, using parametric identification theory, provides a way to evaluate the electrical coupling parameters in multistrand superconducting cables under different conditions (current density and frequency, mechanical loads, etc.). The calculated parameters can be used in analysis of current distribution and cable stability.

QUANTUM FLUCTUATION IN THERMAL VACUUM STATE FOR MESOSCOPIC DISTRIBUTED PARAMETER CIRCUITS

In this paper we consider a non-dissipative distributed parameter circuit at a finite temperature T. We find the unitary operator for diagonalizing the Hamiltonian of the uniform periodic transmission line. The unitary operator is expressed in a coordinate representation. Thermal field dynamic is used in our discussion. It is shown that distributing parameter circuits and quantum fluctuations, which also have distributing properties, are related to both the circuit parameters and the positions and the model of signals and temperature T. The higher the temperature, the more quantum noise the circuit exhibits. The research will be helpful to miniaturize intergreate circuits and electric components. It will be also significant for the futher study of the qualitities of mesoscopic system.

On High-Frequency Circuit Equivalents of a Vertical Ground Rod

Vertical ground rods have been used extensively from the early days of electrical engineering for earth termination of electrical and lightning protection systems. They are usually represented with equivalent circuits with lumped and distributed parameters based on quasistatic approximation, which limits the upper frequency of their validity domain. However, lightning-related studies often require modeling in the megahertz frequency range. Also, emerging technologies, such as power-line communications, require analysis in frequency ranges even up to a few tens of megahertz. The rigorous electromagnetic (EM) field theory approach may be used for such frequency ranges, but equivalent circuits are needed for the usual network analysis methods. In this paper, we look at possibilities to construct simple equivalent circuits that can approximate or match results from the EM model. In particular, we compare a usual homogenous distributed parameter circuit with a nonhomogenous one determined by curve matching with results from the EM model. The analysis is illustrated using numerical simulations.

Density Matrix for Mesoscopic Distributed Parameter Circuits

Under the Born–von-Karmann periodic boundary condition, wepropose a quantization scheme for non-dissipative distributed parametercircuits (i.e. a uniform periodic transmission line). We find the unitaryoperator for diagonalizing the Hamiltonian of the uniform periodictransmission line. The unitary operator is expressed in a coordinaterepresentation that brings convenience to deriving the density matrix ρ(q,q′,β). The quantum fluctuations of charge and currentat a definite temperature have been studied. It is shown that quantumfluctuations of distributed parameter circuits, which also have distributedproperties, are related to both the circuit parameters and the positions andthe mode of signals and temperature T. The higher the temperatureis, the stronger quantum noise the circuitexhibits.

Error in Propagation Velocity Due to Staircase Approximation of an Inclined Thin Wire in FDTD Surge Simulation

This paper presents the result of a study on the error in propagation velocity introduced by the staircase approximation of a thin wire in the finite difference time domain (FDTD) surge simulation. The FDTD method directly solves Maxwell's equations by discretizing the space of interest into cubic cells. Thus, it is suitable for solving very-fast surge phenomena which cannot be dealt with by conventional techniques based on the lumped- and distributed-parameter circuit theories. However, FDTD has a limitation that the shape of a conductive object must be modeled by a combination of sides of cells with forced zero electric fields. This indicates that a thin wire, one of the most important components in the surge simulation, results in a staircase approximation, if the wire is not parallel to any of the coordinate axes used for the discretization. A staircase approximation gives a slower propagation velocity due to the zigzag path which is longer than the actual length of the wire. For precise simulations, the error in propagation velocity has to be clarified quantitatively. In this paper, extensive simulations are carried out to obtain the velocity versus inclination characteristic, and it is deduced that the maximum error in propagation velocity is less than 14%.

Quantum fluctuation of mesoscopic distributed parameter circuits

Under the Born–von-Karmann periodic boundary condition, we propose a quantization scheme for a non-dissipative distributed parameter circuit (a uniform transmission line). Quantum fluctuations of charge and current in the vacuum state are investigated by adopting the canonical transformation and unitary transformation method. Our results indicate that in distributed parameter circuits, quantum fluctuations, which also have distributed properties, are related to both the circuit parameters and the positions and the mode of signals.

A Bulk Current Injection Test Conforming to Statistical Properties of Radiation-Induced Effects

In this paper, a bulk current injection (BCI) immunity test is designed that conforms to the effects induced in the equipment under test (EUT) by a radiated electromagnetic disturbance (EMD). This is done by adopting a statistical description of the EMD and by comparing currents induced by BCI and distributed field-coupling (i.e., radiation) in the input pins of the EUT. Closed-form results are obtained that enforce equivalence of the aforementioned test procedures in terms of specific statistical estimates (e.g., expected value and dispersion) as well as for worst-case radiation-induced effects. A distributed-parameter circuit model of the system under test is adopted, composed by the EUT, auxiliary equipment (AE), and a wiring harness. In the analysis, the EMD is described via plane waves with random parameters and a uniform multiconductor transmission line model is used for the wiring harness. The EUT and AE are represented via lumped impedance matrices. Injection-probe feeding-conditions assuring equivalence are derived analytically, and involve a frequency piecewise-linear profile of the RF voltage source. The proposed BCI immunity test overcomes practical-design difficulties of previous formulations.

Combined modeling of cables and joints/terminations for the electromagnetic analysis of superconducting cables

The electromagnetic models developed in the recent years to study current distribution and ac losses in superconducting magnets have focussed on detailed descriptions of either cables or joints/terminations, usually considered separately. A more accurate physical description of the magnet system requires to model simultaneously the different parts of cable, the joints between them and the cable terminations. In this work we present the coupling of a distributed parameters circuit model of the cable with a simple lumped parameters resistive model of the joints and terminations. The principles and results of the coupling strategy are illustrated and validated by means of a comparison with the analytical solution of the problem found for triplex cables.

Numerically distributed circuit parameters model on microstrip transmission line circuits and its application on CAD

AbstractA new numerical model of microstrip transmission line circuits in terms of distributed circuit parameters is here illustrated. Based on full‐wave electromagnetic results, the extraction methods of these distributed circuit parameters on different types of microstrip transmission line circuits are introduced. As a preparatory experiment, an improved CAD method using this model is tested on microstrip low‐pass filter. Copyright © 2003 John Wiley & Sons, Ltd.

Long-cable effects on conducted emissions levels

A novel frequency-domain distributed-parameter circuit model of the setup for the measurement of conducted emissions (CE) in three-conductor systems is developed in order to predict the effects that an electrically-long power cord connecting the equipment under test (EUT) to the line-impedance stabilization network (LISN) plays on CE levels. To this end, a three-conductor lossless and uniform transmission line model is adopted for the description of the power cord, and modal decomposition of the line voltages and currents to common- and differential-mode voltages and currents is used to derive new closed-form expressions of the CE at the LISN ports. Suitable EUT-to-LISN matrix transfer functions are introduced and it is shown that CE measured at the entrance of the power outlet (i.e., at the LISN ports) may differ significantly from those flowing out of the EUT mains ports, due to propagation and coupling along the power cord. The role played by the mains cable cross section on CE propagation and conversion is investigated, and upper/lower bounds for the power cord effects on CE are derived analytically by applying an asymptote plot analysis to the magnitude of the EUT-to-LISN transfer functions. Direct numerical solution of the transmission line model is used to validate the obtained literal expressions of CE and related bounds, as well as to give explicit indications about the impact of long-cable effects on CE.

Analytical solution for the current distribution in multistrand superconducting cables

Current distribution in multistrand superconducting cables can be a major concern for stability in superconducting magnets and for field quality in particle accelerator magnets. In this article, we describe multistrand superconducting cables by means of a distributed parameters circuit model. We derive a system of partial differential equations governing current distribution in the cable and we give the analytical solution of the general system. We then specialize the general solution to the particular case of uniform cable properties. In the particular case of a two-strand cable, we show that the analytical solution presented here is identical to the one already available in the literature. For a cable made of N equal strands we give a closed-form solution that to our knowledge was never presented before. We finally validate the analytical solution by comparison to numerical results in the case of a steplike spatial distribution of the magnetic field over a short Rutherford cable, both in transient and steady-state conditions.

Evaluation of Resonance Intensities and Frequencies for Piezoelectric Partial-Drive Systems Using Application of Mason's Equivalent Circuit and Complex Series Dynamics

In order to evaluate the `resonance intensities' and resonance frequencies of piezoelectric transducers driven `partially', two mathematical methods are considered: One is the evaluation of `speed of divergence' at the resonance of Mason's equivalent circuit which is applied appropriately using the conventional concept of a distributed-parameter circuit, and the other is a superposition of complex dynamical variable η to form complex infinite geometric series in which |η|2 corresponds to the stored energy in the transducer and in which the way of superposition reflects the electrical and mechanical boundary conditions of the transducer. The resonance intensity is related to the effective power at the resonance. The `partial drive' can induce resonance modes other than a set of odd-degree modes, with various resonance intensities due to a nondissipative cause, on appropriate boundary conditions. The calculation results of the two methods agree with each other satisfactorily, and thus suggest the physical reasonableness of both methods.

A continuum model for current distribution in Rutherford cables

An analysis of eddy currents induced in flat Rutherford-type cables by external time dependent magnetic fields has been performed. The induced currents generate in turn a secondary magnetic field which has a longitudinal periodicity (periodic pattern). The dependence of the amplitude of the pattern on the history of the cable excitation has been investigated. The study has been carried out with two different models for the simulation of current distribution in Rutherford cables, namely a network model, based on a lumped parameters circuit and a continuum model, based on a distributed parameters circuit. We show the results of simulations of the current distribution in the inner cable of a short LHC dipole model in different powering conditions and compare them to experimental data.

磁気マイクロストリップ線路の小型化と構造の最適化

A micro-strip line is an exponent of a distributed parameter circuit. Micro-strip lines are the main components of microwave circuits, and are used in the high frequency range. Magnetic micro-strip lines are constructed by adding magnetic film to micro-strip lines. The characteristics of a stripline depend on its construction and size. The magnetic film contained in it greatly affects the characteristics. This paper describes the characteristics of magnetic micro-strip line. Magnetic micro-strip lines can make miniaturization possible. Some applications, such as in band pass filters, can be expected in view of the unique magnetic characteristics of the strip lines.

Characteristics of a special-isolation transformer capable of protecting from high-voltage surges and its performance

Rapidly expanding computer-control systems and information networks must be protected from high voltage surges and made immune from noise. The usual method employed for this purpose is isolation transformers. Conventional electrostatic-shielded transformers, however, are insufficient for a number of reasons. The first is that many fine and complicated local resonant circuits are created by the inhomogeneously distributed circuit parameters inside the coil. The second is that common-mode surge noises traveling on both the active conductor of the line through some common-mode component, change into normal-mode noise because of the unbalance between their respective impedance values to ground. The third is the problem that component changed into normal mode, propagate due to the electromagnetic inductance from the primary to the secondary coil. In order to remedy this set of problems, one must eliminate the high-frequency magnetic flux linking the primary coil to the secondary coil through the air. In this paper, the authors propose a design for a transformer that does not propagate high-frequency components, even noise in a normal mode. They demonstrate dramatic noise reduction in their experiments with the new design. They thus validate the utility of the coil arrangement for the purpose of noise reduction.