Norton's Circuit Research Articles

Peculiarities of the Norton conversions application when matching impedances with different transformation coefficients

The paper studies the features and consequences of the use of Norton conversions in the process of broadband and narrowband matching of circuit impedances based on filter theory in cases with different transformation ratios. For Norton circuits conversions with different transformation ratios (greater than and less than one), an additional rule is formulated. Using the generalized form of recording the Norton consequence conversions, two examples of reducing the number of elements in bandpass filters are demonstrated. In addition, the consequences that are characteristic of narrow-band applications of transformations are established. Formulas for calculating transformation ratios that depend on frequency are obtained for direct and mirror Г-shaped circuits with different reactivities. It is shown that these circuits can be combined with similar reactivities of Г-shaped circuits with frequency independent transformation ratios. On the basis of the established for the Norton conversions consequences, the step-up and step-down matching circuits of the combined type are synthesized.

The Equivalent Circuits Thévenin and Norton

Abstract The main objectives of this paper are to correctly define the equivalent Thévenin and Norton circuits and to presents the complete and exact proof of Thévenin and Norton theorems. These circuits allow the separation of the linear portions of the electronic circuits from the nonlinear ones and in this way the polarization process of the electronic devices becomes much more efficient. When linear and/or nonlinear analyzed circuits have a small number of nonlinear circuit elements, their analysis, synthesis, and simulation are performed much more efficiently if the nonlinear part of the circuit is separated from the linear one. By determining the equivalent Thévenin or Norton circuits in relation to the load to connected terminals of a system with two or more magnetic coupled coils, that are part of the wireless power transfer systems, optimal load parameters are determined so that the maximum active power is transmitted to the load.

High-Speed Electromagnetic Transient (EMT) Equivalent Modelling of Power Electronic Transformers

The high-speed accurate electromagnetic transient (EMT) simulation of the power electronic transformers (PET) has become a challenge, due to the microsecond-range time steps and the large number of high-frequency semiconductor switches and isolating transformers. Taking the input-series-output-parallel (ISOP) connected cascaded H-bridge (CHB) type dual active bridge (DAB) based PET as an example, this paper proposes a general high-speed equivalent EMT modelling method of PET. First, the isolating transformer within each DAB is discretized into two-port Norton circuits. Second, each CHB-DAB is equivalent to two single-port circuits by eliminating the internal nodes. And the input-side is represented by a Thévenin circuit and the output-side is represented by a Norton circuit. Third, all the CHB-DABs are equivalent to a two-port circuit with all the internal node information preserved. Fourth, the implementation of PET blocking is also considered for startup and fault protective actions. Fifth, the stability of the proposed discrete decoupling method of the PET is verified that it does not introduce specific limitation on the simulation step size. Finally, the developed PET models on PSCAD/EMTDC are shown to be two orders of magnitude faster than the currently available fully-detailed models with negligible loss of accuracy.

Norton Equivalent Circuit for Pulsed Photoconductive Antennas–Part I: Theoretical Model

A novel equivalent circuit for pulsed photoconductive sources is introduced for describing the coupling between the photoconductive gap and the antenna. The proposed circuit effectively describes the mechanism of feeding the antenna by the semiconductor when this latter is illuminated by a laser operating in a pulsed mode. Starting from the classical continuity equation, which models the free carriers’ density with respect to the laser power pump and the semiconductor features, a Norton equivalent circuit in the frequency domain is derived. According to the Norton theorem, the equivalent source representation is decoupled from the antenna. In particular, for photoconductive antennas (PCAs), the Norton circuit takes into account of the electrical and optical properties of the semiconductor material, the features of the laser excitation, as well as the geometrical dimensions of the gap. The presence of the electrodes around the gap is part of the antenna and, therefore, it is taken into account in the antenna impedance. The proposed circuit allows the analysis of the coupling between the photoconductive source and the antenna, providing a tool to analyze and design PCAs.

The strength and phase of the tidal stream

The strength and timing of tidal stream energy in a region is affected both by external hydraulic factors (the driving potential for currents) and by the internal configuration of channels and reservoirs. If we consider a single tidal frequency and take a linear approximation, the dynamics and kinematics can be reduced to an analogous electrical circuit. The external factors can then always be represented by either a voltage source and series impedance (Thévenin circuit) or by a current source and a parallel impedance (Norton circuit). A simple, short channel between two major basins depends on inertia and friction and can be represented simply by a resistor and inductor. Longer channels or channels connected to harbours can be represented using additional circuitry and impedances, including capacitors. The analogy to “capacitance” is provided by wetted area and it is shown that an area of >100km2 is sufficient to alter the strength and timing of the tidal stream for Gigawatt-scale resources. In particular, features in the currents of Pentland Firth can be explained by the capacitive properties of Scapa Flow. Options for extracting tidal energy can be explored by adding load resistors to the circuit.

Fast Transients Analysis of Nonuniform Multiconductor Frequency-Dependent Transmission Lines

In this work, a new model for the simulation of fast transients on nonuniform multiconductor transmission lines is presented. The proposed model is based on the method of characteristics of partial differential equations theory and includes a variation of the electrical parameters with the distance and frequency. In addition, Norton circuits for the transmission line ends, which allow the inclusion of the model into general-purpose programs, are presented. Results obtained with the proposed model are compared with those obtained with the Electromagnetic Transients Program and the Numerical Laplace Transform method.

HiPRIME: hierarchical and passivity preserved interconnect macromodeling engine for RLKC power delivery

This paper proposes a general hierarchical analysis methodology, HiPRIME, to efficiently analyze RLKC power delivery systems. After partitioning the circuits into blocks, we develop and apply the IEKS (Improved Extended Krylov Subspace) method to build the multiport Norton equivalent circuits which transform all the internal sources to Norton current sources at ports. Since there are no active elements inside the Norton circuits, passive or realizable model order reduction techniques such as PRIMA can be applied. The significant speed improvement, 700 times faster than Spice with less than 0.2% error and 7 times faster than a state-of-the-art solver, InductWise, is observed. To further reduce the top-level hierarchy runtime, we develop a second-level model reduction algorithm and prove its passivity.

Multi-port equivalencing of external systems for simulation of switching transients

A multi-port external system equivalent model to simulate switching transients is developed based on direct time domain techniques, as opposed to the currently available models based on frequency domain methods. The model comprises discrete-time filters, which are built using the external system's response at each of the M ports to a multisine excitation signal and solving a system identification problem. At each port, the filters obtained are converted into an equivalent Norton circuit consisting of M current sources (in parallel). A unique feature of the model is that it explicitly incorporates the travel time delay between the ports. The complete M-port model, having M decoupled equivalent Norton circuits, is easily integrated into the discrete-time representation of the study subsystem. The proposed model is validated by simulating the line energization and post-fault transients in a study subsystem connected at two ports to an external system. >

Complete transformer model for electromagnetic transients

A complete, three phase transformer model for the calculation of electromagnetic transients is presented. The model consists of a set of state equations solved with the trapezoidal rule of integration in order to obtain an equivalent Norton circuit at the transformer terminals. Thus the transformer model can be easily interfaced with an electromagnetic transients program. Its main features are: (a) the basic elements for the winding model are the turns; (b) the complete model includes the losses due to eddy currents in the windings and in the iron core; and (c) the solution of the state equations is obtained in decoupled iterations. For validation, the frequency response of the model is compared with tests on several transformers. Applications to the calculation of transients are given for illustration. >

Vector Circuit Theory for Isotropic and Chiral Slabs

This paper discusses modelling of isotropic and chiral slabs by using vector circuits involving dyadic impedances and admittances and tangential field components. The analysis is based on the exact averaging method for the Fourier-transformed field equations of the slab. Then, by considering tangential electric and magnetic fields as voltages and currents, analogous vector circuits, such as equivalent two-port circuits, Thevenin and Norton circuits and T and II circuits, are given for isotropic and chiral isotropic and homogeneous and nonhomogeneous slabs. These vector circuits are most appropriate when calculating propagated and reflected fields for general excitation. In addition, different approximations related to slabs thin either in wavenumbers in the normal or in transversal directions or to slabs with different propagation constant ratios are considered. A case when a slab can be simulated by a sheet is also discussed. The results obtained can be useful in many practical situations, for example, f...

Equilibrium-fluctuation expression for the resistance of a Norton circuit.

In the familiar Green-Kubo expressions, transport coefficients are related to equilibrium fluctuations. The equilibrium ensemble which generates these fluctuations is obtained by setting the thermodynamic force to zero. For the special case of electrical conductivity, we show how the transport coefficient is related to fluctuations in the conjugate equilibrium ensemble where the thermodynamic flux, rather than the force, is set to zero. We show that the conjugate equilibrium correlation function so obtained is the memory function of the flux autocorrelation function.

The Matrix Formulation of Scattering Problems

Two regions in space are coupled through an opening in a perfectly conducting surface. By using a complete set of eigenvectors in the opening, each region can be represented by an equivalent Norton circuit involving a short-circuit current (a vector) and a generator admittance (a matrix). The particular case of a cavity at resonance is investigated. Application to a cavity terminated in a waveguide is considered, and the transformation of the equivalent circuit resulting from the shift of the terminal plane is analyzed. After solving the example of a slotted waveguide, a possible set of eigenvectors for an arbitrary opening is proposed.