Linear Subnetworks Research Articles

An Effective Solution to Count-to-Infinity Problem for both Complex and Linear Sub-Networks

Distance vector routing protocol determines the best route for forwarding information from one node to another node based on distance. For calculating the best route, Distance-vector routing protocols use the Bellman-ford algorithm and the Ford-Fulkerson algorithm. The Bellman-Ford distributed algorithm calculates the shortest path. On the other hand, Routing Information Protocol is commonly used for managing router information management protocol within a Local Area Network or an interconnected Local Area Network group. The main problem with Distance Vector Routing protocols is routing loops. Because the Bellman-Ford Algorithm cannot prevent loops. Moreover, the routing loop triggers a problem with Count to Infinity. This research paper gives an effective solution to the Count to Infinity problem for link down situation and also for the router down situation in both complex and linear sub-network. For the router down situation, when any router goes down, then other nodes will recalculate their routing table with the dependency column. Moreover, the costs are calculated by the shortest path algorithm. If any link is down and all routers are up, then all routers will recalculate their routing table using Dijkstra instead of the Bellman-Ford algorithm. To determine the loops and prevent the loops are the main objectives. This method is mainly based on a routing table algorithm where the Dijkstra algorithm will be used after each iteration and will modify the routing table for each node. Preventing the routing loops will not converge into Count to Infinity Problem.

A network for recursive extraction of canonical coordinates

A network structure for canonical coordinate decomposition is presented. The network consists of two single-layer linear subnetworks that together extract the canonical coordinates of two data channels. The connection weights of the networks are trained by a stochastic gradient descent learning algorithm. Each subnetwork features a hierarchical set of lateral connections among its outputs. The lateral connections perform a deflation process that subtracts the contributions of the already extracted coordinates from the input data subspace. This structure allows for adding new nodes for extracting additional canonical coordinates without the need for retraining the previous nodes. The performance of the network is evaluated on a synthesized data set.

Subspace Based Identification of Broadband Electrical Models from Frequency Response Data

Abstract The generation of broadband equivalent circuit models for time-domain analysis of complex structures or components characterized by frequency-dependent network parameters is of great interest in microwave theory. In this paper, a recently developed frequency-domain subspace identification algorithm is applied to generate multi-port circuit models for passive microwave devices characterized by admittance, impedance, or scattering parameter data. The proposed method combines non-parametric minimal order realization and efficient passivity check. It is suitable for simulating linear sub-networks characterized by frequency response data in a general circuit environment consisting of lumped/distributed elements and nonlinear devices. The synthesized networks are compatible with SPICE-based circuit simulators, as is demonstrated by numerical examples.

On the synthesis of equivalent-circuit models for multiports characterized by frequency-dependent parameters

The synthesis of lumped-element equivalent circuits for time-domain analysis of problems with frequency-dependent parameters is of great interest in microwave theory. This paper presents a systematic approach to generate minimal-order realizations for passive microwave circuits characterized by either admittance, impedance, or scattering-parameter data. In addition, a very efficient method to ensure inherent system properties such as stability and passivity is described. The proposed method is suitable for simulating frequency-response-based linear subnetworks in a general circuit environment consisting of lumped/distributed elements and nonlinear devices. Modeling examples for a two-, four-, and ten-port system with nonlinear and linear terminations, respectively, are given.

Efficient transient simulation of embedded subnetworks characterized by S-parameters in the presence of nonlinear elements

This paper presents an efficient technique for transient simulation of linear subnetworks characterized by S-parameters in the presence of nonlinear components. The proposed method is based on the recently developed model-reduction technique, complex frequency hopping. A new algorithm for computing the moments of S-parameter-based subnetworks is presented. The proposed method is suitable for simulating large number of S-parameter-based subnetworks in a general circuit environment consisting of lumped/distributed elements and nonlinear devices.

Numerical methods and measurement systems for networks containing magnetic nonlinearities

In the last years an increasing interest in computer aided circuit calculation methods could be observed. This can be seen in combination with the short innovation processes in commerical products. Especially there is a need in modelling of nonlinear magnetic elements. In order to overcome these problems, a new method was developed, which makes it possible to calculate the steady state solution of circuits containing nonlinear magnetic elements by the help of an interactive CAD-program. After separating the network into linear and nonlinear subnetworks, it is possible to choose between several models for the nonlinear elements. In applications, where numerical models are insufficient a realtime measurement system can be activated to extract the nonlinear behaviour (dynamic hystersis loops). This concept is discussed for earth-leakage circuit breakers. These networks contain a toroidal highly permeable NiFe-alloy and a relay as nonlinear elements and some resistors, inductors and capacitors as linear elements. AC-signals at the primary winding of the core in any waveform must be regarded as an input, 135 degree phase cut off sinusoidal signals are especially important. These signals with extreme high frequency components make it impossible to use numerical models for the description of the nonlinear behaviour of the core and the relay. Therefore for both elements the realtime measurement system must be used during the iteration process.

Numerical methods and measurement systems for nonlinear magnetic circuits (abstract)

In the past years an increasing interest in calculation methods of circuits containing magnetic nonlinearities could be observed. For this reason a new method was developed which makes it possible to calculate the steady state solution of such circuits by the help of an interactive cad program. The modular concept of the software allows to separate the circuit into nonlinear and linear subnetworks. When regarding nonlinear magnetic elements one can choose between several numerical models for the description of the hysteresis loops or an inbuilt realtime measurement system can be activated to get the dynamic hysteresis loops. The measurement system is also helpful for the parameter extraction for the numerical hysteresis models. A modified harmonic-balance algorithm and a set of iteration schemes is used for solving the network function. The combination of the realtime measurement system and modern numerical methods brings up a productive total concept for the exact calculation of nonlinear magnetic circuits. A special application class will be discussed which is given by earth-leakage circuit breakers. These networks contain a toroidal high permeable NiFe alloy and a relay as nonlinear elements (cells) and some resistors, inductors, and capacitors as linear elements. As input dc signals at the primary winding of the core any curveform must be regarded, especially 135° phasecutted pulses. These signals with extreme higher frequency components make it impossible to use numerical models for the description of the nonlinear behavior of the core and the relays. So for both elements the realtime measurement system must be used during the iteration process. During each iteration step the actual magnetization current is sent to the measurement system, which measures the dynamic hysteresis loop at the probe. These values flow back into the iteration process. A graphic subsystem allows a look at the waveforms of all voltages and current when the iterations take place. One can determine how the steady state is reached, especially when one discusses different iteration methods. All parameters of interest, such as geometric data of the core, number of windings, and the linear elements can vary within the computer program and as a result all voltages and currents in the network stand can be used. With the help of this computer controlled measurement system and several iteration methods fast circuit design and optimization can be done.

Delay and crosstalk simulation of high-speed VLSI interconnects with nonlinear terminations

A method for analysis of VLSI interconnects that contain both lossy coupled transmission lines and nonlinear components is presented. An equivalent time-domain macromodel is derived for the linear subnetworks that contain lossy coupled transmission lines. The macromodel takes the form of a set of ordinary differential equations. The method takes full advantages of the asymptotic waveform evaluation (AWE) technique, which offers two to three orders of magnitude speed-up relative to other methods with comparable accuracy. In addition, it does not require explicit evaluation of the dominant poles of the network. The proposed technique can be easily implemented within the framework of an existing conventional circuit simulator such as SPICE.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Steady-state analysis of nonlinear circuits based on hybrid methods

Two efficient algorithms for calculating the steady-state responses of nonlinear circuits are proposed. They are based on both time-domain and frequency-domain approaches. A nonlinear circuit is partitioned into two subnetworks with substitution sources, and their responses are solved by a combined frequency-domain and time-domain method. The total response of the combined circuit can be calculated by an iterative technique based on either the Newton or the relaxation harmonic balance method. Since the methods are based on both time-domain and frequency-domain algorithms, they are called the Newton and the relaxation hybrid harmonic balance methods, respectively. The methods can be applied efficiently to strong nonlinear circuits containing high-Q subnetworks such as filter circuits and crystal oscillators. When a large-scale circuit is partitioned into large linear subnetworks and small nonlinear subnetworks, the method can also be applied efficiently. >

Evaluation of faulty elements within linear subnetworks

This paper presents a topologically based theoretical background for designing tests for identification of faulty parameter values in linear subnetworks. Nodal voltages are assumed t o be obtainable either by measurements or, indirectly, as a result of a nodal fault analysis. A formulation of nodal fault analysis for subnetworks is presented. It is shown how this approach can be used to evaluate faulty elements within inaccessible faulty subnetworks. The objective of this work is the reduction of the number of required current excitations and, thereby, the number of voltage measurements. The Coates flow-graph representation of a network is used.

Nonlinear circuit analysis through periodic spline approximation

A spline representation is proposed for the current or voltage periodic waveforms at the connections between the linear and nonlinear subnetworks into which the circuit is partitioned. The periodic steady-state analysis is thus reduced to the solution of a nonlinear system whose unknowns are the knot ordinates of these splines.

A piecewise harmonic balance technique for determination of periodic response of nonlinear systems

A new method for the solution of nonlinear periodic networks has been developed. It avoids the time domain solution of the dynamic equations. In the proposed method, the network is decomposed into a minimum number of linear and nonlinear subnetworks. Only frequency domain solutions of the linear subnetworks are required. It is shown that considerable reduction in the size of the computational problem can be achieved by taking advantage of the linearities present in the network.