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Circuit Terminology

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

Network Function of a Circuit

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

Transfer Function to State Space

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...

Bewley Lattice Diagram

Bewley Lattice Diagram

The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.

State Space to Transfer Function

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:

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Updated: Jul 4, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Link-space formalism for network analysis.

David M D Smith¹, Chiu Fan Lee, Jukka-Pekka Onnela

¹Saïd Business School, Oxford University, Oxford, UK. d.smith3@physics.ox.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 4, 2008

Summary

This summary is machine-generated.

We introduce a new link-space formalism to analyze network models, focusing on degree-degree correlations. This method helps understand how node connections impact network structure and degree distributions.

Related Experiment Videos

Last Updated: Jul 4, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Area of Science:

Network Science
Statistical Physics
Graph Theory

Background:

Understanding degree-degree correlations is crucial for characterizing complex network structures.
Existing methods may not fully capture the nuances of node interdependencies in evolving networks.

Purpose of the Study:

Introduce and demonstrate the utility of the link-space formalism for network analysis.
Provide a framework for analytically solving network models with degree-degree correlations.
Investigate the impact of correlations on degree distributions in growing and decaying networks.

Main Methods:

Developed the link-space formalism based on the statistical description of link fractions between nodes of specific degrees.
Applied the formalism to analyze pedagogical models: random attachment, Barabási-Albert preferential attachment, and Erdős-Rényi random graphs.
Utilized the formalism for analytical solutions of network decay models (random link/node deletion) and derivation of nonassortative networks.

Main Results:

The link-space matrix was analytically solved for random attachment, Barabási-Albert, and Erdős-Rényi models.
Demonstrated the effect of degree-degree correlations on degree distribution in a growing network model.
Derived degree distributions for random link and node deletion network decay models.
Characterized the structure of a perfectly nonassortative network.

Conclusions:

The link-space formalism offers a powerful and versatile tool for detailed analysis of network correlations.
This framework facilitates analytical solutions for various network models, including growing and decaying systems.
The formalism provides insights into the formation of specific network structures, such as nonassortative networks.