Electrical network

Lore & Background

An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, current sources, resistances, inductances, capacitances). An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Thus all circuits are networks, but not all networks are circuits (although networks without a closed loop are often referred to as open circuits). Networks are classified by passivity: an active network contains at least one voltage source or current source that can supply energy indefinitely, while a passive network does not contain an active source. By linearity, linear electrical networks consist only of sources, linear lumped elements, and linear distributed elements, and signals are linearly superimposable. Passive networks are generally taken to be linear, but exceptions exist, such as an inductor with an iron core driven into saturation. By lumpiness, discrete passive components are called lumped elements; at high frequencies or for long circuits, the distributed-element model is needed. Sources are classified as independent (maintaining the same voltage or current regardless of other elements) or dependent (depending upon a particular element of the circuit). A number of electrical laws apply to all linear resistive networks, including Kirchhoff's current law, Kirchhoff's voltage law, Ohm's law, Norton's theorem, Thévenin's theorem, and the superposition theorem. These laws result in simultaneous equations that can be solved algebraically or numerically.

Reader's Guide

Electrical networks are foundational to modern electronics, providing the conceptual framework for analyzing and designing circuits ranging from simple resistive networks to complex electronic systems. The classification of networks by passivity, linearity, and lumpiness guides engineers in selecting appropriate analysis methods: linear networks can be analyzed using frequency domain methods such as Laplace transforms, while nonlinear networks require more complex tools. The application of fundamental laws—Kirchhoff's laws, Ohm's law, Norton's theorem, Thévenin's theorem, and the superposition theorem—enables the reduction of complex networks to simpler equivalent forms. These laws extend to networks containing reactances but cannot be used in networks with nonlinear or time-varying components. Circuit simulation software such as SPICE, GNUCAP, and languages like VHDL-AMS and Verilog-AMS allow engineers to design circuits without the time, cost, and risk of building prototypes. Linearization around an operating point and piecewise-linear approximation are techniques used to handle nonlinear elements. The distinction between lumped-element and distributed-element models is critical at high frequencies or for long circuits such as power transmission lines. Overall, electrical networks remain a core subject in electrical engineering education and practice.

Did You Know?

• All circuits are networks, but not all networks are circuits; networks without a closed loop are often referred to as open circuits.
• A resistive network contains only resistors and ideal current and voltage sources, and its analysis is less complicated than networks with capacitors and inductors.
• Passive networks are generally taken to be linear, but an inductor with an iron core can become nonlinear if driven into saturation.
• Norton's theorem states that any network of voltage or current sources and resistors is electrically equivalent to an ideal current source in parallel with a single resistor.