Electrical Network

An electrical network is a collection of interconnected electrical elements (or devices) such as resistors, capacitors, inductors, diodes, transistors, vacuum tubes, switches, storage batteries, transformers, delay lines, power sources, and the like. The behavior (such as the response to a unit impulse) of an electrical network is a function of two factors: (l) the characteristics of each of the electrical elements, and (2) how they are connected together, that is, their topology. It is the latter factor that brings graph theory into the picture.

An electrical element can be

• Lumped or distributed.
• One-port (i.e., two-terminal) or multiport
• Linear or nonlinear.
• Time invariant or time varying.
• Passive or active.
• Bilateral or nonbilateral

To avoid using partial differential equations, a distributed element, such as a transmission line, is either approximated by lumped elements or is con­sidered separately. Thus an electrical network almost by definition implies a network consisting of lumped elements only. Also, a multiport device such as a transformer or a pentode can be replaced by a set of interconnected two-terminal elements, such as resistors, inductors, and dependent power sources. Thus we can confine ourselves to a network of lumped, two-terminal elements.

A two-terminal electrical element is represented by an edge e_k. Associated with each edge are two edge variables, V_k(t) and i_k(t). The variable v_k (t) is called the edge voltage and may be regarded as a cross variable, because it exists across the two end vertices of the edge. The other variable i_k(t) is called the edge current and may be thought of as a through variable, because it flows through the edge. Since the variables are directional, every edge is assigned an arbitrary orientation. The characteristics of each element arc completely described in terms of these two variables. Thus an electrical network for us is a connected directed graph G in which each edge e_k is assigned two variables v_k(t) and i_k(t).

Questionnaire:

• What is electrical network? Explain.