conductanceto

Conductanceto is a term used in electrical engineering and network analysis to describe the conductance between two nodes within an electrical network. In its essential form, it measures how readily current can flow from one terminal to another, and is the reciprocal of the equivalent impedance between those two terminals.

Notation and units

In circuit notation, the conductance between nodes i and j is often written as G_ij and is measured in siemens (S). It represents the ratio of the current I that flows from i to j to the voltage difference V_i − V_j: G_ij = I / (V_i − V_j). When a two-terminal network is analyzed, the total conductance between i and j accounts for all possible paths and components linking the nodes.

Calculation

A standard way to determine G_ij is to apply a known voltage difference between nodes i and j (for example, set V_i − V_j = 1 volt) and compute the resulting current I that flows. The conductance is then G_ij = I. In practice, nodal analysis, circuit reduction, or solving the network’s admittance (Y) matrix is used to find the effective conductance between the chosen terminals. In networks with multiple parallel paths, conductances add. For series elements, appropriate transformations convert the configuration to an equivalent single conductance.

Relation to other concepts

Conductanceto is closely related to admittance, impedance, and the conductance matrix used in nodal analysis. It can describe a node-to-ground conductance (the sum of all admittances connected to a node) as well as a mutual conductance between distinct nodes. In some simulation tools, conductance terms appear as parameters of voltage-controlled current sources or as elements labeled with transconductance values.

Applications

The concept is used in circuit design, network synthesis, and analysis, including SPICE simulations, where effective two-terminal conductances inform impedance matching, signal transfer, and power distribution. See also impedance, admittance, and the conductance matrix.