Dual impedance

Dual networks or dual circuits are electric networks in which currents and voltages are reversed.

Position in theoretical electrical engineering

The duality presented here is a far-reaching structural property of the object of electrical engineering in so far as it allows the systematic comparison of many dual single terms, including:

Dual topology

In the context of graph theory can be used for the case of planar graphs a duality concept grasp, which is closely related to the relationship of cycle and cut space of a graph. As can be seen in the opposite drawing correspond to the edges of both graphs is one-one another, while the nodes of a graph occur in different cycles and vice versa. In terms of electrical cycles than the mesh, the edges as branches ( each with a two pole ), the graph will be called a network or, with focus on the graph theoretical background as topology.

Dual elements

Two poles are dual to each other if their current-voltage legality remains structurally if you switch voltage and current. This is particularly the case with impedances. Thus the basic elements to stand as compared with dual follows.

Dual networks

Two networks are dual to each other if

• Their topology is dual.
• All korrenspondierenden Two poles are dual.

Examples

Series and parallel circuit

The accompanying sketch shows the graphical construction of the duality of series and parallel connection of impedances. Since the circuit is not closed, the connections were alternatively connected with the dashed line. You Ascertain that each dipole has its corresponding dual, and each node lies exactly in a loop of the dual circuit. Further, each of the dual circuits is planar for himself, thus contains no intersecting connections.