Dual impedance

Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance ${\displaystyle Z}$ is its reciprocal, or algebraic inverse ${\displaystyle Z'={\frac {1}{Z}}}$. For this reason, the dual impedance is also called the inverse impedance. Another way of stating this is that the dual of ${\displaystyle Z}$ is the admittance ${\displaystyle Y'=Z'}$.

The dual of a network is the network whose impedances are the duals of the original impedances. In the case of a black-box network with multiple ports, the impedance looking into each port must be the dual of the impedance of the corresponding port of the dual network.

This is consistent with the general notion duality of electric circuits, where the voltage and current are interchanged, etc., since ${\displaystyle Z={\frac {V}{I}}}$ yields ${\displaystyle Z'={\frac {I}{V}}}$^[1]

Parts of this article or section rely on the reader's knowledge of the complex impedance representation of capacitors and inductors and on knowledge of the frequency domain representation of signals.