Dual impedance

This is consistent with the general notion duality of electric circuits, where the voltage and current are interchanged, etc., since

[1] In physical units, the dual is taken with respect to some nominal or characteristic impedance.

[2] The scaling factor R02 has the dimensions of Ω2, so the constant 1 in the unitless expression would actually be assigned the dimensions Ω2 in a dimensional analysis.

There is a graphical method of obtaining the dual of a network which is often easier to use than the mathematical expression for the impedance.

Starting with a circuit diagram of the network in question, Z, the following steps are drawn on the diagram to produce Z' superimposed on top of Z.

This method also demonstrates that the dual of a mesh transforms into a node, and the dual of a node transforms into a mesh.

This dual circuit is not the same thing as a star-delta (Y-Δ) transformation.

Filters designed using Cauer's topology of the first form are low-pass filters consisting of a ladder network of series inductors and shunt capacitors.

Resistor R
Conductor G = R
Conductor G
Resistor R = G
Inductor L
Capacitor C = L
Capacitor C
Inductor L = C
Series impedances Z = Z 1 + Z 2
Parallel admittances Y = Z 1 + Z 2
Parallel impedances 1/Z = 1/Z 1 + 1/Z 2
Series admittances 1/Y = 1/Z 1 + 1/Z 2
Voltage generator V
Current generator I = V
Current generator I
Voltage generator V = I
A star network of inductors , such as might be found on a three-phase transformer
Attaching generators to the three ports
Nodes of the dual network
Components of the dual network
The dual network with the original removed and slightly redrawn to make the topology clearer
The dual network with the notional generators removed
A low-pass filter implemented in Cauer topology
Attaching generators to the input and output ports
Nodes of the dual network
Components of the dual network
The dual network with the original removed and slightly redrawn to make the topology clearer