Principle of Duality:

Two linear circuits are said to be duals of one another if they are described by the same characterizing equations with  dual quantities interchanged.

Network and its dual are same only with respect to the performance, but the elements and connections point of view, they are no equal.

Dual pairs

Resistance R    ⇔     Inductance L

Conductance G ⇔ Capacitance C

Impedance Z  ⇔  Admittance Y

Current i ⇔ Voltage v

Voltage source ⇔ Current source

Node          ⇔           Mesh

Series path  ⇔ Parallel path

Open circuit ⇔ Short circuit


Thevenin ⇔  Norton

Delta network  ⇔ Star network

Ri(t) ⇔  Gv(t)

The number of mesh equations in the original network is equal to the number of nodal equations in its dual network and vice versa. ‘N’ nodal equations represents (N+1) principle nodes.

The following steps are involved in constructing the vith dual of a network:

1. Place a node inside each mesh of the given network. These internal nodes correspond to the independent nodes in the dual network.

2.Place a node outside the given network. The external node corresponds to the datum node in the dual network.

3. Connect all internal nodes in the adjacent mesh by dashed lines crossing the common branches. Elements which are the duals of the common branches will form the branches connecting the corresponding independent node in the dual network.

4. Connect all internal nodes to the external node by dashed lines corresponding to all external branches. Duals of these external branches will form the branches connecting independent nodes and the datum node.

5. A clockwise current in a mesh corresponds to a positive polarity (with respect to the datum node) at the dual independent node.

6. A voltage rise in the direction of a clockwise mesh current corresponds to a current flowing towards the dual independent node.

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