UNIVERSAL COLLEGE OF ENGINEERING &

TECHNOLOGY

Circuits and Networks

E.C Engg.

Parmar Ramendra (140463111001)

Guided by :-

Prof. Dhaval Patel (E.C Department)

Duality

The two networks are said to be dual networks of each other if the mesh (loop) equations of given network are the node equations of other network.

Duality is a transformation in which currents and voltages are interchanged.

Duality

The following pairs of equations also represent dual relations resulting due to the exchange of voltage and current.

e = R i i = G e

e = L di i = C de

dt dt

e = 1 ∫ i dt i = 1 ∫ e dt

C L

Duality

The following pairs of equations represent dual relations resulting due to the exchange of voltage and current.

Following is the list of elements and its duals.

Duality

Sr. No. Element Dual Element

1 Resistance Conductance

2 Capacitance Inductance

3 Inductance Capacitance

4 Series Branch Parallel Branch

5 Mesh Node

6 Closed Switch Open Switch

Duality

Sr. No. Element Dual Element

7 Voltage Current

8 Voltage source Current source

9 Open circuit Close circuit

10 KVL KCL

11 Impedance Admittance

12 Thevenin Norton

Duality

How to Construct Dual Circuits :-

Place a node at the center of each mesh of the circuit.

Place a reference node (ground) outside of the circuit.

Duality

Draw lines between nodes such that each line crosses an element.

Replace the element by its dual pair. Determine the polarity of the voltage

source and direction of the current source.

Duality

Example :- Draw the dual of the following network

shown in the fig.

Duality

Step 1 :- Place a node at the center of each mesh of the circuit.

Duality

Step 2 :- Place a reference node (ground) outside of the circuit.

Duality

Step 3 :- Draw lines between nodes such that each line crosses an element.

Duality

Step 4 :- Replace the element by its dual pair.

Step 5 :- Determine the polarity of the voltage source and direction of the current source.

Duality

Draw Dual circuit :-

Duality

Summary :-

The principle of duality means that the solution to the characterizing equations for one circuit can be applied to its dual circuit.

Duality

The equations that describe the currents and voltages in one circuit are the same set of equations for the its dual, where the variables have been interchanged.

…Thank You…