UNIVERSAL COLLEGE OF ENGINEERING & TECHNOLOGY

Circuits and Networks E.C Engg. Parmar Ramendra ( ) 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 dii = C de dt e = 1 ∫ i dti = 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.ElementDual Element 1ResistanceConductance 2CapacitanceInductance 3 Capacitance 4Series BranchParallel Branch 5MeshNode 6Closed SwitchOpen Switch

Duality Sr. No.ElementDual Element 7VoltageCurrent 8Voltage sourceCurrent source 9Open circuitClose circuit 10KVLKCL 11ImpedanceAdmittance 12TheveninNorton

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…