Transcript Duality - Universal College of Engineering & Technology

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=Ri
e = L di
dt
e = 1 ∫ i dt
C
i=Ge
i = C de
dt
i = 1 ∫ e dt
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.
1
2
3
4
5
6
Element
Resistance
Capacitance
Inductance
Series Branch
Mesh
Closed Switch
Dual Element
Conductance
Inductance
Capacitance
Parallel Branch
Node
Open Switch
Duality
Sr. No.
7
8
9
10
11
12
Element
Voltage
Voltage source
Open circuit
KVL
Impedance
Thevenin
Dual Element
Current
Current source
Close circuit
KCL
Admittance
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…