What Is The Concept Of Duality In Electronic Components?
'Duality' is a property of particular components that allows for their substitution in any given circuits with a 'dual' component. Such dual components function in a complementary manner within the electronic circuit if they are implemented. The concept of duality makes for good time-saving in seeking the solution of numerous circuit problems. The essential reason for this is that the circuits are identical save for the dual elements – and the equations can be said to be 'dual' to one another also, due to the similarity between the circuits. Only certain elements of equations can be treated in such a manner. They include the following:
1. Resistance (exhibited by a resistor) (R) Conductance (G)
2. Inductance (I) Capacitance (exhibited by a capacitor) (C)
3. Voltage (v) Current (i)
4. Voltage Source Current Source
5. Node Mesh
6. Series Path Parallel Path
7. Open Circuit Short Circuit
The above mentioned circuit elements are said to be dual due to the fact that they can interchange with each other according to the circuit equation, and provide a simpler way to solve the problem. The principle of duality creates parallelism among pairs of characterizing circuit equations, and theorems of electronic circuits. This duality principle is applicable to planar circuits and linear quantities only – for example, Power has no dual because it is a non-linear quantity.
Graphical Method to find Dual Circuits:
Duality in circuits is a highly useful concept – if we know the solution of one circuit, we can get the solution of its dual circuit fairly trivially. There is a useful graphical method to find the dual of a given circuit. It consists of following three simple steps:
At the centre of each mesh of a given electric circuit, place a node. Then place a reference node outside the given circuit (this is the ground of the dual circuit).
Draw lines between nodes such that each line crosses a circuit element. Then replace that element with its dual.
A simple rule to recover the polarity of voltage sources and the direction of current sources is:
“If a given voltage source producing a clockwise mesh current has a current source as its dual, the reference direction of this dual current source will be from the ground to the non-reference node of the circuit.”
This article is a guest post by Zain Malik (Electrical Engineer)