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What Is The Concept Of Duality In Electronic Components?

By on June 1, 2012

'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)

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6 Comments

  1. Rich-Orlando

    June 3, 2012 at 6:45 am

    Thanks for that academic exposition.
    It was quite interesting and understandable at the beginning, but somewhere along the lines it become complicated. I suggest such articles could better be understood with a diagram - diagrams are actually the practicality of electronics.
    Thanks all the same.

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    • Jestine Yong

      June 4, 2012 at 3:17 am

      Hi Rich,

      Actually I have asked for the diagram for easy understanding but was told that it was not available.

      Jestine

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  2. chong heng weng

    June 6, 2012 at 10:10 pm

    I am in total agreement with Rich , any technical artical in text follow with diagrams or circuits will make the presentation more easily undersood

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  3. uk electronic components

    June 15, 2012 at 3:59 am

    Thanks for such a nice and informative post.How ever with a diagram would been added a weightage to the post.

    Likes(0)Dislikes(0)
  4. clary josee

    June 26, 2012 at 1:28 am

    I was just going through few sites and blogs yesterday and came across your  site https://www.jestineyong.com/ too. I really liked the way you have presented your site. I was reading some of your content and really found them interesting and informative. So I was just wondering if I can also do something for your site.

    Actually I am a freelance content writer and I love writing articles as a hobby on topics related to EL wire.

    What if I provide you with an unique article as a Guest Post. An article that will be informative for your readers. The article will be related to your website and will be appreciated by your readers.

    It would be great if you can add a small BIO of mine at the end of the article with my related site's links. I guarantee you that the article will be 100% copy scape protected and will be of around 700 words.
     

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    • Jestine Yong

      June 26, 2012 at 7:54 am

      HI Clary,

      Yes sure I need a guest blogger. You can send the article to jestineyong(at)electronicrepairguide.com

      Jestine

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