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Principle of Duality

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gilmanli

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Would some one tell me what is principle of duality at electronic.I only know that changing the circuit from parallel to series ,voltage source to current source,resistance to conductance,capacitor to inductor (vice versa ).
Would some one give me some examples such that I can fully understand this topic.
 
Does this help?
**broken link removed**)

It just seems to be mostly about how two different things are really just different aspects of the same thing stemming or inverses of each other. Supposedly stemming from electricity and magnetism being two different aspects of the same physical phenomena.

Most of it seems more like just people liking to classify and group things and does't seem too important, except for the part about electricity and magnetism being two aspects of the same force.
 
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Inductance & capacitance.
Electric field & magnetic field.
Current & voltage.
Electric charge & magnetic flux.
Series & parallel.
Open circuit & short circuit.
Norton & Thevenin circuits.
 
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Princeple of Duality

Thank you for your information about Princeple of Dulity,the website I had been visited before but no help for me to understand this topic.I need some of examples circuitry to do the conversion or white paper such that I can fully understant the Dulity.
 
Hello there,


It seems that you already know the basics, so lets see if we can build on that a little here.

When it comes to electrical circuits, "duality" is defined on the basis of *mesh* and *nodal* equations:
Two circuits are said to be "duals" of each other if the mesh equations of one circuit have the same form as the nodal equations of the other circuit. They are said to be "exact duals" if the numerical values of the variables of the two systems are the same.

Simply put, one system is defined in terms of currents like i1, i2, while the other system is defined in terms of voltages like v1,v2. If the two systems are duals, the voltage variables v1 and v2 will appear in the equations where the first system had i1 and i2, respectively.

We could probably draw up something like a low pass filter using an R and C and voltage source and then come up with a dual circuit. Im not sure if this is what you want to do though.
 
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Princeple of Duality

Thanks you for your information talking about princeple of duality.I know the princeple of duality just you talked about at this forum.I need some of circuit examples such that I can fully understand princeple of duality at electronic field and do some testing.Have you some of duality circuitry examples post at this forum ?
 
It's not an important or relevant concept. That's why you won't find much on it. THe problem is there's just nothing to understand about it. It's just people grouping similar things together. In electronics have things that complimentary to each other so people like to group them. The grouping exists, but doesn't help in the understanding of anything, or any applications. It does not help in the understanding the individual concepts of electricity, magnetism, voltage, current, resistance, etc.

It's like grouping elements on the periodic table by what colour they are...you can do it, but it doesnt help in the understanding or application of anything.

There is one exception though, and that is the concept of duality in digital logic circuits. That actually is useful because it's a actually a math thereom that helps in the formulation of boolean equations.
 
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Princeple of Duality

Thanks you for your replied about the Priceple of Duality.My ideal is that I am a electronic design engineer on telecommunication product company,some product has design limit for example spacing,if I can fully understand Duality at electronic,I can change a part of circuitry using princeple of duality to fulfill the spacing design limit ( changing high voltage 400VDC and high value 1000uF E cap to a coil ) so I want to understand this topic.Do you know where I can get this material ?
 
Hi again,


Do you know what mesh analysis and nodal analysis are?


Here's an example of dual circuits:

Circuit1:
A voltage source E in series with a resistor R also in series with a capacitor C. The voltage across the cap is vC.

Circuit2:
A current source in parallel to a conductance G also in parallel to an inductor L. The current through the inductor is iL

In circuit 1 we had E,R, and C, and looked at vC, and in circuit 2 we had I, G, and L, and looked at iL.
The circuit 2 elements are related to circuit 1 elements as:
I=E
R=1/R
L=C
iL=vC

So to convert to the new circuit we would use a current source equal to E amps, a resistor equal to 1/R, and an inductor equal to C, and the output would be iL. The response iL(t) would be the same as the voltage response vC(t).

Example:
We have three elements in series, a voltage source E=1v peak, R=100 ohms, and C=100uf, and the dual is a circuit with three elements in parallel, a current source I=1 amp peak, R=1/100 ohms, and L=100uH.
The response of the voltage across the cap in circuit 1 is the same as the current through the inductor in circuit 2. With a frequency of 100Hz, the cap voltage (circuit 1) is about 157mv and the inductor current (circuit 2) is about 157mA.

This illustrates that if you want to change a circuit from using a capacitor to a circuit using an inductor you have to use the same value inductor as the capacitor, a resistance equal to the reciprocal of the original resistance, and change the voltage source to a current source.

Does that help?

It might help more if you told us exactly what circuit you are dealing with and what you want to change to save space or money. In many cases a dual circuit will not work for a number of reasons, even if you swap exactly, because there are other characteristics that change when you go from a cap to an inductor. It really has a lot to do with the actual application.
 
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Princeple of Duality

Thanks you MrAl,
It is very detail to explain the Princeple of Duality for me,I will review Mesh and Nodal analysis such that I can easy to do the circuit change.At your replied you said even I do correct conversion at the circuitry,sometime it does not work exactly I want.Would you mind explian more detail about this ?
 
Hello again,

Well i only meant that there are differences in the inductor compared to the capacitor such as series resistance which could be high for the inductor, so you'd have to take those secondary effects into account also. It's not just a matter of replacing the cap with an inductor, you'd have to look at the circuit very carefully to make sure it worked good enough.
Also, it's not easy to make a current source if you already have a voltage source when dealing with power.

You really need to post your circuit so we can take a better look and advise more precisely.
 
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