network theory

Raj that's a toughie

http://onelook.com/?w=dual&ls=a

Incidentally © doesn't make sense. I presume that's supposed to be "parallel" but then how would the RC circuit be it's own "dual"

Maybe you meant "parallel CR circuit" but sounds nutty

Maybe there's a more sublime and technical meaning for "dual" that a participant with such knowledge will reveal

I will explain first, then I will give the answer.

Here's an excerpt from one of my EE textbooks:



Some dual pairs are listed below:



NOTE: Linearity MUST apply for a dual to exist and even then there may not be a dual. Circuits are duals if they have the same characterizing equations with interchanged dual quantities (as listed).

Since my text explains it so well, I will again reference the method for determining a dual.



Here’s an example from the same book:



Now, as for your specific problem – using the method above, the correct answer to the question of



is



Note, however, that the resistance to be used in the dual was converted from a resistance to conductance; that is, if the resistance was R=5Ω, then the dual resistance is 1/R = G = 1/5 = 0.2Ω.

Wow 24 thanks for that

Since it's a bit beyond me however you might explain the purpose of a dual circuit in simple terms suitable to the average clod (me). For instance, does the dual equivalent of a circuit react the same way to ac, therefore somehow easier to analyze

…which admittedly wouldn't make sense if the dual of an open is a short

The purpose of dual circuits is mostly so that you don't have to re-solve an entire array of mesh or nodal equations on another circuit when it's the dual of one you've already solved (it's already solved for you, you just need to switch the dual quantities).

I've never had to use this technique outside of the class I learned it in (at least not this way); however, this general idea of the duality of electricity and magnetism is very useful in developing circuits where you need an opposite response or the same response in a different quantity (voltage vs. current). For example, high pass filter vs. low pass filter (these are not necessarily dual circuits - they just exemplify the dual nature of the elements).

As far as reacting the same way, the answer appears to be



BUT, you must understand that it is a similar response under dual conditions (current response to voltage response).

For instance, if you were using a voltage source and you were looking at the output voltage over some element, then the dual response would be the same as long as you were looking at the output current through the dual of the same element mentioned in the voltage driven source (again, remember that the dual of a voltage source is a current source).



Using a dual is more useful when using variables (R, L, C, etc.) as a means to quickly obtain the solution of a circuit - from there, the desired values are chosen for the desired response. Often, the dual of one specific circuit will not perform as well as the other, but this comes down to how each element is manufactured and the typical values, tolerances, and power ratings of each device.

And just in case it isn't clear, when you solve for a dual circuit (assuming it has a dual) you must change every element in the network; otherwise, you've altered the response of the circuit.

24 thanks most kindly for that thorough exposition