Reciprocity theorem and LTI systems

[sokrates]

I am looking for good, theoretical references on the reciprocity theorem for resistor networks.

I am trying to find out how general the theorem is and whether it is only limited to LTI systems.

Thanks in advance for the suggestions...

 

[berkeman]

What's the reciprocity theorem for resistor networks?

 

[sokrates]

For instance:

http://mysite.du.edu/~jcalvert/tech/reciproc.htm

 

[waht]

I am trying to find out how general the theorem is and whether it is only limited to LTI systems.

here is a small wiki reference:
http://en.wikipedia.org/wiki/Reciprocity_(electromagnetism)

The general theorem is the Lorentz reciprocity which can be simplified to a linear system by making some assumptions.

 

[berkeman]

What is this theorem used for? What is it's advantage over a standard solution/simulation of the circuit? I wasn't able to figure that out from a quick read of sokrates' link

http://mysite.du.edu/~jcalvert/tech/reciproc.htm

.

 

[waht]

Basically, you can derive a two-port network directly from Maxwell's equations.

1. Start with Maxwell's equations.

2. That leads to Lorentz reciprocity theorem:

the relationship between an oscillating current and the resulting electric field is unchanged if one interchanges the points where the current is placed and where the field is measured (wiki).

3. Make linear approximation

4. And we get the reciprocity theorem which is a simplified version for linear systems only.

5. Using the theorem one can derive two-port network parameters.

Here is another more in depth reference:
http://www.eecs.umich.edu/RADLAB/html/techreports/RL871.pdfAnother application of the theorem is in antenna design. One can prove that a radiation pattern for a transmitting antenna is the same as it would be receiving.

 

[sokrates]

Hi, waht.

Thank you for your insights and references. I am more interested in the resistor network version of the theorem...

Is this the simplifed version? Or would it hold even if my network is not Linear-Time Invariant?These are all good, but I don't need the Maxwell treatment.

 

[waht]

Sorry for the Maxwellian blast, but just trying to illustrate that the reciprocity theorem for resistor networks is just a linear case of a more general theorem, which is non-linear. Reciprocity for resistor networks is time-invariant also.