# Reciprocity theorem and LTI systems

1. Oct 29, 2009

### 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...

2. Oct 29, 2009

### Staff: Mentor

What's the reciprocity theorem for resistor networks?

3. Oct 30, 2009

### sokrates

4. Oct 30, 2009

### waht

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.

Last edited: Oct 30, 2009
5. Oct 30, 2009

### Staff: Mentor

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

.

6. Oct 30, 2009

### waht

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

2. That leads to Lorentz reciprocity theorem:

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:

Another 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.

7. Oct 31, 2009

### 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.

8. Oct 31, 2009

### 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.