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Reciprocity theorem and LTI systems

  1. Oct 29, 2009 #1
    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. jcsd
  3. Oct 29, 2009 #2

    berkeman

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    Staff: Mentor

    What's the reciprocity theorem for resistor networks?
     
  4. Oct 30, 2009 #3
  5. Oct 30, 2009 #4
    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
  6. Oct 30, 2009 #5

    berkeman

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    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

    .
     
  7. Oct 30, 2009 #6
    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:

    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.pdf


    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.
     
  8. Oct 31, 2009 #7
    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.
     
  9. Oct 31, 2009 #8
    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.
     
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