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Violation of Kirchhoff's Laws for a Coherent RC Circuit.

  1. May 11, 2010 #1
    Thank you ZapperZ for introducing these new peer-review papers.
    This one is of particular interest to me.

    I believe I may have some insight into this issue.

    In the normally constructed RC circuits using discrete components, the reactions of the individual components to signal frequency is not normally of concern until the frequency starts to show "skin effect". The higher the frequency, the more the skin effect is evident, and the more care needs to be taken to shield neighboring components from each other.

    The physical construction of the components themselves starts to be the constraint to the circuits operation.

    With a carbon resistors for instance, as the skin effect starts to show, the core of the resistor becomes less and less involved, and the outer surface regions take on more and more of the function, including areas of corrosion, paint, physical blemishes, etc., to the extent that the noise and heat from these eddy current producers and parasitic harmonic resistances eventually cause this device to overheat and destroy the circuit.

    Thin film resistors solve this problem for a while until the frequencies and skin effect once again start to cause damaging and signal interference problems.

    The physical shapes of these devices become more and more important as the skin effect rears its ugly head. Sharp pointed corners and protrusions concentrate EM parasitic harmonic resonances. If anyone has heard these circuit squeals, and whistles, you know what I am referring to. These parasitic harmonic resonances will make component blemishes ring out and transmit EMR to neighboring components that introduce noise and may interfere with proper circuit operation.

    Smooth surfaces, rounded and radius-ed contours, proper component orientation and grouping, all help to keep skin effect under control.

    Component shapes become more important as the frequencies reach the gigahertz range.
    The dimensions of the tracking conventionally used to connect components will cause them to act more and more as wave guides than current conductors.

    As the skin effect becomes thinner and thinner, I believe the surface finish becomes very important to avoid the skipping effect as the energy bridges the gaps and jumps the humps of the blemishes. These blemishes show up in radar wave guides as hot spots or burn out areas.

    Thoughts anyone?
  2. jcsd
  3. May 11, 2010 #2


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  4. May 11, 2010 #3
    Sorry, I missed the entire reference.
    It is
    J. Gabelli et al., Science v.313. p.499 (2006)

    Violation of Kirchhoff's Laws for a Coherent RC Circuit.

    Abstract:What is the complex impedance of a fully coherent quantum resistance-capacitance (RC) circuit at gigahertz frequencies in which a resistor and a capacitor are connected in series? While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on observation of a different behavior. The resistance, here associated with charge relaxation, differs from the usual transport resistance given by the Landauer formula. In particular, for a single-mode conductor, the charge-relaxation resistance is half the resistance quantum, regardless of the transmission of the mode. The new mesoscopic effect reported here is relevant for the dynamical regime of all quantum devices.

    Of course, the significance of this work is not really to show that Kirchhoff's law doesn't work in this regime, but rather to study the behavior of conduction at the mesoscopic scale. This is important since electronics components are getting to be smaller, and quantum computing and circuits will be relevant in future devices. It is vital to know how such components differ from their classical counterparts.


    Edit: They have put this up on ArXiv, so if you don't have access to Science, this is how you can get it:

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