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Lumped element model limitation

Discussion in 'Electronic Basics' started by tsp, Sep 24, 2004.

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  1. tsp

    tsp Guest

    Can somebody tell me why the lumped element model breaks down when
    actual circuit impedances are very low, or when the length of the wire
    approaches the wavelength of the circuit's operating frequency?
  2. Don Kelly

    Don Kelly Guest

    Lumped model circuit theory is a quasi-static approximation of field theory.
    It works well when distances are considerably less than a quarter
    wavelength. However, where it is valid -it is a lot easier than going to
    more complex approaches. Below is a <list>(?) in order of complexity
    Consider a 1 ft length of wire:
    DC and low frequency-lumped model is a resistor.
    Higher frequency- Inductance effects are measurable -lumped model OK
    higher yet- both L and C lumped model works
    Higher- Transmission line models as R, L and C must be considered
    distributed- otherwise errors crop up
    (example 100mile length of unloaded power transmission line will have about
    a 5% higher voltage at the receiving end than at the sending end-lumped
    model doesn't show this). However a lumped T or pi model can be used for a
    specific line and is correct at the ends but not in the middle(10V at each
    end of a 1/4 wavelength line and the mid-line voltage will be about 14V).
    Higher yet and it is necessary to consider the line as a wave guide.
    Beyond that -now you are not using lines- you are using antennae and
    radiating .

    As for the lumped model not being valid for low impedances- not true. The
    breakdown may be that the model is not including all the factors which can
    be ignored at higher impedance levels. For example-at Z=R=0.01 ohms an
    ignored contact or meter resistance of 0.1 ohms can make measurements
    meaningless. If R=100 ohms, the effect is negligible.
  3. Roy McCammon

    Roy McCammon Guest

    I've never heard that.

    Maxwell's equations are operative at all lengths
    (ignoring qm). The question that really needs
    to be answered is why to lumped models work
    at all.
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