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Why the circuit theory works well when a lumped-parameter system has dimensions of one tenth of the electromagnetic wavelength? Why not one third or any other ratio of the electromagnetic wavelength?

Book Ref: Electric Circuits, by James William Nilsson, tenth edition.

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  • \$\begingroup\$ In a lumped parameter system, everything happens at approximately the same time, as opposed to a distributed system where there are significant time delays between events at various locations. Such delays are related to the operating frequency and the distances a signal travels between components, are conveniently measured as fractions (or multiples!) of a wavelength, and are thus readily related to the lengths of PCB tracks, or connecting wires. Perhaps the text should have said 'one tenth of a wavelength or less' \$\endgroup\$
    – Chu
    Commented Mar 25, 2018 at 23:34
  • \$\begingroup\$ The phaseshifts are the concern. \$\endgroup\$ Commented Mar 26, 2018 at 2:17

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When people make calculations or watch already calculated curves on "how much power a piece of wire radiates as a radio wave vs. how large reactive power is inputted to its self capacitance and -inductance" they very easily can make the following decision:

"The proportion of the radiated power starts to grow especially rapidly when the frequency grows and reaches the limit where the length of the wire is ten percent of the wavelength".

No such strict limit actually exists. Its existence is an illusion which depends on used scaling of the radiation resistance vs reactance curves. People also have learned to design well working circuits where that limit seem to be respected (see NOTE1) and ten percent is a convenient number to remember or tell to others.

Wavelength/4 wire is quite effective antenna and that in practice makes that size lumped components useless. The circuits must be well calculated transmission lines to keep the signals in wires and other components.

NOTE1: respected = the longest onboard hf signal path is well below 10% of the wavelength, for example 1 to 2 percent. The circuit works well, but it also radiates very clearly noticeable, if it's not shielded.

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