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There are a total of three postulates of lumped matter discipline.

  1. Rate of change of magnetic flux outside the conductor is zero.
  2. The change of chrage inside a conductor is zero.
  3. Signal timescales must be larger than the delay of propagation of the electromagnetic wave.

 

  1. The magnetic flux is changing will induce a current in a opposite direction inside the conductor.(Faraday's and Lenz's Law.)
  2. No net charge can exist inside the conductor. (Kirchhoff's Current Law)
  3. ???

Am I right? Can someone explain to me the third postulate. I am not sure what it means. Here is the similar answer that I found here. 3rd lumped circuit abstraction postulate

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b) All insulators are dielectrics and all dielectrics can hold a charge. Otherwise they are conductors. A floating conductor can hold a charge but not within a loop circuit. Also KCL defines node current = 0.

c) Signal timescales must be larger than the delay of propagation of the electromagnetic wave

Typically we use path length << 10% of wavelength so that transmission line or antenna effects do not affect conductor impedance significantly. At 1/4 Wavelength impedances invert so short becomes open and open becomes short. In some cases we may consider <1%λ such as -100dB attenuation of screen at RF Faraday cage.

e.g. say a coax has a dielectric constant such that speed of light is 2/3v in air then resistance of 1 meter of coax is say 0 ohms from end to end and open circuit centre to shield from DC up to some frequency. But at f= 1/4 wavelength it becomes the opposite and is often used to make a poor man's RF notch filter and more often fractional wavelengths are used as impedance transformers so the lumped analysis of the conductor and dielectric model is too simple here.

So at what frequency will the wavelength be 10% so that a 1Mohm scope is a poor choice and ought to be terminated with cable impedance = 50 Ohms?

added

In air , EM waves travel at 30 cm/ns or 3e8m/s. and on PCB or coax dielectric , about 2/3 of this speed. Thus conductors , insulators (all dielectrics) and inductors or "lumped elements" get affected by impedance mismatch reflections like ripples. Physical ratios of radius OD/ID determine impedance and thus waveguides and PCB tracks must be very precise in width / gap to ground when approach this pathlength / wavelength ratio . Depending on desired minimal effects thus tolerance keeping this ratio below 5% to 10% or so means it is still a lumped element.

In water waves are very slow but we do see reflections from a hard shore line (impedance mismatch like a short circuit to water) because the width/wavelength is >> 1 , but would be hardly noticeable if <10% and if a river meets a narrowing, the fluid impedance changes. EM waves have a similar yet different property.

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  • \$\begingroup\$ Can I get a more intuitive explanation for c part. I am studying Foundation of Analog Digital by Anant Agarwal & Jeffrey Lang on my own. Just reading book alone. \$\endgroup\$ – Crazy Apr 16 '17 at 14:45
  • \$\begingroup\$ If you understand then you can answer my question. \$\endgroup\$ – Tony Stewart EE75 Apr 16 '17 at 16:00
  • \$\begingroup\$ 2 x 10^9Hz is it? If I am wrong correct me please. \$\endgroup\$ – Crazy Apr 17 '17 at 14:35
  • \$\begingroup\$ Can you explain to me please? \$\endgroup\$ – Crazy Apr 18 '17 at 3:57
  • \$\begingroup\$ lambda = c/f. . \$\endgroup\$ – Tony Stewart EE75 Apr 18 '17 at 4:44

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