[SI-LIST] Concept of Voltage

  • From: Shawn Hermite <shawn.hermite@xxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Sun, 17 Jul 2011 23:06:07 -0700

To SI experts, especially those used Maxwell's equations in their books:
The concept of voltage has been deeply engrained in our minds. It's the
foundation of the circuit theory and electrical engineering at large.
Recently, when collecting materials for a presentation advocating the
importance of signal integrity, I realized that the concept of voltage is
based on the assumption of the electric field being conservative. The
general differential form of Maxwell's equations (the Faraday's Law part in
particular) contains the dB/dt term that ruins the validity of curl {E} =
0.

There are two categories of arguments:
(1) With the integral form of the Faraday's Law, we can treat the
time-varying magnetic flux term as an electromotive-force (like battery),
hence fix the KVL, the general idea of voltage is still being the line
integral of the electric field between two points.
(2) Switching to the frequency-domain, the surface integral of the B-field
is related to the characteristic dimension of the system (D) and the
operating frequency. It goes with some hand-waving arguments, and the claim
is that the unfriendly term is nearly zero when D << wavelength. This
argument also goes hand-in-hand with validity of lumped vs. distributed
element modeling.

I have also observed that in a multi-conductor transmission-line (MTL)
system where the TEM mode is propagating, the E-filed is conservative on
each cross-section, thus voltage is well defined between a signal conductor
and the common-reference conductor.  Here, the general electrodynamic
Maxwell's equations are all satisfied. The MTL theory explains why
RF/microwave testing has to be done using co-ax cables. It also makes sense
why 'port' (instead of circuit node) voltage is used in constructing
S-parameters.

If the second explanation holds true, I am really worried about what the
frequency limit is before we get into trouble with freely applying knowledge
developed with DC or low-frequency circuits.

Any way, looking for a better answer or proof on the validity of the concept
of voltage.

Thanks


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