[SI-LIST] Re: characteristic impedance at DC
- From: Kevin Rhoads <kevin.g.rhoads@xxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Tue, 10 Apr 2012 11:24:36 -0400
On 4/10/2012 11:00 AM, Todd Hubing wrote:
> 1. The concept of characteristic impedance assumes that there is TEM
> propagation on the line. If there are evanescent modes or higher-order modes,
> characteristic impedance is no longer a particularly useful (or well defined)
> concept.
I would rather suggest this should be stated "The concept of
characteristic impedance assumes that there is a single mode of
propagation on the line." That mode is often TEM for multi-conductor
lines, but could be TEnm TMnm or any other non-evanescant mode, so long
as it occurs singly and without significant mode conversion issues.
After all, characteristic impedance has been applied to (for example)
rectangular cross-section waveguides, for which there is no TEM mode.
sequeing into 2)
(Furthermore, while one could consider a characteristic impedance for
each mode in multi-modal propagations, the composite impedance presented
at any port is ill-defined unless the details of amplitude and phase for
each mode at that port and their relative geometric relations to the
point of sampling of voltage difference and current injection are all
well defined and presumably invariant, which is highly unlikely to be
realizable in actuality.)
For 3): "For lossless lines (R=0, G=0), the characteristic impedance is
not a function of frequency ..." given the assumption of TEM in 1) above
this is probably true. When non-TEM modes are considered this is false.
Basically in any situation where dispersion is an issue this statement
is false.
For 4. "For low-loss lines (R<<wL and G<<wC), the characteristic
impedance is nearly independent of frequency." Again likely true for
TEM, but definitely false for modes for which dispersion is an issue.
A good summation in general, albeit a bit overly assumptive of TEM (MHOO)
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