[SI-LIST] Re: characteristic impedance at DC
- From: "Luciano Boglione" <l.boglione@xxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Mon, 9 Apr 2012 20:54:23 -0400
It's a very interesting question, so I'd like to add my 5 cents (not
necessarily answers to Mohammad's questions). So, if I am not mistaken.
. If the fundamental mode is TEM, the corresponding structure does
not support DC - e.g. the fundamental mode of a waveguide is TEM, but no DC
is supported by a waveguide
. The telegraph equation applies to a structure that supports DC
(e.g. cable) and R,L,C,G are AC quantities
. If the line is lossless and the RLCG model is used, then
Zo=sqrt(L/C) even as f->0
. Distributed effects as f->0 occur only if length is comparable to
lambda - i.e. a very long line. If the RLGC model is used and it is valid,
then I would expect to measure Zo (say 50ohm) as f->0 since the line becomes
"invisible".
Just food for thoughts! Within the constraints of a model (e.g. RLGC), I
would expect that the characteristic impedance of the line follows the
resulting equation. However, if there is experimental evidence that Zo
increases as f->0 in microstrip or alike, then the model we are considering
(e.g. RLGC) may not be modeling reality accurately.
Looking forward to following the discussion.
Regards,
Luciano
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Kevin Rhoads
Sent: Monday, April 09, 2012 8:35 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: characteristic impedance at DC
On 4/9/2012 7:55 PM, mohammad haaeri wrote:
> OK, maybe no one has measured or found usefulness of characteristic
> impedance at low frequencies,
Look at the length of the transmission line relative to the wavelength at
the frequency in question.
If the line is as long or much longer than 1/8 of a wavelength, then
characteristic impedance and transmission line effects need to be
considered.
If the line is much shorter than 1/32 of a wavelength then it can and should
be treated as a lumped parameter system.
In between you may be able to do lumped parameter, but maybe not.
Lumped-parameter is the long wavelength limiting case approximation for
transmission lines.
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