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. ------------------------------------------------------------------ To unsubscribe from si-list: <mailto:si-list-request@xxxxxxxxxxxxx> si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: <//www.freelists.org/webpage/si-list> //www.freelists.org/webpage/si-list For help: <mailto:si-list-request@xxxxxxxxxxxxx> si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List forum is accessible at: <http://tech.groups.yahoo.com/group/si-list> http://tech.groups.yahoo.com/group/si-list List archives are viewable at: <//www.freelists.org/archives/si-list> //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: <http://www.qsl.net/wb6tpu> http://www.qsl.net/wb6tpu ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List forum is accessible at: http://tech.groups.yahoo.com/group/si-list List archives are viewable at: //www.freelists.org/archives/si-list Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu