[SI-LIST] Re: characteristic impedance at DC
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: <haaeri@xxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 9 Apr 2012 17:15:15 -0700
Mohammad,
See my answers below.
Best regards,
Yuriy
Yuriy Shlepnev, Ph.D.
President, Simberian Inc.
3030 S Torrey Pines Dr. Las Vegas, NV 89146, USA
Office +1-702-876-2882
Cell +1-206-409-2368
Skype: shlepnev
www.simberian.com
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of mohammad haaeri
Sent: Monday, April 09, 2012 3:31 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] characteristic impedance at DC
Hi,
What is the characteristic impedance of a transmission line at DC? If you
are saying Z0=sqrt(Rdc/Gdc) at DC, since Gdc=0, and Rdc is not zero,
therefore Z0 is infinite. Is it correct?
YS: Yes, this is correct for a lossy line that does not have conductive
losses in the admittance per unit length (technically in dielectric).
Though, there is no waves at DC, for TEM mode we can calculate asymptotes of
the impedance and admittance per unit length and the characteristic
impedance at DC.
How does behavior of L, R, G, and C (line parameters) change vs. frequency
(at low and DC, and at very high frequency)?
YS: It obviously depends on a transmission line type. See analysis for a
microstrip line in this app note
http://www.simberian.com/AppNotes/MicrostripImpedanceAndTDR_2009_04.pdf
Impedance grows at lower frequencies if dielectric model has only
polarization losses. In reality, there are some conductive losses in
dielectric and thus the asymptote of the characteristic impedance ad DC is
not infinity. As someone already noted, the low-frequency growth of the
impedance has small impact on overall behavior of the line. It should also
not be confused with the conductor resistance that is more important to
account at DC. For a microstrip line, the impedance also grows at very high
frequencies.
Can Z0=sqrt(R+jwl/G+jwc) be used for all frequencies?
YS: Yes, as long as the impedance (R+jwL) and admittance (G+iwC) per unit
length are appropriately defined. The formula does not have limitations
neither at low nor at high frequencies, though this is relatively
complicated subject for a short posting.
Thanks,
mohammad
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