# [SI-LIST] Re: characteristic impedance at DC

• From: "Nick Luther" <Nick.Luther@xxxxxxxxxx>
• Date: Mon, 9 Apr 2012 18:45:58 -0500

```Aha!  Now we are zeroing in on the question!  Just to be clear, the TDR
is making an AC measurement.  The TDR pulse has an edge and the rise
time of that edge is related to its bandwidth.

I assume the authors are claiming that they can make better low
frequency Z0 measurements by TDR than they can with a VNA or frequency
domain technique and are claiming the usefulness of that information,
and you're looking to discuss how the information would be useful.  I

If that's the true scope of our discussion, I don't have an example when
I've been concerned with the characteristic impedance of a transmission
line at a very low frequency.  The reason I can cite is that at very low
frequencies the transmission line I'm working with is always
electrically very short, so transmission line effects are negligible,
and the characteristic impedance isn't really seen on either side of the
channel.

-Nick

Sent: Monday, April 09, 2012 6:27 PM
To: Nick Luther
Cc: Weston_Beal@xxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: Re: [SI-LIST] Re: characteristic impedance at DC

Thanks Nick,

I understand characteristic impedance and its usefulness at AC (not DC).
What about very low AC frequencies?

transmission line models with accurate low-frequency response for high
speed system simulations" and they are calculating characteristic
impedance at low frequencies with TDR which is not very high or infinity
as the formula) says and not DC resistance as Weston and Todd are
saying! You can read the paper

On Mon, Apr 9, 2012 at 4:16 PM, Nick Luther <Nick.Luther@xxxxxxxxxx>
wrote:

One quick clarification:

Looking at the two terminals at the input to a transmission line
(consider a center conductor and shield in a coax cable), and with
nothing at the other end (open), you likely will see an open circuit at
DC, just like the "infinite" impedance that Mohammad predicted using his
general equation.  So, in a strict sense, Mohammad was correct.  I want
to point out to Mohammad that he is using the equation correctly, and
this is how he should be interpreting the result that he calculated.

The characteristic impedance is what an AC source would effectively see
at those same two terminals.

Weston and Todd's replies explain why the characteristic impedance
calculation at DC isn't useful.  Mohammad:  I hope that Weston and
should be very useful.  I think you'll find a lot of additional

Nick

--
Nick Luther, P.E.
Design Engineer
Plexus Engineering Solutions
Ship To: 55 Jewelers Park Drive
Mail To: PO Box 677
Neenah, Wisconsin 54957-0677 USA
http://www.plexus.com/

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]

On Behalf Of Beal, Weston
Sent: Monday, April 09, 2012 5:50 PM
To: haaeri@xxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: characteristic impedance at DC

Characteristic impedance applies to propagating EM waves, so it does not
apply to DC.

Or, if you look at the general equation that you cited, you can see that
when jw = 0, the impedance approaches the line resistance. Somewhere in
college I remember seeing a graph of the general impedance equation
compared to actual measurement at low frequency. They are the same above
some kHz, but diverge as frequency decreases.

Weston

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
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?

How does behavior of L, R, G, and C (line parameters) change vs.
frequency (at low and DC, and at very high frequency)?

Can Z0=sqrt(R+jwl/G+jwc) be used for all frequencies?

Thanks,

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