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

• To: "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
• Date: Tue, 10 Apr 2012 00:34:33 +0000

```Ha!  This is the other very common area of confusion.

I would like to illustrate this with a simple practical example
instead of big buzzwords and equations.

Consider measuring the voltage and current of a sinusoidal
Thevenin driver driving a T-line at the point where it is
connected to the T-line.  The Thevenin resistance is perfectly
matched with the (characteristic) impedance of the T-line, say
50 Ohms.  Keep the length of the T-line constant and change the
frequency of the driver.  At certain frequencies the voltage
will go to zero, at certain frequencies the voltage will be
half of the Thevenin voltage source and at certain frequencies
it will be equal to the Thevenin source voltage.  Why?

When the wave comes back with the exact opposite phase, at the input
point of the T-line there will be cancellation.  This looks like
a short to the driver, i.e. the voltage will be zero no matter
how much current the driver pumps into the (lossless) T-line, which
is equivalent to say that electrical impedance of the T-line
is zero.  Yet its characteristic impedance is still 50 Ohms...

When the waveform comes back with the exact same phase, the
voltage at the input of the T-line will be equal to the Thevenin
source voltage, and the current will be zero (if everything is
perfectly lossless).  This looks like an electrical open, i.e.
no matter how many volts the source is driving with the current
is still zero.  This corresponds to an infinite electrical
impedance (while the characteristic impedance is still 50 Ohms).

When there are no reflected waves coming back to the driving
point, you will measure half of the Thevenin source voltage
and a current corresponding to Ohm's law.  This is because in
this situation the driver sees nothing but the characteristic
impedance of the T-line, since there are no electrical waves
coming back from the far and of the T-line to interact with
the driven signal.

I hope this helps...

==================================================================

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Sent: Monday, April 09, 2012 6:55 PM
To: Nick Luther
Cc: Beal, Weston; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: characteristic impedance at DC

OK, maybe no one has measured or found usefulness of characteristic
impedance at low frequencies, but people are simulating and that info (or
L,R,C,G) are necessary (we are not simulating a lumped circuit or a narrow
band signal. It's a wide-band signal from zero to ... and all info are
necessary).
Formula and many are saying infinity, but some people (and the paper I
mentioned) saying not infinity. Which one is correct and why?

On Mon, Apr 9, 2012 at 4:45 PM, Nick Luther <Nick.Luther@xxxxxxxxxx> wrote:

> 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 haven't read the
> paper.****
>
> ** **
>
> 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?****
>
> ** **
>
> Also, I'm reading a paper in DesignCon 2006 "Implementation of Broadband
> 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
>
> ** **
>
> ** **
>
> 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
> literature with a Google search.
>
> 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]
> 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?
>
> 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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> ****
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> ** **
>

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