[SI-LIST] Re: impedance relation with frequency...

Jeff,

Think about your experiment with varying rise times in the frequency=20
domain.  Your comment

         "the TDR and TDT waveforms stabilize at the same level"

answers your question.

If you look at the time it takes for the waveform to stabilize, and conve=
rt that to frequency, you will find that it at a fairly low frequency tha=
t the impedance is measured to be the same.  With really fast edges and g=
ood launches, you can begin to see how impedance varies with frequency.  =
Actually, an alternate way of viewing risetime degradation due to conduct=
or and dielectric losses is as a frequency domain problem, where the impe=
dance changes with frequency. Notice that for long lines the impedance pr=
ofile continues to rise, due to resistance, which is a component of imped=
ance.  There are tranisiton regions, which Dr Johnson discusses in his ne=
w book, where impedance change is dominated by either RC, LC, skin effect=
, or dielectic loss.

If you want to see this with some precision, you can use your VNA and pla=
ce it in delay measurement mode.  You'll need a very good launch and some=
 well known traces with very good impedance control, and nothing nearby t=
hat will resonate.  You'll also need to find a way to de-embed so that th=
e reference plane is extremely close to the trace.  Then you can plot del=
ay vs. frequency.  After having done this, you can convert delay to Er(ef=
fective).  This includes the affect of conductor loss and finite field pe=
netration into the conductor.  You will see that at low frequencies Er(ef=
fective) is much higher than at high frequencies. And even from 1 GHz to =
10 GHz there are some changes in the 5% range.  This is directly related =
to field penetration into conductors which causes the internal inductance=
 to vary with frequency. It turns out that the resistance of a trace and =
the inductance are related, and have to be for the system to be causal.

Now, take the case of semiconductors.  The resistance of the lines are mu=
ch higher, which causes much higher losses and much higher internal induc=
tance with respect to frequency than copper traces on FR-4.  This directl=
y relates to increased change in impedance across what we might consider =
"our" normal operating region of 1 GHz to 10 GHz.  What has happened is t=
hat the increased trace loss has shifted the crossover boundary between t=
he low, mid and high frequency regions of the transmission line.  In addi=
tion, there is another mode that has to be considered at high freqencies =
for silicon, known as the slow-wave mode.  Because silicon is a semi-cond=
uctor, and the conductance of the material is dependent upon the doping l=
evel of the substrate, our normal "approximations" for transmission lines=
 fall apart.  The main assumption that is in every textbook on the subjec=
t is that losses are negligible.  As soon as they are not, we get into se=
cond and third order effects. =20

In the case of silicon, one of those effects is the slow-wave mode, where=
 for inductance purposes, the physical metal structures form the boundari=
es of the loop. That is, the magnetic field is contained and control by t=
he high conductance metal.  But, the capacitance is contained by the sili=
con, and the electric field along with the finite conductivity of the sub=
strate can actually set up a "virtual plane" within the silicon, that doe=
s not penetrate the full depth of the material. In other words, conductan=
ce shunts out the stored electric field. In this way, the electric and ma=
gnetic fields decouple, and capacitance goes way, way up. Until the slow =
wave transition frequency, quasi-TEM propagation exists and the waves tra=
vel at near constant velocity across frequency (with some corrections due=
 to conductor losses and internal inductance).  But once we cross the slo=
w-wave boundary, it is as if the brakes were put on.  I believe Dr. Ed Sa=
yre, III of NESA has quite a bit of expertise in this area.


best regards,

scott



--=20
Scott McMorrow
Electromagnetic Field Wrangler
Teraspeed Consulting Group LLC
2926 SE Yamhill St.
Portland, OR 97214
(503) 239-5536
http://www.teraspeed.com

Loyer, Jeff wrote:

>Hi Andrew,
>I would like some help understanding the difference between board traces=
 =3D
>and "chip lines".  My experience has been that I can TDR a trace using a=
 =3D
>35ps risetime, or through 100 and 400ps filters, and measure the same Z0=
 =3D
>for that trace.  This would seem to be backed up by the fact that there =
=3D
>is no compensation made when measuring traces with different TDRs, =3D
>regardless of their risetime.
>
>I just confirmed that again, measuring the same 3" microstrip trace with=
 =3D
>no filter, and 100ps and 400ps filters, and finding the TDR and TDT =3D
>waveforms stabilize at the same level, regardless of the risetime.  Of =3D=

>course, there's significant impact to the risetime of the TDT, but the =3D=

>Z0 of the trace (as indicated by the DC level of the TDR trace) remains =
=3D
>constant.
>
>This implies to me that the Z0 of the trace is constant for 10GHz , =3D
>3.5GHz, or 875MHz (35ps, 100ps, 400ps risetimes, respectively).
>
>My experience with VNA seems to substantiate this - S11 typically =3D
>remains fairly constant (other than resonances at lambda/4, etc.) while =
=3D
>S21 varies with frequency due to loss effects.
>
>Is there something else I'm missing?
>
>Jeff Loyer
>
>-----Original Message-----
>From: andrew.c.byers@xxxxxxxxxxxxxx
>[mailto:andrew.c.byers@xxxxxxxxxxxxxx]
>Sent: Wednesday, September 17, 2003 12:05 PM
>To: jonpowell@xxxxxxxxxxxx; kbagga31@xxxxxxxxx; si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: impedance relation with frequency...
>
>
>Concerning Zo relation with frequency:
>
>Once again, depends where you live. On boards, typically the
>frequency-dependent impedance change starts leveling out at much lower
>frequencies. Essentially you are approaching the sqrt(L/C) impedance,
>because your omega*L overwhelms your R. *Usually* by 1MHz your Zo curve =
=3D
>is
>flat. But if you are modeling chip lines, your R value for the line =3D
>might be
>comparable (or greater) than omega*L up to a couple GHz or so. Then you
>cannot ignore this frequency dependent behavior. I have seen a typical =3D=

>line
>on chip go from about Zo=3D3D100ohms @100MHz, to Zo=3D3D63ohms @1GHz, to=
 =3D
>Zo=3D3D55ohms
>@10GHz. Measurement, simulation, theory, literature, and gut feel all =3D=

>back
>this up.=3D20
>
>So the bottom line (as it always is in the world of interconnect =3D
>modeling)
>is it depends on how high you go in frequency, the dimensions of line =3D=

>you
>are using, and if you are designing in a narrow band or a wide band.
>HOWEVER, as Jon pointed out, you can often see greater variations due to=

>coupling from nearby traces. Plus you have to remember that impedance
>control is an issue too - usually +/- 10% is as good as it gets for
>run-of-the-mill PCBs out there (but money talks).=3D20
>
>To get a feel for the numbers I got above, you can use a 2D field solver=

>that handles the frequency dependent behavior of R and L (ansoft =3D
>spicelink
>or some other flavor). Or you can dig up equations and plug them into a
>matlab or mathcad. Calculate your R and L and C (usually G is =3D
>non-existant
>or insignificant...) and crunch away.
>
>salud,
>Andy Byers
>
> =3D20
>
>-----Original Message-----
>From: Jon Powell [mailto:jonpowell@xxxxxxxxxxxx]=3D20
>Sent: Wednesday, September 17, 2003 9:09 AM
>To: kbagga31@xxxxxxxxx; si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: impedance relation with frequency...
>
>
>Karen,
>It is my feeling that the frequency related impedance changes on a =3D
>signal
>will be second order considerations compared to the impedance changes =3D=

>caused
>by crosstalk from neighboring wires. These effects can be shown with =3D=

>most
>good SI engines. Intel has often recommended (for instance) calculating =
=3D
>the
>effective impedance when the coupled wires on either side of the target =
=3D
>wire
>switch simultaneously with the target wire in both the same direction =3D=

>(all
>going high and low) and opposite (target going high and low and coupled
>going low and high).
>
>hope this helps (and if I am wrong, I am sure someone will scream at me =
=3D
>so
>wait a couple of minutes).
>
>regards,
>jon
>
>
>-----Original Message-----
>From: si-list-bounce@xxxxxxxxxxxxx
>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of karan bagga
>Sent: Wednesday, September 17, 2003 2:24 AM
>To: si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] impedance relation with frequency...
>
>
>Hi
>
>>From the telegraphic equations on Transmision lines it seems the =3D
>impedance
>of the Trace varies with frequency.
>
>In my design specifications it is specified that my trace should be on =3D=

>(25
>+/- 10%) Ohms.
>How will I do it ? How will I do these kind of analysis?
>
>The frequency of the signal is high and also the rise time is =3D
>significantly
>low.
>Will FFT be of some help here ?
>
>Regards
>Karan.
>
>
>
>---------------------------------
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