[SI-LIST] Re: characteristic impedance at DC
- From: "Oh, Dan" <doh@xxxxxxxxxx>
- To: mohammad haaeri <haaeri@xxxxxxxxx>
- Date: Tue, 10 Apr 2012 08:42:33 -0700
Hi Mohammad,
You are right on everything. Yes, the following formula used to compute Zc at 0
is "wrong":
(1) Zc(f) = (R+jwL)/(G+jwC)
This is a very widely used formula and also supported in Hspice W-element. Many
of EM static field solvers assume more or less similar behavior. We used this
formula to simply demonstrate our case. You can, of course, use a general
formula using the tabular form:
(2) Zc(f) = (R(f)+jwL(f))/(G(f)+jwC(w))
Now the question shift to how to calculate these values at low frequencies?
You need more than simple EM static or fullwave solver as they do not have a
way to calculate these parameter correctly. This is due to the fact that the
assumption used in there conductivity of dielectric as Yuriy Shelpnev pointed
out also. (He may have a right tool to compute this.) Now, your question shift
to finding a method to characterize the dielectric conductivity with accurate
frequency behavior is yet another hard problem. Again, I would suggest using
the formula we provided in the paper to even compute G(f=0) in this case. Our
paper proposal is not limited to eq (1). Again, eq (1) is selected as example.
I am pretty sure even using eq (2) with existing solvers would results in
similar results. For our applications, we found that using either eq (1) or (2)
with static solver in conjunction with our DC correction formula was good
enough.
I guess one person raised the question why we need to talk about Zc which is a
frequency-domain concept. Yes, we do. Any transmission line system can be
represented by Zc, and gamma which can be converted to the impedance,
admittance, or ABCD matrix. Zc and Gamma, equivalently RLGC, are simply one
representation of network parameter in general. As you understand, we need
accurate low frequency network parameter behavior for broadband analysis. Think
as the transmission line parameter as just one way to represent the network
parameter. Of course, circuit simulators will convert Zc to admittance
internally to calculate DC response.
Best,
-Dan Oh
From: mohammad haaeri [mailto:haaeri@xxxxxxxxx]
Sent: Tuesday, April 10, 2012 8:08 AM
To: Oh, Dan
Cc: shlepnev@xxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: Re: [SI-LIST] Re: characteristic impedance at DC
Hi Dan,
I agree about considering loss at DC and calculating it correctly for DC to
have a good time-domain simulation.
I don't agree with what you calculated for characteristic impedance going to 0.
Thanks,
mohammad
On Mon, Apr 9, 2012 at 9:27 PM, Oh, Dan <doh@xxxxxxxxxx<mailto:doh@xxxxxxxxxx>>
wrote:
Hi Mohammad,
My name is Dan Oh and I am one of the coauthors of that paper.
Yes, you have correctly pointed out that we did not consider the TDR cable
frequency dependence nor its loss. However, I believe it's contribution should
be minimal.
I just wanted to clarify why the loss frequency value is very important as we
pointed out in our paper. The low frequency eventually dictates the
static-state behavior. Although it does not affect the transient region which
contains lots dynamics, the static value is very important for digital signals.
I guess you would understand this since you read our paper.
Like Howard mentioned in the later email, if you have set G to be zero, you
will see RC line behavior which reaches to the static value extremely slowly.
You can try this using HSPICE with realistic PCB trace models which typically
have very small G values at low frequency. In most PCB or package traces, this
type of behavior does not make sense as measurements show otherwise. We used
TDR measurement to fix this issue and shows good correlation. This
demonstrates that TDR loss or frequency dependence were very small.
There are several other papers which talks about low frequency modeling issues
besides our paper. They all demonstrate severe issues. I can forward a few
references. If you would like to discuss further, please send me a separate
email. I am very interested to discuss this over with you. FYI, I have been
developing a RLGC solver and transmission line models for many years :).
Best,
-Dan Oh
___________________________________________
Dan (KyungSuk) Oh, Ph.D.
Technical Director of Signal and Power Integrity
Rambus Inc.
(B) 408-462-8363<tel:408-462-8363>
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx<mailto:si-list-bounce@xxxxxxxxxxxxx>
[mailto:si-list-bounce@xxxxxxxxxxxxx<mailto:si-list-bounce@xxxxxxxxxxxxx>] On
Behalf Of mohammad haaeri
Sent: Monday, April 09, 2012 5:34 PM
To: shlepnev@xxxxxxxxxxxxx<mailto:shlepnev@xxxxxxxxxxxxx>
Cc: si-list@xxxxxxxxxxxxx<mailto:si-list@xxxxxxxxxxxxx>
Subject: [SI-LIST] Re: characteristic impedance at DC
Thanks Yuriy for your response, it makes sense.
I think what's been calculated for characteristic impedance at low frequencies
in "Implementation of Broadband transmission line models with accurate
low-frequency response for high speed system simulations" in DesignCon 2006 is
not correct (although it has improved the time domain simulation results!).
They are assuming only the transmission line under test is frequency dependent
and calculate its limit going to low frequencies not the TDR cable (which is
another transmission line and it doesn't have 50ohms going to zero). (page 11,
equation (5)). That's the reason they are coming up with a characteristic of
25.7ohms at DC for a transmission line!
On Mon, Apr 9, 2012 at 5:15 PM, Yuriy Shlepnev
<shlepnev@xxxxxxxxxxxxx<mailto:shlepnev@xxxxxxxxxxxxx>>wrote:
> 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<tel:%2B1-702-876-2882> Cell
> +1-206-409-2368<tel:%2B1-206-409-2368>
> Skype: shlepnev
> www.simberian.com<http://www.simberian.com>
>
>
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx<mailto:si-list-bounce@xxxxxxxxxxxxx>
> [mailto: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<mailto: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.pd
> f 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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