[SI-LIST] Re: RLGC matrices of a differential pair line
- From: Steve Corey <steven.corey@xxxxxxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Thu, 06 Feb 2003 10:53:23 -0800
Hassan -- characteristic impedance alone is not enough to determine
R,L,G, or C. You have to have the information on the propagation
constant(s) as well. Take the single line lossless case, for example,
in which Z=sqrt(L/C). You will note that for a particular value of Z,
the quantities L and C are only determined to within a constant. You
must have the delay as well, in which case T=sqrt(LC) allows you enough
information to compute L and C.
In the case of lossy, differential (i.e., symmetric) lines, you have to
know both the characteristic impedance of each mode, and you have to
know each one's propagation constant. Each of these are typically
complex, frequency-dependent quantities in the lossy case.
My favorite source for such information is "Analysis of Multiconductor
Transmission Lines" by Clayton R. Paul. I consider it to be quite
reliable, and certainly rigorous. It also has equivalent-circuit
information.
Dima has pointed you to one of our app notes. If you want it to apply
to the lossy case, you roughly need to substitute (R+jwL) for (jwL) and
(G+jwC) for (jwC) and "propagation constant" for "delay". If you do
this, and you're willing to deal with complex, frequency-dependent data,
then you can extract the values for R,L,G,C based on the
characteristic impedances and propagation constants of your even and odd
modes.
A word of warning, however -- R and G in a common transmission line
system are second-order or less compared to jwL and jwC behavior, and as
such, they're sensitive to noise and fixture imperfections if you're
starting with measured data. This is why we advise our customers to
stick with lossless calculations for hand analysis, and to rely on
optimization to get accurate loss-related parameters.
-- Steve
-------------------------------------------
Steven D. Corey, Ph.D.
Time Domain Analysis Systems, Inc.
"The Interconnect Modeling Company."
http://www.tdasystems.com
email: steven.corey@xxxxxxxxxxxxxx
phone: (503) 246-2272
fax: (503) 246-2282
-------------------------------------------
Dima Smolyansky wrote:
> Hello, Hassan:
>
> You can not compute R and G from characteristic impedances, but you can
> compute L and C. My guess is that the confusion is because L and C are
> normally computed from even and odd mode impedances, and different people
> define differential and common mode impedances differently. The industry
> standard way is (for a symmetric line pair):
> Zdiff = Zodd * 2, hence, Zodd = Zdiff / 2
> Zcommon = Zeven /2, hence, Zeven = Zcommon *2
>
> You need to first figure out whether your differential and common mode
> impedances were obtained using these definitions or other ones. An easy way
> to tell this will be as follows. For a typical transmission line on the
> board, with a target 100 Ohm differential impedance and in presence of
> coupling, you should expect common mode impedance value to be 25-40 Ohm
> (which would make your even mode impedance about 50-80, and odd mode
> impedance about 50). In any event, odd mode impedance can not be higher than
> even mode impedance (but will be equal to even mode impedance in absence of
> coupling). If your common mode impedance in the given case is in 50-80 ohm
> range, then the assumption used is probably that Zeven=Zcommon.
>
> See our appnote on differential interconnect characterization for equations
> relating Zodd and Zeven with L and C,
> http://www.tdasystems.com/library/appnotes/diff1199.pdf, from which you can
> easily obtain equations for L and C. More appnotes can be found under
> http://www.tdasystems.com/support/applicationnotes/.
>
> Thanks,
>
> ===================
> Dima Smolyansky
> TDA Systems, Inc.
> 4000 Kruse Way Place
> Blvd. 2, Suite 300
> Lake Oswego, OR 97035
> (503) 246-2272
> (503) 246-2282 (fax)
>
> Download new IConnect 3.0 Quick Tour at www.tdasystems.com/products/ !
>
>
>
>
> ----- Original Message -----
> From: "Hassan O. Ali" <hassan@xxxxxxxx>
> To: <si-list@xxxxxxxxxxxxx>
> Sent: Thursday, February 06, 2003 8:44 AM
> Subject: [SI-LIST] RLGC matrices of a differential pair line
>
>
>
>>
>>Hi All,
>>
>>Does anyone have formulas for computing the terms of R, L, G, and C
>>
> matrices for a
>
>>differential pair line using its differential and common-mode
>>
> characteristic impedances?
>
>>There seems to be a confusion of those formulas on the Net.
>>
>>Anyone knows the preferred structure of the equivalent circuit of a
>>
> differential pair
>
>>line of unit length in terms of the per-unit R, L, G, C, parameters? I'm
>>
> particularly not
>
>>sure of where to place the mutual terms in such a network?
>>
>>Thanks.
>>
>>Hassan.
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>
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