# [SI-LIST] Re: off-diagonal resistance and conductance elements

• From: "Issa, Elie" <Elie.Issa@xxxxxx>
• To: <tony_dunbar@xxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
• Date: Wed, 19 Feb 2003 14:11:53 -0600

```Tony:
My understanding also is that L11 is the self inductance.  So I  ran
the XFX field solver to validate my thoughts, a single conductor and =
dual conductor microstrip with=20
10mils spacing microstrip and compare L11.  Here are the reports
Configuration Name: X2  Conductors: 2

Conductor index: 0       name: \$\$GND\$\$=20
Conductor index: 1       name: A=20
Conductor index: 2       name: B=20

i    j      Lij      Cij      Ze     Zo       Se     So      Fwdx   =
Rvsx =20
from  to   (nh/in)  (pf/in)  (ohms) (ohms)   (ns/ft)(ns/ft)   (s/s)  =
(v/v)=20
-------------------------------------------------------------------------=
-
1   1     8.882    2.510    59.91    -       1.78    -        -     -
1   2     1.568    0.199    67.24  51.96     1.86   1.69    0.099  =
0.128
2   2     8.877    2.510    59.89    -       1.78    -        -     -
;

Configuration Name: X1  Conductors: 1

Conductor index: 0       name: \$\$GND\$\$=20
Conductor index: 1       name: A=20

i    j      Lij      Cij      Ze     Zo       Se     So      Fwdx   =
Rvsx =20
from  to   (nh/in)  (pf/in)  (ohms) (ohms)   (ns/ft)(ns/ft)   (s/s)  =
(v/v)=20
-------------------------------------------------------------------------=
-
1   1     8.905    2.505    59.63    -       1.79    -        -     -
;
If I reduce the spacing to 5mils, here are the results..

Configuration Name: XX  Conductors: 2

Conductor index: 0       name: \$\$GND\$\$=20
Conductor index: 1       name: A=20
Conductor index: 2       name: B=20

i    j      Lij      Cij      Ze     Zo       Se     So      Fwdx   =
Rvsx =20
from  to   (nh/in)  (pf/in)  (ohms) (ohms)   (ns/ft)(ns/ft)   (s/s)  =
(v/v)=20
-------------------------------------------------------------------------=
-
1   1     8.756    2.596    59.57    -       1.76    -        -     -
1   2     2.534    0.445    72.44  45.23     1.87   1.65    0.125  =
0.231
2   2     8.756    2.596    59.57    -       1.76    -        -     -
;
Configuration Name: X  Conductors: 1

Conductor index: 0       name: \$\$GND\$\$=20
Conductor index: 1       name: A=20

i    j      Lij      Cij      Ze     Zo       Se     So      Fwdx   =
Rvsx =20
from  to   (nh/in)  (pf/in)  (ohms) (ohms)   (ns/ft)(ns/ft)   (s/s)  =
(v/v)=20
-------------------------------------------------------------------------=
-
1   1     8.905    2.505    59.63    -       1.79    -        -     -
;=20

In both cases, there seem to be only small difference  between the self =
inductance=20
of single line and L11 in the coupled line matrice. =20

Regards
Elie

-----Original Message-----
From: Dunbar, Tony [mailto:tony_dunbar@xxxxxxxxxxx]
Sent: Tuesday, February 18, 2003 4:41 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: off-diagonal resistance and conductance elements

For the purposes of clarification:-

Patrick initially stated "The on-diagonal parameters (e.g., L11) are
typically stated to be the self parasitics, ..."

My understanding is that, rather than being purely "self parasitics", =
they
actually include the effects of coupled neighbors. As a consequence, for
example, L11 will actually be different (lower) than it will be if the =
same
primary structure existed without any coupled neighbors.

Is that correct?

Thanks,
Tony Dunbar

-----Original Message-----
From: Zabinski, Patrick J. [mailto:zabinski.patrick@xxxxxxxx]
Sent: Tuesday, February 18, 2003 2:42 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] off-diagonal resistance and conductance elements

In a coupled-pair of distributed transmission lines (whether =
intentionally
for differential or unintentionally with crosstalk), most (good)
EM simulators produce a 2x2 matrix of capacitance, inductance,
resistance, and conductance (C, L, R, & G).  The on-diagonal
parameters (e.g., L11) are typically stated to be the self
parasitics, which is quite easy to understand.

For the inductance and capacitance matrices, even the off-diagonal
parastics (e.g., L12, C21, ...) are easy to understand and
well published.

However, I have not been able to find a good description nor
treatment on the off-diagonal resistance and conductance
elements.  Can anyone enlighten me a bit? =20

For example, what does R12 respresent?  With the lossless/ideal
case setting R12=3D0, it cannot represent a resistive element
directly between the two traces.  So what is it?

A second yet possibly related question deals with how these
matrices deal with odd- and even-mode using the same matrices.
When looking at any of the common twin-axial cables used
today with Infiniband and other differential protocols, the
two signal conductors are made with "good" (meaning low
loss) materials.  In contrast, the outer shield is often
a much lousier (higher loss) material (either through the metallurgy
or thickness).

For odd-mode signals propagating down one of these twin-ax
cables, we believe the return current for one wire is
effectively captured (at least in part) in the other complement
wire, which would result in reasonably low loss.  In contrast,=20
in even-mode propagation, the return current is within the=20
outer shield, which in turn results in a higher loss than
the odd-mode propagation.  The end result (we have plenty
of measurement data confirming this) is that odd-mode
signals propagate reasonably well, but even-mode signals
attenuate and disperse much more significantly.  (note:
for many applications, this is a very good thing.)

The question is: how can the LRCG matrices be set up such that you=20
use one set of matrices (in the form of a W-element if you wish) that
can accurately represent both cases?  Does the off-diagonal
R & G matrices play a role?

Thanks,
Pat

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