[SI-LIST] Re: off-diagonal resistance and conductance elements
- From: "Bill Beale" <beale@xxxxxxxxxxxxxx>
- To: <zabinski.patrick@xxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Tue, 18 Feb 2003 14:15:04 -0800
Hi Pat,
The answer is "It's all in the Matrix".
Look at any of the transmission line parameters and understand what they =
mean. For a simple example, look at the capacitance matrix:
[Q] =3D [C][V]
This states that the amount of charges on one conductor is proportional =
to the amount of voltage on the other conductors. (In this case, that =
is also why the off diagonal of the capacitance matrix is negative. A =
positive voltage produces negative charges on the other conductors.)
Now look at the resistance matrix:
[V] =3D [R][I]
This states that there is a voltage drop on a neighboring conductor due =
to current 'on yourself'. (Obviously this is frequency dependent:) One =
way to look at it is that the 'coupled' current produces a voltage drop =
on the neighboring line.
To address the odd and even modes, the answer is exactly the same, kind =
of. Any of the transmission line parameters can go through the odd/even =
transformation matrix. You're just changing the basis. (Remember =
linear algebra?)
Hope this helps,
Bill
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Bill Beale Phone: 503-439-3462
Sr. System App. Engineer Fax: 503-477-9472
Accelerant Networks e-mail: bill_beale@xxxxxxxxxxxxxx
On the world wide web @ http://www.accelerant.net
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> In a coupled-pair of distributed transmission lines (whether=20
> 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.
>=20
> For the inductance and capacitance matrices, even the off-diagonal
> parastics (e.g., L12, C21, ...) are easy to understand and
> well published.
>=20
> 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
>=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?
>=20
>=20
> 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).
>=20
> 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.)
>=20
> 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?
>=20
> Thanks,
> Pat
>=20
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>=20
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>=20
>=20
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