[SI-LIST] Re: off-diagonal resistance and conductance elements
- From: "Bill Beale" <beale@xxxxxxxxxxxxxx>
- To: <zabinski.patrick@xxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Wed, 19 Feb 2003 09:55:43 -0800
Again, "The Answer is All in the Matrix".
Look at the capacitance matrix, and a two conductor example:
|Q1| |C11 C12| |V1|
|Q2|=3D|C21 C22| |V2|
By looking at the physics, the diagonal elements represent the total =
amount of charge storage on the conductor. This is the capacitance to =
every other conductor and to ground. The off diagonal elements =
represent the charge storage between the conductors, and as stated =
before, they always have a negative value. Putting one volt on one =
conductor 'attracts' negative charges to the other conductors.
The issue is: How to translate the mathematical capacitance matrix into =
elements of a SPICE file (Or other simulator type of package)?
Answer: =20
1) The algebraic sum of either a row or a column is the capacitance to =
ground.
2) The off diagonal element multiplied by negative one is the =
capacitance between the conductors.
For Example:
Assume the Capacitance matrix has the following values:
[C]=3D|10pf -0.2pf|
|-0.2pf 10pf |
Capacitance to ground:
C11 + C12 =3D 10pf + (-0.2pf) =3D 0.8pf
Capacitance between conductors:
-1*C12 =3D -1*(-0.2pf) =3D 0.2pf
If you're still reading this, (I know I might of lost interest by now :) =
as any good engineer should do, let's take a look at the final answer =
and relate it back to the original matrix:
Looking at one conductor, there is a capacitor of 0.8pf to ground, and a =
capacitor of 0.2pf to the other conductor. This is a total of 10pf of =
charge storage available on the conductor which is the diagonal C11 =
value. =20
A similar comparison to the off diagonal value is left as an exercise =
for the user. :-)
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
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>=20
> No; I don't have anything with a lot of depth.
>=20
> If you look through the W-element section of the
> Hspice manual, they discuss a bit, but they call it
> the "C" matrix (not "B"). I believe the Ansoft manuals
> describe it a bit as well.
>=20
> Anyone else have a good reference?
>=20
> > I haven't heard of this B-matrix before. Do you have any=20
> references?
>=20
>=20
> Pat
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