[SI-LIST] Re: off-diagonal resistance and conductance elements
- From: Ray Anderson <Raymond.Anderson@xxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Wed, 19 Feb 2003 11:09:29 -0800 (PST)
I'm certainly no expert on the matter, but thought I'd contribute my
.02 worth to the discussion.
There are at least 3 common matrix types encountered in the study/discussion
of coupled transmission line capacitance matrices:
1) Branch matrices
2) Maxwell matrices
3) Other Conductors Grounded (OCG) matrices
The branch matrix is accepted by most spice simulators when
it is expecting capacitance matrix numbers. (the U element
for example)
The Maxwell matrix is commonly used internal to the spice
simulator in the capacitance MNA stamp definition. Some field
solvers output this matrix
The OCG matrix defines the capacitance of a conductor with all
other associated conductors grounded. Some types of test equipment
output this. Some field solvers can also output this if requested.
Mathematical transforms allow one to translate between matrix styles.
(See appendix A in the later Hspice model manuals or chapter 21 in
the older Hspice manuals for a discussion and equations)
-Ray Anderson
Sun Microsystems Inc.
>
>You don't need to translate the model if using the W element or equivalent
>which most SI simulators use. This is the ideal way to represent
>transmission
>lines but requires the simulator to "speak the same language".
>
>Best regards,
>
>----- Original Message -----
>From: "Bill Beale" <beale@xxxxxxxxxxxxxx>
>To: <zabinski.patrick@xxxxxxxx>; <si-list@xxxxxxxxxxxxx>
>Sent: Wednesday, February 19, 2003 9:55 AM
>Subject: [SI-LIST] Re: off-diagonal resistance and conductance elements
>
>
>>
>> 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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