[SI-LIST] Re: Even and odd mode capacitances and inductances of coupled lines

Hi Leon,

The formula for even and odd mode is a simple linear
transform, where the two equations are:

[M]*[L]*[M]^1 = transform to odd and even mode inductance
[M]*[C]*[M]^1 = transform to odd and even mode capacitance

This assumes that the capacitance matrix is in the proper
form where:

[Q] = [C]*[V], which is the Maxwell matrix.

The trick is choosing the transformation matrix [M].  As with
any linear transform, it must have the property:

[M]*[M]^-1 = [I]

For the typical 2-line case, 

[M] = (1/sqrt(2))*| 1 -1 |
                  | 1  1 |


Using the above transformation matrix, the odd mode becomes
the upper left entry (11), and the even mode becomes the lower
right entry (22).  The off diagonal is then the mode
conversion, which is non-zero if the coupled line matrix is
asymmetric .

This can be expanded to N number for entries.

Hope this helps,
Bill

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Bill Beale              Phone:  503-439-3462
Sr. App. Engineer         Fax:  503-466-9472
Accelerant Networks    e-mail:  bill_beale@xxxxxxxxxxxxxx
On the world wide web @ http://www.accelerant.net
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx 
> [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Leon Wong
> Sent: Monday, February 23, 2004 6:38 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Even and odd mode capacitances and 
> inductances of coupled lines
> 
> 
> Hi,
> 
> Does anyone know the formula for even and odd mode capacitances and 
> inductances of coupled lines? Is Lodd = L11-L12, Leven=L11+L12, 
> Codd=C11+|C12| and Ceven=C11-|C12|? Thanks in advance!
> 

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