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Toeplitz Matrix as Applied to the Computation of Inductances in Mesh Structures

IP.com Disclosure Number: IPCOM000103711D
Original Publication Date: 1993-Jan-01
Included in the Prior Art Database: 2005-Mar-18
Document File: 3 page(s) / 106K

Publishing Venue

IBM

Related People

Astudillo, FJ: AUTHOR [+3]

Abstract

An advanced packaging module often incorporates mesh-like structures to control the coupled noise. To simulate the delta-I noise, however, one needs to compute the equivalent inductances in these mesh planes. As shown in Fig. 1, the mesh plane is usually modeled by numerous bars connected to each other. The inductances of these bars are computed first [1]. These gigantic inductive networks, which can consist of more than 20,000 inductors just under on chip site, are then reduced to an equivalent circuit [2], so much smaller in size that can be handled by a circuit simulator. Because the CPU time and storage required in doing both the computation [1] and reduction [2] often exceed the available computer resources, the packaging engineers were forced to use simpler or empirical models.

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Toeplitz Matrix as Applied to the Computation of Inductances in Mesh Structures

       An advanced packaging module often incorporates mesh-like
structures to control the coupled noise.  To simulate the delta-I
noise, however, one needs to compute the equivalent inductances in
these mesh planes.  As shown in Fig. 1, the mesh plane is usually
modeled by numerous bars connected to each other.  The inductances of
these bars are computed first [1].  These gigantic inductive
networks, which can consist of more than 20,000 inductors just under
on chip site, are then reduced to an equivalent circuit [2], so much
smaller in size that can be handled by a circuit simulator.  Because
the CPU time and storage required in doing both the computation [1]
and reduction [2] often exceed the available computer resources, the
packaging engineers were forced to use simpler or empirical models.
The following shows that, fully utilizing the property of
block-Toeplitz matrix, one can significantly reduce the CPU time and
storage.  It becomes possible for the packaging engineers to model
the mesh planes under more than one chip site.  Then, the delta-I
noise due to the surrounding chips' activity can be simulated more
accurately than before.

      It is understood that conductors perpendicular to each other
can be de-coupled in both computing and reducing the inductances.
Therefore, let us concentrate on the conductors which are parallel to
each other in the following development.

      In a packaging module, the mesh plants are normally
equi-spaced.  In some instances, solid planes close to the bottom of
the packaging module are used.  These solid planes can be treated
separately in a similar fashion.

      Consider the geometry in Fig. 2.  The inductance matrix [L] can
now be written as:

                            (Image Omitted)

        ...