Difference between revisions of "RCL Circuit Equations"

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Description

These benchmark originate from VLSI circuits. Specifically resistor-capacitor-inductor circuits, which can be represented by first order descriptor systems, following a modeling process based on the two Kirchhoff's circuit laws and the branch constitutive relations.

PEEC Problem

This RCL circuit is a PEEC discretization^[1] and has 2100 capacitors, 172 inductors, 6990 inductive couplings, as well as a resistive source^[2],^[3]. The resulting model has 306 states, and two inputs and outputs.

Package Problem

The second problem models a 64-pin package of an RF circuit. A subset of eight pins carry signals, which leads to sixteen terminals (eight interior and eight exterior)^[4],^[3]. The resulting model has 1841 states, and sixteen inputs and outputs.

Origin

This benchmark is part of the Oberwolfach Benchmark Collection^[5]; see ^[3].

Data

The PEEC problem and package problem are available as MATLAB .mat files, providing the $A$ , $B$ , $E$ matrices, while $C = B^\intercal$ is assumed:

PEEC.zip (32.8KB)
Package.zip (78.7KB)

Dimensions

System structure:

\begin{align} E \dot{x}(t) &= Ax(t) + Bu(t) \\ y(t) &= Cx(t) \end{align}

System dimensions:

$E \in \mathbb{R}^{N \times N}$ , $A \in \mathbb{R}^{N \times N}$ , $B \in \mathbb{R}^{N \times M}$ , $C \in \mathbb{R}^{M \times N}$ .

System variants:

$N = 306$ , $M = 2$ , for the PEEC problem, and $N = 1841$ , $M = 16$ for the package problem.

Citation

To cite this benchmark, use the following references:

For the benchmark itself and its data:

The MORwiki Community, RCL Circuit Equations. MORwiki - Model Order Reduction Wiki, 2019. http://modelreduction.org/index.php/RCL_Circuit_Equations

@MISC{morwiki_convection,
  author =       {{The MORwiki Community}},
  title =        {RCL Circuit Equations},
  howpublished = {{MORwiki} -- Model Order Reduction Wiki},
  url =          {http://modelreduction.org/index.php/RCL_Circuit_Equations},
  year =         {20XX}
}

For the background on the benchmark:

@INCOLLECTION{morFre05,
  author =       {R.W. Freund},
  title =        {RCL Circuit Equations},
  booktitle =    {Dimension Reduction of Large-Scale Systems},
  pages =        {367--371),
  year =         {2005},
  doi =          {10.1007/3-540-27909-1_22}
}

References

↑ A.E. Ruehli, Equivalent Circuit Models for Three-Dimensional Multiconductor Systems, IEEE Transactions on Microwave Theory and Techniques 22(1): 216--221, 1974.
↑ P. Feldmann, R.W. Freund , Efficient linear circuit analysis by Pade approximation via the Lanczos process, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 14(5): 639--649, 1995.
↑ ^3.0 ^3.1 ^3.2 R.W. Freund, RCL Circuit Equations, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 367--371, 2005.
↑ Z. Bai, P. Feldmann, R.W. Freund, Equivalent Stable and Passive Reduced-Order Models Based on Partial Pade Approximation Via the Lanczos Process, Numerical Analysis Manuscript 97(3): 1--17, 1997.
↑ J.G. Korvink, E.B. Rudnyi, Oberwolfach Benchmark Collection, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.

[ruehli1974-1] A.E. Ruehli, Equivalent Circuit Models for Three-Dimensional Multiconductor Systems, IEEE Transactions on Microwave Theory and Techniques 22(1): 216--221, 1974.

[feldmann1995-2] P. Feldmann, R.W. Freund , Efficient linear circuit analysis by Pade approximation via the Lanczos process, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 14(5): 639--649, 1995.

[freund2005-3] 3.0 ^3.1 ^3.2 R.W. Freund, RCL Circuit Equations, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 367--371, 2005.

[bai1997-4] Z. Bai, P. Feldmann, R.W. Freund, Equivalent Stable and Passive Reduced-Order Models Based on Partial Pade Approximation Via the Lanczos Process, Numerical Analysis Manuscript 97(3): 1--17, 1997.

[korvink2005-5] J.G. Korvink, E.B. Rudnyi, Oberwolfach Benchmark Collection, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.

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[2]

[3]

[4]

[5]

@@ Line 93: / Line 93: @@
 <ref name="feldmann1995"> P. Feldmann, R.W. Freund , <span class="plainlinks">[https://doi.org/10.1109/43.384428 Efficient linear circuit analysis by Pade approximation via the Lanczos process]</span>, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 14(5): 639--649, 1995.</ref>
-<ref name="bai1997">Z. Bai, P. Feldmann, R.W. Freund, <span class="plainlinks">[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.7763&rep=rep1&type=pdf Equivalent Stable and Passive Reduced-Order Models Based on Partial Pad e Approximation Via the Lanczos Process]</span>, Numerical Analysis Manuscript 97(3): 1--17, 1997.</ref>
+<ref name="bai1997">Z. Bai, P. Feldmann, R.W. Freund, <span class="plainlinks">[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.34.7763&rep=rep1&type=pdf Equivalent Stable and Passive Reduced-Order Models Based on Partial Pade Approximation Via the Lanczos Process]</span>, Numerical Analysis Manuscript 97(3): 1--17, 1997.</ref>
 <ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection]</span>, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>