RCL Circuit Equations - Revision history

Saak at 16:07, 23 January 2026

2026-01-23T16:07:56Z

← Older revision		Revision as of 16:07, 23 January 2026
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	==Description==		==Description==
	These ~~benchmark~~ originate from [[wikipedia:Very_Large_Scale_Integration\|VLSI]] circuits.		These benchmarks originate from [[wikipedia:Very_Large_Scale_Integration\|VLSI]] circuits.
	Specifically [[wikipedia:RLC_circuit\|resistor-capacitor-inductor]] circuits, which can be represented by first order descriptor systems,		Specifically [[wikipedia:RLC_circuit\|resistor-capacitor-inductor]] circuits, which can be represented by first order descriptor systems,
	following a modeling process based on the two [[wikipedia:Kirchhoff's_circuit_laws\|Kirchhoff's circuit laws]] and the [[wikipedia:Modified_nodal_analysis\| branch constitutive relations]].		following a modeling process based on the two [[wikipedia:Kirchhoff's_circuit_laws\|Kirchhoff's circuit laws]] and the [[wikipedia:Modified_nodal_analysis\| branch constitutive relations]].

Schuetz2 at 05:38, 17 June 2025

2025-06-17T05:38:32Z

← Older revision		Revision as of 05:38, 17 June 2025
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	title = {RCL Circuit Equations},		title = {RCL Circuit Equations},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/RCL_Circuit_Equations}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/RCL_Circuit_Equations}</nowiki>,
	year = {20XX}		year = {20XX}
	}		}

Malhotra: infobox string

2023-11-30T09:39:51Z

infobox string

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 [[Category:SISO]]
 [[Category:Differential_algebraic_system]]
 ==Description==

Lund: remove preliminary warning

2022-08-26T13:03:26Z

remove preliminary warning

← Older revision		Revision as of 13:03, 26 August 2022
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	~~{{preliminary}} <!-- Do not remove -->~~
	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]

Himpe at 12:56, 25 August 2022

2022-08-25T12:56:18Z

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	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
	[[Category:SISO]]		[[Category:SISO]]
	[[Category:~~DAE_order_unspecified~~]]		[[Category:Differential_algebraic_system]]

	==Description==		==Description==

Mlinaric: Fix category name

2021-07-03T18:12:35Z

Fix category name

← Older revision		Revision as of 18:12, 3 July 2021
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	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
	[[Category:SISO]]		[[Category:SISO]]
	[[Category:~~DAE_order_unspecififed~~]]		[[Category:DAE_order_unspecified]]

	==Description==		==Description==

Himpe: fix ref

2019-09-17T12:27:29Z

fix ref

← Older revision		Revision as of 12:27, 17 September 2019
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	<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="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>		<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>

Himpe: init

2019-09-17T12:20:43Z

init

New page

{{preliminary}} 
[[Category:benchmark]]
[[Category:Oberwolfach]]
[[Category:SISO]]
[[Category:DAE_order_unspecififed]]

==Description==
These benchmark originate from [[wikipedia:Very_Large_Scale_Integration|VLSI]] circuits.
Specifically [[wikipedia:RLC_circuit|resistor-capacitor-inductor]] circuits, which can be represented by first order descriptor systems,
following a modeling process based on the two [[wikipedia:Kirchhoff's_circuit_laws|Kirchhoff's circuit laws]] and the [[wikipedia:Modified_nodal_analysis| branch constitutive relations]].

===PEEC Problem===
This RCL circuit is a [[wikipedia:Partial_element_equivalent_circuit|PEEC]] discretization<ref name="ruehli1974"/> and has 2100 capacitors, 172 inductors, 6990 inductive couplings, as well as a resistive source<ref name="feldmann1995"/>,<ref name="freund2005"/>.
The resulting model has 306 states, and two inputs and outputs.

===Package Problem===
The second problem models a 64-pin package of an [[wikipedia:RF_circuit|RF]] circuit.
A subset of eight pins carry signals, which leads to sixteen terminals (eight interior and eight exterior)<ref name="bai1997"/>,<ref name="freund2005"/>.
The resulting model has 1841 states, and sixteen inputs and outputs.

==Origin==

This benchmark is part of the '''Oberwolfach Benchmark Collection'''<ref name="korvink2005"/>; see <ref name="freund2005"/>.

==Data==

The PEEC problem and package problem are available as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] files, providing the <math>A</math>, <math>B</math>, <math>E</math> matrices,
while <math>C = B^\intercal</math> is assumed:

* [[Media:PEEC.zip|PEEC.zip]] (32.8KB)
* [[Media:Package.zip|Package.zip]] (78.7KB)

==Dimensions==

System structure:

:<math>
\begin{align}
E \dot{x}(t) &= Ax(t) + Bu(t) \\
y(t) &= Cx(t)
\end{align}
</math>

System dimensions:

<math>E \in \mathbb{R}^{N \times N}</math>,
<math>A \in \mathbb{R}^{N \times N}</math>,
<math>B \in \mathbb{R}^{N \times M}</math>,
<math>C \in \mathbb{R}^{M \times N}</math>.

System variants:

<math>N = 306</math>, <math>M = 2</math>, for the PEEC problem, and <math>N = 1841</math>, <math>M = 16</math> 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 = <nowiki>{{The MORwiki Community}}</nowiki>,
title = {RCL Circuit Equations},
howpublished = {{MORwiki} -- Model Order Reduction Wiki},
url = <nowiki>{http://modelreduction.org/index.php/RCL_Circuit_Equations}</nowiki>,
year = {20XX}
}

* For the background on the benchmark:

@INCOLLECTION{morFre05,
author = <nowiki>{R.W. Freund}</nowiki>,
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==

<references>

<ref name="ruehli1974">A.E. Ruehli, [https://doi.org/10.1109/TMTT.1974.1128204 Equivalent Circuit Models for Three-Dimensional Multiconductor Systems], IEEE Transactions on Microwave Theory and Techniques 22(1): 216--221, 1974.</ref>

<ref name="feldmann1995"> P. Feldmann, R.W. Freund , [https://doi.org/10.1109/43.384428 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.</ref>

<ref name="bai1997">Z. Bai, P. Feldmann, R.W. Freund, [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], Numerical Analysis Manuscript 97(3): 1--17, 1997.</ref>

<ref name="korvink2005"> J.G. Korvink, E.B. Rudnyi, [https://doi.org/10.1007/3-540-27909-1_11 Oberwolfach Benchmark Collection], Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 311--315, 2005.</ref>

<ref name="freund2005"> R.W. Freund, [https://doi.org/10.1007/3-540-27909-1_22 RCL Circuit Equations], Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 367--371, 2005.</ref>

</references>