Peek Inductor

Peek Inductor

Background
Benchmark ID	peekInductor_n1434m1q1
Category	oberwolfach
System-Class	LTI-FOS
Parameters
nstates	1434
ninputs	1
noutputs	1
nparameters	0
components	A, B, C, E
Copyright
License	NA
Creator	Christian Himpe
Editor	Christian Himpe
Location
NA

Description: Spiral Inductor PEEC Model

Figure 1: Spiral inductor with part of overhanging copper plane

The description of the PEEC model of a spiral inductor can be found in PeekInductor.pdf.

The complex impedance is:

\[ Z(w) = Resis(w)+i*w*Induc(w) = G(i*w)^{-1}=(B^\intercal(-A+i*w*E)^{-1}B)^{-1} \]

A plots of \(Resis(w)\) can be found in PeekInductor-Rspiral_skin.pdf and a plot of \(Induc(w)\) in PeekInductor-Lspiral_skin.pdf.

Origin

This benchmark is part of the Oberwolfach Benchmark Collection; No. 38891, see .

Data

The model is of order \(N=1434\) and of the form: \[ \begin{array}{rcl} E \dot{x}(t) &=& Ax(t) + Bu(t) \\ y(t) &=& B^\intercal x(t) \end{array} \]

and can be downloaded as PeekInductor-dim1e3-spiral_inductor_peec.tar.gz (10.5 MB).

Short Matlab files to:

• plot \(Resis(w)\) and \(Induc(w)\),
• perform a PRIMA reduction of order 50,
• produce symmetrized standard state-space system\[\dot{x}(t) = A_{symm}x(t)+ B_{symm}u(t)\], \(y(t) = B_{symm}^\intercal x(t)\), where \(A_{symm}\) is symmetric.

can be found in PeekInductor-plot_spiral.tar.gz

Dimensions

System structure:

\[ \begin{align} E \dot{x}(t) &= Ax(t) + Bu(t) \\ y(t) &= B^\intercal x(t) \end{align} \]

System dimensions\[E \in \mathbb{R}^{1434 \times 1434}\], \(A \in \mathbb{R}^{1434 \times 1434}\), \(B \in \mathbb{R}^{1434 \times 1}\).

Citation

To cite this benchmark, use the following references:

• For the benchmark itself and its data:

The MORwiki Community, Peek Inductor. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Peek_Inductor

@MISC{morwiki_peek,
  author =       {{The MORwiki Community}},
  title =        {Peek Inductor},
  howpublished = {{MORwiki} -- Model Order Reduction Wiki},
  url =          {https://modelreduction.org/morwiki/Peek_Inductor},
  year =         {20XX}
}

• For the background on the benchmark:

@INCOLLECTION{morLiK05,
  author =       {J.R. Li, M. Kamon},
  title =        {PEEC Model of a Spiral Inductor Generated by Fasthenry},
  booktitle =    {Dimension Reduction of Large-Scale Systems. Lecture Notes in Computational Science and Engineering},
  volume =       {45},
  pages =        {373--377},
  year =         {2005},
  doi =          {10.1007/3-540-27909-1_23}
}