Peek Inductor

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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 LiKamon.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 Rspiral_skin.pdf and a plot of $Induc(w)$ in 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 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 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:

$E \in \mathbb{R}^{1434 \times 1434}$, $A \in \mathbb{R}^{1434 \times 1434}$, $B \in \mathbb{R}^{1434 \times 1}$.