### Abstract

A numerical simulation program, QvalueC, was developed
for the design of planar inductors on lossy substrates in
two-dimensional geometry. Integral equations are used for
the estimation of the overall impedance of a circular
inductor at a given frequency. The program computes the
current density distribution in the wire that has a
finite electric conductivity. This so called magnetic
computation gives the series inductance and series
resistance of the coil. By using Green functions,
integral equations are derived for equivalent surface
charges that represent the conductor in the electric
problem. From the surface charges the parallel
capacitance and the parallel resistance are obtained. The
code is written with the view to designing planar coils
in four dielectric layers, but also solenoids with
multilayered conductors can be computed. The approach
taken allows an accurate simulation of the following
dissipation mechanisms affecting the Q-value: ohmic
losses in the wire, skin-depth effect, proximity (eddy
current) effect, and losses in supporting dielectric but
conductive layers via capacitive coupling. Simulated and
measured results from planar inductors on lossy silicon
and other substrates show a good agreement.

Original language | English |
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Place of Publication | Espoo |

Publisher | VTT Technical Research Centre of Finland |

Number of pages | 31 |

ISBN (Print) | 951-38-5641-0 |

Publication status | Published - 2000 |

MoE publication type | Not Eligible |

### Publication series

Series | VTT Tiedotteita - Meddelanden - Research Notes |
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Number | 2017 |

ISSN | 1235-0605 |

### Keywords

- numerical simulation program
- design of planar inductors
- planar coils

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## Cite this

Varpula, T. (2000).

*Optimising planar inductors*. VTT Technical Research Centre of Finland. VTT Tiedotteita - Meddelanden - Research Notes, No. 2017