### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the 63rd European Study Group Mathematics with Industry |

Subtitle of host publication | Enschede, The Netherlands, 28 January – 1 February, 2008 |

Editors | Onno Bokhove, Johann Hurink, Gjerrit Meinsma, Chris Stolk, Michel Vellekoop |

Place of Publication | Amsterdam |

Publisher | Centrum voor Wiskunde en Informatica |

Pages | 65-84 |

Number of pages | 20 |

ISBN (Print) | 978-90-365-2779-8 |

Publication status | Published - 28 Jan 2008 |

Event | 63rd European Study Group Mathematics with Industry, SWI 2008 - University of Twente, Enschede, Netherlands Duration: 28 Jan 2008 → 1 Feb 2008 Conference number: 63 |

### Publication series

Name | CWI Syllabus |
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Publisher | CWI (Centrum voor Wiskunde en Informatica) |

### Conference

Conference | 63rd European Study Group Mathematics with Industry, SWI 2008 |
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Abbreviated title | SWI |

Country | Netherlands |

City | Enschede |

Period | 28/01/08 → 1/02/08 |

### Fingerprint

### Keywords

- MSC-34K28
- EWI-14950
- METIS-255156
- MSC-74A60
- IR-65338
- CR-G.1

### Cite this

*Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008*(pp. 65-84). (CWI Syllabus). Amsterdam: Centrum voor Wiskunde en Informatica.

}

*Proceedings of the 63rd European Study Group Mathematics with Industry: Enschede, The Netherlands, 28 January – 1 February, 2008.*CWI Syllabus, Centrum voor Wiskunde en Informatica, Amsterdam, pp. 65-84, 63rd European Study Group Mathematics with Industry, SWI 2008, Enschede, Netherlands, 28/01/08.

**Some studies on the deformation of the membrane in an RF MEMS switch.** / Ambati, Vijaya Raghav; Asheim, Andreas; van den Berg, Jan Bouwe; van Gennip, Yves; Gerasimov, Tymofiy; Hlod, Andriy; Planqué, Bob; van der Schans, Martin; van der Stelt, Sjors; Vargas Rivera, Michelangelo; Vondenhoff, Erwin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Some studies on the deformation of the membrane in an RF MEMS switch

AU - Ambati, Vijaya Raghav

AU - Asheim, Andreas

AU - van den Berg, Jan Bouwe

AU - van Gennip, Yves

AU - Gerasimov, Tymofiy

AU - Hlod, Andriy

AU - Planqué, Bob

AU - van der Schans, Martin

AU - van der Stelt, Sjors

AU - Vargas Rivera, Michelangelo

AU - Vondenhoff, Erwin

N1 - http://eprints.ewi.utwente.nl/14950

PY - 2008/1/28

Y1 - 2008/1/28

N2 - Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.

AB - Radio Frequency (RF) switches of Micro Electro Mechanical Systems (MEMS) are appealing to the mobile industry because of their energy efficiency and ability to accommodate more frequency bands. However, the electromechanical coupling of the electrical circuit to the mechanical components in RF MEMS switches is not fully understood. In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch. We investigate the present problem along two lines of attack. First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO. Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.

KW - MSC-34K28

KW - EWI-14950

KW - METIS-255156

KW - MSC-74A60

KW - IR-65338

KW - CR-G.1

M3 - Conference contribution

SN - 978-90-365-2779-8

T3 - CWI Syllabus

SP - 65

EP - 84

BT - Proceedings of the 63rd European Study Group Mathematics with Industry

A2 - Bokhove, Onno

A2 - Hurink, Johann

A2 - Meinsma, Gjerrit

A2 - Stolk, Chris

A2 - Vellekoop, Michel

PB - Centrum voor Wiskunde en Informatica

CY - Amsterdam

ER -