## Abstract

The interpolation and extrapolation of complex S-parameter data using the Cauchy method is described. An approximation of the complex S-parameter data is accomplished by a ratio of two polynomials. By applying the Cauchy method, an electromagnetic system is represented by a set of poles and zeros in the s-plane. The Total Least Squares (TLS) implementation of the Singular Value Decomposition (SVD) is used to estimate the dimension of the null space and hence calculate the value of the coefficients of the polynomials. Once these coefficients are computed, the complex S-parameter data can be interpolated or extrapolated over other frequencies of interest. A numerical example is provided to show the applicability of the Cauchy method in interpolating or extrapolating the complex S-parameter data over a whole frequency band including the pass and the stop bands.

Original language | English (US) |
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Title of host publication | Proceedings of the 2018 IEEE/MTT-S International Microwave Symposium, IMS 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 330-333 |

Number of pages | 4 |

Volume | 2018-June |

ISBN (Print) | 9781538650677 |

DOIs | |

State | Published - Aug 17 2018 |

Event | 2018 IEEE/MTT-S International Microwave Symposium, IMS 2018 - Philadelphia, United States Duration: Jun 10 2018 → Jun 15 2018 |

### Other

Other | 2018 IEEE/MTT-S International Microwave Symposium, IMS 2018 |
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Country | United States |

City | Philadelphia |

Period | 6/10/18 → 6/15/18 |

## Keywords

- Cauchy Method
- extrapolation
- interpolation
- QR decomposition
- Singular Value Decomposition (SVD)
- Total Least Squares (TLS)

## ASJC Scopus subject areas

- Radiation
- Condensed Matter Physics
- Electrical and Electronic Engineering