### Abstract

The capacitance per unit length of a microstrip transmission line is obtained using a spectral-domain Method-of-Moments (MoM) formulation. The paper emphasizes this problem as a teaching tool to introduce students of electromagnetics to this technique. Firstly, the derivation of the spectral-domain Green's function is outlined. Using this, the relevant integral equation is derived to which the Galerkin MoM approach is then applied. The MoM problem is solved in the spectral domain by also transforming the expansion and weighting functions. The inverse Fourier transform is then applied to find the spatial-domain charge distribution, and, hence, capacitance. The issues that arise here - both of selecting how much of the spectrum to include, and how to choose the number of integration points - are discussed, and the results of typical numerical experiments are presented. The time required to compute the elements of the immittance matrix is shown to be O(N^{3}); the use of translational symmetry (and thus Toeplitz matrix structure) to reduce this is outlined. Classroom experience with this material is discussed. Finally, a hybrid spectral/spatial-domain formulation, introducing asymptotics, is outlined to accelerate the evaluation of the immittance matrix.

Original language | English (US) |
---|---|

Pages (from-to) | 11-19 |

Number of pages | 9 |

Journal | IEEE Antennas and Propagation Magazine |

Volume | 46 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2004 |

### Fingerprint

### Keywords

- Electromagnetic engineering education
- Green function
- Microstrip
- Moment methods
- Numerical analysis
- Spectral domain analysis
- Toeplitz matrices

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Antennas and Propagation Magazine*,

*46*(3), 11-19. https://doi.org/10.1109/MAP.2004.1374083

**An introduction to spectral domain Method-of-Moments formulations.** / Davidson, David B.; Aberle, James.

Research output: Contribution to journal › Article

*IEEE Antennas and Propagation Magazine*, vol. 46, no. 3, pp. 11-19. https://doi.org/10.1109/MAP.2004.1374083

}

TY - JOUR

T1 - An introduction to spectral domain Method-of-Moments formulations

AU - Davidson, David B.

AU - Aberle, James

PY - 2004/6

Y1 - 2004/6

N2 - The capacitance per unit length of a microstrip transmission line is obtained using a spectral-domain Method-of-Moments (MoM) formulation. The paper emphasizes this problem as a teaching tool to introduce students of electromagnetics to this technique. Firstly, the derivation of the spectral-domain Green's function is outlined. Using this, the relevant integral equation is derived to which the Galerkin MoM approach is then applied. The MoM problem is solved in the spectral domain by also transforming the expansion and weighting functions. The inverse Fourier transform is then applied to find the spatial-domain charge distribution, and, hence, capacitance. The issues that arise here - both of selecting how much of the spectrum to include, and how to choose the number of integration points - are discussed, and the results of typical numerical experiments are presented. The time required to compute the elements of the immittance matrix is shown to be O(N3); the use of translational symmetry (and thus Toeplitz matrix structure) to reduce this is outlined. Classroom experience with this material is discussed. Finally, a hybrid spectral/spatial-domain formulation, introducing asymptotics, is outlined to accelerate the evaluation of the immittance matrix.

AB - The capacitance per unit length of a microstrip transmission line is obtained using a spectral-domain Method-of-Moments (MoM) formulation. The paper emphasizes this problem as a teaching tool to introduce students of electromagnetics to this technique. Firstly, the derivation of the spectral-domain Green's function is outlined. Using this, the relevant integral equation is derived to which the Galerkin MoM approach is then applied. The MoM problem is solved in the spectral domain by also transforming the expansion and weighting functions. The inverse Fourier transform is then applied to find the spatial-domain charge distribution, and, hence, capacitance. The issues that arise here - both of selecting how much of the spectrum to include, and how to choose the number of integration points - are discussed, and the results of typical numerical experiments are presented. The time required to compute the elements of the immittance matrix is shown to be O(N3); the use of translational symmetry (and thus Toeplitz matrix structure) to reduce this is outlined. Classroom experience with this material is discussed. Finally, a hybrid spectral/spatial-domain formulation, introducing asymptotics, is outlined to accelerate the evaluation of the immittance matrix.

KW - Electromagnetic engineering education

KW - Green function

KW - Microstrip

KW - Moment methods

KW - Numerical analysis

KW - Spectral domain analysis

KW - Toeplitz matrices

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U2 - 10.1109/MAP.2004.1374083

DO - 10.1109/MAP.2004.1374083

M3 - Article

VL - 46

SP - 11

EP - 19

JO - IEEE Antennas and Propagation Society Newsletter

JF - IEEE Antennas and Propagation Society Newsletter

SN - 1045-9243

IS - 3

ER -