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

David B. Davidson, James Aberle

Research output: Contribution to journalArticle

23 Citations (Scopus)

### 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(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.

Original language English (US) 11-19 9 IEEE Antennas and Propagation Magazine 46 3 https://doi.org/10.1109/MAP.2004.1374083 Published - Jun 2004

### Fingerprint

Method of moments
Capacitance
Inverse transforms
Charge distribution
Galerkin methods
Green's function
Integral equations
Electric lines
Fourier transforms
Teaching
Students
Experiments

### 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

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

In: IEEE Antennas and Propagation Magazine, Vol. 46, No. 3, 06.2004, p. 11-19.

Research output: Contribution to journalArticle

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