AntennaDesign.wikiAntenna design, explained

What is the method of moments?

From Antenna Design Wiki · By the · Published · Last reviewed · How we research

The method of moments (MoM) solves an integral equation for the unknown currents on an antenna by expanding the current in N basis functions and enforcing the equation with N testing functions, giving a dense matrix equation [Z][I] = [V]. Harrington’s 1968 book established the framework for electromagnetics; NEC applies it to wire antennas and RWG basis functions to arbitrary triangulated surfaces.[1][2][3]

Which integral equations are used?

For thin wires, Pocklington’s and Hallén’s equations relate the axial current to the incident field on the wire surface. For surfaces, the electric-field integral equation (EFIE), magnetic-field integral equation (MFIE) and their combination (CFIE) are used; layered-media Green’s functions make planar MoM efficient for printed antennas.[4][1]

What are the strengths and limits?

Only conductors (and sometimes dielectric surfaces) are meshed, and radiation to infinity is built into the Green’s function, so open problems need no absorbing boundaries. However, the dense N × N matrix costs O(N²) memory and O(N³) direct solution time; fast multipole and related methods reduce this for large problems. Complex inhomogeneous dielectric bodies are less natural for MoM than for FEM or FDTD.[1][5]

What are RWG basis functions?

Rao, Wilton and Glisson defined basis functions on pairs of triangles sharing an edge, with normal current continuity across the edge, enabling MoM analysis of arbitrarily shaped surfaces.[3]

Frequently asked questions

Why is MoM good for wire antennas?

Only one-dimensional segments are meshed, so models are small and fast.

What is a segment?

A short section of wire carrying one basis function, typically λ/10 to λ/20 long.

Does MoM handle ground?

Yes, with image theory for perfect ground and Sommerfeld integrals for real ground in NEC.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

  1. “Field Computation by Moment Methods”. R. F. Harrington, Macmillan (IEEE Press reprint 1993). 1968.
  2. “Numerical Electromagnetics Code (NEC) — Method of Moments, Tech. Rep. UCID-18834”. G. J. Burke and A. J. Poggio, Lawrence Livermore Laboratory. January 1981.
  3. “Electromagnetic Scattering by Surfaces of Arbitrary Shape”. S. M. Rao, D. R. Wilton and A. W. Glisson, IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409-418. May 1982.
  4. “Antenna Theory: Analysis and Design, 4th ed.”. C. A. Balanis, Wiley. 2016.
  5. “Antenna Engineering Handbook, 4th ed.”. J. L. Volakis (ed.), McGraw-Hill. 2007.
Categories: Simulation