The method of moments (MOM) expands the currents on an antenna (or scattering object) in a linear sum of simple basis functions. The approximate solution is a finite series of these basis functions:
 (1)We compute the coefficients by solving integral equations to satisfy boundary conditions on the surface of the antenna (or object). The integral equation can be expressed in the form , where L is a linear operator, usually a scalar product using an integral , the unknown currents given by Eq. (1), and g the known excitation or source function. We substitute the summation of Eq. (1) into the linear operator equation and use the scalar product integral to calculate the terms in a matrix equation. The solution of the matrix equation determines the coefficients of current expansion. The MOM produces filled matrices that require time-consuming numerical methods for inversion. The art of the MOM is in choosing basis functions and deriving efficient expressions for evaluating the fields using the basis function currents. Common basis functions are simple staircase pulses, overlapping triangles, trigonometric functions, or polynomials.
The method does not satisfy boundary conditions at every point, only over an integral average on the boundaries. By increasing the number of basis functions, the method will converge to the correct solution. We need to judge how many terms are required for an adequate engineering evaluation. Spending excessive time on the solution cannot be justified if it greatly exceeds our ability to measure antenna performance accurately using real hardware. |
