 Another design approach, particularly suitable for CAD because it is a numerical method, is to decompose the filter into a number of finite elements. These elements are a large number of simple steps and ridges. A number of methods are available to analyse the individual elements. The mode matching technique expands the field equations of the element into a series of eigenfunctions and then for each mode matches the field at the interface between elements. The Galerkin method expands the field equations into polynomial functions such as Gegenbauer polynomials or Chebyshev polynomials. These methods can be mixed according to what is convenient for a particular type of element. Whichever analysis method is used, the final output needed is the scattering parameters matrix for each element. The overall filter response is then found from the combined scattering matrix of all the individual element matrices. This method is analytic rather than synthetic, that is, a trial design must first exist in order to be analysed unlike synthesis methods where the starting point is a prescribed transfer function from which a design is synthesised.
