Frequency domain transfer functions of microwave systems are usually calculated either directly in the frequency domain or in the time domain in combination with a Fourier analysis. The computation of loss-free linear devices based on eigen"elds (resonant "elds) o!ers an alternative to obtaining broadband frequency characteristics with a high accuracy. Such methods are very e!ective for problems with multiple narrow resonances as many points in frequency domain have to be calculated to sample the maximas, or time domain computations have to deal with long transients. We describe a method of this type and then an improvement that leads directly to transfer functions, which are very accurate even if only modes in the chosen frequency range are taken into account.
Generalized macroscopic parameters are introduced as input and output quantities, which are related to conventional quantities such as discrete currents and voltages, wave parameters, or even beam currents and voltages (as de"ned in accelerator physics for beams of ultra-relativistic charged particles). When the generalized input/output parameters are causal they are related to each other and to state parameters of the eletromagnetic "elds by a di!erential equation with time independent system matrices. The input/output transfer matrix in the frequency domain is an impedance matrix, which is derived from the system matrices of the discretization as well as from a series expansion using eigensolutions. The number of eigenmodes is typically three times the number of meshpoints, but good approximations can be achieved even with a much smaller set of eigenvalues around the frequency range of interest. Another approach to characterizing the system response is based on the output/input relation described by an admittance matrix. Combining both approaches, the error of the approximations can be estimated and signi"cantly reduced. The application of the method is shown for several examples.