## 1 Introduction  
Characterizing the performance of communications devices in a certain frequency band can be done by discretizing the frequency band into a number of discrete points, and repeatedly characterizing the response of the device in each one of these points. However, if the response of this device is complex, many points are needed to properly characterize the response, and thus this discrete frequency sweep becomes a time consuming process. Therefore, fast frequency sweep techniques are necessary to speed up the simulation process. A fast frequency sweep technique must provide an accurate response of the device with small error when compared with the discrete frequency sweep response, and it must do so consuming as little time as possible. Many fast frequency sweep techniques have been proposed in the technical literature. In [1], the asymptotic waveform evaluation (AWE) and the complex frequency hopping (CFH) techniques are both used for performing a fast frequency sweep in the analysis of substrate integrated waveguides (SIW). In the asymptotic waveform evaluation [2; 3; 4], the whole frequency response is approximated from the computation of the accurate response in only one single frequency point inside the bandwidth of interest. A Pade approximation to a reduced order rational polynomial is performed, and this approximation is used to interpolate over the whole frequency band with a certain degree of accuracy. The AWE technique has also been applied for the fast calculation of the radar cross-section [5], to the solution of general mixed circuit and electromagnetic problems with a full-wave method of moments solver [6], and to the characterization of an arbitrary two-dimensional dielectric waveguide using the tangential-vector finite-element method (TVFEM) [7]. However, the desired bandwidth in which the device has to be characterized is frequently so wide that it is not possible to get an accurate approximation from a single point. A possible solution to this problem is to use more than one point to develop such approximation. The main drawback of this strategy is that it is difficult to find the appropriate points for these partial AWE sub-expansions. To find these points, the complex frequency hopping (CFH) technique [8; 9] can be used. Applying this technique can guarantee that the approximation will be as good as desired. The width of the analyzed frequency range will not affect the precision of the results, but the cost will be proportionally increased, since the accurate response of the device will have to be computed in more than one discrete point (as many as necessary to obtain accurate results). As the authors of this work already experienced when implementing the AWE and the CFH techniques in [1], these techniques are complex and difficult to implement. Thus, a more straightforward fast frequency sweep would be desirable. Another fast frequency sweep technique is the vector fitting technique [10], which approximates the frequency response by a rational function and replaces a set of starting poles with an improved set of poles via a scaling procedure. This technique can approximate complex functions, but, as in the case of AWE and CFH, it also requires complex computations in order to obtain the poles of the approximated rational function. Other fast frequency sweep techniques have also been presented, such as the balanced truncation proper orthogonal decomposition (BT-POD) [11], which uses an adaptive frequency sampling method that allows a speed-up of 16 times when compared with discrete sweep, although this is a technique that is dependent on the electromagnetic solver, and can only be used in conjunction with the BT-POD. The same happens with the fast sweep technique presented in [12], which presents an adaptive multi-point method that chooses several frequency points called expansion frequencies for implementing a reduced order model in a finite element solver. The methods in [11; 12] are intrusive, requiring access to the frequency-dependent system representation.