#### 5.2.6.3. Frequencies

RF3p solves for the fields and circuit parameters in the model at a set of discrete frequency points, using either a separate analysis at each frequency or an asymptotic method that evaluates a set of adjacent points with one analysis.

When performing the discrete frequency analysis, RF3p determines the fields and associated circuit parameters by solving a separate finite-element problem at each frequency. For each frequency the user-specified number of modes are extracted at each port using an eigenanalysis of the port, and the finite-element matrix equation is solved once for each mode at each port. Each resulting solution vector contains both the fields that result from the excitation of the corresponding port/mode, and also the associated column in the generalized S-matrix. In a discrete sweep, each frequency is effectively treated as a separate problem, and as such, discrete sweeps make efficient use of multiple processors since solving for each frequency can proceed independently.

In addition to discrete analysis, RF3p can compute results at a set of frequency points using an asymptotic method known as the Galerkin Asymptotic Wave Expansion (GAWE). This technique allows much faster treatment of problems with a large number of frequencies, where discrete frequency treatment would be prohibitive. Processing associated with individual GAWE expansion points is independent, so when multiple processors or cluster nodes are used each can work on a distinct expansion point, which allows for efficient parallel processing. In preparation for a fast sweep the system analyzes any waveports over the complete frequency spectrum using a subset of the total number of frequency points and creating expansions that are used in the sweep. The sweep itself initially does discrete solves at the frequency endpoints and also at a point near the middle of the band. An expansion is done about the middle point and evaluated/compared at the endpoints to determine if additional expansion points are needed. If the agreement is not good enough at the low frequency end, then an additional discrete solve/expansion frequency point is added in the interval below the mid-point, and likewise for the interval above the mid-point. Interval subdivision continues until the solution is sufficiently accurate over the entire band. Individual expansion points can be solved independently so if multiple processes are being used, the first 3 frequency points are done concurrently. After that the number of concurrent expansions is determined by the process evolution, but generally the more expansion points required, the more parallelism can be exploited.

To set a particular frequency sweep type, choose one of the options under Frequency Sweep Type in the simulation properties dialog box under the Solver tab. If you specify the sweep type as Automatic the solver uses either GAWE or Discrete, depending on which is likely to be faster for the simulation frequency count, port count, and parallel configuration. You can also force the use of one or the other by specifying it instead of Automatic. GAWE is usually faster than the discrete sweep when the frequency count is large compared to the number of ports, especially when only a few processors are available. Even with GAWE, however, you generally do not want to ask for more frequencies than you need, as even for fast sweeps there is an additional computational burden for each frequency point. GAWE also requires more computer memory than the discrete sweep because of the need to store matrix expansions and basis vectors. The amount of time it takes for the fast sweep to finish is a function of the number of ports/modes, since expansions must be formed for each source in the problem.

The finite-element method used by RF3p is appropriate for high frequencies, and it loses accuracy at very low frequencies. To protect against simulation at frequencies that are too low, RF3p defines a minimum solved frequency (default value is 0.01 GHz) below which it does not apply the finite-element method. You may change the minimum frequency value in the simulation properties dialog box Solver tab, under Minimum Solved Frequency (GHz). Adjust this value with care, however: results for simulations run at very low frequencies may lose accuracy.

If you attempt to simulate at a frequency below the minimum solved frequency, RF3p extrapolates the results from above the minimum solved frequency using a cubic polynomial fit. Previous versions of RF3p simply replaced all frequencies below the minimum solved frequency with the minimum solved frequency; to obtain this behavior, set Extrapolate Toward DC to None in the simulation properties dialog box Solver tab. Since the results below the minimum solved frequency are obtained by extrapolation and not through application of electromagnetic principles, the low-frequency results should be viewed with some skepticism. These results are provided for convenience only, and are not intended to provide true physical insight. Nevertheless, if the lowest frequency you request is close to the minimum solved frequency, the extrapolation will often provide good results.