前言

• 6.1求解设置介绍的驱动类型的求解设置中“Gneral选项卡”关于Solution Frequency（称为求解频率或自适应网格剖分频率）的选择有三种类型：分别是single，Multi-frequency，broadband。
• 无论选择哪种求解频率设置，都要设置相应的扫频方式，而HFSS中对应的扫频方式有三种，分别是：Fast，Discrete，Interpolating。

自适应网格剖分频率类型

• If a single frequency sweep is solved, an adaptive analysis is performed only at the solution frequency. If you want to solve over a range of frequencies, define a frequency sweep or a Multi-Frequency or Broadband solve. You must first assign an excitation for the Mult-Frequencies and Broadband options to appear on the setup.
• In multiple frequencies solve, port adapt is at the highest frequency and lambda refine is based on an algorithm that uses the highest and lowest user frequencies to allow maximum reuse of solved data. The lambda refinement frequency is the “nominal frequency”.
• The mesh at each pass is solved at multiple frequencies and energy error from all frequencies points are used to drive the mesh refinement for the next pass.
• The adaptive solution is converged when the simulation reaches the maximum number of passes or when all frequency points reach the targeted maximum delta S. The minimum converged passes and minimum number of passed parameters apply as the total requested passes.

单频点（Single）

单频点很好理解，就只是在该频率点处进行网格剖分，对于如何选择单频点的频率值，可以参考了李明洋的《HFSS电磁仿真设计…》这本书。

• 点频或者窄带问题：自适应网格剖分频率可以直接选择工作频率；
• 宽带问题：对于宽带问题，应该选择最高频率作为自适应网格剖分频率；
• 滤波器问题：对于滤波器问题，由于阻带内电场只存在于端口处，所以自适应网格剖分频率选择在通带内的高频段；
• 若扫频设置选择了Fast类型，通常将扫频范围的中心频率设置为自适应网格剖分频率；

• Note: For Fast sweeps, HFSS uses the solution frequency as the center frequency if it is within the frequency range (greater than the start frequency and less than the stop frequency.) Otherwise the middle of the frequency range is used as the center frequency.
• 如果扫频设置为Fast类型，若求解频率设置在扫频范围内，则HFSS会用求解频率作为中心频率。否则，中心频率会设置为扫频范围的中点。

多频点（Multi-frequency）

• 多频点实际上没有什么复杂的内容，实际上就是单频点的扩展。如果你已提前了解你所设计的结构，需要在哪些频段提供哪些自适应网格收敛的频率点，可以采用这种方法。实际上也可以创建多个Setup，然后采用Single 求解类型代替。

宽带（Broadband）

• The meshing frequencies include the Low and High with the remaining points determined automatically by HFSS. When the user requests DC as the low frequency, the lowest frequency solved by the adaptive meshing process is determined by an algorithm that looks at the range of frequencies you entered.
• 用于网格剖分的点，包括低频和高频，其余频率点则由HFSS自动确定。

• The Broadband setup enables HFSS to intelligently determine the appropriate frequencies at which to adapt the mesh.
• 设置宽带求解频率类型后，HFSS会自动地确定合适的频率来收敛网格；
• The virtue of automatic broadband adaptive meshing lies in eliminating uncertainty in choosing the best frequency for adapting the mesh. You need only specify the highest and lowest frequencies of the range and HFSS determines the frequencies at which to adapt the mesh. The mesh is always adapted for a minimum of three frequencies within the specified frequency range. Adaptive meshing at additional frequencies require enabling the high performance computing (HPC) feature and availability of sufficient computational resources.
• 自动宽带自适应网格剖分的优点在于消除了关于选择最佳自适应网格剖分频率的不确定性。你只需要确定频率范围的高低频，HFSS就会自己来决定自适应网格剖分的频率。网格的自适应收敛至少会采用在频率范围内的三个频率点。额外频率点下的自适应网格剖分需要启用高性能计算（HPC）功能和有足够可用的计算资源。

• The adaptive mesh refinement process occurs at various frequencies within the specified frequency range until the convergence criterion is met. In this case, the values of Maximum Delta S between consecutive solves are calculated for each frequency. The weighted average of Maximum Delta S across all frequencies must be below the specified magnitude of Maximum Delta S for the simulation to converge. You also have the option to set Maximum Number of Passes as the stopping criterion.
• 自适应网格细化过程发生在指定频率范围内的不同的频率上，直到满足收敛标准。在这种情况下，将针对每个频率计算连续求解之间的Maximum Delta S值。 所有频率的Maximum Delta S的加权平均值必须低于Maximum Delta S的指定幅度，仿真才能收敛。 您还可以选择设置最大迭代次数作为停止条件。
• For Broadband adapt, HFSS prompts you with an interpolation sweep predefined by a range of frequencies identical to the Broadband frequency range. In addition, the algorithm chooses the adapt frequencies in a way that they can also be reused in the frequency sweep. This increases the efficiency of the solution process.
• 对于Broadband的自适应收敛，HFSS会提示你在扫频设置的时候使用interpolation sweep插值扫频，并且把插值扫频的频率范围设置到和宽带求解的频率范围一致。除此之外，用在宽带求解确定自适应网格剖分频率点的算法也同样会应用在插值扫频中，提高了求解的效率。

• Broadband frequency setup does not allow viewing the fields for the adapted frequencies. You can define a discrete sweep including the adapt frequencies and solution data will be provided without re-solving.

所以从Help文档可以总结宽带求解的一些特点：

• 在宽带求解下，自适应网格剖分频率点至少选取三个点，其中两个是频率范围的最高和最低点，另外的频率点是由HFSS自己来确定的，而确定其他频率点的方法与扫频设置中“插值扫频”所使用的方法相同；（这个方法见后文插值扫频的介绍）
• 自适应网格收敛的时候，需要所有自适应网格剖分频率点都达到收敛才能停止网格细分（mesh refinement）；
• 由于宽带求解的自适应网格收敛中由多个自适应网格剖分频率点，所以可以开启HPC并行求解来加速收敛；

仿真和收敛

• In multiple frequencies modes, when frequency point p convergences prior to frequency point q,
  keep adapting at p until q and all other points achieve convergence.
• 对于多频率点的求解设置时，当频率点p先于频率点q达到收敛时，会继续对频率点p进行迭代，直到频率点q也收敛后一起停止迭代。
• The convergence data in the solution data dialog for single frequency mode is calculated in the same way as before. In multiple frequencies mode, the convergence plotted on the convergence display item corresponds to the global maximum delta S. Convergence data such as “Max. Delta S” appear in the reporter as standard solution quantity so that you can easily plot the maximum delta S for each frequency point vs. pass.

数据后处理报告

• For multiple frequencies adapted solutions, the S-Matrix solution display let you to view matrix data across different frequencies of its AdaptivePass and LastAdaptive solutions.
• In “Broadband” mode, the nominal frequency is solved and its results are available for all post processing, Optimetrics and expression cache setup. In this mode, results of other solved frequencies will be shown in the S-Matrix solution display but will not be available in reporter, Optimetrics and expression cache setup.
• In “Muti-Frequencies” mode, all post postings of the AdaptivePass and LastAdaptive will be extended to support results at all user-specified frequencies. Creating a report with solution across multiple frequencies will be the same as creating such report with a sweep solution.

存在的疑惑

• 关于多频率点类型（Multi-frequency、Broadband），使用HFSS plot mesh查看，最后显示所剖分的网格只有一个，也就是说，无论是单频点还是多频率点类型的，最后自适应网格细分后只存在一个。只不过对于多频率点类型来说，这个网格同时满足了所有频率点Max. Delta S该收敛标准。

自适应网格剖分频率与扫频频率的区分

• 自适应网格剖分频率：自适应网格剖分频率也可以称为求解频率，HFSS自适应网格剖分是在用户设定的求解频点（solution frequency）上进行的，网格剖分完成后，同一个求解设置项下其他频点的求解，都是基于前面设定频点上所剖分完成的网格来进行的（举个栗子，设置求解频率类型为“single”，那么此时网格剖分是基于该频点的，而扫频范围中其他频点则都是基于该频点的网格来求解，不会再进行网格剖分）。

Note：通常，自适应网格剖分频率设置的越高，网格剖分的越细，网格个数就越多，计算结果也相应地更加准确。但同时，网格剖分越多，所耗费的内存就越大

• 通过求解设置，可以对模型结构进行自适应网格剖分，并计算在指定的网格剖分频率点处的S参数和场解。但这只是分析一个频点处的S参数和场解，如果要分析或计算某个频段范围内的S参数和场解，则需要进行频率扫描设置。
• 求解频率设置和扫频设置所影响的HFSS运行流程范围如下图所示；
  

扫频设置

Gneral选项卡

频率扫频类型（Sweep Type）

快速扫频（Fast）

• Generates a unique full-field solution for each division within a frequency range.
  Best for models that will abruptly resonate or change operation in the frequency band. A Fast sweep will obtain an accurate representation of the behavior near the resonance. Fast sweeps are disabled if an anisotropic boundary condition is present.
• HFSS uses the center frequency of the frequency range to select an appropriate eigenvalue problem with which to generate a solution for the entire Fast sweep. It then uses an Adaptive Lanczos-Padé Sweep (ALPS)- based solver to extrapolate the field solution across the requested frequency range from the center frequency field solution.
• HFSS always uses the middle of the frequency range and the center frequency.
• Be aware that HFSS uses the finite element mesh refined during an adaptive solution at the solution frequency or, if you did not request an adaptive solution, the initial mesh generated for the problem. It uses this mesh without further refinement. Also, the field solution at the center frequency is the most accurate. Depending upon the desired level of accuracy you require throughout the frequency range, you may wish to perform additional Fast sweeps at other center frequencies.
• The full-field solution is saved only at the center frequency, while the S-parameters are saved for every frequency point; however, the Fast sweep allows the you to post process fields for any frequency entries to the sweep range.
• The time and memory required for a Fast sweep may be significantly greater than the time and memory required for a single frequency solution.

下图为Fast类型频率扫描的过程：

总结：

• 快速扫频适用于谐振问题和高Q值问题的分析，使用快速扫频可以得到场在谐振点附近行为的精确描述；
• 使用快速扫频，一般选择频带中心频率作为自适应网格剖分频率，进行网格剖分，计算出该频点的S参数和场分布，然后使用基于ALPS算法的求解器从中心频率处的S参数解和场解来外推整个频带范围的S参数和场解。
• 使用快速扫频，计算时只会求解中心频点处的场解，但在数据后处理时整个扫频范围内任意频点的场都可以显示。
• 存在疑惑：如果不以扫频范围的中心频率作为自适应网格剖分频率的话，对结果的影响？上述结论中，扫频范围的中心频点设置为自适应网格剖分频率（solution frequency），然后自适应网格收敛过程中，把solution frequency的S参数和场解求解出来了，接着使用基于ALPS算法的求解器从该频率点的S参数和场解来外推整个频带范围的S参数和场解。所以猜想就算solution frequency不是扫频范围的中心频点，但只要它在扫频范围内，工作的流程依然如上述执行，只不过扫频范围内离solution frequency越远的点，S参数和场结果不是那么精确。

离散扫频（Discrete）

• 用solution frequency细化后的网格对频率范围内，每一个频率进行独立的解算；
• For example, if you specify a range of 1000 MHz to 2000 MHz, then a Step Size of 2.5, the result（S parameters and field） would be solutions at 1000, 1250, 1500, 1750, and 2000 MHz.
• 默认情况下，离散扫频只保存最后计算的频率点的解，比如上述example中只保存2000MHz的场解，如果需要保存所有discrete点的场解，勾选后面的 Save fields(All frequencies) 选项；
• 离散扫频适用于那种整个频带范围内，只关注或者说只需要有限个频率点就能精确表示的情况；

插值扫频（Interpolating）

• 插值扫频使用二分法来计算整个频段内的S参数和场解。
  • 举例，（有时间再仔细更新）

• *Choose an Interpolating sweep if the frequency range is wide and the frequency response is smooth with the exception of a few resonances, or if the memory requirements of a Fast sweep exceed your resources.
• An Interpolating sweep’s time requirement may be much less than a Discrete sweep’s because a solution for the entire frequency range is interpolated based on solutions for a minimal number of frequency points. The maximum time required for an Interpolating sweep is the time required for a single frequency solution multiplied by the maximum number of solutions.

• 使用插值扫频适用于那种频率响应较为平坦的问题的分析
• 插值扫频会多出一个选项卡interpolation
  • Max Solutions：插值点最多设置为多少个；
  • 注意如果General选项卡中插值扫频选择了
  • Error Tolerance：最小的插值误差收敛标准
  • 上述两个都是判断插值扫频的停止标准，达到其中任一个就会停止插值。

Frequency Sweeps（频率扫描方式）

• Frequency Sweeps. You specify sweeps in terms of Distribution type, which can be Linear Step, Linear Count, Log Scale, Single Point, or Single Point Sweep, which adds a set of 10 Single Point Sweeps, defaulting from 1 GHz to 10 GHz in increments. The Add Above, and Add Below buttons permit you to add additional sweeps, including mixed sweep types. This feature provides flexibility. For example, you can define sweeps with log scale at lower frequencies, and linear step at higher frequencies. You can edit the Distribution, Start and End fields for any sweep.
• 频率扫描方式支持线性步长，线性计数，对数比例，单点，单点扫描共五种，注意选择不同的Sweep Type，其支持的频率扫描方式也不同，比如选择离散扫频（discrete），则上述五种扫频方式都可以选择，而选择快速扫频（Fast），则仅支持Linear Step和Linear Count。

• 如果对扫频方式不理解，直接打开Preview选项卡，可以看到扫频点是多少。
  
• 需要注意的地方：
  • 选择了插值扫频方式（interpolating），那么Distribution设置的频率点和Interpolation选项卡里面的Max Solutions的扫频频率点需要协调，最好是Max solutions的频率点大于扫频频率点。