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請善用CST幫助文件。 
請參考CST MWS幫助文件《Material Overview (HF)》及相關鏈接文件。

In CST MICROWAVE STUDIO®, several different material properties are considered to allow realistic modeling of practical simulation problems. The two basic materials available are PEC (Perfect Electrically Conducting material) and Vacuum. Other more complex materials may be defined in the Material Parameters dialog. Each material is distinguished by its unique name and can be visualized in a selectable color and transparency.  
Considering linear behavior, in the frequency domain the dielectric and magnetic material parameters determine the ratio of the electric field and flux density and of the magnetic field and flux density, respectively:  
 
and 
The material properties can be defined either as normal, describing isotropic media or with consideration of anisotropic behavior.  
In the following section, some special material declarations are discussed.  
Conducting materials  
 
Introducing material losses leads to complex permittivity or permeability values, respectively. This means that the material parameters have a real and an imaginary part, both frequency dependent. The losses are specified by the dielectric or magnetic loss angle or its corresponding tangent delta values:  
 
and  
 
Consequently, the tangent delta value is given as the negative ratio between imaginary and real part of the complex permittivity or permeability, respectively:    
 
and  
 
In general, every linear material behavior is described with help of the expressions above. Besides the special dispersive models explained later, different possibilities for loss definitions are available in CST MICROWAVE STUDIO®.  
 
One definition is the following conductivity model:  
 
This model realizes a broadband constant conductivity, however, the corresponding tangent delta value is frequency dependent, as displayed in the right picture.  
 
To realize an almost constant tangent value, or to set up a specific tangent delta curve, an internal dispersive first order Debye model (see below) will be fitted to the tangent delta input. The green curve on the right demonstrates the tangent delta dispersive behavior of such a model. Obviously, it is less frequency dependent than the conductivity model.  
 
Please note that no material exists in reality, providing a broadband perfectly-constant tangent delta value.  
 
Lossy metal: This material type simulates the penetration of electromagnetic fields inside a very good but not perfect electrically conductor by use of an internal one-dimensional surface impedance model. This offers the possibility to take the so-called skin effect into account without refining the mesh for these materials. However, please keep in mind that this model is physically reasonable only for a specific frequency range, defined by the solid's dimension and its material properties: the conductivity k and the permeability m . As mentioned above, on one hand the material has to represent a very good conductor, that means a material with a high conductivity value or, in other words, a material with a  high tangent delta value:  
 
Obviously this defines an upper limit for valid frequencies, but on the other hand the frequency dependent skin depth of the fields  
 
has to be smaller than the thickness d of the corresponding metal solid. This then defines a limit for the lowest applicable frequency:  
 
using a weight factor of approximately 0.2.  
 
Both constraints define together the valid frequency range for this material type, thus to take lower frequencies into account the material should be modeled applying a normal material type in connection with an electric conductivity. Consequently, for broadband simulations the frequency range should be split into two intervals.  
 
Note that this kind of material type is also available as a boundary condition to suppress unwanted box resonances of the structure model.  
 
Dispersive materials  
 
To consider frequency-dependent material behavior in broadband simulations, the most common models up to second-order dispersions are available. This includes relaxation and resonance effects as well as plasma or even gyrotropic media. In each case the microscopic material behavior is represented by a macroscopic description of the permittivity or permeability in the frequency domain. Hereby the static parameter limit is indicated by the subscript 's' and correspondent to this the high frequency limit by infinity symbol.  
 
Relaxation process: The relaxation process, also called first-order Debye model is characterized by the following formulation for the relative permittivity, containing the relaxation time t:  
 
The second-order Debye model is a superposition of two different first-order models sharing the same high frequency limit.  
 
Resonance process: The resonance behavior of a material is described by the Lorentz model, containing the resonance frequency w0 and the damping factor d:  
 
Relaxation Process  
Resonance Process  
 
In the pictures above, the real and imaginary parts of the relative permittivity are shown. On the left a typical relaxation process is visualized by a Debye first-order dispersion model. The relaxation time determines the frequency range of significant changes. In contrast to this is a Lorentz resonance curve on the right,  demonstrating the material resonance at the resonance frequency. Both models are also available for magnetic dispersions, i.e., for frequency dependent permeability.  
 
Cold plasma media: A special material behavior is given by cold plasma, also known as Drude dispersion. This model describes the characteristics of an electrically conducting collective of free positive and negative charge carriers, where the thermic movement of electrons is neglected. Damping is obtained by the collision of the particles among each other, described with help of the collision frequency nc. Considering the specific plasma frequency wp the correspondent relative permittivity is given as  
 
General dispersion models: All dispersion models mentioned above can be described in form of a general polynomial formulation, either as a first or a second order model. In case of a dielectric dispersion the corresponding expressions are given as  
 
and  
, respectively.  
 
The parameters of these two general models can be directly defined in the Dispersive Material Parameters dialog or by applying an automatic fitting scheme to a list of material data values in the Dielectric Dispersion Fit or Magnetic Dispersion Fit dialog.  
 
Biased plasma (electric gyrotropic) media: When a homogeneous magnetic biasing field is present in addition to the assumptions for the cold plasma, the effective material properties can be described by a gyrotropic permittivity tensor. If a z-directed biasing field is assumed, the correspondent permittivity tensor is given by  
 
with the elements  
 
and  
 
and finally  
 
where  
 
Here, the plasma frequency is again wp, and the cyclotron frequency wb arises from the circular trajectory of electrons with charge e and mass me in the constant biasing field B0. Damping is again due to the collision of the particles among each other, as described by the collision frequency nc.  
 
Biased ferrite (magnetic gyrotropic) media: Applying a static magnetic field to ferrite material causes dispersive and anisotropic permeability parameters. In fact, this material behaves strongly non-reciprocally and is significant for many microwave applications like circulators or one-way transmission devices. Such materials are called magnetic gyrotropic or simply gyromagnetic and are described by the following permeability tensor, assuming a magnetization above saturation in the z-direction:  
 
with the elements  
 
and 
Here, the Larmor frequency wl = G m0H0  (with H0 as the biasing static field) and the gyrotropic frequency wm = G MS  are coupled to the magnetic flux density and saturation magnetization by use of the gyromagnetic ratio G = (g e) / (2 me). This factor is calculated from the Landé factor g in connection with the charge and mass value of an electron. Beyond it the damping factor a is determined by the resonance line width DH as  
 
Note that this material description is given in SI units. However, the ferrite parameters often appear in Gauss units referring to the input parameters Landé factor, saturation magnetization and resonance line width. Thus, for convenience, the Dispersive Material Parameters dialog offers both possibilities.  
 
For Time-Domain solver runs, a homogeneous biasing field can be assigned to each material.  
 
 
Inhomogeneously biased ferrite media:  
 
For cases where the inhomogeneity of the biasing field needs to be considered, the Frequency Domain Solver with tetrahedral mesh features a convenient way to automatically calculate the magnetostatic field before the high frequency solver run. The solver then applies this biasing field to determine the ; varying material properties of the ferrites. Set up low and high frequency materials and sources in a single model, and then activate the Calculate static B-field for Ferrites option in the Special Frequency Domain Solver Parameters, and start the solver.  
 
The material properties specified in the Dispersive Material Parameters dialog influence the initial mesh even if the magnetic field vector or the biasing direction and the Larmor frequency are overwritten with the corresponding values for the local magnetostatic field.  
 
It is recommended to enter the material properties in the Gauss system, where the Landé factor can be specified directly. The C; frequency is proportional to the biasing field's magnitude, with the factor containing the Landé factor. The latter is then assumed to be equal to two if the material properties are given in the SI system (which approximately holds for many ferrites.)  
 
Corrugated walls  
 
Corrugated wall surface impedance models are only available for the general purpose frequency domain solver with tetrahedral mesh. The surface impedance is given by  
 
with the gap width w, the tooth width t (which should be less than one tenth of the gap width), and the corrugation depth d, which must be much larger than the corrugation width for the model to be valid. The number of corrugations per wavelength should be large, with ten per wavelength being the lower limit. There is a resonance in the effective material behavior when the corrugation depth is close to a quarter wavelength.  
 
Note: The validity of the corrugated wall surface impedance model for a given simulation cannot be checked by the solver. Therefore, it is mandatory to compare the results obtained with the equivalent material (i.e., the corrugated wall) to the full model at least once for a given problem type.  
 
Weight density  
 
Besides the mentioned electric and magnetic material properties also the density value of a can be defined. This is necessary to perform SAR calculation as a postprocessing step.  
 
See also  
 
Modeller View, Material Parameters  

謝謝大家，我看了幫助文件?？墒鞘怯⑽牡?，還是不是很明白。 
 
有沒有中文資料，或者大概給解釋下。謝謝

各向同性；各向異性；有耗金屬；非線性