**2.1. EM field basics**

Electromagnetic Field can be described using well known Maxwell's equations (for more information on Maxwell's equations please refer to any book dealing with EM field theory).

$$\begin{cases} DdS = Q \\ \oint BdS = 0 \\ \oint Edl = -\frac{d\Phi}{dt} \\ \oint Hdl = I\_0 + I\_c \end{cases} \tag{1}$$

Simply by solving those equations EM field can be completely described at all points of space and time. This leads us to complete description of EM field using only phasors of intensity of electric and magnetic field *E* and *H* (or *D* and *B* where *D = εE* and *B = µH*). This means that output of conventional commercial simulator is in the form of time dependent vectors that have components in axis *x*, *y* and *z*. These vectors are defined for each part of computational domain (e.g. when using FDTD (Thomas et. al., 1994), vectors are defined for each voxel – block discretizing computational domain).

We can see that this type of data can be extracted in form of matrices (multi-dimensional, e.g. 4D). Now, we shall look closer at those matrices.

#### **2.2. Data structure**

As we mentioned in previous chapter, results from simulators of EM field are represented as matrices, which directly predestines them to be processed in Matlab, which is the perfect tool for matrix operations.

There is a sample of data obtained from simulation in the following table. It depicts x-component of vector of intensity of electric field [V/m] in y-axis section in a part of some model.



Following graphical representation can help us shed some more light on the structure of data we obtained. These data are represented as four dimensional matrices (for phasors *E* and *H* separately) depicting whole computational domain and they are time dependent.

**Figure 1.** Data structure

20 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

explanation of advantages provided by presented solutions.

**2. Rough results from EM field simulator** 

briefly go through some EM field basics.

**2.1. EM field basics** 

**2.2. Data structure** 

model.

tool for matrix operations.

in particular regions of simulation domain, visualization of results in many ways (pcolor, slices, histograms, multiple iso-surface, surf interpretation on various shapes according to specific task etc.). We will provide detailed examples with practical applications and

As mentioned above, in this chapter we suppose that we have obtained rough data from any numerical simulator of EM field and now we want to interpret them. First of all we should look at how the structure of this data looks like. To get the full understanding we shall

Electromagnetic Field can be described using well known Maxwell's equations (for more information on Maxwell's equations please refer to any book dealing with EM field theory).

*DdS Q*

*BdS*

 

 

each voxel – block discretizing computational domain).

e.g. 4D). Now, we shall look closer at those matrices.

*<sup>d</sup> Edl*

0

Simply by solving those equations EM field can be completely described at all points of space and time. This leads us to complete description of EM field using only phasors of intensity of electric and magnetic field *E* and *H* (or *D* and *B* where *D = εE* and *B = µH*). This means that output of conventional commercial simulator is in the form of time dependent vectors that have components in axis *x*, *y* and *z*. These vectors are defined for each part of computational domain (e.g. when using FDTD (Thomas et. al., 1994), vectors are defined for

We can see that this type of data can be extracted in form of matrices (multi-dimensional,

As we mentioned in previous chapter, results from simulators of EM field are represented as matrices, which directly predestines them to be processed in Matlab, which is the perfect

There is a sample of data obtained from simulation in the following table. It depicts x-component of vector of intensity of electric field [V/m] in y-axis section in a part of some

*dt Hdl I I*

*c*

  (1)

0

 

Generally we can describe phasors as follows.

$$
\widehat{V}\_{\left(x,y,z,t\right)} = V\_{\left(x,y,z\right)} e^{j\alpha t} \tag{2}
$$

Note: It may be necessary to convert data to suitable matrix form (e.g. rough data are in the form of a row vector with axial information for each element). We will look into it in the chapter 3.

Now that we know what our data source looks like we can simply process it to view the results and highlight some of their aspects according to our needs (see Table 2. for axial information).

**Figure 2.** Extraction of Axes (in our example)
