8

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SOLVING ELECTROMAGNETIC FIELD PROBLEMS USING HOBBIES

8.0 SUMMARY

Modeling and simulation of basic electromagnetic (EM) field problems are introduced in this chapter. The most fundamental modeling problem in an EM simulation is to analyze metallic wires, surfaces, and wire-surface junctions. Therefore illustrative examples are first presented at the beginning of this chapter, related to these topics. Then modeling of dielectric structures are illustrated, followed by simulation examples dealing with composite structures consisting of both metallic and dielectric bodies. For the case of pure dielectric structures, homogeneous, inhomogeneous, and multilayered dielectric structures are discussed.

Examples using different impedance loadings are also demonstrated in this chapter, which involves use of both distributed and concentrated loadings. Real material properties of wires and metallic surfaces (e.g., finite conductivity) can be taken into account by adding distributed loadings over the wires and surfaces, or by treating the structure as a lossy dielectric. Lumped elements inserted at the junction of a wire with other wires or surfaces can be modeled by concentrated loadings.

Anti-symmetry, symmetry, perfect electric conductor (PEC), and perfect magnetic conductor (PMC) settings are also presented. Symmetry properties can be used to speed up the analysis if both the geometry and the excitation are symmetrical or anti-symmetrical with respect to the same basic coordinate plane (xOy, xOz, and/or yOz plane). Also, the effects of a real ground influencing the properties of an antenna are discussed. Examples including radiation patterns and impedances of antennas above a real ground, which is treated as a finite dielectric slab with the far-fields calculated using the reflection coefficient method and an infinite dielectric ground plane, are also described.

Finally, an imaging technique is described, which can be applied to improve the quality of the analysis for microstrip structures or for structures coated with a thin dielectric layer. A microstrip patch antenna array is used to illustrate the advantages of using this imaging technique.

The Higher Order Basis Based Integral Equation Solver (HOBBIES) examples presented in this chapter are not very complicated. However, these examples represent most of the principal applications of HOBBIES. With the HOBBIES functions demonstrated in this chapter, users can perform very complicated EM simulations, which will be discussed in Chapter 9.

All examples introduced in this chapter have the name starting with HOBBIES (e.g., HOBBIES0111). Users can load these projects from the “infoexamples” folder, which is under the HOBBIES installation folder, and can get all the details about the model and the simulated results.

As mentioned in the previous chapter, this academic version of HOBBIES has a limit of a maximum of 3000 nodes for generating the geometry and 5000 sampling points for displaying the results in post-processing. Examples presented in this chapter are simulated with this limitation.

8.1 METALLIC STRUCTURES

Any metallic structure can be modeled as a combination of wires and plates. A metallic structure is characterized by four entities: nodes, wires, surfaces, and junctions, which need to be specified by the user. There are three types of junctions: wire-to-wire junctions, surface-to-surface junctions, and wire-to-surface junctions. First two of these junctions are automatically recognized by HOBBIES, while the third type should be specified by the user.

For excitations, one can use either a radiation or a scattering mode of operation. Scattering problems are excited by plane waves, and radiation problems are excited by delta function generators operating at a single frequency.

All metallic structures are grouped into three classes:

1. Wire structures
2. Surface structures
3. Combined wire and surface structures

8.1.1 Wire Structures

HOBBIES treats wire structures consisting of arbitrarily shaped wires interconnected in a general way. Wires can be:

• Straight or curved. In this section, only straight wires are considered (curved wires are modeled by a sequence of straight wires).
• Of constant radii or of variable radii (e.g., cylindrical and conical wires). In this section, both cases are considered.
• Thin or thick when the radii are compared with their length. In this section, relatively thick wires are used so that three-dimensional (3D) drawings of the wires are more illustrative.
• Solid or hollow. There is no difference between solid and hollow wires if they are thin enough. The thick hollow wires are more precisely modeled as pipes made of surfaces. HOBBIES also enables precise modeling of solid wires by considering the wire-end effects. In this section, the wire-end effect is not included.

All wire-to-wire junctions are presented as junctions of wire ends.

8.1.1.1 Linear Wire Scatterer Project: HOBBIES0111

The structure includes two nodes, a single wire and a plane wave excitation (Figure 8.1). The geometry of a cylindrical wire is modeled by a right-truncated cone of equal radii. The wire has a length of 0.5 m and a radius of 25 mm. The model is simulated from 100 MHz to 400 MHz using the Bistatic RCS mode. The user can load the project HOBBIES0111 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is listed in Figure 8.2. Figure 8.2 (a) provides the node list describing the structure. Figure 8.2 (b) lists the segment that composes the wire modeled by a truncated cylinder with the same value of the radius at both ends. Figure 8.2 (c) shows the wave list that lists the plane wave defined in the model. Figure 8.2 (d) shows the scattering pattern window that defines the directions in the spherical coordinates, along which the radiation or scattering is to be calculated. Figure 8.2 (e) is the frequency window defining the start frequency, stop frequency, and number of frequencies between them for the simulation. Figure 8.2 (f) defines the mode of operation for the model.

Figure 8.1. A linear wire scatterer model.

Figure 8.2. Information windows describing the model: (a) Node list, (b) Wire list, (c) Wave list, (d) Pattern for the scattered fields window, (e) Frequency window, (f) Operation mode window.

Results: Simulate the model by clicking the Run button , and wait until the simulation is finished, then go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the scattering patterns of the fields over a frequency band as shown in Figure 8.3. The maximum value for σ/λ² is obtained when the wire length is approximately half the wavelength of the incident wave. The value for the wire thickness also affects the results. If the wire is thick, the effective wire length is increased by approximately one wire radius, resulting in a resonant frequency slightly smaller than the one obtained for a thin wire with a zero thickness of the same length (260 MHz instead of the theoretical value of 300 MHz for a thin wire).

Figure 8.3. Bistatic radar cross section (RCS) for the linear wire scatterer.

8.1.1.2 Linear Dipole Radiator Project: HOBBIES0112

A linear dipole antenna consists of two cylindrical wires, and each wire has the length of 0.25 m and the radius of 25 mm. The model is simulated in the frequency range of 100 MHz to 400 MHz using the All generators mode and is excited by a point generator at the interconnection of the wires, as shown in Figure 8.4. The user can load the project HOBBIES0112 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.5. Figure 8.5 (a) provides the node list, followed by the wire list in Figure 8.5 (b). The generator list is provided in Figure 8.5 (c) and the radiation pattern setting in Figure 8.5 (d). Finally, the frequency and the options information are described in Figures 8.5 (e) and (f).

Figure 8.4. A linear dipole antenna model.

Figure 8.5. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Window providing the input for the radiation pattern, (e) Frequency window, (f) Options window.

Junction of two wires: Two or more wires having a common node are considered interconnected (i.e., there is a current flow through the common node). Such junctions are automatically determined by HOBBIES and need not be specified by the user.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the network parameters. Choose Z(Imped.) for the parameter to observe the input impedance, and the Real component from the Data tab within the Left Panel. Then click the button and choose Z(Imped.) for the input impedance and the Imag. component. Change the values for the range to be between −210 and 110 using the Range tab to obtain a view shown in Figure 8.6 (a). To view the S parameters, choose the S(Scat.) parameter and the Mag. component from the Data tab within the Left Panel. Figure 8.6 (b) plots the input S parameter. To view the 3D radiation pattern, click the button. Choose Gain (dB) from the Data tab within the Left Panel, and change the Scalar factor to be 0.4 from the Options tab to display the pattern of Figure 8.7. The Z, S parameters and the 3D radiation pattern are shown for a/h = 0.1. Because of this value of a/h, the resonant frequency is about 260 MHz, a bit lower than the theoretical value of 300 MHz.

When the dipole radius to the height ratio, a/h, tends to zero, a minimum value of S₁₁ is obtained for a half-wavelength dipole and Re(Z) decreases to the theoretical value of 73.1 Ω at 300 MHz (see Table 8.1 – results are obtained with grade Enhanced 3 for HOBBIESOptionsCurrent Expansion). Also, the radiation pattern practically does not depend on the wire radius for a constant height.

Figure 8.6. A linear dipole antenna: (a) real and imaginary parts of the input Z parameter, (b) magnitude of the input S parameter.

Figure 8.7. 3D radiation pattern (Gain in dB) of the dipole antenna at 260 MHz.

Table 8.1. Real part of Z parameter with respect to a/h at 300 MHz.

8.1.2 Surface Type Structures

HOBBIES can handle surface type structures consisting of arbitrarily oriented surfaces interconnected in a general way. In this example, the thickness of the surface is infmitesimally thin. The surface is composed of a perfect conductor. There is no field inside a closed conducting structure. Hence, a structure modeled by a closed surface represents either a solid or a hollow metallic body at high frequencies. An infmitesimally thin surface can also model a real surface of finite thickness. Note that in this case the current on the infmitesimally thin surface is the sum of currents over both sides of the real surface. A more precise model of a real surface would be a body, made of several infmitesimally thin Non-Uniform Rationale B-Spline (NURBS) surfaces, with the dimensions (height, width, and thickness) of the observed real surface.

All surface-to-surface junctions are presented as connections between the edges of the surfaces. There are two classes of such surface-to-surface junctions:

1. All surfaces at a junction have two common nodes, defining a common edge. This class is considered in this section.
2. Electrically short edges of all surfaces do not coincide and are situated in an electrically small junction domain. This class is modeled in a similar way as the class of wire-to-surface junctions.

Finally, note that HOBBIES requires that a generator be assigned to a wire and not to a surface. Scatterer Modes can analyze metallic objects consisting of surfaces and wires. To solve a radiation problem, a portion of a wire has to be introduced in the model to place the generator.

8.1.2.1 Cube Scatterer Project: HOBBIES0121

A PEC cube scatterer is composed of six surfaces with a side length of 2 m. The cube is excited by a plane wave at 100 MHz, as shown in Figure 8.8. The user can load the project HOBBIES0121 from the “infoexamples” folder under the HOBBIES installation folder. The bistatic RCS is calculated. The information about the model is shown in Figure 8.9. Figure 8.9 (a) provides the node list, followed by the surface list in Figure 8.9 (b). The wave list is provided in Figure 8.9 (c) and the near-field setting in Figure 8.9 (d). Finally, the frequency setting and the mode of operation information are described in Figures 8.9 (e) and (f). To have a better view of the model, the user can click the button to rotate the model and switch between the mesh view and the Geometry view through ViewModeMesh/Geometry.

Modeling of closed metallic bodies: There is no field inside a closed structure. Hence, a structure made by a closed surface represents a good model for either a solid or a hollow metallic body at high frequencies.

Figure 8.8. A cube scatterer model.

Figure 8.9. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wave list, (d) Near field setting window, (e) Frequency window, (f) Operation mode window.

Junction of two surfaces: Two or more surfaces with two common nodes that define their common edge are considered electrically interconnected. This means that there is a current flow across the common edge joining the two surfaces. Such a junction is automatically characterized by HOBBIES. (The user does not need to define these junctions.)

Two surfaces with only a part of an edge in common, as shown in Figure 8.10 (a), are not considered electrically interconnected. To interconnect these two surfaces, you must subdivide them, as shown in Figure 8.10 (b). Two surfaces with only one common node, as shown in Figure 8.10 (c), or two common nodes, without common edges, in Figure 8.10 (d), are also not electrically interconnected.

Figure 8.10. Junctions of two surfaces.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the distribution of the electric field around and inside the cube. Inside the cube, the electric field is zero. The fields are large in the front of the cube due to an interaction between the incident and the reflected fields, whereas it is small in the shadow region, as shown in Figure 8.11.

Figure 8.11. Near-field distribution around and inside the cube scatterer.

8.1.3 Composite Wire and Surface Structures

In general, any metallic structure can be modeled as a composite wire and surface structure. All composite wire and surface structures can be grouped into two main classes:

• Structures without wire-to-surface junctions
• Structures with wire-to-surface junctions

Note that a composite wire and surface structure without a wire-to-surface junction represents a combination of a wire structure and a surface structure. Such a structure can be modeled using the techniques outlined in Sections 8.1.1 and 8.1.2. The case of a composite wire and surface structures with wire-to-surface junctions requires a wire-to-surface junction. All wire-to-surface junctions can be grouped in two classes:

• Simple wire-to-surface junctions
• Combined wire-to-surface junctions

The simple wire-to-surface junction contains the end of one wire and one short surface edge situated in an electrically small domain. Any other wire-to-surface junction can be represented as a combination of simple wire-to-surface junctions. Hence, they are referred to as combined wire-to-surface junctions.

All combined wire-to-surface junctions can be grouped into three subclasses:

• The junction of a wire and a surface corner or a surface vertex
• The junction of a wire and a surface edge or a surface wedge (that is not electrically short)
• The junction of a wire intersecting a surface at some location other than a surface edge or vertex

However, all combined wire-to-surface junctions are defined in the same way. Finally, note that all wire-to-surface junctions belong to the group of junctions (see Section 1.4.4).

8.1.3.1 Biconical Antenna Project: HOBBIES0131

The antenna consists of two wires and four regular cones, as shown in Figure 8.12 (a). And the model after the mesh is generated is shown in Figure 8.12 (b). The size of the mesh is 0.0545 and the Automatic correct sizes option is chosen to be Normal in the Preferences window (refer to Appendix A). The wires between the cones have a length of 1 cm and a radius of 1 mm. The model is excited by a point generator at the center of the two wires between the cones and is simulated from 100 MHz to 400 MHz using the All generators mode. The user can load the project HOBBIES0131 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.13. Figure 8.13 (a) provides the node list, followed by the surface list in Figure 8.13 (b). The wire list is provided in Figure 8.13 (c) and the junction list in Figure 8.13 (d). Figure 8.13 (e) provides the generator list. Finally, the operating frequency and the current display setting information are described in Figures 8.13 (f) and (g).

Figure 8.12. A biconical antenna: (a) the antenna model before meshing, (b) the model after meshing.

Figure 8.13. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wire list, (d) Junction list, (e) Generator list, (f) Frequency window, (g) Current display setting window.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the current distribution on the antenna. Total current along the top of the cone tends to zero at the tip, as shown in Figure 8.14 (a). Click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component from the Data tab within the Left Panel. Then click the button and choose the Y(Admit.) parameter and the Imag. Component shown in Figure 8.14 (b). To view the S parameters, choose the S(Scat.) parameter and the Real component from the Data tab within the Left Panel. Then click the button and choose the S(Scat.) parameter and the Imag. component for comparison. Figure 8.14 (c) gives the results for S parameter.

Figure 8.14. A biconical antenna: (a) current distribution on the antenna, (b) Y parameter of the antenna, (c) S parameter of the antenna.

8.1.3.2 Bowtie Antenna Project: HOBBIES0132

A bowtie antenna consists of two wires driven by a generator at their interconnection and two trapezoidal surfaces, as shown in Figure 8.15 (a). The center wire has the length of 18 mm and a radius of 3 mm. The model is simulated from 300 MHz to 600 MHz using the antenna mode. The trapezoidal surfaces have their short sides connected to the free wire ends. The user can load the project HOBBIES0132 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.16. Figure 8.16 (a) provides the node list, followed by the wire list in Figure 8.16 (b). The junction list is provided in Figure 8.16 (c) and the generator list in Figure 8.16 (d). Finally, the frequency setting and the options setting information are described in Figures 8.16 (e) and (f). The results shown in Figure 8.17 are obtained with grade Enhanced 3 for HOBBIESOptionsCurrent Expansion.

Figure 8.15. A bowtie antenna: (a) the antenna model, (b) the simple wire-to-surface junction.

Figure 8.16. Information windows describing the model: (a) Node list, (b) Wire list, (c) Junction list, (d) Generator list, (e) Frequency window, (f) Options window.

Simple wire-to-surface junction: A simple wire-to-surface junction contains one wire end and one short surface edge situated in an electrically small domain, as shown in Figure 8.15 (b). The wire and the surface have no common nodes. Hence, such a junction belongs to the class of localized (nontrivial) junctions.

In general, a localized (nontrivial) junction is a junction between the ends of a wire and/or short surface edges that have no common nodes and are situated in an electrically small domain. This domain is referred to as a junction domain. The physical contact between the ends of the wires and edges of the surfaces is not defined, but it is assumed. It is also assumed that all these ends are interconnected satisfying the Kirchhoff's current law (i.e., the total current coming out of all these ends and edges is equal to zero).

A simple wire-to-surface junction is completely defined by three nodes contained in the junction domain, one defining the end of the wire and the other two nodes defining the short surface edge.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the network parameters. To view the S parameters, choose the S(Scat.-dB) parameter from the Data tab within the Left Panel, to obtain Figure 8.17 (a). To view the 3D radiation pattern, click the button, choose Gain (dB) from the Data tab within the Left Panel, choose 447 MHz from the Freq. drop-down list, change the Scalar factor to be 0.4 from the Options tab, change the radiation pattern range from the Range tab, and the user can get the plot of Figure 8.17 (b). A bowtie antenna has a 2 dB gain, length of 216 mm, and a resonant frequency at 447 MHz, as shown in Figure 8.17. A corresponding half-wave dipole would have a length of 336 mm. By using the bowtie antenna, we obtain the same gain as for an electrically shorter antenna.

Figure 8.17. A bowtie antenna: (a) S parameter of the antenna, (b) 3D radiation pattern of the antenna.

8.1.3.3 Monopole Antenna Mounted on a Cube Project: HOBBIES0133

A monopole antenna mounted on a cube includes one wire and six surfaces, as shown in Figure 8.18 (a). The wire has a length of 0.75 m and a radius of 50 mm. The cube has a side of length 2 m. The model is excited by a generator at the interconnection between the wire and the top surface of the cube and is simulated at 100 MHz using the antenna mode. The user can load the project HOBBIES0133 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.19. Figure 8.19 (a) provides the node list, followed by the surface list in Figure 8.19 (b) and the wire list in Figure 8.19 (c). The junction list is provided in Figure 8.19 (d) and the generator list in Figure 8.19 (e). Finally, the frequency setting and the mode of operation are described in Figures 8.19 (f) and (g).

Figure 8.18. A monopole antenna mounted on a cube: (a) the antenna model, (b) the combined wire-to-surface junction viewed in the post-process window.

Figure 8.19. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wire list, (d) Junction list, (e) Generator list, (f) Frequency window, (g) Operation mode window.

Wire-to-surface junction: Any wire-to-surface junction can also be modeled as a combination of several wire-to-surface junctions. Hence, they are referred to as combined wire-to-surface junctions. This modeling includes a specific segmentation technique that divides the surfaces into two or more subsurfaces. The segmentation is automatically performed by HOBBIES, as shown in Figure 8.18 (b).

There are three types of combined wire-to-surface junctions:

• The junction of a wire and a surface corner or a surface vertex
• The junction of a wire and a surface edge or a surface wedge (which is not electrically short)
• The junction of a wire and the middle part of a surface

Any combined wire-to-surface junction is completely defined by the node at the end of the wire contained in the junction region.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the current distribution around the interconnection, as shown in Figure 8.20.

Figure 8.20. Current distribution around the junction.

8.1.3.4 Nonconnected Plates and Wire Scatterer Project: HOBBIES0134

A nonconnected plates and wire scatterer includes two wires and three surfaces, as shown in Figure 8.21 (a). The center wire has a length of 1.54 m and a radius of 50 mm. The model is excited by a plane wave excitation at 225 MHz using the Monostatic RCS mode. The user can load the project HOBBIES0134 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.22. Figure 8.22 (a) provides the node list, followed by the wire list in Figure 8.22 (b) and the wave list in Figure 8.22 (c). The scattering pattern setting is provided in Figure 8.22 (d). Finally, the frequency setting and the mode of operation are described in Figures 8.22 (e) and (f).

General non-trivial junction: It is possible to define junctions between wires and surfaces that are not physically interconnected. Such a junction is shown in Figure 8.21 (b). Enter the order numbers of the surface's nodes in the vicinity of the wire and nodes of the wire that belong to the junction in the Junction list window, as shown in Figure 8.23. The junction is automatically assembled by HOBBIES transparent to the user.

Figure 8.21. A nonconnected wire and plates scatterer: (a) the model, (b) the junction.

Figure 8.22. Information windows describing the model: (a) Node list, (b) Wire list, (c) Wave list, (d) Scattering pattern window, (f) Frequency window, (g) Operation mode window.

Figure 8.23. Junction list window for the nonconnected plates and wire scatterer.

Result: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the 3D RCS pattern. Choose RCS (dB) from the Data tab within the Left Panel, change the Scalar factor to be 0.2 from the Options tab, and users can get the display of Figure 8.24 (a). Also, users can click the button to view the 2D RCS pattern, as shown in Figure 8.24 (b).

Figure 8.24. RCS plot of the nonconnected wire and plates scatterer: (a) 3D monostatic RCS, (b) 2D monostatic RCS in Phi = 0° cut-plane.

8.2 COMPOSITE METALLIC AND DIELECTRIC STRUCTURES

Any linear antenna, scatterer, or a microwave device represents a combination of metallic and dielectric bodies. In addition, metallic bodies can be considered of composite wire and surface structures. The main task of the user in electromagnetic modeling of composite structures is to create an appropriate geometric model of the structure and to define the excitation for the model. The rest is done by HOBBIES.

A composite structure is determined by five entities: domains, nodes, wires, surfaces, and junctions. When compared with modeling of metallic structures, the new entities are domains. A domain consists of all bodies made of the same material. Modeling of these bodies is the same as in the case of metallic structures, except that for each surface the user defines to which domains it belongs.

The domain consisting of all bodies made of PEC is designated as the 0th domain. Outer space is designated as the 1st domain. By default, the 1st domain is filled by vacuum, and each surface belongs to the 0th and 1st domains, as in the case of metallic structures. In the case of a composite structure, particular care should be devoted to these entities.

All composite structures can be divided into the following three classes:

• Pure metallic structures (as explained before)
• Pure dielectric structures
• Combined metallic and dielectric structures

8.2.1 Pure Dielectric Structures

In general, HOBBIES can handle any arbitrarily shaped inhomogeneous dielectric body located in vacuum. Such a body can be represented by a proper combination of homogeneous dielectric bodies, if the body has a layered structure.

The homogeneous dielectric body is completely specified by the shape of its boundary surface, and by electrical parameters of the material from which the body is made. The boundary surface of a dielectric body is modeled by NURBS surfaces. This surface represents a boundary surface between two dielectric domains, and because of that, it is called a dielectric surface.

The field inside a homogeneous dielectric body is completely determined by equivalent electric and magnetic currents over the surface of the body. Hence, a dielectric surface is accompanied by electric and magnetic current sheets. Note that these currents create zero fields outside the body.

8.2.1.1 Inhomogeneous Dielectric Cube Scatterer Project: HOBBIES0211

An inhomogeneous dielectric cube scatterer is composed of eight subcubes, as shown in Figure 8.25. Each subcube is of the same size, and each side has a length of 0.3 m. And each subcube is filled with one dielectric material that is specified in the domain list. The model is excited by a plane wave and is simulated from 100 MHz to 300 MHz using the Bistatic RCS mode. Project HOBBIES0211a is used for comparison purposes. The only difference between the two projects is that in project HOBBIES0211a, the real parts of all permittivities are set to 4.25, as shown in Figures 8.26 (a) and (b). The user can load both projects HOBBIES0211 and HOBBIES0211a from the “infoexamples” folder. The information about the model is shown in Figure 8.27. Figure 8.27 (a) provides the node list, followed by the wave list in Figure 8.27 (b) and the surface list in Figure 8.27 (c). The scattering pattern setting is provided in Figure 8.27 (d). Finally, the frequency setting and the mode of operation information are described in Figures 8.27 (e) and (f).

Figure 8.25. An inhomogeneous dielectric cube scatterer.

Figure 8.26. Domain list: (a) eight different dielectric cubes with eight different permittivities in project HOBBIES0211, (b) eight different cubes with the same value of the permittivity as illustrated in project HOBBIES0211a.

Figure 8.27. Information windows describing the model: (a) Node list, (b) Wave list, (c) Surface list, (d) window dealing with parameters to plot the scattering pattern, (e) Frequency window, (f) Operation mode window.

Dielectric structures: Dielectric structures are modeled the same way as metallic structures, using NURBS surfaces. In general, the model of a homogeneous dielectric body must be a closed surface. The definition of the geometry and domain specification is explained in Chapters 4 and 6, respectively. A domain is fully specified by its geometry and electrical properties of the material that fills it.

Inhomogeneous dielectric structures: An inhomogeneous dielectric is modeled by piecewise homogenous dielectric bodies. This means that an inhomogeneous dielectric body should be subdivided into two or more bodies in such a manner that any of the subbodies can be considered to be made of homogenous dielectric materials.

The question is how small a subbody should be, in order to be considered homogeneous. Most often, even for highly inhomogeneous dielectrics, satisfactory results are obtained if the maximum dimension of each subbody does not exceed 0.1 λ. An inhomogeneous dielectric filling such a subbody is replaced by a homogenous dielectric, whose electrical parameters represent the mean value of the electrical parameters of the inhomogeneous dielectric materials. In HOBBIES0211a, the real parts of all the permittivities are set to 4.25.

Multiple dielectric junctions: Three or more dielectric domains can be interconnected through a common edge. Such an edge is called a multiple dielectric junction. Such a junction is automatically determined by HOBBIES. It is not necessary to define these junctions.

Results: For project HOBBIES0211 and HOBBIES0211a, the user needs to run both of the projects to compare the results. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the 2D RCS pattern. Then click the button to add or superimpose the results of project HOBBIES0211a. The user needs to simulate that project first and then load the file through folder HOBBIES0211a.gid POST HOBBIES0211a.ral. Check the Group Mode checkbox within the Left Panel, which enables the user to change the parameters for all displayed graphs. For Figure 8.28 (a), choose 100 MHz from the Freq. drop-down list, and change the scattering pattern range to be between 0 and 0.04 from the Range tab. For Figure 8.28 (b), choose 200 MHz from the Freq. drop-down list, and for Figure 8.28 (c), choose 300 MHz and change the scattering pattern range to be between 0 and 14. The Results for the two models show acceptable agreement at 100 MHz and 200 MHz. A distinct difference is observed at 300 MHz because the maximum dimension of each subbody far exceeds 0.1 λ.

Figure 8.28. Comparison of RCS along ϕ = 0 cut-plane at different frequencies for a dielectric cube scatterer: (a) 100 MHz, (b) 200 MHz, (c) 300 MHz.

8.2.1.2 Multilayered Dielectric Cube Scatterer Project: HOBBIES0212

A multilayered dielectric cube is modeled as a dielectric cube immersed in a slightly larger cube made of another dielectric material, as shown in Figure 8.29. The outer and the inner cubes have the side length of 0.6 m and 0.4 m, respectively. The model is excited by a plane wave and is simulated at 100 MHz using the Bistatic RCS mode. The user can load the project HOBBIES0212 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.30. Figure 8.30 (a) provides the node list, followed by the surface list in Figure 8.30 (b) and the wave list in Figure 8.30 (c). The domain and near-field setting is provided in Figures 8.30 (d) and (e), respectively. Finally, the frequency setting and the mode of operation information are described in Figures 8.30 (f) and (g).

Figure 8.29. A multilayered dielectric cube scatterer model.

Figure 8.30. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wave list, (d) Domain list, (e) Near-field setting window, (f) Frequency window, (g) Operation mode window.

Multilayered dielectric structures: A multilayered dielectric body is modeled as a dielectric body immersed in a larger dielectric body. This larger body may be further immersed inside another body, and so forth. The number of layers created in such a manner can be unlimited.

Evaluation of the near-field in a multidomain structure: Data defining the points at which the near-field is to be evaluated are edited into the Near-Field dialog box. The Domains combo box is set to All, which represents the default mode. It means that the total near-field is evaluated at all the specified points. This default mode can be used for all near-field evaluations.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. The results for the electric and magnetic fields and the Poynting vector are shown in Figure 8.31. In the post-processing window, click the button to view the near-field distribution around and inside the cube. To view the electric field distribution, choose the E component from the Data tab within the Left Panel. Similarly, choose the H and P component to view the magnetic field and the distribution of the Poynting vector, separately. To compare the intensity of the electric field at a boundary surface of two dielectrics, or between a dielectric and air, users can obtain their ratio using the boundary conditions for the vector D (D₁ = D₂).

Figure 8.31. A multilayered dielectric cube scatterer: (a) electric field distribution, (b) magnetic field distribution, (c) Poynting vector.

8.2.2 Combined Metallic and Dielectric Structures

Any linear antenna, scatterer, a microwave device, and so on, can be modeled as a composite metallic and dielectric structures. All such structures can be grouped into two main classes:

• Structures without metallic-to-dielectric junctions
• Structures with metallic-to-dielectric junctions

A composite structure without metallic-to-dielectric junctions represents a simple combination of pure metallic and pure dielectric structures. In that case, the metallic structure is simply placed near the dielectric object or immersed in the dielectric object.

There are three types of metallic-to-dielectric junctions:

• Composite metallic and dielectric junction
• Protrusion of a wire through a dielectric surface
• Protrusion of a metallic surface through a dielectric surface

Pure metallic structures (metallic structures in vacuum) are always modeled by wires and metallic surfaces accompanied by a single current sheet. A real surface of finite width is modeled by a single infinitesimally thin surface, whose current represents a sum of the currents placed over both sides of the real surface. In the same way, one can model metallic structures immersed in any dielectric domain. Such metallic surfaces, accompanied by a single current, are identified as simple metallic surfaces.

A single infinitesimally thin surface also models a real surface of finite width, placed between two dielectric domains. However, this surface is accompanied by two independent current sheets, since currents placed over its opposite sides act in two different dielectric domains. Two overlapping basic metallic surfaces, immersed in different dielectric domains, can replace such a surface. Hence, such a metallic surface is identified as a composite metallic surface.

8.2.2.1 Coated Surface Scatterer Project: HOBBIES0221

A coated surface scatterer consists of one metallic surface coated with a dielectric, or equivalently, the metallic structure is placed inside a dielectric box, as shown in Figure 8.32 (a) for project HOBBIES0221. The box has the size of 2 m by 2 m by 0.2 m. And the surface is of dimension 2 m by 2 m. The model is excited by a plane wave and simulated at 150 MHz using the Bistatic RCS mode. As a comparison, Figure 8.32 (b) and Figure 8.32 (c), which are for projects HOBBIES0221a and HOBBIES0221b, display that for the models, the metal plate is outside and inside the dielectric box, respectively. All three projects have the same size of the box and the plate. The user can load projects HOBBIES0221, HOBBIES0221a, and HOBBIES0221b from the “infoexamples” folder under the HOBBIES installation folder. The information of the model for project HOBBIES0221 is shown in Figure 8.33. Figure 8.33 (a) provides the domain list. Figure 8.33 (b) provides the node list, followed by the surface list in Figure 8.33 (c) and the wave list in Figure 8.33 (d). The setting of the scattered field is provided in Figure 8.33 (e). Finally, the frequency setting and the mode of operation information are given in Figures 8.33 (f) and (g).

Figure 8.32. A coated surface scatterer: (a) a metallic surface coated with a dielectric, (b) a metallic surface placed in the vicinity of a dielectric box, (c) a metallic surface immersed inside a dielectric box.

Figure 8.33. Information windows describing the model: (a) Domain list, (b) Node list, (c) Surface list, (d) Wave list, (e) Scattering pattern window, (f) Frequency window, (g) Operation mode window.

Coated structures: Since the geometry of both metallic and dielectric objects are defined by their surfaces, it is equally easy to model a metallic plate in the vicinity of a dielectric object or if the metallic plate is embedded in the dielectric object. In the second case, the metallic plate is immersed inside the first domain (vacuum) – surface domain specification (1 0), while for the third case, it is immersed inside the specified dielectric domain – surface domain specification (2 0). To move the metallic surface from vacuum into the dielectric body or vice versa, it is enough to shift all the nodes of the surface the same distance and to change the order numbering of the domain of the first surface.

Results: To compare the results of project HOBBIES0221, HOBBIES0221a, and HOBBIES0221b, the user needs to run all the three projects. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. Click the button to view the 2D RCS pattern. Then click the button to add the graph for HOBBIES0221a. To load the file containing the results of project HOBBIES0221a, users need to simulate that project first and then load through HOBBIES0221a.gid POST HOBBIES0221a.ral. Similarly, click the button and load the graph for HOBBIES0221b. Furthermore, change the range of the scattered fields to be between 0 and 11 from the Range tab and change the Resolution to be 11 to obtain the plot shown in Figure 8.34.

It is expected that one would obtain similar results for the RCS in the case of a metallic plate embedded inside a dielectric box, a metallic plate touching a dielectric box, and a metallic plate placed in the vicinity of the box, as the dielectric material is lossless. A significant difference is observed in the results when the plate is immersed in the dielectric.

Figure 8.34. Comparison of RCS for the three cases.

8.2.2.2 Scatterer Coated with a Lossy Dielectric Project: HOBBIES0222

A coated scatterer consists of one metallic surface touching or encased by a dielectric box made of a lossy material. The model is the same as in HOBBIES0221 {Figure 8.32 (a)}, with a different specification for the dielectric domain, as shown in Figure 8.35. The user can load the project HOBBIES0222 from the “infoexamples” folder under the HOBBIES installation folder.

Lossy dielectric: A regular surface of loss free dielectric scatters the incident wave from both sides of the surface. In addition, there is a reflection at the dielectric to the vacuum boundary surface. To eliminate the reflection at the boundary surface, we modify the dielectric to have the same characteristic impedance as of vacuum. For example, we choose ε_r = μ_r = 4 − j4. Also, we expect a part of the electromagnetic wave to be absorbed by the dielectric material, eliminating the reflection from one side of the surface.

Figure 8.35. Window displaying the list of Domains.

Results: To compare the result for project HOBBIES0222 and HOBBIES0221, the user needs to run both of them. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. To view the 2D RCS pattern, click the button. And click the button to add the result of project HOBBIES0221. Choose the Theta-cut option and select θ = 0° from the Data tab within the Left Panel and the user can obtain the view shown in Figure 8.36. The result shows that the presumption is correct. If we compare the RCS from a lossy material with that in HOBBIES0222, we see that it is decreased by more than 10 dB on one side of the surface.

Figure 8.36. Comparison of RCS for the coated surface both with and without loss.

8.2.2.3 Composite Prism-Shaped Scatterer Project: HOBBIES0223

A composite prism-shaped scatterer is made of a metallic prism and two dielectric prisms, as shown in Figure 8.37 (a). These two dielectric prisms are filled with different dielectric materials, which are specified in the domain list. The model is excited by a plane wave at 250 MHz using the Bistatic RCS mode. The user can load the project HOBBIES0223 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.38. Figure 8.38 (a) provides the domain list. Figure 8.38 (b) provides the node list, followed by the surface list in Figure 8.38 (c) and the wave list in Figure 8.38 (d). Finally, the frequency setting and the mode of operation information are described in Figures 8.38 (e) and (f).

Figure 8.37. A composite prism scatterer: (a) the scatterer model, (b) composite metallic and dielectric junction.

Figure 8.38. Information windows describing the model: (a) Domain list, (b) Node list, (c) Surface list, (d) Wave list, (e) Frequency window, (f) Operation mode window.

Composite metallic and dielectric junction: Two or more dielectric domains and the 0th domain can be interconnected through a common edge, as shown in Figure 8.37 (b). Such an edge is termed a composite metallic and dielectric junction. This junction is automatically determined by HOBBIES and does not have to be specified by the user.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the and button to view the electric current and the magnetic current distribution on the structure, respectively. The distribution of the electric and magnetic currents over a dielectric surface at the boundary surfaces of different domains determines the field distribution, as shown in Figures 8.39 (a) and (b), respectively. At the interconnection of two dielectrics and metal, the electric current is of high density, while the magnetic is very small.

Figure 8.39. A composite prism scatterer: (a) electric current over a dielectric surface, (b) magnetic current over a dielectric surface.

8.2.2.4 Dipole Antenna Protruding from a Dielectric Cube Project: HOBBIES0224

The model consists of a dielectric cube and a dipole antenna half immersed in the dielectric, as shown in Figure 8.40. The dipole is formed of two wires, and each wire has a length of 0.25 m and a radius of 25 mm. Each side of the cube has a length of 0.6 m. The model is excited by a generator at the interconnection of the wire and the top surface, and is simulated from 100 MHz to 400 MHz using the antenna mode. The relative dielectric constant is set to be ε_r = 4 (HOBBIES0224). As a comparison, in project HOBBIES0224a, the dielectric constant is set to be ε_r = 1. And in HOBBIES0224b, the dielectric is removed and only the dipole antenna is left in air. The user can load projects HOBBIES0224, HOBBIES0224a, and HOBBIES0224b from the “infoexamples” folder under the HOBBIES installation folder. The information of the model for project HOBBIES0224 is shown in Figure 8.41. Figure 8.41 (a) provides the domain list. Figure 8.41 (b) provides the node list, followed by the surface list in Figure 8.41 (c) and the wire list in Figure 8.41 (d). Finally, the junction information is described in Figure 8.41 (e).

Figure 8.40. A dipole antenna protruding from a dielectric cube.

Figure 8.41. Information windows describing the model: (a) Domain list, (b) Node list, (c) Surface list, (d) Wire list, (e) Junction list.

Wire inside, outside, and between dielectric bodies: Since the geometrical modeling is performed with surfaces, it is equally easy to model the wire near the dielectric object as it is to model a wire embedded in the dielectric object. In the first case, the wire is surrounded by the first domain (vacuum), while in the second case, it is surrounded by a specified dielectric domain. To move the wire from vacuum into the dielectric body or vice versa, it is enough to shift both the nodes of the wire and change the order number of the wire domain.

Wire protruding from the dielectric box: Wire protruding from a dielectric surface is modeled by two wires placed on the opposite sides of the dielectric surface, with a common node placed at the dielectric surface. The dielectric surface represents the boundary between two domains, and both wires are immersed in one of these two domains. The dielectric surface and wires create a nontrivial junction. The common node for these two wires must be specified in the Junction list.

Results: To compare the results for projects HOBBIES0224, HOBBIES0224a, and HOBBIES0224b, the user needs to run all of them. Go to the post-processing mode and click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component from the Data tab within the Left Panel. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Then change the parameter range to be between 0 and 18 from the Range tab and change the Resolution to be 9 to obtain a view as shown in Figure 8.42 (a). To compare the results for projects HOBBIES0224a and HOBBIES0224b, the user needs to run these two projects first. Then go to the post-processing window, and click the button to view the network parameters. Similarly, load the real part and the imaginary part of the Y parameter for project HOBBIES0224a. Then click the button to add the curve for project HOBBIES0224b through HOBBIES0224b.gid POST HOBBIES0224b.ral, and get the plot shown in Figure 8.42 (b).

For a cube, with ε_r = 1 (HOBBIES0224a), good agreement with results for the dipole antenna in HOBBIES0224b is observed, as shown in Figure 8.42 (b). Setting ε_r = 4 (HOBBIES0224), the dipole becomes electrically longer, and the second resonance appears in the frequency range, as shown in Figure 8.42 (a).

Figure 8.42. A dipole antenna protruding from a dielectric cube: (a) Y parameters of project HOBBIES0224, (b) comparison with the Y parameters for projects HOBBIES0224a and HOBBIES0224b.

8.2.2.5 Conducting Plate Protruding from a Dielectric Box Project: HOBBIES0225

A conducting plate protruding from a dielectric box is composed of the dielectric box and two metallic surfaces, as shown in Figure 8.43. The dielectric box has the size of 1.2 m by 2.4 m by 2.4 m, and the square plate has the side length of 2 m. The model is excited by a plane wave and is simulated at 150 MHz using the Monostatic RCS mode. In project HOBBIES0225, the relative dielectric constant is set to ε_r = 2 . As a comparison, in project HOBBIES0225a, the dielectric constant is set to ε_r = 1. And in HOBBIES0225b, the dielectric box is removed and only the metallic plate is left. The user can load projects HOBBIES0225, HOBBIES0225a, and HOBBIES0225b from the “infoexamples” folder under the HOBBIES installation folder. The information of the model for project HOBBIES0225 is shown in Figure 8.44. Figure 8.44 (a) provides the domain list. Figure 8.44 (b) provides the node list, followed by the surface list in Figure 8.44 (c) and the wave list in Figure 8.44 (d). The scattered field pattern setting is provided in Figure 8.44 (e). Finally, the frequency setting and the mode of operation information are described in Figures 8.44 (f) and (g).

Figure 8.43. A square conducting plate protruding from a dielectric box.

Figure 8.44. Information windows describing the model: (a) Domain list, (b) Node list, (c) Surface list, (d) Wave list, (e) window to input the pattern for the scattered fields window, (f) Frequency window, (g) Operation mode window.

Surface protruding from a dielectric surface: The surface protruding from a dielectric surface is modeled by two metallic surfaces placed on the opposite sides of the dielectric interface, and having a common edge placed at the dielectric interface. The dielectric interface represents a boundary surface between the two domains, and each of the two metallic plates is immersed in one of these domains.

Results: To compare the results for projects HOBBIES0225, HOBBIES0225a, and HOBBIES0225b, the user needs to run all of the projects. In the post-processing window, click the button to view the 3D RCS pattern. Choose the RCS parameter from the Data tab within the Left Panel, and the user can get the view shown in Figure 8.45 (a). Also, the user can click the button to view the 2D RCS pattern. Then click the button to add the result for project HOBBIES0225a. To load the results of project HOBBIES0225a, the user needs to simulate that project first and then load the file through HOBBIES0225a.gid POST HOBBIES0225a.ral. Similarly, the user can load the result of project HOBBIES0225b. Then, check the Group Mode checkbox within the Left Panel, which enables the user to change the parameters for all displayed graphs. Then choose the RCS (dB) parameter and select the ϕ = 0° cut-plane from the Data tab within the Left Panel, change the scattering pattern range to be between −30 and 15 dB, and change the Resolution to be 9 to obtain a view shown in Figure 8.45 (b).

The influence of the dielectric is visible in Figure 8.45 (b) as the RCS changes compared to the conducting plate without the dielectric box in HOBBIES0225b. In HOBBIES0225a, the permittivity of the dielectric is set to 1. If we compare results for the air dielectric with HOBBIES0225b, there is little noticeable difference, as shown in Figure 8.45 (b).

Figure 8.45. A square conducting plate protruding from a dielectric box: (a) 3D monostatic RCS of the scatterer, (b) comparison of the 2D RCS pattern for projects HOBBIES0225, HOBBIES0225a, and HOBBIES0225b.

8.3 LOADINGS

By default, wires and metallic surfaces are considered to be composed of perfect electric conductors. Real material properties of wires and metallic surfaces (e.g., having finite conductivity) can be taken into account by adding a distributed loading over the wires and the metallic surfaces. These loadings are defined in the Distributed loading list.

Lumped elements inserted at the junction of a wire with other wires or surfaces are modeled by concentrated loadings. These loadings are defined in the Concentrated loading list. The loading editing windows are opened from the menu HOBBIESLoadingsDistributed/Concentrated.

8.3.1 Distributed Loadings

8.3.1.1 Electrically Short Dipole Antenna Project: HOBBIES0311

The antenna shown in Figure 8.46 (a) is made of copper with a conductivity of σ = 57 MS/m. The material property is specified in the Skin tab of the Distributed Loading list window as shown in Figure 8.46 (b). The wire has a length of 0.25 m and a radius of 2.5 mm. And the model is simulated between 0.001 MHz and 60 MHz using the antenna mode. As a comparison, project HOBBIES0311a is the same dipole but without the loading. The user can load both projects HOBBIES0311 and HOBBIES0311a from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.47. Figure 8.47 (a) provides the node list, followed by the generator list in Figure 8.47 (b). The radiation pattern setting is provided in Figure 8.47 (c). Finally, the frequency and options setting information are described in Figures 8.47 (d) and (e).

Figure 8.46. A dipole antenna: (a) the antenna model, (b) skin tab of distributed loading list.

Figure 8.47. Information windows describing the model: (a) Node list, (b) Generator list, (c) Radiation pattern window, (d) Frequency window, (e) Options window.

In the general case, the radiation and loss resistance of a short dipole are analytically given by:

where l = 250 mm and is the length of a dipole arm. is the phase coefficient, and a = 2.5 mm is the wire radius. For these specific data, the resistances are:

Results: To compare the results for projects HOBBIES0311 and HOBBIES0311a, the user needs to run both models. Wait until the simulation is finished, and then go to the post-processing mode by clicking the button. Click the button to view the network parameters. Choose the Z(Imped.) parameter and the Real component from the Data tab within the Left Panel. And change the parameter range to be between 0 and 0.0035 and the Resolution to be 7 from the Range tab. Also change the Frequency range to be between 0 and 1, to obtain a view shown in Figure 8.48 (a).

To compare the gain over frequency for the two projects, the user needs to click the button. Then click the button to add the result for project HOBBIES0311a. To load the result file of project HOBBIES0311a, the user needs to simulate that project first and then load the file through folder HOBBIES0311a.gid POST HOBBIES0311a.ral. Change the radiation pattern range to be from −0.3 to 2.2 and the Resolution to be 5 from the Range tab. Also change the Frequency range to be between 0 and 1, to obtain a view shown in Figure 8.48 (b). Similarly, change the Frequency range to be between 1 and 60, to obtain a view shown in Figure 8.48 (c).

In Figure 8.48 (b), if there are no losses, we would expect a gain of 1.5, from project HOBBIES0311a. However, R_loss >> R_rad at low frequencies, and hence, the efficiency is very low, resulting in low values of the gain, as shown in Figure 8.48 (c).

Figure 8.48. An electrically short dipole antenna: (a) Z parameter of the antenna with losses, (b) comparison of gain over frequency of 0.001 MHz to 1 MHz for projects HOBBIES0311 with losses and HOBBIES0311a without losses, (c) comparison of gain over 1 MHz to 60 MHz band for projects HOBBIES0311 with losses and HOBBIES0311a without losses.

8.3.1.2 Dipole Antenna Inside a Dielectric Radome Project: HOBBIES0312

A dielectric radome (project HOBBIES0312) of permittivity ε_m = 4ε₀ and thickness δ = 20 mm is shown in Figure 8.49 (a). Inside it is a dipole antenna that is simulated from 230 MHz to 330 MHz using the antenna mode. The model has three symmetry planes for xOy-, xOz-, and yOz-planes and requires 674 unknowns. As a comparison, in HOBBIES0312a the dielectric ellipsoid is replaced with a single metallic ellipsoid with distributed loading, as shown in Figure 8.49 (b). The user can load both projects HOBBIES0312 and HOBBIES0312a from the “infoexamples” folder under the HOBBIES installation folder. The information about the model for project HOBBIES0312 is shown in Figure 8.50. Figure 8.50 (a) provides the node list. Figure 8.50 (b) provides the list of wires, followed by the list of surfaces in Figure 8.50 (c). Finally, the domain list is displayed in Figure 8.50 (d) and the generator list is in Figure 8.50 (e).

Figure 8.49. A dipole antenna inside a radome: (a) dielectric radome, (b) metallic radome with distributed loading.

Figure 8.50. Information windows describing the model: (a) Node list, (b) Wire list, (c) Surface list, (d) Domain list, (e) Generator list.

The surface impedance for the dielectric layer is given by Z_s = 1/[jω(ε_m − ε)δ] (see Table 6.2 in Section 6.5.1 in Chapter 6). Since the frequency range is relatively small (230–330 MHz), we can use a central frequency (280 MHz) in the above expression for Z_s. Then, we obtain Z_s = jX_s = −j1071 Ω. Select Srfc tab in the Distributed Loadings list window, and type −1071 in the X_s edit field, as shown in Figure 8.51. These data exist in project HOBBIES0312a.

Figure 8.51. Srfc tab of Distributed loadings list.

Results: To compare the results for projects HOBBIES0312 and HOBBIES0312a, the user needs to run both of them. Go to the post-processing and click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Then click the button to add the result for project HOBBIES0312a through HOBBIES0312a.gid POST HOBBIES0312a.ral. And change the parameter range to be between −5 and 20 and the Resolution to be 5 from the Range tab to obtain a view shown in Figure 8.52. If we compare the results, we observe good agreement between the results. The number of unknowns needed for HOBBIES0312a is only 94, compared to 674 for HOBBIES0312.

Figure 8.52. Comparison of Y parameter for projects HOBBIES0312 and HOBBIIS0312a.

8.3.1.3 Capacitively Loaded Dipole Antenna Project: HOBBIES0313

Capacitive loading is realized by inserting a dielectric rod of permittivity ε_m = 9ε₀, into each of the arms of the dipole, as shown in Figure 8.53 (a). Wires of radius a = 25 mm are modeled by cylindrical surfaces. The total length of the wire is 0.5 m. The model is excited by a generator located at the center of the wire and is simulated from 200 MHz to 800 MHz using the antenna mode. This model, given by project HOBBIES0313, requires 329 unknowns.

The same model can be made entirely of wires with distributed loadings added to wires 11 and 12, as shown in Figure 8.53 (b). Since thickness σ_m = 0, the surface impedance of the dielectric rod is Z_s = 2/[jω(ε_m − ε)a] (see Table 6.3 in Section 6.5.1 in Chapter 6). The user can load both projects HOBBIES0313 and HOBBIES0313a from the “infoexamples” folder under the HOBBIES installation folder. The information about the model for project HOBBIES0313 is shown in Figure 8.54. Figure 8.54 (a) provides the surface list. Figure 8.54 (b) provides the wire list, while Figure 8.54 (c) provides the domain list in. Finally, the junction list is given in Figure 8.54 (d) and the generator list is in Figure 8.54 (e).

Figure 8.53. A capacitively loaded dipole antenna: (a) the antenna model, (b) the antenna with distributed loadings.

Figure 8.54. Information windows describing the model: (a) Surface list, (b) Wire list, (c) Domain list, (e) Junction list (e) Generator list.

According to Eq. (6.4), Z_s is given by Z_s = 1/(jωC_s), with C_s = (ε_m − ε)a/2. In this case, C_s = 8.8542×10⁻¹³ F. This is inputted into the C_s edit field of the RLC tab, as shown in Figure 8.55. Configuration can be either Parallel or Series.

Figure 8.55. RLC tab of Distributed loading list.

Results: To compare the results for projects HOBBIES0313 and HOBBIES0313a, the user needs to run both of them. Go to the post-processing mode and click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Then click the button to add the result for project HOBBIES0313a. To load the results of project HOBBIES0313a, the user needs to simulate that project first and then load the file through folder HOBBIES0313a.gid POST HOBBIES0313a.ral. If we compare the results, we see the agreement between the two results, as shown in Figure 8.56. The number of unknowns needed for HOBBIES0313a is only 15, compared to 329 for HOBBIES0313.

Figure 8.56. Comparison of the Y parameter for projects HOBBIES0313 and project HOBBIES0313a.

8.3.2 Concentrated Loadings

A concentrated loading is an element inserted at the junction of a wire with other wires or surfaces. It is completely determined by the two nodes of the wire to which it is connected and by its value for the impedance. It is placed at the first of the two specified nodes. It can model lumped elements such as resistors, inductors, capacitors, or their combinations. A concentrated loading represents a special case of distributed loading, when the loading is distributed over a surface or length whose dimensions are much smaller than the wavelength.

8.3.2.1 Parallel Configuration of Two Impedances Project: HOBBIES0321

The model is generated by connecting two wire loops. The impedances Z₁ = (50 + j50) Ω and Z₂ = (50 − j50) Ω are realized as concentrated loadings connected to the wires and the circuit is excited by a voltage generator, as shown in Figure 8.57. The model is simulated from 0.1 MHz to 1 MHz using the antenna mode. The user can load the project HOBBIES0321 from the “infoexamples” folder under the HOBBIES installation folder. The information of the model for project HOBBIES0321 is shown in Figure 8.58. Figure 8.58 (a) provides the node list. Figure 8.58 (b) provides the wire list, followed by the generator list in Figure 8.58 (c). Finally, the frequency information is described in Figure 8.58 (d).

Figure 8.57. The circuit model of parallel configuration of two impedances.

Figure 8.58. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Frequency window.

The impedances are defined in the R + jX tab of the Concentrated loading list window (Figure 8.59). The impedance seen by the generator should be

Figure 8.59. R + jX tab of Concentrated loading list.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the network parameters. Choose the Z(Imped.) parameter and the Real component. Then click the button and choose the Z(Imped.) parameter and the Imag. component. Then change the parameter range to be between 0 and 60 and the Resolution to be 6 from the Range tab to obtain a view shown in Figure 8.60. It can be seen that the computed impedance deviates from the theoretical value as the frequency increases. This can be explained by the effects of the wires that connect the generator to the impedances. This can be eliminated by decreasing the length of connecting wires.

Figure 8.60. Equivalent Z parameter of the model.

8.3.2.2 Monopole Antenna over a PEC Plane Project: HOBBIES0322

A monopole antenna is set to operate at 300 MHz and with an input impedance matched to 50 Ω. A lumped capacitor of C = 1.5587 × 10⁻¹¹ F (Figure 8.62) in series with the antenna (used to match the input impedance to 50 Ω) is realized as a concentrated loading at the location of the generator as shown in Figure 8.61. The user can load the project HOBBIES0322 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.63. Figure 8.63 (a) provides the node list, followed by the wire list in Figure 8.63 (b). The generator list is provided in Figure 8.63 (c). Finally, the frequency and the symmetry information are described in Figures 8.63 (d) and (e).

Figure 8.61. A monopole antenna over a PEC plane.

Figure 8.62. RLC tab of the Concentrated loading list.

Figure 8.63. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Frequency window, (e) Symmetry window.

Results: Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. To view the S parameters, choose the S(Scat.-dB) parameter and the Real component from the Data tab within the Left Panel to get the view shown in Figure 8.64, where S₁₁ has the minimum value at 300 MHz.

Figure 8.64. S parameter of the antenna.

8.3.2.3 Resistor Project: HOBBIES0323

A resistor is modeled as a resistive cylindrical rod of conductivity σ = 63.66 S/m. The bases are covered with thin metallic layers, as shown in Figure 8.65 (a). The resistance is 50 Ω. It takes 100 unknowns for the analysis. As a comparison, in HOBBIES0323a, a resistor is modeled as a wire of equal radius with distributed loadings. The per-unit-length impedance of the wire is Z′ = 5kΩ/m, corresponding to a surface impedance of Z_s = 10 π Ω, according to Eq. (6.3). The model is shown in Figure 8.65 (b) and requires eight unknowns for the analysis. Loadings are specified in the Srfc tab of the Distributed loading list window (open from the menu HOBBIESLoadingDistributed), as shown in Figure 8.66. The user can load both projects HOBBIES0323 and HOBBIES0323a from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.67. Figures 8.67 (a), (b), and (c) provide the node list, surface list and wire list, respectively. The junction list is provided in Figure 8.67 (d) and the generator list is described in Figure 8.67 (e). Finally, the domain list and the frequency information are provided in Figures 8.67 (f) and (g).

Another way of modeling a resistor of 50 Ω is by using concentrated loadings. Open project HOBBIES0323b. One can see that the resistor is replaced by a short wire with concentrated loadings placed between nodes 5 and 6, as shown in Figure 8.68. Loadings are specified in the R + jX tab of the Concentrated loading list window (the menu to open this window is HOBBIESLoading Concentrated), as shown in Figure 8.69. This model requires eight unknowns for the analysis. The user can load the project HOBBIES0323b from the “infoexamples” folder under the HOBBIES installation folder.

Figure 8.65. A resistor: (a) a resistive cylindrical rod, (b) a wire of equal radius with distributed loadings.

Figure 8.66. Srfc tab of the Distributed loading list.

Figure 8.67. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wire list, (d) Junction list, (e) Generator list, (f) Domain list, (g) Frequency window.

Figure 8.68. A resistive cylindrical rod.

Figure 8.69. R + jX tab of Concentrated loading list.

Results: To compare the results for projects HOBBIES0323, HOBBIES0323a, and HOBBIES0323b, the user needs to run all of them. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. Click the button to view the network parameters. Choose the Z(Imped.) parameter and the Real component. Then click the button and choose the Z(Imped.) parameter and the Imag. component. Then click the button to add the result of project HOBBIES0323a through HOBBIES0323a.gid POST HOBBIES0323a.ral. Similarly, the user can load the result of HOBBIES0323b. And change the parameter range to be between 0 and 800 and the Resolution to be 5 from the Range tab to obtain a view shown in Figure 8.70.

It is seen that the results from HOBBIES0323 and HOBBIES0323a practically coincide. However, there is a slight difference in the results for HOBBIES0323b at higher frequencies, as shown in Figure 8.70.

Figure 8.70. Comparison of the Z parameter for projects HOBBIES0323, HOBBIES0323a, and HOBBIES0323b.

8.4 USE OF SYMMETRY IN THE ANALYSIS OF A PROBLEM

In this section, several structures are analyzed based on the application of a symmetry plane. The main advantage of this method is to reduce the number of unknowns so as to shorten the overall computation time.

8.4.1 Dipole Antenna (xOy Anti-Symmetry) Project: HOBBIES0410

The analysis of a linear dipole antenna (project HOBBIES0112) has been introduced in Section 8.1. This dipole antenna has a total length of 0.5 m and a radius of 25 mm. In this section, a simulation for the same dipole antenna using the feature of symmetry is introduced. The antenna is oriented along the z-axis and symmetrical with respect to the xOy-plane. When symmetry is considered, the dipole antenna only needs to be 0.25 m long (i.e., half of its original length), while the other half is given by the symmetry. It is anticipated that the number of unknowns and the simulation time can be significantly reduced. In addition, various kinds of symmetries in the excitation source or the property of the symmetry plane can be defined. These options include Anti-Symmetry, Symmetry, PEC, and PMC as illustrated in Figure 8.71. Anti-symmetry and Symmetry is used to set the excitation anti-symmetrical or symmetrical with respect to the coordinate plane (i.e., the xOy-plane is used as a reference in this example). PEC and PMC refer to the use of a perfect electric conductor or a perfect magnetic conductor symmetry plane, respectively.

Figure 8.71. A dipole antenna: (a) xOy anti-symmetry, (b) xOy symmetry, (c) xOy PEC, (d) xOy PMC (note that the xOy plane has a different color depending on the menu).

The symmetry option can be set in the pull-down menu HOBBIES, and the Anti-Symmetry option for the xOy-plane is first chosen. In this example, both the current distribution and the far-field radiation are analyzed from 100 MHz to 400 MHz. The generator is a voltage source (type = 4) with an amplitude of 1.0 V. The details of the antenna model information and simulation parameter settings can be seen in Figure 8.72. Figure 8.72 (a) provides the node list, followed by the wire list in Figure 8.72 (b). The generator list is described in Figure 8.72 (c). The symmetry plane and the frequency information are shown in Figures 8.72 (d) and (e). Finally, the current distribution setting and the radiation pattern setting are plotted in Figures 8.72 (f) and (g).

Users can load the project HOBBIES0410 from the “infoexamples” folder under the HOBBIES installation path for the dipole antenna under consideration, which is Anti-Symmetrical with respect to the xOy-plane. Furthermore the same dipole antenna with xOy Symmetry, xOy PEC, or xOy PMC parameter is analyzed in the project HOBBIES0410a, HOBBIES0410b, and HOBBIES0410c, respectively. The model of these four projects are shown in Figures 8.71(a)-(d) and their respective xOy planes is shown in different colors for illustrating the use of different types of symmetry options.

Figure 8.72. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Symmetry window, (e) Frequency window, (f) Current window, (g) Radiation pattern window.

Results: To compare the results for projects HOBBIES0410, HOBBIES0410a, HOBBIES0410b, and HOBBIES0410c, the user needs to run all of them. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. In the post-processing window, click the button to view the current distribution on the dipole. The current distribution at 100 MHz under a setting of Anti-Symmetry is given in Figure 8.73 (a), while that of Symmetry is shown in Figure 8.73 (b). In addition, these four simulations are compared with the analysis of only the dipole antenna that is modeled without using any symmetry, project HOBBIES0112. Comparisons in admittance and gain (in unnamed units) are shown in Figures 8.73 (c) and (d).

For project HOBBIES0410, click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Then click the button to load the result of the other four projects to get the view shown in Figure 8.73 (c). Then click the button to view the variation of the gain with frequency. Also, load the results of all five projects for comparison to get the view shown in Figure 8.73 (d).

It can be found that the Anti-Symmetry case (HOBBIES0410) generates similar results for both the admittance and the gain, but the value of the current is doubled with respect to the dipole-only case (HOBBIES0112). However, when the Symmetry (HOBBIES0410a) or PMC (HOBBIES0410c) option is used, one obtains a zero current distribution, admittance, and gain. This is because when a generator is placed in a symmetric fashion, the effect of the generator and its image generated by the symmetry plane cancel result in a zero current distribution. When a PEC symmetry plane is used (HOBBIES0410b), the current distribution, admittance, and gain (in unnamed units) are all doubled with respect to the original dipole antenna (no symmetry). From this example, one can observe that the total computation time can be significantly reduced when a symmetry option is used.

Figure 8.73. A dipole antenna: (a) electric current distribution for project HOBBIES0410, (b) electric current distribution for project HOBBIES0410a, (c) comparison of the Y parameter, (d) comparison of gain.

8.4.2 Dipole Antenna (xOy Symmetry) Project: HOBBIES0420

A dipole antenna with a length of 0.25 m and a radius of 25 mm is oriented along the y-axis and various symmetry options with respect to the xOy plane are studied. The Symmetry option for the XY plane is chosen first. In this example, both the current distribution and the far-field radiation from this antenna are analyzed from 100 MHz to 400 MHz. The generator is a coaxial transverse electromagnetic (TEM) frill excitation (type = 2) with 1.0 V amplitude, with a 25-mm inner radius and a 75-mm outer radius.

Users can load the project HOBBIES0420 from the “infoexamples” folder under the HOBBIES installation path for the above dipole antenna with xOy Symmetry. Also the same dipole antenna using a PMC symmetry plane is analyzed in the project HOBBIES0420a. The model used for these two projects are shown in Figures 8.74 (a) and (b), different symmetry options are represented by different colors of the xOy-plane. The details of the antenna model and the parameters related with the simulation are shown in Figure 8.75. Figure 8.75 (a) provides the node list, followed by the wire list in Figure 8.75 (b). The generator list is given in Figure 8.75 (c). The symmetry plane and the frequency information are presented in Figures 8.75 (d) and (e). Finally, the current distribution and the radiation pattern settings are shown in Figures 8.75 (f) and (g).

Figure 8.74. A dipole antenna: (a) xOy- a plane of symmetry, (b) xOy- a PMC plane.

Figure 8.75. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Symmetry window, (e) Frequency window, (f) Current window, (g) Radiation pattern window.

Results: To compare the results of the projects HOBBIES0420 and HOBBIES0420a, the user needs to run both of them. Go to the post-processing and click the button to view the current distribution on the dipole. The current distribution at 100 MHz under a setting of Symmetry is given in Figure 8.76 (a), while that of using a PMC is shown in Figure 8.76 (b). In addition, comparisons of the two simulations in terms of admittance and gain (in unnamed units) are shown in Figures 8.76 (c) and (d).

For project HOBBIES0420, click the button to view the network parameters. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Then click the button to load the result of project HOBBIES0420a to get the view shown in Figure 8.76 (c). Click the button to view how the gain varies with frequency. By loading the results of both projects for comparison, one can obtain the display shown in Figure 8.76 (d).

It is found that the current distributions for the cases (Symmetry and PMC) are equal; however, their admittances and gains are quite different. The admittance of the PMC case is half of that of the Symmetry case, whereas the gain is doubled. Using the Anti-Symmetry or PEC symmetry plane does not yield reasonable results because the newly created (image) elements annul the effect of the existing elements.

Figure 8.76. A dipole antenna: (a) electric current distribution for project HOBBIES0420, (b) electric current distribution for project HOBBIES0420a, (c) comparison of the Y parameters, (d) comparison of the gain.

8.4.3 Dipole Antenna with a Corner Reflector (yOz Anti-Symmetry, xOz Symmetry) Project: HOBBIES0430

This example illustrates the use of a symmetry and an anti-symmetry plane using a dipole antenna with a corner reflector. The use of symmetry allows only a quarter of the structure to be modeled rather than the whole, and it is called the quarter model. The quarter model using the symmetry planes is illustrated in Figure 8.77 (a).

To model the dipole antenna, the user can simply create a wire of length 0.25 m and a radius of 25 mm aligned along the x-axis. A rectangular PEC plate will serve as a quarter of the corner reflector. To create this rectangular surface, one can first create the nodes (1, 1, 0), (0, 1, 0), (1, 0, -0.5), and (0, 0, −0.5) and then connect them together. Based on this quarter of the reflector, a user can obtain the full reflector structure using symmetry. By introducing Anti-Symmetry and Symmetry with respect to the YZ- and XZ-planes, respectively, to this quarter of a reflector, the full model of the corner reflector can be created. In this example, the radiation from this structure is analyzed at 200 MHz. The generator is a voltage source (type = 4) with amplitude of 1.0 V. The details of the model and the parameters associated with this simulation can be seen in Figure 8.78. Figure 8.78 (a) provides the node list, followed by the wire list in Figure 8.78 (b). The generator list is in Figure 8.78 (c), and the surface list is in Figure 8.78 (d). The symmetry plane and the frequency information are described in Figures 8.78 (e) and (f). Finally, the far-field radiation pattern setting is shown in Figure 8.78 (g).

Users can model the reflector using half of its structure and using Anti-Symmetry with respect to the yOz-plane. This is called the half model and is defined by the project HOBBIES0430a. And project HOBBIES0430b is the half structure configuration using the xOz symmetry. These two structures are shown in Figures 8.77 (b) and (c). Users can load projects HOBBIES0430, HOBBIES0430a, and HOBBIES0430b from the “infoexamples” folder under the HOBBIES installation path.

Figure 8.77. A dipole antenna using: (a) yOz anti-symmetry and xOz symmetry, (b) yOz anti-symmetry, (c) xOz symmetry.

Figure 8.78. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Surface list, (e) Symmetry window, (f) Frequency window, (g) Radiation pattern data window.

Results: To compare the results for projects HOBBIES0430, HOBBIES0430a, and HOBBIES0430b, the user needs to run all of them. Go to the post-processing and click the button to view the 2D radiation pattern. Choose the Gain parameter along the ϕ = 0° cut-plane. Then click the button to load the results of project HOBBIES0430a and HOBBIES0430b, as shown in Figure 8.79.

It is shown that one can obtain the same radiation pattern using different symmetry schemes. Moreover, the quarter model in HOBBIES430 contains 47 unknowns, while the half model in HOBBIESS430a has 97 unknowns. Hence, use of symmetry can be used to simplify the modeling and it can also reduce the number of unknowns and therefore the computation time.

Figure 8.79. Comparison of gain for three cases.

8.4.4 Linear Antenna Array (xOz Symmetry) Project: H0BBIES0440

A linear antenna array of two dipoles, each having a length of 0.5 m and a radius of 25 mm and placed vertically on the YZ-plane, is considered. Their radiation-properties are studied by using various symmetry options with respect to the XZ-plane.

To generate the model for this structure, users can simply create two wires with the same specified length and radius. The option Symmetry is chosen with respect to the XZ-plane. In this example, both the current distribution and the radiation from this antenna array are analyzed from 240 MHz to 260 MHz. Each dipole is excited by a voltage source (type = 4) with an amplitude of 1.0 V.

Project HOBBIES0440 is the same linear antenna array with the xOz Symmetry setting, while project HOBBIES0440a is the same array but using a PMC symmetry plane. The models of these two projects are shown in Figures 8.80 (a) and (b). The difference for the symmetry options are illustrated by the color coding of the xOz-plane. Users can load both projects HOBBIES0440 and HOBBIES0440a from the “infoexamples” folder under the HOBBIES installation path. The details of the antenna model and the parameters for the simulation can be seen in Figure 8.81. Figure 8.81 (a) provides the node list, followed by the wire list and the generator list in Figures 8.81 (b) and (c). The mode of operation and the symmetry plane information are described in Figures 8.81 (d) and (e). Finally, the current display and the radiation pattern information are given in Figures 8.81 (f) and ((g). Note that the antenna operation mode is set to the All generators mode. HOBBIES does not image port excitations that are not on the symmetry plane, such as generator 2 in Figure 8.80, and it is not possible to use the operation mode of One generator at a time.

Figure 8.80. A linear antenna array using: (a) xOz symmetry, (b) xOz PMC plane.

Figure 8.81. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Operation mode window, (e) Symmetry window, (f) Current window, (g) Radiation pattern window.

Results: To compare the results for projects HOBBIES0440 and HOBBIES0440a, the user needs to run all of them. Go to the post-processing mode and click the button to view the current distribution on the dipole array. The current distribution at 240 MHz under a setting of Symmetry for the xOz-plane is given in Figure 8.82 (a), while that of using a PMC plane is shown in Figure 8.82 (b). The comparisons of admittance and gain are shown in Figures 8.82 (c) and (d).

For project HOBBIES0440, click the button to view the variation of gain with frequency. Then click the button to load the result for project HOBBIES0440a. Check the Group Mode checkbox and choose the direction of ϕ = 180°, θ = 0°, to get the view shown in Figure 8.82 (c).

To view the network parameters, click the button. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Similarly, click the button again to load the Mag. component. Then click the button to load the result for project HOBBIES0440a, to get the view shown in Figure 8.82 (d).

As observed, the current distributions obtained using the Symmetry plane (HOBBIES0440) and the PMC plane (HOBBIES0440a) are equal. The gain for the PMC case is doubled, while the magnitude of the admittance is halved. Note that the same results can be obtained using the full model without using any symmetry planes.

Figure 8.82. A linear antenna array: (a) electric current distribution for project HOBBIES0440, (b) electric current distribution for project HOBBIES0440a, (c) comparison of gain, (d) comparison of the Y parameter.

8.4.5 Linear Array Antenna (xOy Anti-symmetry) Project: HOBBIES0450

A one-dimensional linear array of three identical dipoles is studied. The antennas of this array are placed vertically in the XY-plane separated by a distance of 0.25 m. Each antenna has a length of 0.5 m and a radius of 25 mm. The symmetry with respect to the XY-plane and the options xOy Anti-Symmetry and xOy PEC will be used in this section.

In this example, both the current distribution and the radiation from this antenna are analyzed from 240 MHz to 260 MHz. Each dipole is fed with a generator that is a voltage source (type = 4) with an amplitude of 1.0 V. The operation mode should be selected as the Antenna (One generator at a time). The imaging of ports situated in the symmetry plane is possible, with the setting xOy Anti-Symmetry, as shown in Figure 8.83 (a). Also, the same array antenna with a setting of the xOy PEC symmetry plane is given in the project HOBBIES0450a, as shown in Figure 8.83 (b). The difference in the symmetry options is illustrated by the color of the xOy-plane.

The details of the antenna model and the information about the parameters of the simulation are described in Figure 8.84. Figure 8.84 (a) provides the node list, followed by the wire list in Figure 8.84 (b). The generator list is in Figure 8.84 (c). The mode of operation and the symmetry plane information are described in Figures 8.84 (d) and (e). Finally, the current display and the radiation pattern information are given in Figures 8.84 (f) and (g). Users can load projects HOBBIES0450 and HOBBIES0450a from the “infoexamples” folder under the HOBBIES installation path.

Figure 8.83. A linear antenna array using: (a) xOy-plane as an anti-symmetry plane, (b) xOy as a PEC plane.

Figure 8.84. Information windows describing the model: (a) Node list, (b) Wire list, (c) Generator list, (d) Operation mode window, (e) Symmetry window, (f) Current window, (g) Radiation pattern window.

Results: To compare the results for projects HOBBIES0450 and HOBBIES0450a, the user needs to run all of them. Go to the post-processing mode and click the button to view the current distribution on the dipole array. The current distribution at 240 MHz under a setting of Anti-Symmetry is given in Figure 8.85 (a), while that for a PEC plane is shown in Figure 8.85 (b). Comparisons in admittance and gain (in unnamed units) are shown in Figures 8.85 (c) and (d).

To view the network parameters, click the button. Choose the Y(Admit.) parameter and the Real component. Then click the button and choose the Y(Admit.) parameter and the Imag. component. Similarly, click the button again to load the Mag. component. Then click the button to load the result for project HOBBIES0450a, to get the view shown in Figure 8.85 (c).

For project HOBBIES0450, click the button to view the variation of gain with frequency. Then click the button to load the result for project HOBBIES0450a. Check the Group Mode checkbox and choose the direction of ϕ = 180°, θ = 0°, to get the view shown in Figure 8.85 (d).

It is found that current distributions for the cases (Anti-Symmetry and PEC) are equal; however, their admittance and gain are different. The admittance and gain for the Anti-Symmetric case is one half of that of the PEC case. Note that the same results of HOBBIES0450 can be obtained when the full model without symmetry planes is used and under the operation mode of One generator at a time.

Figure 8.85. A linear antenna array: (a) electric current distribution for project HOBBIES0450, (b) electric current distribution for project HOBBIES0450a, (c) comparison of the Y parameter, (d) comparison of gain.

8.4.6 Corner Reflector (xOz Symmetry) Project: HOBBIES0460

A corner reflector consists of two rectangular plates acting as a scatterer. The common edge of the two plates is oriented along the z-axis. The scatterer model is created by first generating a rectangular surface inclined with the xOz-plane, and the other surface is given by using symmetry (called the half model). The symmetry options Symmetry, Anti-Symmetric, PEC, and PMC with respect to the xOz-plane are studied in this example.

The scatterer plate has the size of 1 m by 2 m. The option Symmetry for the xOz-plane is first chosen. In this example, the bistatic RCS of this corner reflector is analyzed at 100 MHz, given an incident θ –polarized wave (situated in the symmetry plane) with 1 V/m amplitude. The details of the scatterer model and the parameters for the simulation are displayed in Figure 8.87. Figure 8.87 (a) provides the node list, followed by the surface list in Figure 8.87 (b). The wave list is provided in Figure 8.87 (c) and the scattering pattern setting is shown in Figure 8.87 (d). Finally, the mode of operation and the symmetry information are described in Figures 8.87 (e) and (f).

When symmetry is not used, both rectangular plates are required to create the scatterer model (called the full model) and with the setting of No Symmetry. The details of the information about the model are shown in Figure 8.88. The symmetry information is provided in Figure 8.88 (a). Figure 8.88 (b) provides the node list, followed by the surface list in Figure 8.88 (c). The same structure with a setting of xOz Symmetry, xOz PMC, xOz Anti-Symmetry, xOz PEC, and No Symmetry are given in projects HOBBIES0460, HOBBIES0460a, HOBBIES0460b, HOBBIES0460c, and HOBBIES0460d, respectively. The structures for these five projects are shown in Figures 8.86 (a)–(e), and the difference in the symmetry options are illustrated by the color of the xOz-planes. Users can load these projects from the “infoexamples” folder under the HOBBIES installation path.

Figure 8.86. A corner reflector using: (a) xOz symmetry, (b) xOz PMC, (c) xOz anti-symmetry, (d) xOz PEC, (e) no symmetry.

Figure 8.87. Information windows describing the model: (a) Node list, (b) Surface list, (c) Wave list, (d) Scattering pattern window, (e) Operation mode window, (f) Symmetry window.

Figure 8.88. Information windows describing the model: (a) Symmetry window, (b) Node list, (c) Surface list.

Results: To compare the results for all five projects, users first need to run all of them. For project HOBBIES0460, click the button to view the 2D RCS pattern. Then click the button to load the result of all the projects, HOBBIES0460a, HOBBIES0460b, HOBBIES0460c, and HOBBIES0460d. Check the Group Mode checkbox and choose ϕ = 0° cut-plane, to get the view shown in Figure 8.89. Compared with the No Symmetry plane case (HOBBIES0460d), the RCS in dB for the Symmetry case (HOBBIES0460) is equal but that of the PMC plane case (HOBBIES0460a) is increased by 6 dB. For the Anti-Symmetry plane case (HOBBIES0460b) and the PEC plane case (HOBBIES0460c), symmetrical incident wave and images of the incident wave are respectively used to annul the excitation of the original wave, resulting in zero gain. The results for Scatterer (monostatic RCS) are the same as for Scatterer (bistatic RCS) if the incident wave is located in a symmetry plane as shown in Figure 8.86 (a). Otherwise, the scatterer is excited by two waves.

Figure 8.89. Comparison of RCS for the different cases.

8.4.7 Corner Reflector (xOz Anti-Symmetry) Project: HOBBIES0470

The same corner reflector of Section 8.4.6 is assumed. In this example, the bistatic RCS of this corner reflector is analyzed at 100 MHz, given an incident ϕ –polarized wave (orthogonal to the symmetry plane) with 1 V/m amplitude. The symmetry options Anti-symmetry and PEC with respect to the xOz-plane are studied. The scatterer model and the simulation parameters are almost the same as that in Section 8.4.6, except the setting of the incident wave.

The corner reflector with xOz Anti-Symmetry, PEC, and No Symmetry setting are given in projects HOBBIES0470, HOBBIES0470a, and HOBBIES0470b, respectively. The details of the setting for project HOBBIES0470 are seen in Figure 8.91. Figure 8.91 (a) provides the symmetry information, followed by the wave list in Figure 8.91 (b). When symmetry is not used, both rectangular surfaces are required to generate the scatterer model (called the full model). The information about the details of the full model and the information about the symmetry is seen in Figure 8.92. Figure 8.92 (a) provides the symmetry information. Figure 8.92 (b) provides the node list, followed by the surface list in Figure 8.92 (c). The models for the three projects are shown in Figures 8.90 (a)–(c), the difference in the symmetry options are illustrated by the color of the xOz-plane. Users can load all three projects from the “infoexamples” folder under the HOBBIES installation path.

Figure 8.90. A corner reflector using: (a) xOz anti-symmetry, (b) xOz PEC, (c) no symmetry.

Figure 8.91. Information windows describing the model: (a) Symmetry window, (b) Excitation Wave list.

Figure 8.92. Information windows describing the model: (a) Symmetry window, (b) Node list, (c) Surface list.

Results: To compare the results of all three projects, first the user needs to run all of them. For project HOBBIES0470, click the button to view the 2D RCS pattern. Then click the button to load the result for projects HOBBIES0470a and HOBBIES0470b. Check the Group Mode checkbox and choose the ϕ = 0° cut-plane, to get the view shown in Figure 8.93.

It is found that the RCS (in dB) for the Anti-Symmetry plane is equal to that of the full model, whereas for the PEC plane case, it is increased by 6 dB when compared with the full model.

Figure 8.93. Comparison of RCS for the different cases.

8.5 ANTENNA ABOVE A REAL GROUND

The real ground influences the properties of an antenna placed above it in two ways:

• It modifies the distribution of the currents along the antenna
• It modifies the radiation pattern of the antenna

The radiation pattern is modified not only because the original distribution of the current is modified, but also because the ground acts as a reflector. If the height of the antenna above the ground plane is greater than 0.1λ–0.25λ, the original current distribution does not change much. In that case, the radiation pattern is simply obtained starting from the original current distribution and calculating the sum of the direct and the reflected far field. This method will be presented in Section 8.5.1.

For the case when the height of the antenna above the ground plane is less than 0.1λ–0.25λ, the modified current distribution on the structure should be calculated first.

Usually, the evaluation of this modified current distribution is carried out using the classical Sommerfeld formulation [1-3]. In that case, the real ground is modeled as a half-space. However, only a part of the ground placed below the antenna significantly influences the antenna current distribution. So, a finite, truncated part of the ground is modeled in the present discussion. In HOBBIES, this finite ground is modeled as a dielectric layer with a finite size. Typically, the size of this finite ground should be at least five times the height of the total structure located on top of it. Under this condition, dominant currents reside on the upper surface of this finite dielectric plate and the weak currents underneath the plate can be neglected. Thus, only the upper surface of the dielectric plate makes the contribution and is modeled as an open dielectric surface in HOBBIES. The details are discussed in Section 8.5.2.

8.5.1 Influence of the Ground on the Radiation Pattern Project: HOBBIES0510

To take into account the influence of the ground on the radiation pattern, it is enough to specify that the 2nd domain has the parameters of a real ground, except that the conductivity is written with a minus sign. Note that the 2nd domain then is reserved for a real ground, if it exists.

Let us consider a monopole antenna mounted at the corner of a rectangular conducting plate, as shown in Figure 8.94. The data for this antenna exist in the project HOBBIES0510. The wire is 1.85 m long, and the radius is 18.5 mm. The plate has a size of 2.3 m by 1.3 m. The plate is situated above a real ground at a height of 1.5 m. The antenna operates in the frequency range from 30 MHz to 100 MHz. As a comparison, project HOBBIES0510a is the same model but without the setting of the 2nd domain as the ground. The user can load both projects HOBBIES0510 and HOBBIES0510a from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.95. Figure 8.95 (a) provides the node list, followed by the wire list in Figure 8.95 (b) and the junction list in Figure 8.95 (c). The domain list is provided in Figure 8.95 (d) and the generator list in Figure 8.95 (e). Finally, the information about the frequency and the radiation pattern are presented in Figures 8.95 (f) and (g).

Figure 8.94. A monopole antenna connected to a conducting plate over the ground.

Figure 8.95. Information windows describing the model: (a) Node list, (b) Wire list, (c) Junction list, (d) Domain list, (e) Generator list, (f) Frequency window, (g) Radiation pattern window.

The electrical parameters of the ground are ε_r = 12, μ_r = 1, and σ =0.001S/m. To take into account the influence of the ground into the radiation pattern of the antenna, it is enough to specify the parameters of the 2nd domain in the Domains table as Re{ε_r} = 12, Im{ε_r} = 0, Re{μ_r} = 1, Im{μ_r} = 0, and σ = −0.001 S/m. The conductivity is written with a negative sign “−”, indicating that the HOBBIES model has a real ground and so care should be taken in the evaluation of the radiation pattern. It is assumed that a real ground fills the lower half-space (i.e., for all space z ≤ 0), and so the reflection coefficient method can be used to evaluate the radiation patterns using a positive value for the ground conductivity.

Results: The computations of the gain (dB) for the horizontal and vertical far-field components at 30 MHz are given in Figure 8.96. To compare the results for projects HOBBIES0510 and HOBBIES0510a, the user needs to run both of them. In the post-processing window, click the button to view the 2D radiation pattern. Then click the button to add the result of project HOBBIES0510a. To load the result file of project HOBBIES0510a, the user needs to simulate that project first and then load through HOBBIES0510a.gid POST HOBBIES0510a.ral. Check the Group Mode checkbox within the Left Panel, which enables the user to change the parameters for all displayed graphs. Then choose the Gain (dB) parameter and the E-Theta component by selecting the Theta-cut plane. Change the Radiation Pattern Range to be between −40 and 0 and the Resolution to be 8 from the Range tab to obtain a view, shown similar to Figure 8.96 (a) (the result for the Sommerfeld formulation is taken from the references and not included in this code).

Similarly, choose the E-Phi component, and change the Radiation Pattern Range to be between −70 and 0 and the Resolution to be 7 from the Range tab to obtain a view, similar to Figure 8.96 (b).

At this frequency, the plate is situated 0.15λ above the ground. It is clearly seen that the results from HOBBIES (HOBBIES0510) taking the effect of the real ground only in the calculation of the far-field agree well with those calculated using the more accurate Sommerfeld formulation. If the effect of ground is not considered (HOBBIES0510a), then the results from HOBBIES are markedly different from the others.

8.5.2 Influence of the Ground on the Current Distribution Project: HOBBIES0520

When the antenna structure is close to the ground plane, then one cannot assume, as done in the previous section, that the current distribution will not be affected by the ground. In this situation, the sign “−” used in the specification of the conductivity for the 2nd domain indicates to HOBBIES that all objects with nonpositive z-coordinates:

• Will be taken into account for the evaluation of the current distribution of the antenna structure
• Will not be taken into account for the evaluation of the radiation pattern

Figure 8.96. Gain (dB) of the monopole antenna: (a) vertical component, (b) horizontal component.

In this case, the ground is modeled as a finite dielectric plate, as shown in Figure 8.97. A good rule of thumb, is that the size of the dielectric plate should extend approximately five times the height in all directions away from the projection of the antenna structure to the dielectric ground. Two different models for the grounds are possible for the ground model, as shown in Figure 8.98. Project HOBBIES0520 applies the modeling of the ground as shown in Figure 8.98 (a).

The user can load the project HOBBIES0520 from the “infoexamples” folder under the HOBBIES installation folder. The information about the model is shown in Figure 8.99. Figure 8.99 (a) provides the node list, followed by the wire list in Figure 8.99 (b) and the surface list in Figure 8.99 (c). The junction list and the domain list are shown in Figures 8.99 (d) and (e). The generator list is given in Figure 8.99 (f). Finally, the frequency and the information about the radiation pattern are described in Figures 8.99 (g) and (h).

Figure 8.97. A monopole antenna connected to a metal plate located over a finite ground.

Figure 8.98. Two finite dielectric plates modeling ground: (a) GROUND_1, (b) GROUND_2.

Figure 8.99. Information windows describing the model: (a) Node list, (b) Wire list, (c) Surface list, (d) Junction list, (e) Domain list, (f) Generator list, (g) Frequency window, (h) Radiation pattern window.

Results: Load the project HOBBIES0520. Click the Run button , and wait until the simulation is finished. Go to the post-processing mode by clicking the button. The computed results for HOBBIES0520 are compared with those for HOBBIES0510 along with the results generated using the more accurate Sommerfeld formulation, as displayed in Figure 8.100. (To compare the results for projects HOBBIES0520 and HOBBIES0510, the user needs to run both of them. For project HOBBIES0510, please read Section 8.5.1.)

In the post-processing window, click the button to view the 2D radiation pattern. Then click the button to load the file through folder HOBBIES0510.gid POST HOBBIES0510.ral. Check the Group Mode checkbox within the Left Panel, which enables the user to change the parameters for all the displayed graphs. Then choose the Gain (dB) parameter. Also choose to display the Theta-cut plane. Change the Radiation Pattern Range to be between −36 and −31 from the Range tab to obtain a view similar to Figure 8.100 (the results for the Sommerfeld formulation are taken from the references).

The result for HOBBIES0520 is more accurate than that for HOBBIES0510 for most far-field angles, because the influence of the ground on the antenna structure is taken into account more accurately in HOBBIES0520. However, the number of unknowns for HOBBIES0520 is much more than that for HOBBIES0510, because of the finite dielectric ground plate introduced and generates a large number of unknowns. This methodology can also be used when the height of the antenna above the ground plane is greater than 0.1λ–0.25λ, but the improvement in the radiation pattern is insignificant for most cases.

Figure 8.100. Total gain (dB) of the monopole antenna with different ground modeling.

8.6 USE OF IMAGING FOR GENERATING AN ACCURATE SOLUTION

In this section, we illustrate how the accuracy of the analysis of a microstrip patch array is improved by using a special type of meshing through the use imaging.

8.6.1 Analysis of a Microstrip Patch Array Project: HOBBIES0600

Suppose a small plate is placed very close to a large plate, as shown in Figure 8.101 (a). The small plate strongly affects the current distribution on the large plate placed just below the small plate. Divide the large plate into subplates, so that a fast variation of the current distribution over the large plate can be properly taken into account. The first of these subplates corresponds to the projection of the small plate onto the large plate (i.e., the first subplate represents the image of the small plate), as shown in Figure 8.101 (b). This procedure is called imaging. This technique can be applied to improve the quality of the analysis for microstrip structures and other classes of structures, such as those described in Section 8.5.2.

Figure 8.101. A small plate above a large plate: (a) the original model, (b) imaging the small plate onto the large plate to generate a mesh.

EXAMPLE: A 2 × 2 patch antenna defined by the HOBBIES0600 project is shown in Figure 8.102. The ground plane of this structure is given in Figure 8.103 (a). In addition, the ground plane is modeled using the image of the conducting strips, as shown in Figure 8.103 (b). The model with an imaged mesh exists in the project HOBBIES0600a. The substrate is also subdivided according to the patch size of the upper plate. For each patch, the substrate plate has the size of 30 mm by 30 mm with a thickness of 0.8 mm. And the metallic patch is of 14 mm by 9.6 mm with a zero thickness. The permittivity of the dielectric substrate is 4.34. Each patch is excited by a thin wire that connects the patch and the ground. The radius of the wire is 0.04 mm. The complete model is simulated at 4.97 GHz using the All Generators mode option.

Users can load both projects HOBBIES0600 and HOBBIES0600a from the “infoexamples” folder under the HOBBIES installation folder. The model information for project HOBBIES0600 is shown in Figure 8.104. Figure 8.104 (a) provides the node list, followed by the wire list in Figure 8.104 (b) and the surface list in Figure 8.104 (c). The junction list is provided in Figure 8.104 (d) and the generator list in Figure 8.104 (e). Finally, the operation mode setting and the frequency setting information are described in Figures 8.104 (f) and (g).

Figure 8.102. A microstrip patch antenna array: (a) perspective view, (b) top view.

Figure 8.103. Bottom view of the microstrip patch array: (a) meshing without imaging, (b) meshing with imaging.

Figure 8.104. Information windows describing the model: (a) Node list, (b) Wire list, (c) Surface list, (d) Junction list, (e) Generator list, (f) Operations mode window, (g) Frequency window.

Results: To compare the results of project HOBBIES0600 and HOBBIES0600a, users need to run both of them. In the post-processing window, click the button to view the 2D radiation pattern. Then click the button to add the result of project HOBBIES0600a. To load the result of project HOBBIES0600a, users need to simulate that project first and then load it through HOBBIES0600a.gid POST HOBBIES0600a.ral. Check the Group Mode checkbox within the Left Panel, which enables users to change the parameters for all the displayed graphs. Click the icon to change the view with the polar coordinate. Then choose the Gain (dB) parameter. Figure 8.105 shows the comparison of the radiation pattern after normalization for the HOBBIES result with/without using the imaging technique and the results obtained from using a finite-difference time-domain (FDTD) algorithm. From the comparison of the figures, the results with the imaging technique agree well with the results of the FDTD using an extremely fine mesh. It is seen that the imaging technique improves the accuracy of the simulation (the result for the FDTD algorithm is taken from another source and not included in this code).

Figure 8.105. Comparison of the radiation pattern of the patch array displayed with and without imaging and FDTD result: (a) along the xOz-plane, (b) along the yOz-plane, (c) along the xOy-plane (θ = 0° starts from the z-axis in the xOz-plane).

8.7 CONCLUSION

Electromagnetic modeling of various structures in HOBBIES has been described in this chapter, so that users can generate models for any complex structures with ease. Examples in this chapter have dealt with structures containing metallic wires and surfaces along with composite metallic and dielectric structures. In addition, distributed and concentrated loadings, use of the appropriate symmetry planes, effects of a real ground, and introduction of an imaging technique in the generation of a mesh are described through various examples.

REFERENCES

[1] T. K. Sarkar, “Analysis of Radiation by Arrays of Parallel Vertical Wire Antennas over Plane Imperfect Ground (Sommerfeld Formulation),” IEEE Transactions on Antennas and Propagation, Vol. AP-24, No. 4, pp. 544–545, Jul. 1976.

[2] T. K. Sarkar, “Analysis of Arbitrarily Oriented Thin Wire Antennas over a Plane Imperfect Ground,” AEU, Band 31, Heft 11, pp. 449–457, 1977.

[3] A. R. Djordjevic, M. B. Bazdar, T. K. Sarkar, and R. F. Harrington, AWAS Version 2. 0: Analysis of Wire Antennas and Scatterers, Software and User 's Manual, Artech House, Norwood, MA, 2002.