Simulation of Coaxial Structures
In the following, we will demonstrate the simulation of a coaxial step structure as shown in Figure J.1. Basically, we need to create 4 entities: one cylindrical tube for the inner conductor, one cylindrical tube for the smaller outer conductor, one cylindrical tube for the larger outer conductor and one ring for joining the two outer conductors.
Figure J.1. The longitudinal cross-sectional view of the coaxial step structure.
First we define the basic parameters:
unit length = mm.
grid size = 1 mm
substrate parameters (free space):
No.0 layer, z=0, permittivity = 1, permeability = 1, conductivity = 0
No.1 layer, z=1.0e+10, permittivity = 1, permeability = 1, conductivity = 0
metallic strip parameters:
No.1 type, thickness = 0.01 mm, conductivity = 4.9e+7 (s/m)
discretization parameters:
highest frequency = 1 GHz, Number of cells per wavelength = 20
The second step is to create the inner conductor:
Select Conical Tube in Entity menu and define the following parameters:
x-direction for the tube
number of segments = 12
starting point = 0.5
center x-coordinate = 0 mm
center y-coordinate = 20 mm
center z-coordinate = 10 mm
length = 50 mm
initial radius = 3 mm
end radius = 3 mm
We define the inner conductor to be longer so we can define the port on it without mixing the edges with those on the outer conductor. We select x-direction because we want the coaxial to be on the x-axis. We define the starting point = 0.5 because we want to have at least one polygon to be horizontal. The Extension for MMIC de-embedding scheme requires at least one edge to be from a horizontal polygon. Figure J.2 shows the top view of the cylindrical tube on MGRID. The tube is from x = 0 mm to x = 50 mm. If you do not get similar view, you may have entered something wrong. For example, you may see a circle if you forgot to change the default z-direction to the x-direction. If you define the start point = 0 instead of 0.5, there will be no horizontal polygon. Whenever something is wrong, you can select Undo in Edit menu to recover.
Figure J.2 The inner conductor (the center strip with different color
is the horizontal polygon).
The third step is to create the smaller outer conductor:
Select Conical Tube in Entity menu and define the following parameters:
x-direction for the tube
number of segments = 12
starting point = 0.5
center x-coordinate = 5 mm
center y-coordinate = 20 mm
center z-coordinate = 10 mm
length = 20 mm
initial radius = 6.9 mm
end radius = 6.9 mm
The result is shown in Figure J.3.
Figure J.3. Top view of the inner conductor and the smaller outer conductor.
The fourth step is to create the larger outer conductor:
Select Conical Tube in Entity menu and define the following parameters:
x-direction for the tube
number of segments = 12
starting point = 0.5
center x-coordinate = 25 mm
center y-coordinate = 20 mm
center z-coordinate = 10 mm
length = 20 mm
initial radius = 8.86 mm
end radius = 8.86 mm
The result is shown in Figure J.4.
Figure J.4 Top view of the inner and outer conductors.
The fifth step is to create the ring joining the outer conductors:
Select Ring in Entity menu and define the following parameters:
x-direction for the tube
number of segments = 12
starting point = 0.5
center x-coordinate = 25 mm
center y-coordinate = 20 mm
center z-coordinate = 10 mm
inner radius = 6.9 mm
outer radius = 8.86 mm
The result will be similar to Figure J.4 except there are some red dots on the junctions of the outer conductors.
The sixth step is to define the ports:
We must use the Extension for MMIC scheme for coaxial structures. We also need to define the positive and negative ports using the Port for Edge Group in Port menu. Figure J.5 shows the structure with the positive and negative ports defined.
Figure J.5 The structure with the ports defined.
The seventh step is to shorten the inner conductor.
We use the Select Vertices and Move Object commands in Edit menu to move the vertices on both ends of the inner coaxial. The offsets for the left end are dx = 5 mm and dy = 0. The offsets for the right end are dx = -5 mm and dy = 0 mm. The final result is shown in Figure J.6.
Figure J.6 The structure with the inner conductors aligned with the outer conductors.
The final structure is saved in c:\ie3d\samples\coaxstep.geo.
. Dividing Polygon into Multiple Sub-Polygons and
Connecting a Vertex to an Edge Vertically
Sometimes, you need to break a polygon into a group of polygons for better control over the meshing or editing. There are manual and automatic ways to divide polygons. Let’s use the chamfered bend shown in Figure K.1 as an example. If we use a normal 20 cells per wavelength guideline for meshing, we will end up with the discretization as shown in Figure K.2.
Figure K.1 A chamfered bend.
Figure K.2 Normal meshing of the bend.
In case we want to mesh the structure into 3 cells in the transverse direction, we can use the Automatic Edge Cell feature in the meshing. Another simple way is to define more cells per wavelength. Figure K.3 shows the meshing with 80 cells per wavelength. The structure is meshed into 3 cells in the transverse direction.
The automatic ways certainly can mesh a structure into smaller cells. However, they meshed all the polygons into smaller cells without exception. In practical applications, we may want to reduce the number of cells in order to improve the efficiency. We will try to use one cell in the transverse as much as possible, and we only mesh those polygons really need 3 cells in transverse direction. In such a case, we need to use the manual control over the meshing. For the bend structure in Figure K.1, we can insert some vertices on the edges manually to control the meshing.
What we want to do is to divide the polygons along point 1 to point 2 and port 3 to point 4 as shown in Figure K.4. There are vertices at point 1 and point 3. We need to insert vertices at point 2 and point 4. Let’s demonstrate how to divide the polygon along the line from point 1 to point 2.
Move the mouse to point 1 and click the left mouse button. Confirm the connection to the vertex at point 1. The next step is to insert a vertex at point 2. We want to insert the vertex 2 such that the line from point 1 to point 2 is vertical to the edge where the point 2 is on. What you can do is to select Connect to Edge Vertically in Inputmenu (or type ALT+C). You will see the upper right child window will indicate “Connect Vertically”. Then, you move the mouse to the edge where the point 2 is on and click the left mouse button. MGRID will insert the vertex on the edge without prompt you. If MGRID prompts you that the vertex is close to an edge and whether you like to connect to an edge, it means that you did not do “Connect to Edge Vertically” correctly. After we insert the vertex at point 2, we have entered an edge from point 1 and point 2. We want to cut the polygon along the edge. We select Divide Polygon in Edit menu (or ALT+D). The polygon will be divided into two as shown in Figure K.5. We can do the same thing to divide the polygon along the line from point 3 to point 4. To make it faster, you can even enter a series edges to connect vertices 1, 2, 3 and 4. Then, you select Divide Polygon in Edit menu. The polygon will be divided along vertices 1 and 2, 3 and 4. However, the vertices 2 and 3 will not divide the polygon because the edge between vertices 2 and 3 is cutting some edge of the polygon.
Figure K.3 Structure meshed into 3 cells in the transverse direction.
Figure K.4
After we divide the polygons into 3 sub-polygons, we can insert vertices on the edges on both ends of the bend and the edges from point 1 to point 2 and point 3 to point 4. Figure K.6 shows the discretization result after the polygon is divided into 3 sub-polygons and appropriate vertices are inserted onto the edges. As you can see, the structure is meshed into 3-cells in the transverse direction and the meshing density is not changed in the longitudinal direction.
Figure K.5 The polygon is divided into two.
Figure K.6 The normal meshing of the final result.
As you have seen, inserting vertices manually really can help improving the accuracy while still keeping the number of unknowns as small as possible. The problem is that it may be very time consuming if we have a big structure. Fortunately, we have implemented an automatic way to do it. In the following, we will discuss the automatic way.
For a structure as shown in Figure K.1 or any more complicated structure, we can break it into multiple rectangle dominant polygons easily. What we need to do is to select Rectanglizationin Process menu. The result is shown in Figure K.7. It can be seen the polygon is broken down into two rectangles and one polygon on the bend. The procedure alone does not offer much since the automatic meshing program can do it in the meshing process. This process will help the process of automatic inserting edge vertices very much.
We select the two rectangles using the corresponding menu item in Edit menu. Figure K.8 shows the two rectangles are selected (blackened). Then, we select Add Edge Vertex in Edit menu. MGRID will prompt you the default for adding vertices on the edge.
We select the two rectangles using the corresponding menu item in Edit menu. Figure K.8 shows the two rectangles are selected (blackened). Then, we select Add Edge Vertex in Edit menu. MGRID will prompt you the default for adding vertices on the edge. There are two options for adding the edge vertices:
Option 1: 90 degree vertex only or non-180 degree vertex.
Option 2: connected edges only, disconnected edges only, and any edge.
Figure K.7 The result of rectanglization.
Figure K.8 Two rectangles are selected.
We should always set Option 1 as 90 degree vertex only. We usually should not select the non-180 degree vertex because it should not do any thing good to the meshing. For Option 2, we should select connected edges only or any edge. The edge width is the parameter controlling the width of the edge cells in Figure K.6. For our case, it is 0.025 mm (1 grid on MGRID). Figure K.9 shows the comparison for different selections of Option 2. It should be noted that whenever a port is defined on an edge, the edge is considered as a connected edge. We can see that we can not get good result by selecting connected edges only without defining the ports on the edges. We get good meshing by selecting any edge. However, it will also add some additional vertices you do not need. The best result is created when we define the ports on the ends of the bend and select connected edges only for Option 2.
Therefore, the procedures to insert edge vertices to control the meshing are the following: (1) delete all the ports (This procedure is required for rectanglization on); (2) select Rectanglization in Process menu; (3) define the ports; (4) select the polygons you want to add edge vertices; (5) select Add Edge Vertices in Edit menu with option 1 as 90 degree vertices only, option 2 as connected edges only. Procedure (5) is usually good for inserting vertices on the edges in simulating coupled line structures. For filter design, you may need to use the option 2 as any edge because you may have some open-end polygons. They are not connected together and we want to add edge vertices on them. In such a case, we will select any edge for option 2 in procedure (5). Certainly, the above procedure can be replaced by the Automatic Edge Cells feature if you want to control the meshes of all the polygons.
(a) Option 2 for connected edges only.
original result meshed result
(b) Option 2 for any edge.
original result meshed result
(c) Option 2 for connected edges only with ports defined at the end of the bends.
original result meshed result
Figure K.9 Comparison for different selections of option 2.
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