Optional Parameters, Modeling Lossy Dielectrics and Choosing the Right Matrix Solver

Optional Parameters, Modeling Lossy Dielectrics and Choosing the Right Matrix Solver

            The optional parameters are grouped into the dialog in Optional Parameters in Param menu.  Correct setup of the Optional Parameters will make your use of the IE3D more convenient and accurate. The dialog for the optional parameters is shown in Figure A.1.

 The Optional Parameters dialog

            You may have realized that we define the infinite ground plane as a substrate with high conductivity.  In the other word, a substrate with high conductivity will be considered as a ground plane.

            From (3) of Chapter 3, we know that the conductivity s is really related to the e_{r, total} in the equation. For HTS superconductor, the s in the formula is small. However, |Im( e_r )| is a big number. Therefore, our criterion for infinite ground plane is actually big  |e_{r, total}|.  Due to the s to e_{r, total}’s contribution is frequency dependent. We will use the |e_{r, total}(freq=1GHz)| for our criterion. We define the Conductor Assumption Limit for Dielectric Constant (CAL).  When |e_{r, total}(freq=1GHz)| < CAL, we consider the dielectrics as normal dielectrics. When |e_{r, total}(freq=1GHz)| ³ CAL, we consider the dielectrics as ground plane.

           

            Because we compare the CAL to |e_{r, total}(freq=1GHz)|, we would not know directly whether a lossy substrate with finite s is considered as a ground plane or just a normal lossy substrate. For most circuits with the s of the ground plane about 10⁷ (s/m), we really want to consider it as a ground plane. For some semi-conductor substrate, there might be some dielectric layer with the s about 1000 (s/m). This dielectric layer will be on top of the true ground plane with the s of the ground plane about 10⁷ (s/m). In such a case, you may want to model the effect of the semi-conductor substrate. You should define the right CAL until you see the horizontal line on the metal layer on the interface of the semi-conductor substrate disappears.

            Saved in c:\ie3d\samples\cal1.geo is an example. The dielectric setup for the structure is shown in Figure A.2. When you open the file on MGRID, you should see 2 metal layers in the layer window: the No.1 layer is z = 0.25 mm and the No.2 layer is z = 0.5 mm. When you set the CAL in the Optional Parameters in Param menu to 1500, you will see there is a line across the No.2 layer with z = 0.5 mm. It means that the interface at z = 0.5 mm is the interface of a high conductivity conductor. For our case, the dielectrics from z > 0.5 mm is considered as the top ground plane. If we set the CAL in Optional Parameters in Param menu to 10000, we will see the lines across the No.2 layer with z = 0.5 mm disappear. Then, the dielectrics above z = 0.5 mm is correctly considered as a lossy dielectric layer.

Figure A.2  The dielectric setup for c:\ie3d\samples\cal1.geo.

            Another important Optional Parameter is the selection of matrix solvers. There are quite some matrix solvers available on the IE3D. Interested users should read Chapters 12 and 13 for more information on different matrix solvers. We would like to give more comments on the Separation Distance (SD) in the following paragraph. The SD is used in the partial matrix solvers and iterative matrix solvers.

            For IE3D, the matrix is always a full matrix. However, it is a diagonal dominant matrix. Many off-diagonal elements are insignificant especially for large structures. Each matrix element is corresponds to the coupling between 2 cells as shown in Figure A.3.  The coupling between the cell 1 and cell 3 is much weaker than the coupling between cell 1 and cell 2. The coupling between the cell 1 and cell 4 is even much weaker. The difference might be a few orders in the corresponding matrix elements. Because the coupling between cell 1 and cell 4 is so weak compared with other couplings, we may not need to consider it because it can be negligible. If we neglect the coupling between 2 far away cells, we will obtain a sparse matrix. We will denote the matrix solver for the sparse matrix as Partial Matrix Solver (PMS) in order to distinguish it from SMS. We introduce a parameter called Separation Distance (SD) to identify which coupling is negligible. As it is shown in Figure A.3, for any cell with a distance to cell 1 smaller than the SD, the coupling between this cell and cell 1 will be considered.  When a cell with a distance to cell 1 larger than the SD, the coupling between the cell and cell 1 will be neglected. Same rule applies to any cell in the layout. Starting from IE3D 8.0, the SD is defined as number of cells. Normally, we recommend users to choose the SD = 5 to 15 cells.

  A 2-element patch antenna array.

            The selection of SD is very critical to the accuracy of the PMS and the convergence of the IMS. There is no way to guarantee a SD with converged IMS. Apparently, when we choose the SD to be 0, the IMS will always diverge. When we choose the SD to be the largest distance between cells, the IMS is basically FMS and the iteration always converges, and it also defeats the purpose of IMS. We need to choose the right SD so that we can fast convergence with the least memory and time.

            The Iteration Relative Error, Iteration Absolute Error, Maximum Iterations, AIMS Epsilon are for controlling the convergence of the iterative matrix solvers. They should not be changed normally. The Buffer Size should not be changed either.

            For planar circuits and antennas, a good suggestion for SD is about 10 times of the substrate thickness. For 3D structures, the SD should be chosen to be larger because the off-diagonal terms do not decay so fast.

            Other optional parameters are Automatic Edge Cell and the settings for the initial display. If we check it, every time we start MGRID, it will take the default settings. The Optional Parameters are saved into the file mgrid9_0.ini file in the system automatically.