Verification on Lossy Dielectric Modeling

   Verification on Lossy Dielectric Modeling

         IE3D is implemented with the capability to model lossy dielectrics. We will use some well-defined examples to verify the robustness and accuracy of the lossy dielectric modeling.

            As you may know, the transmission properties of coaxial structures are independent of the environment surrounding it, regardless the shape of the cross-section. IE3D’s basic formulation is for open structures. We will demonstrate the accuracy of the IE3D in modeling coaxial structures and verify the modeling of lossy dielectrics, by  using some rectangular coaxial structures.

            Saved in c:\ie3d\samples\rcoax.geo is a rectangular coaxial structure. The size of the outer conductor is 0.1 mm. The size of the inner conductor is 0.05 mm. The coaxial length is 0.5 mm. The coaxial structure is embedded into an infinite dielectrics of e_r = 6 - j 6. Building the structure is quite simple. The most important issue is the definition of the balanced port. As modeling of coaxial structures will be discussed in Appendix J, we will not provide any detail on building the rectangular coaxial structure.

            We simulated the structure and saved the result in c:\ie3d\samples\rcoax.sp. We expect the  e_reff should be the same as e_r = 6 - j 6. We can find out the transmission parameters of the rcoax.sp using MODUA: (1) Run MODUA. (2) Select Display Parameter Module to display rcoax.sp. (3) Select Display Toggle in Control for the design display. (4). Select Find Transmission Line Parameters in Process menu and enter the Transmission Line Length as 0.5 mm. MODUA will save the transmission parameters into c:\ie3d\samples\rcoax.tra.  Open the rcoax.tra file on a text editor. You will see the IE3D calculated e_reff = 6.0138 - j 6.00937 at 20 GHz which is very close to supposed value of  ( 6 - j 6 ).

            For c:\ie3d\samples\rcoax.geo, we built the whole space as a single dielectrics with e_r = 6 - j 6. Certainly, we can get very accurate modeling of lossy dielectrics. The question is how accurate the lossy dielectric modeling will be for multi-layer lossy dielectrics. Saved in c:\ie3d\samples\rcoax1.geo is an example of the rectangular coaxial with multilayer lossy dielectrics. Theoretically, rcoax1.geo’s result should be identical to that of rcoax1.geo because the dielectrics enclosed by the coax is still the same. Only the outer environment is changed. Practically, rcoax1.geo is more challenging check on the lossy dielectric modeling. The simulation result of rcoax1.geo is saved in c:\ie3d\samples\rcoax1.sp. The transmission parameter file is saved in c:\ie3d\samples\rcoax1.tra. The IE3D predicted  e_reff = 5.92003  - j 5.82743 at 20 GHz. The error is about 2%. We can claim that the result is quite accurate, considering the e_reff is the most sensitive parameters to numerical error (2% error in e_reff corresponds to 1% error in frequency). For rcoax1.geo, we also have a coarse meshing. Each side of the rectangular coaxial is only meshed into 1 to 2 cells. The outer conductor will have difficulty to completely stop field from penetrating into the air region that is just outside the outer conductor. When field is slightly penetrating into the air, we naturally will see some small drop in the  e_reff.

                                          RCOAX.GEO                                             RCOAX1.GEO

Figure C.1    The cross-sections and dielectric setup of the RCOAX.GEO and RCOAX1.GEO. In the IE3D simulation, only 1-2 cells are used on each side of the rectangular coaxials.

. Changing the Default Display Settings on MODUA

            After the IE3D (or FIDELITY) finish the simulation for the s-parameters, the IE3D will invoke the MODUA for graphic display of the parameters in a specific form. Different users may prefer different display form for the data. In Chapter 3 of the IE3D manual, we assume the default display form is the Smith Chart. However, users can change the default display form. To change the default display form on the MODUA, please select Optional View Settings in the View menu, then change the Default Display Settings to whatever you like.

Files Involved in the IE3D

            Many different files are created during the setup, simulation and post-processing of the IE3D.

Table E. 1  The different types of files on IE3D

Name	Source	Important	Description
*.geo	MGRID/ IE3DLIBRARY	Yes	It is the geometry file created by MGRID. It also can be created by IE3D after an optimization.
*.sp	IE3D	Yes	It is the simulation s-parameter file. It is the primary result of the IE3D. It is compatible with the HP/EEsof’s Touchstone™ format.
*.spt	IE3D	Yes	It is the original s-parameter file when Adaptive Intelli-Fit is used.
*.dsg	MODUA	Yes	It is the design file for MODUA. It describes the connections between different elements.
*.spm	MODUA / IE3D	Yes	It is the simulation results from MODUA or from IE3D with setup from MODUA
*.sim	MGRID / MODUA	Possibly	It is the simulation input file carrying simulation or optimization setup information. Starting from IE3D 7.0, it can be retrieved from MGRID / MODUA.
*.lib	MODUA	Yes	It is the result of the LC-equivalence. It is in the SPICE format.
*.cur	IE3D	Possibly	It is the current distribution file. It can be used to view the current distribution and generate radiation patterns. It is important to antenna designers.
*.pat	IE3D, CURVIEW or PATTERNVIEW	Possibly	It is the radiation pattern file. It carries the information about the radiation pattern.
*.ary	CURVIEW	Possibly	It is the array factor file created and used by CURVIEW for pattern display.
*.arr	PATTERNVIEW	Possibly	It is the array factor file created and used by PATTERNVIEW.
*.ctp	MGRID	Possibly	It is the template file created and used by MGRID for importing.
*.fld	FIELD	Possibly	It is the near field file.
*.log	IE3D	Possibly	It is the log file for the simulation. You can check it for any intermediate data created by the IE3D.
*.tra	MODUA	Possibly	It is the file for the transmission line information calculated on MODUA.
*.ect	MODUA / IE3D	Possibly	It is the excitation file. It is used to find out the port voltage, current and power.
Ie3d.tp? Ie3d.tq? Ie3d.tr? Io?????? Is??????	IE3D	No	They are temporary files created. They are useless after the simulation. Normally, they should be removed automatically. Abnormally termination of the IE3D may leave them there. You should delete them if you are sure their corresponding IE3D processes are terminated.
*.cif	MGRID	Possibly	It is the CIF file for import/export.
*.gds	MGRID	Possibly	It is the GDSII file for import/export.
*.dxf	MGRID	Possibly	It is the DXF file for import/export.
*.3dt	MGRID	Possibly	It is the 3D text file for import/export
*.zfw	MGRID	Possibly	It is the FIDELITY file created by MGRID.
*.ie3	IE3DLIBRARY	Yes	It is the IE3DLIBRARY file.

.     Plane-Wave Excitation and Radar Cross-Section

            Plane wave incident problems can be solved by the IE3D now. You can define a plane wave incident from any angle at the upper half space. To define or change an incident plane wave, you select the menu item Plane Wave Excitation in Port menu and define the incident angles.  After you define the plane wave excitation, MGRID will indicate the incident angles at the lower right corner. Simulation of plane wave excited structures is the same as simulating a circuit structure. IE3D will only create the current distribution data. It will not create the network parameters even though you may have defined ports on the structure.

            There are two polarization schemes for the plane wave incident scattering. The two cases are shown in Figure F.1. You are not required to specify which polarization the incident wave is on MGRID. You can change it any time on the MGRID/CURVIEW.

					H
	E-plane incident

 

Figure F.1

If you define ports on the structure with plane wave excitation, you can change the port excitation and termination as well as the incident wave polarization and magnitude. You can also change the port excitation and termination such as the parameters of a diode tie to the port in order to get the maximum radiation or the radar cross-section.

Radiation pattern in the full 3D space instead of the upper half space is available to those structures with the lower half space defined as air. Radar cross section is available only when the full 3D radiation pattern is available.

Comparative, Symbolic and Mixed-Parameter Optimization

            We have demonstrated how to optimize the shapes of the structures for some specified goals. You may have noticed that the goals we have discussed are direct goals. What direct goal means is that the goal is a known constant. There are cases for in-direct goals. Table G.1 shows the differences between direct goals and in-direct goals. Implementing in-direct goals is relatively difficult. For simplicity in implementation, we implement the symbolic goals instead of in-direct goals. Symbolic goals can achieve the same as in-direct goals. Comparative goals can also be used to replace in-direct goals. Symbolic goals can do the same and more. As the implementation in IE3D 7.0, a comparative goal can be defined on maximum 4 parameters. However, a symbolic goal can be defined on as many as you like.

Table G.1  Direct goals, in-direct goals, symbolic goals and comparative goals.

Direct Goal Examples	In-Direct Goal Examples	Symbolic Goals	Comparative Goal
dB[S(1,1)] = -20 dB	N/A	N/A	N/A
dB[S(1,1)] < - 20 dB	N/A	N/A	N/A
N/A	Ang[S(2,1)] = Ang[S(3,1)]	Ang[S(2,1)] = S0 Ang[S(3,1)] = S0	Ang[S(2,1)] / Ang[S(3,1)] = 1 or Ang[S(2,1)]–Ang[S(3,1)]= 0
N/A	dB[S(2,1)] < dB[S(3,1)]	dB[S(2,1)] = S0 dB[S(3,1)] > S0	dB[S(2,1) – dB[S(3,1)] < 0
N/A	dB[S(2,1)] =dB[S(3,1)]+10	DB[S(3,1)] = S0 dB[S(2,1)] = S0 + 10	dB[S(2,1)-dB[S(3,1)] = 10

            Lets take the Y-junction in c:\ie3d\samples\y.geo as an example. We want to optimize the Ang[S(3,1)] = Ang[S(2,1)] by adjusting the length of the port 3 arm (or arm 3). In fact, if we can make the length of the arm 3 to be the same as the arm 2 (the port 2 arm), we should be able to get the Ang[S(2,1)] = Ang[S(3,1)]. We just use this simple example to illustrate how we define comparative goals and symbolic goals. We have defined the length of the arm 3 as optimization variable. We are going to define either the comparative goal of Ang[S(2,1)] - Ang[S(3,1)] = 0 or the symbolic goal for Ang[S(2,1)] = Ang[S(3,1)].

(1)     Comparative Optimization:

Step 1     Run MGRID and open c:\ie3d\samples\y.geo. Select Set Optimization in Process menu. Enter Start Freq = 10, End Freq = 20, Number of Freq = 2. Select Enter to define the two frequencies.  Disable the Adaptive Intelli-Fit. Select Add button to define the goals. MGRID will prompt you for the goal.

Step 2     Select Ang(S) for the Parameter Type. Select (2, 1) for the 1^st Parameter. Select Minus for the Operator. Select (3,1) for the 2^nd Parameter. Select Optimization Quantity = Objective1 for Objective Type. Enter 0 for Objective 1. Select OK to define the goal. Select OK to perform the optimization. The IE3D will be invoked to perform the optimization. It will be finished in tens of seconds and the optimized geometry will be saved in c:\ie3d\samples\ym.geo.

(2)     Symbolic Optimization:

Step 1     Open c:\ie3d\samples\y.geo. Save it as c:\ie3d\samples\y1.geo. Select Set Optimization in Process menu. All the parameters are still there.

Step 2     Select Remove All to remove the comparative goal we defined earlier. Select Add button and we are going to define the symbolic goals for it. MGRID will prompt for the goal.

Step 3     Select Ang(S) for the Parameter Type. Select (2,1) for the 1^st parameter. Select By Itself for the Operator. Select Optimization Quantity = Symbol + Constant for Objective Type. Enter 0 for the Constant. Select OK to continue. MGRID will add the symbolic goal into the list. Then, it continues to prompt you for the next goal for the same symbol.

                Explanation:

                            MGRID will continuously prompt you for the next goal for the same symbol until you select Cancel. If you Cancel it after you define the 1^st symbolic goal, the symbolic goal will have no effect. At least two goals need to be defined for one single symbol if you want the goals to be effective.

Step 4     Change the 1^st parameter to (3,1). Select OK to accept the other parameters. The 2^nd goal will be included in the list. MGRID will prompt you for the 3^rd goal definition for the same symbol.

Step 5     Select Cancel to stop the symbol. MGRID will list the two goals as shown in Figure G.1. They are on the same symbol S0.

Figure G. 1  The symbolic goals.

                Explanation:

                            The 1^st line in the list (or the 1^st goal) defines that Ang[S(2,1)] = S0 + 0. The 2^nd line defines that Ang[S(3,1)] = S0 + 0. Then, we will have Ang[S(2,1)] = Ang[S(3,1)].

Step 6     Select OK to start the symbolic optimization. The IE3D will be invoked to perform the optimization. It will also take tens of seconds only.

            As it is demonstrated, the comparative optimization and symbolic optimization expand the optimization capability of the IE3D very much.

(3). Mixed-Parameter Optimization:

            The improvement on the IE3D 7.0 optimization capability is not only limited to comparative and symbolic optimization. On the IE3D 7.0, we can also optimize different parameters simultaneously. For examples, we can optimize the s-parameters, z-parameters and y-parameters simultaneously. We can also optimize the directivity, the efficiency and axial ratio of an antenna simultaneously. We cannot illustrate many examples here. Interested users can explore the flexible and powerful optimization capability of the IE3D by themselves.

Electric, Magnetic and Periodic Walls

            Electric, magnetic and periodic walls are implemented to take advantage of symmetry. Basically, we use images to represent the walls. When there is one wall in the x-direction, we will have one image. The image will give the exact solution to the wall. The same statement applies to the case with the wall in the y-direction. When there are two walls in either the x-direction or the y-direction, there will be infinite number of images. Numerically, we cannot take infinite number of images. You need to provide how many images you want. Usually, we can define the number of images in x-direction or y-direction as 4. It should be able to capture the coupling effect of the walls. Using the image theory, it will be very difficult to capture the resonant effect of the enclosure.

Figure H.1 Absolute equivalent solution with one wall in x-direction.

Figure H.2 Absolute equivalent solution with one wall in both x- and y-directions.

            To define a wall is very simple. You just select the menu item Enclosure Walls in Entity menu. You can define left wall, right wall, top wall, or bottom wall as either electric or magnetic wall. There are some limitations on the wall definition. If you do not define the wall correctly, the IE3D will not simulate the structure.

            It is interesting to note that we can simulate a symmetrical structure as half of the structure. It will reduce the size of the problem to half of the original structure as shown in Figure H.5. One comment on the equivalence in Figure H.5 is that the current at the port in Figure H.5A is twice as much as that in Figure H.5B. We need to do a conversion on the s-parameter files in order to get the correct s-parameters. In order to get the result of  A from B, we can connect two module B’s together on MODUA (see Figure H.5). Another comment on the equivalence is that MGRID will yield the same radiation pattern for both A and B.

Figure H.3 Structures allowed on IE3D 2.15.

Figure H.4   Structures not allowed.

Figure H.5 Symmetrical structure equivalent in solution.

            Periodical walls are specially designed for the simulation of large uniform infinite arrays. Periodical walls must come with pair: left and right, or top and bottom. Figure H.6 shows an antenna with left and right periodical walls.

Figure H. 6   A probe-fed patch antenna with left and right periodical walls.

            There are 4 additional parameters for the periodical walls: 2 for the periodical walls parallel to the y-axis, and 2 for the periodical walls parallel to the x-axis. For the left and right walls, which are parallel to the y-axis, the 2 additional parameters are the X-Phase Increment in degree and the X-Image Index.

            Assuming we define Number of Images Along X = 4, then the structure in Figure H.6 is equivalent to the one in Figure H.7. The X-Phase Increment is the excitation phase difference between the Patch 1 and Patch 0. For example, if the phase difference is - 30° and the Patch 0 is of phase of 0, then, the Patch 1 is of phase -30°, Patch 2 is of phase - 60°, Patch 3 is of phase -90° and Patch 4 is of phase -120°.

Figure H.7  The equivalent structure to Figure H.6 with 4 images.

            In treating the images of the periodical walls, we assume the current distribution is the same except there is a phase difference. Then, the voltage will be different at the port of each patch. So, we introduce the X-Images Index. If we specify the X-Image Index = 0, we are looking at the input impedance of the Patch 0. If we specify the X-Image Index = 2, we are looking at the input impedance of the Patch 2. In this way, we can calculate the input impedance of a patch in a large uniform phase array, no matter whether the patch is inside the array or on the boundary of the array.

                Starting from the IE3D 8.0, we have the precise modeling of periodic and electric walls implemented when the 4 walls are periodic or electric. In the simulation, infinite number of images will be included. However, for pattern calculation, a user still needs to enter the X-Pattern Images and Y-Pattern Images. They control how many images are used in the pattern calculate