6 Domain decomposition with PMC boundaries and port interfaces

The proposed cavity model for the simulation of the parallel-plane field inside the enclosure has been optimized for this purpose by a reduction of the general Maxwell equations in Chapter 4. This reduction is only admissible under the conditions (4.4) and (4.5), which are fulfilled inside the enclosure, but not in the external device environment. Thus, an interface between the cavity model and another simulation model of the external environment is necessary for the consideration of external influences on the internal cavity field. An interface which enables separate simulations of the external and the internal model and an integration of both simulation results in a common network simulation is established by utilizing equivalent source theory. Figure 6.1 depicts the subject of equivalent source theory, that the external field outside of an object is preserved, when the object is replaced by a PMC object of the same shape with electric currents on the surface, which are obtained from the initial field. Alternatively, the object can be replaced by a PEC object with magnetic currents on the surface, also preserving the external field [102].

Figure 6.1: Equivalent source theory. Electric current sources and a PMC boundary condition on the surface of an obstacle cause the same fields. Magnetic current sources and a PEC boundary condition cause also the same fields.

Another valid model preserves the field inside the object and replaces the external environment of the object by PMC material and electric currents on the object surface. PEC in the volume outside of the object and magnetic currents on the object surface will preserve the internal fields accordingly. A PMC surface with an electric surface current is, from a circuit point of view, equivalent to an ideal current source, while a PEC surface with a magnetic surface current is equivalent to an ideal voltage source.
The described equivalent source theory enables a general simulation domain separation with every standard full-wave simulation tool that supports PMC boundary conditions and electric current ports, or PEC boundary conditions and magnetic current ports. A separate domain simulation of the internal and the external domains of an object and integration of both results can be performed with the following simulation procedure:

1. Replace the object in the simulation model with a PMC object of the same shape.
2. Arrange electric current ports parallel to the outer object surface
   (i.e. on a triangular mesh).
3. Simulate the external model with three-dimensional full wave simulation or obtain
   an analytical solution.
4. Obtain a port impedance network from the simulation results.
5. Return to the initial model and remove the external environment.
6. Declare a PMC boundary at the surface of the object.
7. Arrange electric current ports parallel to the inner object surface
   (i.e. on a triangular mesh).
   The ports must be positioned identically to the ports in the previous simulation to
   enable a correct connection.
8. Simulate the internal model with three-dimensional full wave simulation,
   or with the cavity model (if the object is an enclosure).
9. Obtain a port impedance network from the simulation results.
10. Implement both network models in a standard network simulation program.
11. Perform a network simulation to obtain joint domain results.

Alternatively to a PMC boundary together with an electric current port, PEC boundaries together with magnetic current ports may also be used. Since the external and the internal simulation are separated, the external simulation can be performed with either PMC boundaries together with electric current ports, or PEC boundaries together with magnetic current ports, while the internal simulation can be performed with a different boundary and port current definition. The described procedure is general and can be performed on every three-dimensional object. The number of ports which have to be arranged along the object's surface to obtain accurate results depends on the maximum frequency of the simulation and the object size. Ports must not be declared on metallic walls of the object. High frequency fields decay rapidly inside a metallic wall and cannot excite the other domain. Therefore, these surfaces are modeled as they are. This significantly reduces the necessary number of surface ports, if the object is an metallic enclosure. At slim enclosure apertures ports must only be arranged perpendicular to the slot edges, due to the vanishing electric field tangential along the metallic edges. Thus, this domain separation approach is efficient for emission and shielding effectiveness simulations even on large metallic enclosures.

The inner domain of devices as described in Chapter 1 is simulated by using the cavity model (4.13) with PMC boundaries at the slot surfaces and multiple ports between the upper and lower planes just in front of the PMC surface inside the enclosure. The result of this simulation is an impedance matrix (4.17) model of the internal device domain. Although energy dissipation is caused by radiation and coupling to cables from enclosure slots, the PMC boundary condition is a much more realistic model of the slot than a PEC boundary. An enclosure model with PMC surfaces and no surface current ports does not consider emissions from the slot. However, this ideal model has nearly the same cavity modes as a model that considers the emissions, and thus provides good first order information about the resonance frequencies. Therefore, it is proposed to implement the interface at the slots with a PMC boundary condition and electric currents on the slot surface.
Another simulation has to be performed for the external device domain using PMC or PEC boundaries at the slots with electric or magnetic current ports respectively at the same slot positions, but outside of the enclosure.
Every available three-dimensional full-wave simulation tool can be used for this simulation. The results of both the internal model and the external model simulations are combined in a network simulation program according to the previously described procedure. As an alternative to the numerical simulation of the external enclosure domain, an analytical model for the free space radiation loss is obtained in Section 7.2, utilizing magnetic current sources at the slot. A port admittance matrix from this analytical solution is introduced into the cavity model for the consideration of the slot radiation in the calculation of the field on the inside of the enclosure. With the field on the enclosure slot and the external free space radiation solution, the radiation of the slot from a slim enclosure is expressed analytically. This purely analytical application of the domain decomposition method provides a powerful method for predesign investigations.

Advantages of the proposed domain decomposition approach:

• Numerically stable separate simulation of both domains.
• Applicable with every three-dimensional full-wave simulation tool which supports
  either PMC boundaries and electric current ports, or PEC boundaries and magnetic
  current ports.
• A change in one of the separated models requires only a new simulation of this model.
  This enables efficient device optimization.
• Models of different tools and methods can be combined.
• Significant reduction of interface ports at metallic enclosures.
• External environment influences can be considered in the cavity model (4.13).
• The results of a separated device provide insight into pure device properties which
  are not overlaid from external influences (i.e. resonances).
• Different environment models can be connected with a device model.
  The behavior of the device in different environments can be studied efficiently.

C. Poschalko: The Simulation of Emission from Printed Circuit Boards under a Metallic Cover