**RADIOING.com - eEngineer**

**Simulation Methods**

Several different simulation or modeling methods were found in current EMI simulation software packages. The most common of these are the Method of Moments (MOM), Finite Difference Time Domain (FDTD), Uniform Theory of Diffraction (UTD), Frequency Domain Finite Differences (FDFD), and Finite-Difference Time-Domain (FDTD). Each of these methods has its recommended area of application for maximum efficiency as well as those areas of deficiency where analysis becomes very time consuming and inaccurate. The software packages that combine desirable techniques into a multiple stage modeling or simulation suite are most efficient in dealing with all of the different PCB design problems.

**Method of Moments (MOM)**

The MOM technique is commonly used for analysis of radiated electric field emissions caused by the common mode currents on the enclosure/box, connectors, and cables resulting from the PCB emissions. It is a frequency domain technique that supports straight, thin-wire segments, small surface patches, segments and patches together, and segments whose end points have been attached to the centers of patches. A structure is usually divided into segments that are small compared to the wavelength of interest. Both wire segments and surface patches can be loaded with conductivity. Segments can also receive "lumped" loads and voltage sources. MOM problems can also utilize a ground plane model based on Fresnel reflection coefficients. Models can be created from which RF currents at selected frequencies on the wires and conductors may be observed. Far-field and/or near-field can be calculated and presented as an entire complex structure. Maximum field strength patterns can be observed while seeing the interaction of radiation patterns, RF current distribution and the radiating-source impedance. MOM is only applicable to the modeling of structures and not the surrounding space. Discrete components are easily inserted into a model as impedance assignments to a given wire segment. MOM is particularly well suited for applications involving metallic structures such as near the outside of a PCB shielded enclosure or box, including any cables and connectors. It assumes that the current on a surface patch or wire segment to be the same throughout its depth. Therefore, it is difficult to use for aperture effects and for dielectric materials. Also, this frequency domain technique can become inefficient for use over a large frequency range. Multiple frequencies require additional simulation runs and more software resources.

**Finite Difference Time Domain (FDTD)**

The FDTD technique is commonly used for the simulation of a printed circuit board (PCB) and its associated components and connectors within the interior of the shielded enclosure or box. It is a time domain technique that easily supports multiple frequencies with a single simulation using a differential time domain numerical modeling method. Maxwell’s equations are modified in differential form with the E-field and H-fields being solved alternately in time. The time derivative of the E-field (E-field change) is dependent on the “curl” of the H-field (H-field change) across space. Models are based on the determination of the E-fields and H-fields within a defined simulation space. The simulation space cells can consist of any material such as air or free space, metal and dielectrics. The excitation source can be a plane wave, electric current or field. The output results are the E-field or H-field at any point(s) within the computational domain space. FDTD is particularly well suited for applications involving different materials within a computational domain, shielding effects, fields inside/outside of structures, and aperture effects. FDTD calculates the E and H fields within a gridded computational domain using grids that are small compared to the smallest wavelength and model feature. Therefore, far fields and some models with with extended features such as wires may not be applicable due to large domains with excessive computational times.
**Uniform Theory of Diffraction (UTD)**

The UTD technique is useful for direct rays, reflected rays, diffractions from edges and corners, and waves around curved surfaces. UTD uses modeling elements of flat plates, cylinders of elliptical cross-section, and the end caps of each cylinder that may be tilted.
**Frequency Domain Finite Differences (FDFD or FD)**

FDFD/FD solves for electromagnetic fields at points in closed regions using a specialized form of Householder's Method of Modified Matrices. FD boundaries are specified by the UTD modeling elements.

**MOM/UTD**

MOM/UTD Hybrids allow for modeling structures with both MOM and UTD elements. It usually requires MOM matrix methods and UTD ray tracing for achieving solutions. A simple example of a MOM/UTD hybrid is a monopole antenna (MOM segments) attached to a finite size ground plane (UTD plate).

**MOM/UTD/FD**

MOM/UTD/FD Hybrids allow for modeling problems with more than one region, such as an interior and an exterior. FD is used to model the interior region(s), while MOM or MOM/UTD is used to model the exterior region. The physics of each region is reduced to a matrix format with boundary conditions across the areas.

**Software Suite Architecture**

A modeling or simulation suite consists of two or more modeling methods configured in stages. For example, a two-stage suite may be used to model the external radiated emissions originating at the PCB level within an enclosure. The combined technique may utilize the results of an FDTD technique as a source for MOM simulation.

A simplified computational sequence of events for most EMC simulation software is as follows:

1. Processing of the input PCB design data. This is usually in the form of circuit design and routing information via one of the software interfaces.

2. Time domain currents are simulated for all PCB nets.

3. A fast Fourier Transform is used to provide the harmonic content of time domain waveforms.

4. Nets are numerically divided into elemental antenna segments with consideration for the patch or segment location and direction.

5. The emissions from all pins, vias, and transmission line nets are included.

6. The value of the electromagnetic fields are computed in the models for three dimensions by integration over all current elements at an arbitrary height above the board.

7. Highly radiating "hot spots" are mapped at each frequency.

8. Nets that are the principal contributors to establishment of the hot spots are highlighted. This identifies the conductors producing the emissions.

9. Circuit terminations and "what-if" scenarios can be performed to determine appropriate solutions.