- 1 Motivation and Objectives
- 2 State of the art
- 2.1 The three-dimensional full wave simulation approaches
- 2.2 The semi-analytical approach based on EMI source multipole macro modeling
- 2.3 Analytical and numerical modeling of the EMI effects to classify sources and coupling paths regarding their potential to exceed emission limits
- 2.4 Analytical model for the free space radiation of a cubical enclosure intended for fast predesign investigations
- 2.5 Modeling of the common mode coupling from ICs to the cavity field

- 3 Electromagnetic emissions mechanisms from PCBs
- 4 Cavity model of the electromagnetic field between PCB and metallic cover
- 4.1 Derivation of the two-dimensional Helmholtz equation model
- 4.2 Analytical solution methods for the two-dimensional Helmholtz equation
- 4.3 Inductance, capacitance, resistance (LCR) grid solution method for the two-dimensional Helmholtz equation
- 4.4 FEM solution for the two-dimensional Helmholtz equation

- 5 Introduction of sources and PCB layout structures to the cavity model
- 5.1 Calculation of
K
_{couple}with mode decomposition - 5.2 Expression of
K
_{couple}by a distance ratio factor - 5.3 Validation of the trace introduction by HFSS
^{®}simulations - 5.4 Independence of the common mode coupling from the horizontal trace routing
- 5.5 Link of the common mode coupling to the near field above the PCB
- 5.6 Modeling the coupling from integrated circuits
- 5.7 Link to the current driven common mode mechanism and the common mode inductance of a trace inside a cavity.
- 5.8 Design consequences
- 5.9 Necessity to consider the influence of the external environment at the cavity field simulation

- 5.1 Calculation of
K
- 6 Domain decomposition with PMC boundaries and port interfaces
- 7 Analytical model for the radiated emissions from the slot of a rectangular enclosure:
- 7.1 Analytical cavity model for a rectangular enclosure with three closed edges and one open slot
- 7.2 Analytical consideration of the radiation loss and a model for the free space radiation from the enclosure slot
- 7.2.1 Calculation of the far field from the slot field distribution
- 7.2.2 Derivation of an admittance matrix for the consideration of the radiation loss at the cavity field simulation
- 7.2.3 Introduction of the radiation loss admittance matrix into the cavity model matrix
- 7.2.4 Summary of the equations for the introduction of the radiation loss into the cavity model and the far field calculation

- 7.3 Comparison of the analytical model results to HFSS
^{®}simulations and measurement results - 7.4 Radiation diagrams for the rectangular enclosure with a slot on one edge

- 8 Design rules for PCBs inside a metallic enclosure with apertures
- 8.1 Rule 1: Trace placement symmetric to the enclosure symmetry reduces the coupling up to the second enclosure resonance
- 8.2 Rule 2: Trace placement parallel and close to metallic enclosure walls reduces EMI, trace placement orthogonal and close to enclosure walls increases EMI
- 8.3 Rule 3: Trace placement in the middle of the enclosure slot reduces the EMI at the first resonance
- 8.4 Rule 4: Reduction of the trace height d above the ground plane reduces EMI
- 8.5 Rule 5: Single source placement closer to an enclosure wall reduces EMI
- 8.6 Rule 6: Shielding reduces the common mode coupling
- 8.7 Rule 7: A ground plane under an IC reduces EMI
- 8.8 Summary of the design guidelines

- A. Validation of the analytic common-mode coupling factor d/h

- Bibliography