Planar Circuits for Microwaves and Lightwaves

The Field of Power/Ground Planes influenced by the HPEM Source, and its Damage Reduction

“…The size in the horizontal direction is much greater than the height. So this structure can be modeled as the pair of power/ground planes [5,6]. The incident electromagnetic wave induces the electric field over the gap between the top and bottom planes and this becomes the voltage source that causes the electromagnetic penetration(EMP) into the enclosure.…”

“…Considering the material and geometry of a flat factory, it looks like a pair of power/ground planes(parallel plates) of a multi-layered PCB without loss of generality. The power/ground planes are a rectangular cavity that has resonance modes due to the boundary conditions of a dielectric sandwiched between the top and bottom PEC planes [5]. With this geometrical model, using the modal analysis method for this particular cavity problem, the field inside the wide rectangular box is characterized with a high power voltage source, in this paper.…”

Coupling between Vias and the PCB Power-Bus

“…The impedance of the PB Z P B can be calculated approximately and analytically with a quite fast and accurate method. The modified modal summation Dickmann, 2005, 2007) is based on the cavity-model for an unpopulated rectangular PB, which solves the 2-D-Helmholtz equation by using a series expansion of orthogonal modes (Okoshi, 1984), (Lei, 1999) and leads to a double summation expression for the impedance of a populated rectangular PB with dimensions W x ×W y and thickness W z :…”

“…They can be calculated with analytic formulas for the assumed quasi-TEM propagation on the microstrip lines in the frequency range of interest (Gupta, 1979), (Zinke, 2000).…”

Multiport Analysis by Pad㉠Approximation

“…During these calculations, the Green's function infinite series is truncated to the extent that the summation is sufficiently convergent to the true value. Once the Green's function is determined, the multiport impedance matrix can be obtained [15][16][17]. This impedance matrix defines the mutual and self-impedances among the ports and can be obtained analytically only for regularly-shaped patches such as rectangular, triangular and circular patches.…”