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Interconnects in rigid and flexible boards can be formalized and simulated as transmission lines: strip, microstrip, coplanar, single-ended, or differential. The number of conductors in transmission line models is two for single-ended and three for differential lines. The signal conductors in the electrical model correspond to the interconnect traces, and the reference conductors correspond to one or two reference planes. Static or quasi-static field solvers are usually used to extract modal (impedance, attenuation, and phase delay) and per-unit-length (RLGC) parameters for analyzing data links. These models may be accurate up to very high frequencies depending on the geometry and material models. Reference planes in such models are assumed to be solid. That is usually correct assumption for most of the rigid-board interconnects (except BGA fields in some cases).

But most of the flexible interconnects have meshed or hatched planes; the reference conductors have periodic cutouts. The question is how do you build accurate models for such structures? It turns out that the traces over conductors with periodic cutouts can be effectively simulated as periodic structures; that requires a 3D electromagnetic analysis of a small segment instead of the analysis of a cross-section or complete link. Similar to the regular transmission lines, periodic structures can be characterized with per-unit-length impedance, admittance, and the modal parameters: attenuation, phase delay, characteristic impedance. That is very convenient for building models for interconnects with arbitrary length. This article shows what one can learn from this analysis using a particular example. Simbeor software was used for the analysis of interconnects with meshed planes.

**Electromagnetic Waves in Traces Over Planes With Periodic Cutouts**

In general, a periodic structure is made up of repetitions of a unit cell in one, two, or three dimensions. For instance, Figure 1 provides a simple example of the periodic repetition of a rectangular cutout in transmission line reference plane. The cutouts are repeated in two dimensions, but for the wave propagating along the trace, it is essentially a one-dimensional periodic structure (it becomes 2D for leaky-mode investigation). To extract the per-unit-length and modal parameters of such a structure, 3D electromagnetic analysis is needed due to the non-TEM structure of the waves propagating along the traces.

Most of the transmission lines in PCB or packaging interconnects have so-called quasi-TEM waves with the electric and magnetic fields mostly perpendicular or transverse to the propagation direction. Parameters of such transmission lines can be accurately approximated with the analysis of a single cross-section in a 2D field solver. With the cutouts in the reference plane, the waves become non-TEM and not even quasi-TEM due to the presence of the longitudinal components in the electric and magnetic fields.

*To read this entire article, which appeared in the January 2019 issue of Design007 Magazine, click here.*