Power loss due to periodic structures in high-speed packages and Printed Circuit Boards

In this paper we apply the basic principles of electromagnetic wave propagation in periodic media to explain the high frequency power loss resonances of Printed Circuit Board (PCB) interconnects observed in recent simulations and measurements. For this purpose we consider a simplified PCB trace buried in a one dimensional periodic media consisting of alternating dielectric materials resembling glass weave and resin patterns found in a typical PCB. We formulate distributions of electric and magnetic field components in each homogeneous region and solve them to get the relationship between fields in TE and TM waves in two equivalent layers with the same effective dielectric constant. We apply Floquet´s theorem to relate the fields in similar periodic structure media and find the dispersion relationship between frequency (ω), propagation constant (β) and Bloch wave number (k) separately for TE and TM modes. From this relationship we identify regions where k is purely real and where k becomes complex, which corresponds to propagating and evanescent wave modes respectively. These modes result in resonant power losses, observed in simulations and measurements. To validate this theory we create a parameterized, full-wave simulation model of a typical glass-resin substrate using ANSYS´ HFSS™ and HFSS-Transient™ to resemble the theoretical assumptions. Resonant power losses are clearly observed through the simulated s-parameter plots in the frequency domain and the simulation results are well matched to theoretical predictions. Finally we also discuss the importance of considering resonant power loss frequency regimes in the design of high-speed packaging and PCB design.