Unit cell approach to full-wave analysis of meander delay line using FDTD periodic structure Modeling method

Unit cell modeling is performed to determine the effect of electromagnetic coupling on the propagation characteristics of a meander delay line, which is widely used in printed circuit boards and packages. Since the design of a delay line must guarantee a several tens of picosecond timing margin in modern highspeed packages and board level interconnections, a penetrating understanding of the meander effect is essential. The propagation delay, the characteristic impedance, and the stop-band characteristic of the meander delay line have been carefully investigated based on a full-wave analysis using the finite-difference time-domain (FDTD) periodic structure modeling method. The periodicity of the meander line is utilized based on Floquet's theorem, resulting in a reduction of the computational domain in the FDTD simulation and providing a unit cell model of the meander line. The unit cell modeling of the meander delay line shows the effect of electromagnetic coupling in meander line structure on the reduction of the propagation delay. Also, an analysis based on the unit cell modeling was confirmed by time-domain reflection/transmission measurements. To investigate the effects of variation of substrate thickness (H) and trace width (W) generated during the manufacturing process, the propagation delay and the characteristic impedance were analyzed with different values of H and W. The unit cell modeling approach based on Floquet's propagation mode analysis produces a transmission line model of the meander delay line, which gives the dispersion relation and the characteristic impedance. This work should prove useful for high-speed digital circuit board designers.