Accurate solution of periodic microstrips for digital applications

This paper presents a conformal-mapping analysis of periodic microstrips (PMSs) with zero-thickness strips. The analysis yields closed-form expressions for the common-mode and alternate-differential-mode capacitances, characteristic impedances, and effective dielectric constants of PMSs. The accuracy of the capacitances against electromagnetic simulations is found to be better than 4% in three test cases. The accuracy of approximating the differential-mode capacitance of PMSs using their alternate-differential-mode one is also found to be within 4%. In the case of an air substrate, the capacitances and impedances become exact. These expressions allow a quick estimate of crosstalk-induced impedance and velocity changes on a signal line at or near the center of a data bus consisting of multiconductor microstrips in digital design. A cell of the periodic structure in an alternate differential mode is actually a single microstrip (SMS) with sidewalls and, therefore, the alternate-differential-mode results are equally useful in the design of such an SMS. As expected, calculated alternate-differential-mode data for a large strip spacing approach corresponding common-mode ones and those of a corresponding SMS without sidewalls.