Analysis and measurement of small inductance of loops and vias on printed circuit board

Printed circuit board (PCB) design has become a crucial issue for high density packaging of power electronics circuits. The traces, loops and vias on the PCB all introduce parasitic inductance, which causes high frequency ringing in the circuit and thus additional losses. In this paper, the inductance of several typical loops and vias on PCB is analyzed using Neumann formula. Studies show that the self-inductance of the rectangular loop is related to the length/width ratio, the trace width as well as the rectangular area. The mutual inductance between two loops is related to their relative position as well as their common area. When a loop contains vias, they may introduce additional inductance due to the additional cross-sectional area formed by the vias, while the vias themselves have little contribution to the inductance in the switching frequency domain. A simple and accurate test circuit was built based on oscillation method to measure the small inductance of loops on the PCB. Experimental results match the theoretical prediction with acceptable errors. Finally, some useful design guidelines are presented to optimize the layouts.