A new closed form formula for inductance calculation in microstrip line spiral inductor design

The on-going explosive development in wireless communication has renewed the interests in spiral inductor study, primarily due to the fact that spiral inductors are the fundamental building blocks for various microwave/RF circuits. Common methods for designing square spiral inductors are either based on electromagnetic field (EM) simulation or on inductor library data. Although both of them are very accurate, they have their own limitations. EM simulation based design is typically time consuming; while the inductor library data based design is lack of flexibility. In this paper a new formula based on the Bryan´s equation is proposed for inductance calculation. This new formula established a closed form relation between inductance and three independent geometric variables of a spiral inductor. Once physical layout of a spiral Inductor is given, the inductance can be directly calculated using this new formula. Therefore the new formula provides both design flexibility and simplicity. The accuracy of the formula is verified by 4 sets of inductor library data with total 139 square spiral inductors. Excellent agreement was found between the measured and calculated inductance values