Two-Layer Planar Rectangular Inductors and Their Electrical Models for Increased Inductance Density and Figure-of-Merit

This article presents two-layer planar rectangular inductors for increased inductance density and figure-of-merit (FOM). The equivalent lumped electrical models of the proposed inductors are developed. The model consists of the mutual inductance, parasitic capacitance, and self-inductance of the inductor. The closed-form expression for the mutual inductance is derived using the magnetic field law. Two different inductor geometries are developed and fabricated on FR4 substrate, and these are doubly wound top bottom (DWTB) and singly wound top bottom (SWTB) inductors. Four different geometries of DWTB and SWTB inductors are fabricated for analytical and experimental verification. Close agreement is observed between simulated and experimentally measured inductance. Among both, the measured results show that the proposed DWTB inductor has the highest inductance density of 24.43 (nH/mm) for an inductance of 122.2 nH, and a quality factor of 55.06. In addition, the FOM of the proposed SWTB inductor is 52.44, with a self-resonance frequency (SRF) of 386 MHz, and within outer dimension of 4 mm. The proposed inductor design is applicable to any dielectric substrate and scalable for different frequencies of operation.