Fractal Loop Inductors

Abstract

We report a significant fractal-scaled increase in inductance for conductive pathways oriented in a fractal loop-based layout for a suite of planar inductors, which effectively occupy the same layout space and require only a single fabrication layer. These are closely predicted using a fractal scaling model for generalized loop-based inductors elucidated in this paper. Single-layer planar fractal structures were investigated with the loop inductor serving as the base construct. Thin sub-200 nm Cr/Au metal films compatible with flexible and stretchable substrates were used. It was found that while higher fractal orders did improve the inductive performance (over nine times from zeroth to third order), it is met with increased resistance. However, when compared with its equivalent series orientation, the effective sheet resistance of the simple fractal strategy demonstrated a clear advantage of up to four times. When the inductor is normalized for thickness, a quality factor Q greater than 40 is observed for all structures. Finally, the inductance quality gain figure of merit showing the optimal geometrical approach is introduced to quantify the quality of the structure's inductance over its resistance.

Design of an Inductive Spiral-Loop Loaded Unit Cell in a Mushroom-Shaped High Impedance Surface for Sub-GHZ Applications

“…Fractal geometries would also be employed to achieve high inductance for a HIS [19,20]. For example, a fractal loop inductor has considerable long electrical traces because of its a mathematical fractal pattern [21,22]. Thus, without significant increase of its dimensions, the fractal loop inductor can provide much higher inductance than the previous multi-turn SSLL.…”

Fractal Parallel Stacked Inductor using Modified Hilbert Space Filling Curve for RFIC

“…Inductor designed using fractal geometry were highly area efficient [11]- [12]. An intuitive study of mathematically defined fractal space filling inductors was carried out in [13]- [14]. The unique property of space filling curves significantly increases the inductance value within the limited area.…”

Design of multi-layer fractal inductor for RF applications

“…In literature fractal geometry successfully applied to electrical components like high capacitive fractal capacitors [5] and fractal inductors with high inductance value based on well known space filling curves [6][7] [8].…”