Optimisation of chirped and tapered microstrip Koch fractal electromagnetic bandgap structures for improved low-pass filter design

This study presents electromagnetic bandgap (EBG) structures in microstrip technology based on one-dimensional Koch fractal patterns (Koch fractal EBG (KFEBG)). This fractal geometry allows to adjust the radius r and distance a between patterns so that a low-pass filter response is obtained when the ratio r/a is higher than 0.5. However, in such case undesired strong ripples appear in the low bandpass region. We demonstrate that the performance in the passband of this filter can be improved by applying a tapering function to the Koch fractal dimensions and to the width of the microstrip line, while simultaneously chirping (modulating) the Koch fractal periodic pattern distance (a) so as to maintain a constant r/a ratio. Several tapering functions scaled by a factor K are presented, and the results of their application to the KFEBG microstrip structure are compared by means of relevant characteristic parameters. Optimal performance has been obtained for the Kaiser and Cauchy distributions applied to the Koch fractal pattern, combined with a rectangular and Cauchy distribution applied to the microstrip width, respectively.