**6. Comparison with other fractal-based filter models**

In this chapter, the modified Minkowski fractal geometry has been adopted to design the proposed BPF filter. The modified Minkowski fractal geometry is with better space-filling property to achieve more miniaturization as compared with the conventional Minkowski fractal geometry. However, an attempt has been carried out to compare the performance of the proposed filter with those modeled using other fractal geometries with high space-filling properties.

For this purpose, Peano and Moore fractal geometries have been adopted to design two BPFs based on the presented design idea. In the modeling of the proposed BPF filters, the same substrate and the same resonator dimensions are used. **Figures 16** and **17** illustrate the filter structures together with their performance

**43**

**Figure 18.**

*Photos of the fabricated prototype (a) the top and (b) the bottom views.*

region.

*Fractal Geometry: An Attractive Choice for Miniaturized Planar Microwave Filter Design*

responses. It is clear that both filters offer resonant responses at a higher frequency than that provided by the Minkowski fractal-based BPF. This means that the Minkowski fractal-based BPF possesses a higher size reduction. It is worth to note that the BPF based on Peano fractal geometry offers dual-band resonant response which can be tuned to a certain extent by the filter elements. However, further

A prototype of the fractal-based defected ground structure band-pass filter has been manufactured. The fabricated prototype uses an identical substrate with a relative permittivity of 2.65 and thickness of 1.0 mm. **Figure 18** shows photos of the manufactured filter. The measured and simulated scattering coefficient responses,

The simulated and measured results of the modeled and the fabricated bandpass filters well agree with each other. Some deviation, between the measured and the simulated results, is noticed. The shift of the lower edge of the passband response of the *S*21 responses is slight, while that of the upper edge is hardly visible. Furthermore, the measured results reveal attenuation in the passband

The production technique might cause dimensional tolerance which, in turns, leads to the differences observed between the measured and the simulated results. Employing more advanced manufacturing methods, besides the selection of a substrate having a more stable parameter, will result in a closer agreement.

*DOI: http://dx.doi.org/10.5772/intechopen.81353*

investigation of this filter has to be conducted later.

**7. Fabricated model and the measured results**

*S*11 and *S*21, are depicted in **Figures 19** and **20**, respectively.

#### **Figure 16.** *Moore fractal-based DGS BPFs together with performance responses.*

**Figure 17.** *Peano fractal-based DGS BPFs together with performance responses.*

*Fractal Geometry: An Attractive Choice for Miniaturized Planar Microwave Filter Design DOI: http://dx.doi.org/10.5772/intechopen.81353*

responses. It is clear that both filters offer resonant responses at a higher frequency than that provided by the Minkowski fractal-based BPF. This means that the Minkowski fractal-based BPF possesses a higher size reduction. It is worth to note that the BPF based on Peano fractal geometry offers dual-band resonant response which can be tuned to a certain extent by the filter elements. However, further investigation of this filter has to be conducted later.
