Koch Snowflake Fractal Antenna Design in the Deep Space Bands for a Constellation of Cubesat Explorers

This paper presents the design and simulation of a Koch curve fractal antenna, developed according to the second iteration of the Koch snowflake fractal for S-band, C-band, X-band and Ku-band. The simulated antenna shows good performance for the operating frequencies and desirable gain, bandwidth and VSWR parameters. Being a compact antenna, it has a size, geometry and characteristics that go in accord with the CubeSat’s structure standards. The antenna was fabricated on a 1.5 mm thick FR-4 substrate. The VSWR achieved values are lower than 1.4 for the frequencies used (2.1 GHz to 2.4 GHz and 7.4 GHz to 8.9 GHz) with a simulated omnidirectional radiation pattern. A maximum gain of 6.8 dBi was achieved. As this antenna works optimally in the S, C and X bands, it is adequate for deep space applications, especially in low-power consumption systems. This approach would be ideal for constellations of Cubesat explorers.

Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

Network and Field Analysis of Koch Snowflake Fractal Geometry Radiofrequency Coils for Sodium MRI

Sodium is one of the most abundant physiological cations and is a key element in many cellular processes. It has been shown that several pathologies, including degenerative brain disorders, cancers, and brain traumas, express sodium deviations from normal. Therefore, sodium magnetic resonance imaging (MRI) can prove to be valuable for physicians. However, sodium MRI has its limitations, the most significant being a signal-to-noise ratio (SNR) thousands of times lower than a typical proton MRI. Radiofrequency coils are the components of the MRI system directly responsible for signal generation and acquisition. This paper explores the intrinsic properties of a Koch snowflake fractal radiofrequency surface coil compared to that of a standard circular surface coil to investigate a fractal geometry’s role in increasing SNR of sodium MRI scans. By first analyzing the network parameters of the two coils, it was found that the fractal coil had a better impedance match than the circular coil when loaded by various anatomical regions. Although this maximizes signal transfer between the coil and the system, this is at the expense of a lower Q, indicating greater signal loss between the tissue and coil. A second version of each coil was constructed to test the mutual inductance between the coils of the same geometry to see how they would behave as a phased array. It was found that the fractal coils were less sensitive to each other than the two circular coils, which would be beneficial when constructing and using phased array systems. The performance of each coil was then assessed for B1+ field homogeneity and signal. A sodium phantom was imaged using a B1+ mapping sequence, and a 3D radial acquisition was performed to determine SNR and image quality. The results indicated that the circular coil had a more homogeneous field and higher SNR. Overall while the circular coil proved to generate a higher signal-to-noise ratio than the fractal, the Koch coil showed higher versatility when in a multichannel network which could prove to be a benefit when designing, constructing, and using a phased array coil.

SOLUTION OF THE TWO-DIMENSIONAL WAVE DIFFRACTION PROBLEM ON FRACTAL BODIES BY THE PATTERN EQUATIONS METHOD

The solution of the two-dimensional wave diffraction problem for infinite cylinder of complex cross-section was considered by using the pattern equations method (PEM). A triangle and a Koch snowflake of first iteration were chosen as the geometry of the cross-sections of the cylinder. The numerical algorithms of the PEM for a single scatterer and for a group of bodies with the Dirichlet condition on their boundary are briefly presented, and the results of numerical calculations of the scattering characteristics for the above geometries are obtained using the PEM and the method of continued boundary conditions (MCBC). To check the convergence of the numerical algorithm in both methods, the optical theorem was used. The limits of applicability of the PEM for fractal scatterers are established. It is shown that for all convex bodies the algorithm of the PEM is sufficiently stable and allows obtaining calculation results with an accuracy acceptable in practice. In the case of a non-convex body, namely, a Koch snowflake, the algorithm of the PEM for a single scatterer turns out to be unstable and the acceptable accuracy can be obtained only if this geometry is considered as a group of bodies composed of convex geometries (for example, triangles).