Performance analysis of first iteration koch curve fractal log periodic antenna of varying flare angles

Similar documents
Design And Performance Analysis of Minkowski Square Loop Fractal Antenna

Compact Log-Periodic Dipole Antennas using Peano Fractal Cuvres

LOG PERIODIC FRACTAL KOCH ANTENNA FOR UHF BAND APPLICATIONS

Design and Analysis of a Multiband Koch Fractal Monopole Antenna

Bandwidth optimization of compact microstrip antenna for PCS/DCS/bluetooth application

Fractal Monopoles: A Comparative Study

Comparison of the Radiation Characteristics of Triangular and Quadratic Koch Fractal Dipole Wire Antennas

Design of Fractal Antenna for RFID Applications

Keywords-, Folded Slot antenna, Fractals, Koch fractal antenna, Coplanar waveguide (CPW) feed, Finite Element Method (FEM).

Miniaturized Ultra Wideband Microstrip Antenna Based on a Modified Koch Snowflake Geometry for Wireless Applications

Performance Analysis of Different Ultra Wideband Planar Monopole Antennas as EMI sensors

Review of Antennas Deploying Fractal Slot Geometries

DESIGN OF MULTIBAND MICROSTRIP PATCH ANTENNA FOR WIRELESS 1 GHz TO 5 GHz BAND APPLICATIONS WITH MICROSTRIP LINE FEEDING TECHNIQUE

Chapter 7 Design of the UWB Fractal Antenna

A Printed Log-Periodic Koch-Dipole Array (LPKDA)

Keywords-Microstrip, Fractal, Sierpinski.

Design of CPW Fed Ultra wideband Fractal Antenna and Backscattering Reduction

Slotted Octagonal shaped Antenna for Wireless Applications

On the Design of CPW Fed Appollian Gasket Multiband Antenna

Dual Band Fractal Antenna Design For Wireless Application

Octagonal Fractal Antenna Design using Koch Curve

We are IntechOpen, the world s leading publisher of Open Access books Built by scientists, for scientists. International authors and editors

Modified Sierpinski Gasket for Wi-Fi and WLAN Applications

Multiband Cross Dipole Antenna Based On the Triangular and Quadratic Fractal Koch Curve

Rupender Kaur 1, Navpreet Kaur 2 1,2 ECE Department, Punjab Technical University, Punjab. IJRASET 2015: All Rights are Reserved

Design of E-Shape Fractal Simple Multiband Patch Antenna for S-Band LTE and Various Mobile Standards

Design and Analysis of Triangular-Circular Fractal Antenna for UWB Applications

Progress In Electromagnetics Research, PIER 93, , 2009

Radiation Performance of Log Periodic Koch Fractal Antenna Array with Different Materials and Thickness

Design and Implementation of Pentagon Patch Antennas with slit for Multiband Wireless Applications

Wideband Octagonal Shaped Iterated Fractal Antenna with DGS for Wireless Applications

Design and Development of a 2 1 Array of Slotted Microstrip Line Fed Shorted Patch Antenna for DCS Mobile Communication System

A New Fractal Based PIFA Antenna Design for MIMO Dual Band WLAN Applications

Proximity fed gap-coupled half E-shaped microstrip antenna array

SIERPINSKI CARPET FRACTAL ANTENNA ARRAY USING MITERED BEND FEED NETWORK FOR MULTI-BAND APPLICATIONS

Design and Simulation of Miniaturized Multiband Fractal Antennas for Microwave Applications

Improved Multiband Triangular Fractal Patch Antenna for Wireless Communication

Broadband and Gain Enhanced Bowtie Antenna with AMC Ground

Multi-Band Microstrip Rectangular Fractal Antenna for Wireless Applications

New Design of CPW-Fed Rectangular Slot Antenna for Ultra Wideband Applications

A COMPACT MULTIBAND MONOPOLE ANTENNA FOR WLAN/WIMAX APPLICATIONS

INTERNATIONAL JOURNAL OF PURE AND APPLIED RESEARCH IN ENGINEERING AND TECHNOLOGY

Plus Shape Slotted Fractal Antenna for Wireless Applications

A Fractal Circular Polarized RFID Tag Antenna

Design and analysis of Slot Fractal Antenna Using Koch Curve

A New Microstrip Bandpass Filter Design Based on Hilbert Fractal Geometry for Modern Wireless Communication Applications

Design of A PIFA Antenna with Slots on Ground to Improve Bandwidth

International Journal of Scientific & Engineering Research, Volume 4, Issue 8, August ISSN

Cross Dipole Hybrid Koch Fractal Antenna for Wireless Communication

A Self-Similar Fractal Antenna with Square EBG Structure

Design of a Fractal Slot Antenna for Rectenna System and Comparison of Simulated Parameters for Different Dimensions

Designing of Microstrip Feed Antenna by Combining Circular and Square Microstrip Antennas

Bandwidth and Gain Enhancement of Multiband Fractal Antenna using Suspended Technique

δ = Where h represents the side length of the square patch fractal antenna and n is a natural number represents the number of iteration.

A Miniaturized Wide-Band LTCC Based Fractal Antenna

DESIGN OF OMNIDIRECTIONAL HIGH-GAIN AN- TENNA WITH BROADBAND RADIANT LOAD IN C WAVE BAND

An X-Fractal Patch Antenna with DGS for Multiband Applications

COMPACT WIDE-SLOT TRI-BAND ANTENNA FOR WLAN/WIMAX APPLICATIONS

Analysis and Design of Rectangular Microstrip Patch Antenna using Fractal Technique for Multiband Wireless Applications

HIGH GAIN KOCH FRACTAL DIPOLE YAGI-UDA ANTENNA FOR S AND X BAND APPLICATION

Design of a Compact and Low-Cost Fractal-Based UWB PCB Antenna

COMPACT FRACTAL MONOPOLE ANTENNA WITH DEFECTED GROUND STRUCTURE FOR WIDE BAND APPLICATIONS

The Effect of Aspect Ratio and Fractal Dimension of the Boundary on the Performance of Fractal Shaped CP Microstrip Antenna

MINIATURIZED CROSSED-DIPOLE CIRCULARLY PO- LARIZED FRACTAL ANTENNA

A NOVEL DESIGN OF MULTIBAND SQUARE PATCH ANTENNA EMBEDED WITH GASKET FRACTAL SLOT FOR WLAN & WIMAX COMMUNICATION

A MODIFIED FRACTAL RECTANGULAR CURVE DIELECTRIC RESONATOR ANTENNA FOR WIMAX APPLICATION

On the Design of Tree-type Ultra Wideband Fractal Antenna for DS-CDMA System

BROADBAND SERIES-FED DIPOLE PAIR ANTENNA WITH PARASITIC STRIP PAIR DIRECTOR

Plus Shape Fractal Antenna with EBG Structure for Wireless Communication

Efficient Design of Sierpinski Fractal Antenna for High Frequency Applications

DESIGN OF A NOVEL WIDEBAND LOOP ANTENNA WITH PARASITIC RESONATORS. Microwaves, Xidian University, Xi an, Shaanxi, China

Design and Simulation of Fractal Antenna with DGS structure for Multiband Applications

Fractal Dimension versus Quality Factor: Modelling with NEC. José M. González and Jordi Romeu. Total number of pages: 17

Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 14 No. 1, June 2015

Ultra-Wideband Coplanar-Fed Monopoles: A Comparative Study

SAUSAGE MINKOWSKI SQUARE PATCH ANTENNA FOR GPS APPLICATION

Perturbed Rectangular Sierpinski Carpet Geometry Based Miniaturized Fractal Patch Antenna

Characterization of Series Iteration Log-periodic Fractal Koch Printed Antenna Equipped with Balun Unit

Design and analysis of T shaped broad band micro strip patch antenna for Ku band application

International Journal of Engineering Trends and Technology (IJETT) Volume 49 Number 6 July 2017

QUAD-BAND MICROSTRIP ANTENNA FOR MOBILE HANDSETS

Stacked Configuration of Rectangular and Hexagonal Patches with Shorting Pin for Circularly Polarized Wideband Performance

Analysis and Implementation of Fractal Antenna

Fractal Hexagonal Disc Shaped Ultra Wideband Antenna

DESIGN OF A NOVEL MICROSTRIP-FED DUAL-BAND SLOT ANTENNA FOR WLAN APPLICATIONS

A Review- Microstrip Patch Antenna Design

SELF-COMPLEMENTARY CIRCULAR DISK ANTENNA FOR UWB APPLICATIONS

PYTHAGORAS TREE: A FRACTAL PATCH ANTENNA FOR MULTI-FREQUENCY AND ULTRA-WIDE BAND- WIDTH OPERATIONS

L-slotted Microstrip Patch Antenna for WiMAX and WLAN Applications

Analysis and Design of Microstrip Patch Antenna For Triple Band Applications

Posts and Telecommunications, Mailbox 280#, 66 Xinmofan Road, Nanjing , China

COMPOSITE STRUCTURE FRACTAL WIDEBAND MONOPOLE ANTENNA FOR ISM BAND APPLICATIONS

Design of a Sierpinski Gasket Fractal Bowtie Antenna for Multiband Applications

DUAL WIDEBAND SPLIT-RING MONOPOLE ANTENNA DESIGN FOR WIRELESS APPLICATIONS

Design & Fabrication of Sierpinski Fractal Antenna for Multiband Wireless Application

Venu Adepu* et al. ISSN: [IJESAT] [International Journal of Engineering Science & Advanced Technology] Volume-6, Issue-2,

A New Approach to Optimal Design of T-shaped Tri-Band Fractal Microstrip Patch Antenna for Wireless System Applications

Modified Inverted fork Patch Antenna for Microwave Applications

HIGH GAIN AND LOW CROSS-POLAR COMPACT PRINTED ELLIPTICAL MONOPOLE UWB ANTENNA LOADED WITH PARTIAL GROUND AND PARASITIC PATCHES

An Annular-Ring Microstrip Patch Antenna for Multiband Applications

Transcription:

Cent. Eur. J. Eng. 3(1) 2013 51-57 DOI: 10.2478/s13531-012-0040-2 Central European Journal of Engineering Performance analysis of first iteration koch curve fractal log periodic antenna of varying flare angles Research Article Ashutosh K. Singh 1, Reneez A. Kabeer 1, Z. Ali 2, V.K. Singh 2, M. Shukla 3 1 Department of Electronics Engineering, Indian Institute of Information Technology, Allahabad, India 2 Department of Electronics Engineering, Bundelkhand University, Jhansi, India 3 Department of Electronics Engineering, Harcourt Butler Technological Institute, Kanpur, India Received 07 August 2012; accepted 08 September 2012 Abstract: Miniaturization has always been a crucial challenge in the field of antenna engineering. In the recent past a number of researchers have shown that fractal geometry have potential to design smaller, broad band and multi band antennas. In this proposed work performances of log periodic fractal antennas of different flare angles have been investigated. Simulation results show that fractal log periodic antenna gives better performance in terms of gain, return loss and directivity. Performance of log periodic fractal antenna has also been investigated for flare angles 30, 45, 60, 70 and 80. In this proposed work fractal antenna gives best performance with 60 flare angle. Keywords: Koch Curve Fractal antenna Gain; Bandwidth Versita sp. z o.o. 1. Introduction In the field of wireless communication, antenna size and space occupied by it are very crucial factors. The antenna has to be compact as well as feasible, as long as fabrication is concerned, along with having an improvement or a nonconsiderable degradation in its radiation patterns and performance. This is where fractal geometry comes into the picture with fractal antennas. A fractal is a fragmented geometric shape which is made of reduced-size copies of itself. In other words, fractals are self-similar structures or shapes. Fractal antennas are those antennas which use this self-similarity property of E-mail: ashutosh_singh@iiita.ac.in fractals on each of its elements to form a fractal antenna. The first of its kind was the log periodic antenna. These fractal antennas are composed of many reduced-size copies of itself in it and hence provide a wider range of operational frequencies. The general rule of antenna length being near target frequency wavelength does not apply itself in the same way with fractal antennas. Although effective electrical length of the elements of fractal antenna is longer, the fractal antennas are themselves physically smaller. Thus these fractal antennas, due to their compact size and multi-band properties, are very useful in cellular telephone and microwave communications. There are various types of fractal structures and geometrical shapes introduced. Some of the examples are Koch Curve, Serpinski triangle, T-Square, Gosper Island, etc. The Koch curve is one of the earliest mathematical curves described according to fractal geometry and can have infi- 51

Performance analysis of first iteration koch curve fractal log periodic antenna of varying flare angles 2. Related work Figure 1. Koch curve fractal and its 4 iterations. nite number of iterations. The Koch fractalization is done to an element by dividing the element into three equal parts a, b, c of length l and replace the center element b with two elements joint together at a flare angle 60, as in Figure 1. The log periodic Koch fractal antenna uses the above mentioned Koch curve fractal to modify the various elements of the conventional log periodic dipole antenna. The different iterations of these antennas can be denoted as K0 and K1 being 0 th and 1 st iterations. In the 1 st iteration, the angle at which the center two elements meet is called the flare angle. This flare angle can be of any magnitude, but conventionally is maintained at 60 to maintain a constant overall length of element. The conventional log periodic antenna can also be called the 0 th iteration log periodic Koch fractal antenna. The log periodic Koch fractal antenna is shown to be more compact than the conventional log periodic antenna while maintaining its overall performance characteristics with minimal degradation in input impedance and return loss [1]. Most of the research work in antenna designing is done improving the performance of the antenna keeping size similar or miniaturizing the antenna with very less difference in performance. In [1] the authors have used Koch curve fractal over a conventional Log Periodic dipole antenna to show the difference in performance. This was the first application of Koch pre-fractal elements in a miniaturized wideband antenna design. In [2], the concept of fractal antenna was employed to achieve the necessary height reduction, while keeping its radiation characteristics nearly constant. Research paper [3] deals with a type of fractal shape known as Serpinski triangle and its use on a monopole antenna. The PKG (Penta-Gasket-Koch) fractal has been implemented to design a planar monopole antenna with satisfying input impedance match and gain in [4]. In the paper Fractal log-periodic Antenna [5], the authors have discussed the effect of Koch fractal on the conventional log periodic antenna along with simulated patterns and results. They describe how each of these iterations causes an increase in the electrical length of the antenna while keeping the size of the antenna almost constant. And also how the fractals affect the input impedance and return loss parameters. In the field of antenna design, the topic of fractal geometry and fractal designs have recently gained a considerable amount of interest. One such example is the paper [6], in which, an improvement has been made to the fractal tree structure applied to a log periodic antenna, published in paper [7]. Yet another example of the advantages of fractal geometries and fractal structures on dipoles has been studied in the paper [8]. Log periodic antenna is very widely used in VHF/UHF range for commercial purposes. Therefore its size reduction was very crucial step in antenna designing field as shown in paper [9]. In 1996, D.H. Werner, P.L. Werner and A.J Ferraro discussed the frequency independent properties of fractal structures [10] or structures which possessed the selfsimilarity property. The paper has shown how these fractal shapes and geometrical structures can be used to develop multi band linear array radiators whose directive gain is a log periodic function of frequency. This antenna is the one commonly used today as the log periodic dipole array antenna (LPDA). In 1997, an author, N. Cohen, [11] published an article on the applications of fractal geometry to antenna elements for smaller, resonant multiband/broadband antennas which are simple and cost-effective to fabricate. In this paper, N. Cohen has also explained how these fractal shapes on antennas can help in the miniaturization of size and provide better resonance. The paper also shows 52

A.K. Singh, R.A. Kabeer, Z. Ali, V.K.Singh, M. Shukla Figure 2. LPKFA with flare angle 0. Figure 4. LPKFA with flare angle 45. Figure 3. LPKFA with flare angle 30. Figure 5. LPKFA with flare angle 60. the multi-banded nature of such fractal antennas and the expansion in bandwidths. In paper [12], the authors have designed different iterations of Koch dipole log periodic antenna for size reduction. Recently work was done on a multi-fractal antenna combining the Koch fractal and the Serpinski fractal for application over a dipole antenna [13]. 3. Proposed work In this paper, the computer software CST Microwave Studio is used to design and simulate a Log Periodic Koch fractal antenna of 1 st iteration. First, a conventional Log Periodic antenna is designed or a 0 th iteration Log Periodic Koch fractal antenna. Then, the 1 st iteration antenna is going to be designed by applying Koch fractal to the conventional antenna. The designs are going to be for different flare angles namely at 30, 45, 60, 70 and 80. Finally, all the designs are simulated in the simulation software to get the required antenna performance parameters. These results for different flare angles are compared to provide a conclusion to this paper. The above figures (Figure 2 to Figure 7) are of the designed log periodic Koch 1 st iteration fractal antenna with flare Figure 6. LPKFA with flare angle 70. Figure 7. LPKFA with flare angle 80. 53

Performance analysis of first iteration koch curve fractal log periodic antenna of varying flare angles Figure 8. Dimensional difference due to difference in flare angle. angles at 0, 30, 45, 60, 70 and 80. The difference in dimensions caused by the different flare angles are shown in the order of the flare angles 0, 30, 45, 60, 70 and 80. Figure 8 shows dimensional differences due to difference in flare angles of fractal antennas. As seen in the above Figure 8, there is a reduction in size of the antenna as angle goes below 60. This reduction can also be used in the miniaturization of the antenna size. Figure 9. Radiation pattern for LPA. 4. Simulation results The simulation of the above structures have yielded a great number of results showing the far field radiation pattern, gain (in db), directivity (in dbi), return loss parameter (S 11 ) and VSWR (voltage standing wave ratio). The simulation is run on CST Microwave Studio using the Transient analysis method at various frequencies ranging from 0.4 GHz to 2.9 GHz. The following radiation patterns have been taken for the frequency at 1.37 GHz for the different designed antennas. Figures 9, 10, 11, 12, 13 and 14 show the radiation patterns for flare angles 0, 30, 45, 60, 70 and 80 degrees respectively. Figure 9 shows the radiation pattern of normal log periodic antenna at 1.37 GHz. Having a maximum gain of 5.6 db, the radiation pattern is very poor in terms of directivity and the direction of main lobe. As this is an end-fire radiation antenna, the main lobe (maximum gain) should be towards the smaller elements (toward bottom of the diagram). But this is not the case. Hence, it shows poor radiation characteristics. Figure 10 shows the radiation pattern of the LPKFA with 30 flare angle at 1.37 GHz. It is clear from the figure that the main lobe is towards the smaller elements with Figure 10. Radiation pattern for 30. maximum gain of 7.35 db. But it is also seen from the figure that there are too many side lobes and the back lobe is too great in magnitude. This also results in unwanted radiation and thus a very poor radiation. Figure 11 shows the radiation pattern of LPKFA with 45 flare angle at 1.37 GHz. As seen in figure, even though there is an increase in the width of the main lobe (with maximum gain of 7.47 db) in comparison to Figure 10, there is still the presence of large unwanted side lobe radiations. Figure 12 shows the radiation pattern of LPKFA with flare angle 60 at 1.37 GHz. It can be seen from the figure that 54

A.K. Singh, R.A. Kabeer, Z. Ali, V.K.Singh, M. Shukla Figure 11. Radiation pattern for 45. Figure 13. Radiation pattern for 70. Figure 14. Radiation pattern for 80. Figure 12. Radiation pattern for 60. there is a major increase in the width of the main lobe towards the smaller elements and also optimal back lobe magnitude with increase in main lobe gain magnitude to 7.57 db. Figure 13 shows the radiation pattern of LPKFA with 70 flare angle at 1.37 GHz. It is seen that there is a decrease in the main lobe magnitude (maximum gain of 7.23 db) in comparison to Figure 12 with almost no change in the back lobe magnitude. Figure 14 shows the radiation pattern of LPKFA with 80 flare angle at 1.37 GHz. This pattern also shows a further reduction in the main lobe magnitude in comparison to Figure 12 and 13 with almost no change in the back lobe magnitude. From the above patterns of Figure 9 14, it can be observed that the antenna with 60 flare angle provide the best radiation pattern with a maximum gain of 7.575 db. The above table.1 of readings show that the antenna with the flare angle 60 give the best possible radiation pattern while keeping the size of the antenna almost constant. Figure 15 shows variation of gain with different flare angles. We find that maximum gain is obtained near 60 flare angle. Similarly Figure 16 shows variation of directivity with different flare angles. In Figure 17 variation of gain is shown for different frequencies. 55

Performance analysis of first iteration koch curve fractal log periodic antenna of varying flare angles Table 1. Simulated gain and directivity at 1.37 GHz. Flare Angle (degrees) Gain (db) Directivity (dbi) LPA 5.609 5.671 30 7.352 7.420 45 7.472 7.525 60 7.575 7.623 70 7.230 7.276 80 7.199 7.249 Figure 15. Chart showing variation in Gain vs. Flare angle. Figure 16. Chart showing variation in Directivity (dbi) vs. Flare angle (degrees). This antenna with 60 provides a very good radiation pattern with very minor difference in the return loss parameter as compared to the conventional log periodic antenna. The Figure 17 shows the gain variation of the antenna with 60 flare angle at various frequencies. The simulated return loss parameter of the antenna, with 60 flare angle, is compared to the conventional log periodic antenna. The Figure 18 shows the S 11 parameter of the antennas with S 11 along y-axis ranging from 35 db to 0 db and frequency in GHz along x-axis ranging from 0 3 GHz. As seen in Figure 18, there is only a slight variation in return loss parameter between the fractal antenna and the conventional log periodic antenna. As seen, the bands of frequencies providing more negative S-parameter (in db) have been improved too. The Figure 19 shows the VSWR parameter of the 60 flare angled LPKFA with VSWR along y-axis ranging from 0 to 120 and frequency in GHz along x-axis ranging from 0 to 3 GHz. The graph in Figure 19 shows that this log periodic Koch fractal antenna with 60 flare angle provides a VSWR = 1.3711695 at 1.37 GHz and VSWR (minimum) = 1.0698082 at 0.425 GHz. The simulated Quality Factor of this antenna, Q = 5332.1. 5. Conclusion Figure 17. Chart showing variation in Gain (db) vs. Frequency (GHz) for 60 flare angle antenna. In this paper, we used the CST Microwave Studio to design and simulate the log periodic Koch fractal antenna at various flare angles along with the traditional log periodic antenna. We find that the Koch Fractal antenna provides a better performance than the normal antenna and also that the antenna with a flare angle of 60 gives optimum performance in terms of radiation pattern, gain and directivity. This 60 flare angled Koch fractal antenna also provides a return loss parameter of up to 29 db and a VSWR < 2, which gives very high radiation efficiency. 56

A.K. Singh, R.A. Kabeer, Z. Ali, V.K.Singh, M. Shukla Figure 18. S-parameter (db) plots of log periodic antenna (dotted line) and log periodic Koch fractal with 60 flare angle Vs. Frequency (GHz). Figure 19. VSWR of Log Periodic Koch Antenna with 60 flare angle Vs. Frequency (GHz). References [1] Anagnostou D.E., Papapolymerou J., Tentzeris M.M., Christodoulou C.G., A printed log-periodic koch-dipole array (LPKDA), IEEE Antennas and Wireless Propagation Letters, 7, 2008, 456 460 [2] Sharma S.K., Shafai L., Investigations on miniaturized endfire vertically polarized quasi-fractal log-periodic zigzag antenna, IEEE Transactions on Antennas and Propagation, 52 (8), 2004, 1957 1962 [3] Song C.T.P., Hall P.S., Ghafouri-Shiraz H., Shorted fractal Sierpinski monopole antenna, IEEE Transactions on Antennas and Propagation, 52 (10), 2004, 2564 2570 [4] Naghshvarian-Jahromi M., Novel Wideband Planar Fractal Monopole Antenna, IEEE Transactions on Antennas and Propagation, 56 (12), 2008, 3844 3849 [5] Strycek M., Hertl I., Fractal log-periodic Antenna, In: IEEE proc., 2007, 1 3 [6] Wang B., Chen A., Su D., An improved fractal tree log-periodic dipole antenna, In: IEEE proc., 2008, 831 834 [7] Qiu J., Lin S., Yang C., You Q., A novel printed fractal log-periodic dipole antenna, In: IEEE proc., 2005, 50 53 [8] Tang P., Scaling property of the Koch fractal dipole, In: IEEE proc., 2001, 3, 150-153, [9] Moallemizadeh A., Hassani H.R., Nezhad S.M.A., Wide bandwidth and small size LPDA antenna, In: IEEE proc., 2012, 1 3 [10] Werner D.H., Werner P.L., Ferraro A.J. Frequency independent features of self-similar fractal antennas, In: IEEE proc., 2006 3, 2050 2053 [11] Cohen N., Fractal antenna applications in wireless telecommunications, In: IEEE proc., May 1997, 43 49, [12] Karim M.N.A., Rahim M.K.A., Majid H.A., Ayop O., et al., Zubir log periodic fractal Koch antenna for UHF band applications, PIER 100, 2010, 201 218 [13] Li D.T., Mao J.F., Koch-like sided Serpiski gasket mutifractal dipole antenna, PIER, 126, 2012, 399 427 57