A Microstrip Second-Iteration Square Koch Dipole Antenna for TT & C Downlink Applications in Small Satellites

1CONACYT, Centro de Investigación y Desarrollo en Telecomunicaciones Espaciales, Universidad Autónoma de Zacatecas, Ramón López Velarde 801, Zacatecas, ZAC, Mexico 2Coordinación General de Investigación Cient́ıfica, Universidad de Colima, Gonzalo de Sandoval 444, Colima, COL, Mexico 3Facultad de IngenieŕıaMecánica y Eléctrica, Universidad de Colima, Carr. Colima-Coquimatlan Km 8.5, Coquimatlán, COL,Mexico 4Centro de Investigación y Desarrollo en Telecomunicaciones Espaciales, Universidad Autónoma de Zacatecas, Ramón López Velarde 801, Zacatecas, ZAC, Mexico


Introduction
Satellites are objects or devices that orbit a planet, which can be either natural or artificial.Regarding artificial satellites, thousands of them orbit the earth and have become a very important technology for modern life [1].Today, this space infrastructure offers telecommunication services such as television, telephony, and Internet.Satellites also allow us to predict weather, track hurricanes, monitor agricultural activities, understand population growth, and assess pollution levels [2].With respect to classification, satellites are classified based on some specific characteristics such as their mass, which classifies them from picosatellites (0.1-1 kg) to large satellites (>1000 Kg) [3].
Within the category of picosatellites are CubeSats, miniaturized satellites first developed by Bob Twiggs from Stanford University and Jordi Puig-Suari from California Polytechnic State University in 1999.CubeSats work typically in low earth orbits and have been used primarily by universities for research and space exploration, and they, as well as larger satellites, provide a wide range of research projects and applications.CubeSats are subject to a design protocol that specifies maximum outer dimensions equal to 100 × 100 × 100 mm 3 and it is worth mentioning that their electronic equipment is made of commercial off-the-shelf components [4][5][6].The main reason for miniaturizing satellites is primarily to reduce deployment costs, since larger satellites require larger rockets of greater cost to finance.Small satellites are not short of technical challenges, because they use innovative propulsion, attitude control, computer, communication, and power systems.Small satellites, as any wireless telecommunication system, also need to include antenna structures to perform core satellite functions [4].Each of these functions requires different antenna configurations, which have commonly been helices, monopoles, and patches.CubeSats commonly work at bands for amateur satellite communication purposes such International Journal of Antennas and Propagation as 434.8-438 (70-centimeter band), 1260-1270, and 2400-2450 MHz bands [5][6][7].
Requirements as operating frequencies for CubeSats can be achieved using microstrip antennas, which are manufactured by means of standard printed-circuit-board (PCB) techniques.Many advances in terms of printed antennas for small satellites have been presented, which is evidence of their importance.An example of these advances is the one referring to planar antennas at 2.225 GHz for small satellites in 1994 where optimization of the area between solar cells and microstrip antennas was achieved [8].Other examples of microstrip antenna structures for small satellites are the patch antennas for the USUsat, including patch antennas for the up/downlinks resonating at 450 MHz and 2.26 GHz, respectively [9], and the square patch low-gain microstrip antenna at 2.45 GHz to optimize antenna placement for the ESEO and SSETI-Express [10].Most antenna implementations target either the TTC or the payload data downlink subsystem [4] although recently a study on intersatellite cross-link antennas for picosatellites operating at 10.5 GHz has been conducted; this study consisted of modified Van Atta retrodirective arrays [11].
Printed antennas for small satellites have advantages such as integrating them into the structure, but, in scenarios like CubeSats, a challenging task is to print them on their reduced faces (100 × 100 mm 2 ) and make them resonate at relatively large wavelengths (70-centimeter band), since conventional /2 dipoles working at those frequencies are about 35 cm long and could not fit within those limited areas [4][5][6].The aforementioned design challenge can be solved by using fractal antennas whose geometry is created through the successive iteration of a generator shape to a simple basis shape [12], using conventional antennas of size less than a quarter wavelength of the radiation bandwidth, and hence the efficiency is reduced [13].Fractal antennas are multiband and optimize dimensions, making antennas at relatively small spaces possible work at relatively low frequencies.Fractal geometries were first studied by Mandelbrot during the 1970s and characteristics that define them include self-similarity, where small regions of the geometry duplicate the overall geometry on a reduced scale, which is generally interpreted as a measure of the space-filling properties and complexity of the fractal shape [14][15][16][17].
In this work, a planar and low-cost antenna for TTC (telemetry, tracking, and command) subsystems of CubeSat satellites is presented.The antenna consisted of a microstrip second-iteration square Koch dipole fractal antenna working at centimeter band, which shows characteristics that make it suitable for this kind of application.

Materials and Methods
This work was based on a methodology, which considered four critical stages.The stages were (i) antenna design and configuration, (ii) simulation, (iii) antenna fabrication, and (iv) measurements and implementation.These stages are described in Sections 2.1 to 2.4.

Antenna Design and Configuration.
The antenna design consisted of a microstrip fractal dipole with its 2 arms formed by square Koch curves in its second iteration ( = 2).The square Koch curve is obtained by repeatedly replacing each line segment composed of four quarters with the generator consisting of eight pieces, each one-quarter long.Koch curves, as other fractals, allow the optimization of the total antenna length making it possible to have antennas resonating at 70-centimeter band on a CubeSat face [18].In this case, the Koch antenna was built on the total diagonal of a 100 mm × 100 mm commercial PCB card which will act as one of the CubeSat faces.The second iteration Koch antenna occupies the entire diagonal  0 = 14.14 cm and had a total length of  2 = 56.56cm considering both antenna arms and the feed gap, since this total dipole length of the th iteration "  " is given by   = 2   0 , where "" is the integer iteration number within 0 ≤  < ∞.Regarding the microstrip segments that form the Koch dipole, it could be mentioned that they were made of copper on a bakelite substrate and they were 1.5 mm wide and 4.4 mm long.Also, it is important to note that, with that segment width, reaching iteration  = 3 would hinder the construction of the PCB antenna because the length of such segments would be 1.1 mm (shorter than the width), which is why iteration  = 2 was chosen.The fractal antenna is matched to a 50 Ω SMA coaxial connector that in turn is connected to a 50 Ω UHF transceiver through a 50 Ω coaxial cable.Figure 1 shows (a) iterations  = 0,  = 1, and  = 2 for a square Koch curve generated using Wolfram Demonstrations Project available in [19], (b) the top side of the printed fractal antenna, and (c) the bottom side of the printed fractal antenna.

Simulation.
In order to computationally evaluate the performance of the antenna design, it was decided to simulate it using the finite element method considering for the model two subdomains: one to simulate far-field free-space conditions which in turn was subdivided into two regions and the other one to simulate the 2 mm thick bakelite substrate.Also, an infinite sphere of radiation was considered.On the substrate, three negligible-thickness sheets were considered: two of them for the antenna arms set as finite conductivity and the other one for a 50 Ω lumped port which simulates the antenna feed.A frequency sweep considering 101 points from 400 to 500 MHz was performed in order to evaluate frequency-dependent parameters as reflection coefficient  11 , standing wave ratio VSWR, and input impedance which are defined as follows [12]: where   =   +   is the input impedance of the antenna and  0 is the impedance to which the designed antenna was connected.Also, an individual analysis setup at 436.5 MHz was considered to know the gain radiation patterns which are defined by where (, ) is the antenna gain and   (, ) is called the realized gain that takes into account the reflection/mismatch losses due to the connection of the antenna element to the transmission line.If the antenna is matched to the transmission line, that is, the antenna input impedance   is equal to the characteristic impedance  0 of the transmission line (| 11 | = 0), then the two gains are equal (  = ).Likewise,   and   are the reflection and radiation efficiencies, respectively (both dimensionless), (, ) is the directivity (dimensionless), (, ) is the radiation intensity, and  rad is the radiated power [12].Radiation patterns were simulated at 436.5 MHz because that is the center frequency at which the transceiver used for the satellite implementation described in Section 2.4 works.

Antenna Fabrication.
The fabrication step was conducted by using conventional PCB techniques.For the design of the antenna geometry, EDA (electronic design automation) software for the creation of professional schematics and printed circuit boards was used [20].This fabrication process included an SMA (SubMiniature version A) connector, which was connected directly to the antenna arms.As it was mentioned before, the microstrip Koch fractal antenna was built on the total diagonal of a 100 mm × 100 mm single-sided commercial PCB card shown in Figure 1(b). of the frequency channels at which the transceiver TR2M-436.50-10-ARSfrom Radiometrix5 works.TR2M-436.50-10-ARSwas used to build the communications stage for the small satellite and the receiving card for the ground station.Polarization of transmitting and receiving antennas was set to be matched so that losses due to polarization mismatch were minimized.Figure 3 shows the diagram of the prototype satellite link implemented.It is important to highlight that, in this scenario, there were no surrounding structures and multipaths occur due to ground reflections.However, due to the distance between the transmitter and the receiver and because a narrowband signal was transmitted, the multipath waves could be neglected.

Results and Discussion
Regarding frequency-dependent parameters, such as reflection coefficient  11 , VSWR, and input antenna impedance in the range of 400 to 500 MHz (70-centimeter band), it can be highlighted that simulation results were very similar to those obtained in measurements with the VNA, in both cases observing resonance frequencies with reflection coefficients below −20 dB, VWSR under 2, and impedance with magnitude very close to 50 ohms.Figure 4 shows the antenna behavior in terms of (a) reflection coefficient, (b) VSWR, and (c) input antenna impedance.
In order to highlight the results observed in the above graphics, emphasis on the resonance frequencies and their bandwidths around them was done, so in Table 1 a summary of the antenna performance in terms of frequency-dependent parameters is shown.
As it was mentioned in Sections 2.2 and 2.4, two frequencies of interest in this work are 436.5 MHz and 436.675MHz: the central frequency of transceiver TR2M-436.50-10-ARSand the frequency channel selected for the practical satellite implementation, respectively.Although these are not optimum frequencies for the fractal antenna, frequencydependent parameters remain within acceptable limits.Table 2 shows the fractal antenna behavior at 436.5 MHz and 436.675MHz.
In this work, it was decided to design this linearly polarized fractal antenna on the diagonal of one side of a CubeSat in order to make the most of its limited dimensions compared with wavelengths at 70-centimeter band.Although the fractal antenna does not have its resonance frequency within the TR2M-436.50-10-ARSband, the performance is acceptable without designing one that resonates exactly at those frequencies, a design where the main constraint is the total length that would be greater retaining the same iteration.
As it was mentioned before, regarding radiation patterns for the printed fractal antenna at 436.5 MHz, they were obtained both by simulations and by measurements.The fractal antenna was placed vertically so that the PCB formed a diamond with respect to the floor, considering the PCB plane as the "" plane with the "-axis" perpendicular to this plane.Figure 5 shows (a) the 3D simulated total gain pattern with respect to the PCB geometry and the corresponding magnitude of the current distribution on the antenna surface, (b) plots for 2D simulated normalized total gain pattern for the main antenna planes, and (c) plots for 2D measured normalized patterns (power at the receiver) for the main antenna planes inside an anechoic chamber.
In Figure 5, it can be seen that both the simulated and the measured radiation patterns show similar behaviors, although it should be mentioned that simulation case was ideal, while measurements were performed using different antennas at the transmitter and at the receiver.Anyway, in both cases, the typical behavior of dipole antennas is observed, which leads to classifying it as an omnidirectional  antenna [12].At 436.5 MHz, simulated and measured radiation patterns have nulls on the -plane at 90 ∘ and 270 ∘ while they have main lobes at 0 ∘ and 180 ∘ .At 436.5 MHz, the maximum total gain computed by numerical simulations was  max = 1.391 = 1.433 dBi, while at 462 MHz it was  max = 1.433 = 1.565 dBi which is the simulated resonance frequency between 400 MHz and 500 MHz.Simulated radiation efficiencies were 98.56% and 98.77% at 436.5 MHz and 462 MHz, respectively.An aspect to emphasize with respect to the small satellites is that if they lack an on-board stabilization system, this results in a polarization mismatch between the involved antennas.Figure 6 shows simulated components (a)   () and (b)  0 () of the antenna gain at 462 MHz for different values of 0 from 0 ∘ to 180 ∘ where the different radiation patterns can be appreciated and in order to see polarization discrimination.
Finally, with regard to the implementation of the prototype satellite link working at 436.675 MHz, telemetry data from the picosatellite including temperature, altitude, and acceleration were received successfully at the ground station.Similarly, it was decided to take measurements of received power with an N9913A spectrum analyzer [24], where it was observed that the received power was   = −57.526085dBm = 1.7676 nW.This received power level is acceptable considering that losses due to connectors, adapters, and cables used during this implementation exceed 5 dB.Also, a receiving antenna gain of approximately 5.56 dBi, separation between transmitter and receiver of 938.81 m, and transmitted power of 27.31 dBm = 538.27mW were considered which led to the estimation of a transmitting antenna gain that resembles the one computed by simulations using the Friis equation under ideal conditions [25]. Figure 7 shows (a) the antenna design connected to the picosatellite, (b) the ground station with its UHF vertical monopole antenna getting telemetry data, and (c) the UHF vertical monopole antenna connected to the spectrum analyzer.

Conclusion
In this work, the use of fractal geometries for designing printed antennas at the 70-centimeter band for TT&C downlink applications in small satellites has been demonstrated.It is probed that an antenna working at 70-centimeter band can be printed on the limited surfaces of CubeSat faces (100 mm × 100 mm), since, for example, conventional /2 dipoles working at those frequencies are about 35 cm long and could not fit within those areas.The design was a second-iteration fractal dipole antenna printed on a 100 mm × 100 mm commercial PCB card with bakelite substrate and having a total length including the feed gap of 56.56 cm.where an approximate link budget considering losses gives a maximum gain similar to that obtained through simulations.These parameters make this antenna geometry suitable for TTC subsystems in CubeSat satellites, which leaves as future work the experimentation with other types of substrates in order to improve the antenna characteristics.

Figure 1 :
Figure 1: (a) Iterations  = 0,  = 1, and  = 2 for a square fractal curve used as dipole arms; (b) top side of the PCB for the designed antenna; (c) bottom side of the printed fractal antenna.

Figure 2 :Figure 3 :
Figure 2: Experimental setup using an anechoic chamber: (a) diagram and (b) a photo of the inside of the chamber.

Figure 5 :Figure 6 :Figure 7 :
Figure5: Radiation patterns at 436.5 MHz: (a) 3D simulated total gain pattern with respect to the PCB geometry and its corresponding magnitude of the current distribution on the antenna surface, (b) 2D plots for simulated normalized total gain patterns for the main antenna planes, and (c) 2D plots for measured normalized power patterns for the main antenna planes inside an anechoic chamber.

Table 2 :
Frequency-dependent parameters for the designed Koch antenna at 436.5 MHz and 436.675MHz.