The Electrical Design of a Membrane Antenna for Lunar-based Low-frequency Radio Telescope

Detecting primordial fluctuations from the cosmic dark ages requires extremely large low-frequency radio telescope arrays deployed on the far side of the Moon. The antenna of such an array must be lightweight, easily storable and transportable, deployable on a large scale, durable, and capable of good electrical performance. A membrane antenna is an excellent candidate to meet these criteria. We study the design of a low-frequency membrane antenna for a lunar-based low-frequency (<30 MHz) radio telescope constructed from polyimide film widely used in aerospace applications, owing to its excellent dielectric properties and high stability as a substrate material. We first design and optimize an antenna in free space through dipole deformation and coupling principles, then simulate an antenna on the lunar surface with a simple lunar soil model, yielding an efficiency greater than 90% in the range of 12-19 MHz and greater than 10% in the range of 5-35 MHz. The antenna inherits the omni-directional radiation pattern of a simple dipole antenna in the 5-30 MHz frequency band, giving a large field of view and allowing detection of the 21 cm global signal when used alone. A demonstration prototype is constructed, and its measured electrical property is found to be consistent with simulated results using |S11| measurements. This membrane antenna can potentially fulfill the requirements of a lunar low-frequency array, establishing a solid technical foundation for future large-scale arrays for exploring the cosmic dark ages.


INTRODUCTION
The concept of building a radio astronomical observatory on the far side of the moon has been considered since as early as 1965 [1].This is especially vital for the frequency band below 30 MHz, which remains largely unexplored because ground-based observations are severely affected by the strong reflection and absorption of Earth's iono-sphere, together with ubiquitous radio frequency interference (RFI).Conducting low-frequency radio observations on the lunar far side or in lunar orbit not only avoids the influence of Earth's ionosphere but also leverages the moon's shielding to block the otherwise substantial terrestrial electromagnetic interference [2].The opening up of this new window of astronomical observation holds vast potential for new discoveries and promises great scientific value.One of the most fascinating potential uses of such a telescope is the observation of the cosmic dark ages.This is the era after recombination of the hot plasma following the Big Bang, and before the formation of first generation stars and galaxies [3].The exploration and study of the cosmic dark ages may give insights into the early evolution of the universe and the nature of dark matter and offer the opportunity to observe primordial fluctuations generated during the inflationary era before their nonlinear evolution, elucidating the origin of the universe [4][5][6].Additionally, the ultra-long wave band can also be used for researching solar radio emissions, exoplanet radio emissions, the solar system's local environment in the galaxy, galaxy medium distribution,and the origins of cosmic rays, among other subjects [7].
In 1972, the US RAE-2 satellite, equipped with a lowfrequency inverted-V antenna, carried out observations of ultra-long wave signals in lunar orbit, confirming extreme electromagnetic quietness on the lunar far side [8].Subsequently, a number of spacecraft have carried lowfrequency payloads to make space-based observations, primarily aimed at solar or planetary sources(see e.g.[2,6,7] for further discussions ).During Chinese Chang'e-4 mission, low frequency radio experiments have also been carried out by the lander [9], the relay satellite [10], and the Longjiang-2 lunar micro-satellite [11].
Currently, a number of lunar radio astronomy mission concepts are under development, including lunar orbit single satellites such as The Dark Ages Polarimeter Pathfinder (DAPPER) [12], or satellite arrays like Discovering Sky at the ongest Wavelength (DSL) [13][14][15][16].It is also a consideration in lunar surface project concepts, such as the Lunar Surface Electromagnetics Experiment (LuSEE) [17] , the Lunar Crater Radio Telescope (LCRT) [18], and the Farside Array for Radio Science Investigations of the Dark ages and Exoplanets (FARSIDE) [12] proposed by the USA, the Astronomical Lunar Observatory(ALO) project [6] , and the Large Array for Radio Astronomy on the Farside (LARAF) proposed by China [19].Projects based in lunar orbit are typically simpler in terms of space engineering, but the lunar surface provides certain advantages; telescopes can be deployed on solid ground, making control, communication, and data analysis simpler, especially if they include a large number of array elements.
Constructing a radio telescope with a large receiving area and a large number of elements on the lunar far side surface is a great engineering challenge due to the prohibitive expense of shipping the material to the Moon and the severely restricted amount of labor and tools available for deployment and construction.A logical way to alleviate these problems is to construct the antenna using thin films, which are lightweight and easy to fold and store for shipping [20].Unlike on Earth, where a film needs to be fastened against the wind, lunar deployment is simplified by the lack of a significant lunar atmosphere.This is therefore considered as a major design option for most current lunar surface low-frequency radio astronomy projects [21][22][23].Membrane antennas have previously also been used on Earth for other applications (e.g., cellphone antennas or biomedical antennas), though typically on a much smaller scale [24].
In this paper, we conduct a preliminary study on the electrical design and performance of a membrane antenna in the context of constructing a lunar surface low-frequency array.The paper is organized as follows: in Section 2, we present the design of the membrane anAtenna; in Section 3, we describe our electromagnetic simulation and experiment test.We summarize and conclude in Section 4.

ELECTRICAL DESIGN OF A MEMBRANE ANTENNA
A lunar surface radio telescope can either be a reflector, such as the LCRT [18], an array of dipoles, or any variation or combination of these.A membrane can be applied in the construction of any type.Here we primarily consider the dipole array type, which is simpler to deploy and construct and is more flexible for large-scale applications.The membrane itself can be made with printed conducting layers, which can function as the antenna or connection wire.Being lightweight, a relatively large geometric size can be achieved, at least along one dimension.Before deployment, the membrane can be rolled to reduce its size for storage.It can then be carried by a lunar rover to the desired site, before being unrolled onto the lunar surface.A number of materials can be used for making such a membrane.Polyimide film, for example, exhibits excellent electrical properties(ϵ ∼ 3.1−3.5,tan δ ∼ 0.001−0.01)and has good stability in the ambient temperature extremes of the lunar surface [25].Consequently, we selected it as the antenna substrate considered in this study.
In the design of membrane antennas, apart from seeking a larger impedance-matched bandwidth, some engineering and technical specifications must also be satisfied.Here, we assume that for the convenience of rapid deployment on the far side of the moon, using a reel on the lunar rover, the width of the antenna is limited, i.e., we assume the film is a long strip.Wider films will require special design to fold and deploy, which we do not consider here.

Simple Dipole Antennas
We start with a simple dipole antenna made with the membrane.as shown in Figure 1-A, with a length of 20 meters, and a thickness of less than 1 millimeter, the impedance of feed port is 50 Ω.We consider a number of different widths, including 0.01 m, 0.25 m, 0.5 m, 0.75 m, and 1 m.On each, we perform an electromagnetic simulation of its electric performance, first in free space, then with a lunar surface model (described in Section 3.2) to investigate its impact on the dipole antenna.
The simulation results of |S 11 | parameter, as shown in Figure 2, demonstrate that the simple dipoles exhibits narrow resonances in free space.Fig. 2A compares dipoles with different widths in free space.The thinnest has the narrowest resonances, with the fundamental frequency occurring where the total length is equal to λ/2 =total length (for λ/2 = 20m, the corresponding frequency is 7.5 MHz), Higher resonances are observed at odd multiples of the fundamental frequency, with the next falling at 3 × 7.5MHz = 22.5MHz.For dipoles with larger widths, resonance frequencies are lower, with broader widths.We select the 0.25 m width model as our reference model, with its resonance occurring at approximately 7 MHz.
we observed that under the influence of the lunar surface (bottom panel of Fig. 2), the resonance points of the dipole antenna shift to lower frequencies compared to free space.This is because the lunar surface environment increases the effective permittivity of the environment in which the dipole is located, compared with free space.
Simulated antenna beam patterns are shown in figure 3 for free space , and Figure 4 for the lunar surface.In free space, the antenna maintains a broad dipole pattern.As the frequency increases, the two-lobed beam pattern splits into four lobes, due to the reverse currents on the antenna at shorter wavelengths.The presence of the lunar surface causes the antenna pattern under the lunar surface almost disappear.Owing to the effect of surface loss, the peak gain of the dipole antenna on the lunar surface is usually below 0 dBi.At higher frequencies, the antenna pattern will split further, giving more lobes.

Design Schemes of Membrane Antennas
A simple dipole has a narrow working band which requires a small |S 11 |, making it not very suitable for the purpose of observing low frequencies in a range of astronomical applications.This is a general problem in the design of low-frequency receivers.These have a large relative variation of frequencies, making it difficult to maintain well-matched impedance of the antenna and receiver over a wide frequency range.Here, we try to design a system to achieve good impedance matching over a relatively wide bandwidth.
In the design process, we first improve and optimize the antenna structure with various design patterns.We initially considered adopting the logarithmic spiral structure (Figure 1-B),with a feed port impedance of 200 Ω, capable of achieving ultra-wide band matching.However, for storage and deployment on the Moon by a single rover, a long strip of film wrapped around a spool is the most convenient form to use.With this in mind, we devote most of this study to designs in this form, such as the dipole square spiral and helical dipole as shown in Figure1-(C,D), However, these still require a large width to work effectively.
We find that the planar-coupled design can effectively expand the bandwidth of the antenna.Planar coupling refers to certain conductive layer portions of the antenna that are not directly connected, but are designed around the antenna to change its impedance through interaction of the electromagnetic field.The additional radiation paths and effective electromagnetic modes are significantly increased by the planar-coupled structure, thereby expanding the bandwidth of the antenna [26].By using a balun for impedance transformation, a planarcoupled wide-band dipole membrane antenna can be a good candidate.A possible design is shown in Figure 1-E.Two triangular regions at the bottom of the center are radiation blades, and other areas are planar-coupled structure which are not connected with each other.The feed port impedance is 300 Ω.
To simplify the simulation process and reduce simulation time, we first consider the free space background for the membrane antenna design and parameter optimization.Performance and optimization of the membrane antenna are then discussed and optimized with a simple lunar soil model, based on current lunar measurement data.

Parameter Optimization
After extensive simulations using the Computer Simulation Technology (CST) and FEKO(FEldberechnung beiKörpern mit beliebiger Oberfläche) software suites, on a number of different designs, we propose a lightweight, foldable, planarcoupled design.The main body of the membrane antenna is made up of isosceles triangular-shaped structures of conducting area, with a connection balun placed    the antenna's impedance bandwidth.This allows the membrane antenna, though a geometrically narrow structure, to have a large impedance bandwidth.The sizes of various structures and thickness of the membrane antenna are marked in Figure 5 and given in Table 1.The base material use for the bottom layer of the membrane is polyimide.The middle layer is metallic copper acting as the radiating layer, and the top layer is a coating layer used for preventing copper oxidation.Because this top layer is very thin, it is difficult for the software to simulate it accurately.Because the top layer of paint has minimal impact on the thin-film antenna, it is omitted from the simulation.An aerial photograph of the actual prototype, placed on the ground, is shown in the Figure 6.
The size of the membrane antenna is determined by several parameters.We focus on scanning and optimizing a few primary parameters, with the impedance bandwidth serving as the principal criterion, to achieve a larger impedance bandwidth below 30 MHz, and employ the CST simulation software for parameter scanning.Figure

Balun
The membrane antenna requires a balun structure for balanced-to-unbalanced conversion, as well as impedance transformation.With many types of balun structures available, choosing a suitable design is crucial to the performance of the antenna.A transformer balun exhibits superior performance in this band and can achieve an ultralarge bandwidth, so choose this variety of balun for the membrane antenna and use impedance transformation to widen the impedance bandwidth.
The test model of transformer used here is a MABA011040, manufactured by MACOM, with an impedance transformation ratio of 1:6. Figure 8 shows a photograph of the transformer balun, with dimensions L 7 =2.4 cm and W 4 =3.1 cm.The size of the balun was minimized to reduce insertion loss and lessen the impact on the mechanical structure of the membrane antenna.Measurement of the balun's S-parameters was performed using a back-to-back cascade approach with a Copper Mountain TR1300/1 vector network analyzer (VNA).

SIMULATION
Here, we consider simulations of our antenna models.We first make a validation test by simulating a membrane antenna model on the terrestrial ground, which can be compared with the measurement data.We then describe the model for the lunar soil and use it to simulate the performance of the antenna on the lunar surface.

Terrestrial Validation Test
We first validate our simulation by using terrestrial measurements of the membrane antenna.A membrane antenna with a feed port impedance of 300 Ω is connected via a 1:6 impedance-transforming balun transformer, and tested in an open field near the Hongliuxia observatory in Balikun County, Xinjiang, where the Tianlai experiment is located [27].The |S 11 | parameter is measured with a portable VNA.The relative permittivity and conductivity of the ground at the site is also measured.The measurement of the relative dielectric constant is conducted using the Time Domain Reflectometry method [28], and the conductivity measurement is performed using the Four-point probe method which was originally developed for semiconductor material [29].We model the testing site ground as an infinitely large ground plane, with the underground filled by a media with a relative permittivity of 3.60, and a conductivity 0.064 S/m, per our measurements.Fig. 10: The measured |S 11 | on the ground Figure 10 shows the terrestrial measurement and simulation results.showing that the measured |S 11 | is below -5 dB in the 10-35 MHz frequency band, with a resonance point at around 13 MHz, this is generally consistent with the simulation, though there is still some difference in the magnitude of |S 11 |, probably due to the simplification of the ground model.Real soil may have different conductivity and permittivity at different depths, leading to some discrepancy between the simulation and real measurements.This general agreement between the ground measurement and simulation gives us confidence that we can use the simulation for our design, provided we use a reasonably good lunar surface model.

The Lunar Surface Model
To use the membrane antennas on the surface of the moon, it is necessary to understand the impact of the dielectric properties of lunar soil on its performance.The dielectric constant is a complex number: where ε ′ is the real part of the complex dielectric constant, ε ′′ is the imaginary part,where ε 0 is the vacuum permittivity, ε r is the relative permittivity, σ is the electrical conductivity, ω is the angular frequency.The imaginary part of the permittivity is generally characterized using the loss tangent, defined as: The dielectric properties of lunar surface materials vary with different locations and depths.from existing research on the dielectric properties of lunar samples obtained from the Apollo and Luna missions [30], the real part of the permittivity of lunar soil is primarily related to density, showing little correlation with chemical composition and mineral constituents, while the loss tangent is associated with density and the proportion of FeO and TiO 2 [30]: tan δ = 10 0.038(FeO+TiO2)%+0.312ρ−3.26(5) Recent Chinese lunar missions, namely Chang'e 3, 4, and 5, user ground-penetrating radar to infer the complex permittivity of the lunar surface, yielding similar results [31][32][33].Chang'e 4, in particular, was the first to land on the far side of the moon, offering valuable reference data for future low-frequency exploration.Chang'e 4 measured the complex dielectric constants of the lunar surface down to a depth of 10 m, showing the relative permittivity to be between 2.64 and 3.85, with a loss tangent between 0.0032 and 0.0044 [31].Chang'e 6 is intended to return the first soil samples from the lunar far side, potentially allowing the lunar surface model to be further improved as new data becomes available.The loss tangent also increases with density; although, the correlation is not as strong, and it is also related to the material content, particularly ilmenite concentration [9].The loss tangent also changes with frequency, with the lowest resonant point occurring around 10 MHz, which is also temperature-dependent [30].On the whole, the loss tangent on the lunar surface is extremely small, indicating excellent insulation and for membrane antennas their radiation efficiency would not be much affected.
The lunar surface material consists of both regolith and rocks.Here, we model it as two plane layers, using the FEKO infinite multilayered medium simulation.The first layer consists of weathered regolith , which typically has an average thickness of 4-5m in lunar maria and 10-15m in highland regions [34].Here we consider the average thickness of 8.5 m, with density increasing gradually from 1.49 at the surface to 2.07 g•cm −3 at a depth of 8.5 m.With depth,the corresponding relative permittivity increases from 2.64 to 3.85 [31], with an average value of 3.25.This aligns with the sample's average loss tangent of 0.0091.The second layer, the rock layer, is modeled with an effectively infinite thickness.Its complex permittivity is primarily derived from Chang'e 4's ground-penetrating radar measurements, with a density in the range of 2-2.6 g•cm −3 at depths of 10-45 m.The average relative permittivity is taken to be 5.61,based on the data presented in Figure 11, with a loss tangent of 0.0246 and thickness taken as infinite.This structure is illustrated in Figure 12.

Simulation with the Modeled Lunar surface
For a simulation in free space, the |S 11 | parameter and the power beam pattern are shown in Figure 13.yielding |S 11 | is below -10 dB in the 15-27 MHz frequency band with a relative bandwidth of 57%.As the membrane antenna designed in this work is a type of dipole antenna, the directional pattern is essentially consistent with that of a dipole, maintaining a characteristic a wide beam throughout the entire frequency band with a peak gain of about 2.5 dBi.The E-plane directional pattern splits slightly at the maximum frequency of 30 MHz.This occurs because the antenna size exceeds the half wavelength, resulting in the splitting of the main lobe due to the presence of reverse currents, though the direction of the lobes does not change significantly.The H-plane directional pattern is essentially omni-directional in the entire frequency band.
Our simulation uses the simplified lunar surface model described above, in Section 3.2.The top panel of Figure 14 width of 48.2%.However, as mentioned before, the maximum impedance bandwidth occurs under a 1:6 impedance transformation in free space, indicating that the optimal balun impedance transformation ratio varies between free space and the lunar surface.
In the simplified lunar surface model, shown in Figure 12, the dielectric properties of the first layer of lunar soil (or regolith) predominantly affect the performance of the membrane antenna.However, because the dielectric properties of the lunar surface vary with location and depth.We examine a range of relative permittivity and loss tangent.Figure 15 shows the influence of complex dielectric properties on the performance of the membrane antenna on lunar surface.The relative permittivity affects the |S 11 | parameter of the antenna significantly.As it increases, the resonance points shift towards lower frequencies,as expected.The influence of loss tangent on |S 11 | is less noticeable, mainly due to the very low loss tangent value in the regolith.Observable changes only occur when they reach to a threshold level.
Simulated beam patterns are shown in Figure 16.These beam peaks in the zenith direction, with a peak gain is less than 1 dBi, somewhat smaller than the free space case due to Ohmic loss on the lunar surface.There are some ripples modulating on top of the dipole pattern due to apparent chromaticity, i.e. the beam pattern changes with frequency.These effects are relatively minor and can be easily accommodated in conventional astronomical observations.However, observation of 21 cm fluctuations in the cosmic dark ages requires extremely high precision, and such variations and ripples may introduce complications.Further efforts will be required to compensate these effects.
Figure 17 shows the impact of different permittivity values on the beam pattern at 15 MHz.An increase in relative permittivity results in increased ground loss and decreased gain for the membrane antenna in both the Eplane and the H-plane.
the pattern also changes with the variation of the loss tangent, as shown in Figure 18,with an increase in loss tangent leading to a weak decrease in antenna gain.This influence is negligible while the loss tangent is below a threshold level, becomes very obvious at higher values.

Antenna efficiency
Antenna efficiency here is determined primarily by antenna Ohmic loss, ground loss and impedance mismatching.For membrane antenna on lunar surface, Ohmic loss and ground loss are both small, making impedance mismatching the dominant consideration for antenna efficiency.Efficiency from impedance mismatching is calcu-lated using the relationship where η is the antenna efficiency and Γ is the reflection coefficient.
For frequency bands below 35 MHz, the sky signal is mostly from the synchrotron radiation of the Milky Way.The brightness temperature of the synchrotron radiation exceeds ∼ 10 4 K at 30 MHz, and can be in excess of ∼ 10 7 K at a few MHz, so it is the dominant component of system temperature.For an antenna efficiency of 10%, the signal-induced antenna temperature still far exceeds the environment temperature of the system, so a good signalto-noise ratio can still be obtained.we take the bandwidth of the 10% antenna efficiency as workable bandwidth for the lunar antenna.
Figure 19 shows a comparison between the efficiency in free space and on the lunar surface, indicating that this membrane antenna can achieve efficiency greater than 10% in free space at 7.4-35 MHz and efficiency greater than 90% at 15-27 MHz.The lunar surface simulation results show that the membrane antenna's efficiency exceeded 10% at 5-35 MHz and the efficiency exceeded 90% at 12-19 MHz.

SUMMARY
Lunar-based radio astronomy, as an important astronomical goal, is crucial for studying the epochs of the Cosmic Dark Ages and Cosmic Dawn.In such projects, the membrane antenna could play an important role.It has a number of favorable properties, such as light weight, compact collection volume, easy deployment, and no need to be fastened against wind in the lunar environment, making it well suited for use on a lunar mission.The receiving circuit can be directly mounted on the membrane antenna, forming an integrated receiver.
In this study, we investigate the electrical design of membrane antennas, noting that polyimide films have been used for previous space-based applications.However, in using this material for an antenna on the lunar surface, performance and durability still need to be investigated under the extreme variations in temperature and radiation exposure present on the surface of the moon.The goal is to construct a large radio interferometer array for ultra-longwavelength astronomy, i.e., at frequencies below 30 MHz.The antenna unit must have a wide beam and a broad working bandwidth, in order for the array to achieve a large field of view with the potential to be used in a wide variety of astronomical research, including observing the early universe.Here, we primarily consider designs in the   form of a long, narrow strip, as the most practical form to store, transport, and deploy.
Our antenna adopts a planar-coupling broadband dipole design, capable of achieving an antenna efficiency greater than 10% in free space from 7.4-35 MHz and greater than 90% antenna efficiency from 15-27 MHz while maintaining a very wide radiation pattern in frequency bands below 30 MHz.Informed by results from previous Fig.19: Comparison of antenna efficiency of membrane antennas in free space and on the lunar surface lunar missions, we create a simplified lunar soil model and simulate the membrane antenna performance when successfully deployed.On the lunar surface, the antenna efficiency is predicted to be greater than 10% at 5-35 MHz and greater than 90% at 12-19 MHz, with the radiation pattern maintaining a dipole form at 5-30 MHz.As noted in Section 3.3, for observations at such low frequencies, the sky temperature is very high, meaning that a 10% antenna efficiency is sufficient for astronomical observations with a good signal-to-noise ratio.
This study still has a number of limitations.It assumes the antenna membrane to be laid on a perfectly flat and uniform ground plane and adopts a highly simplified model for the lunar ground.In reality, it is unlikely to be deployed on a flat surface, and a more complex distribution of subsurface material may be present.While we vary our ground model parameters, such more complicated cases are not considered here.Additionally, the membrane antenna itself may also have bends and folds.Such issues will be addressed in future work.Nevertheless, the work presented here provides a good foundation for the design of a lunar-based radio telescope and can be used to aid in the design of antenna arrays on the lunar far side.

Fig. 1 :
Fig. 1: Several designs of membrane antennas.A: dipole, B: logarithmic spiral, C: square spiral dipole, D: helical dipole, E: Planar-coupled dipole.The red arrows show the feed port of each antenna

Fig. 2 :
Fig. 2: |S 11 | of the dipole membrane antenna.Top: different width in free space, Bottom: Comparison of the 0.25 m width dipole in free space and with lunar ground.

Fig. 3 :
Fig. 3: The beam pattern of the dipole model on the Eplane (top) and H-plane (bottom),simulated in free space.

Fig. 4 :
Fig. 4: The beam patterns of the dipole model on the Eplane (top) and H-plane (bottom), simulated on a modeled lunar surface.

Fig. 7 :
Fig. 7: Optimization of membrane antenna parameters.(topleft) The parameter scan of L1. (top right) The parameter scans of L2 and L3.(lower left)The parameter scan of W. (lower right)The parameter scan of W1.The red curve represents the optimal parameter set.

Figure 9
shows that |S 11 | < −18 dB, and |S 21 | > −0.55 dB across the entire frequency band.Through actual measurement, the 1:6 transformer balun exhibits excellent impedance matching and low transmission loss, meeting the requirements of the membrane antenna for ultrawideband.

Fig. 8 :
Fig. 8: Illustration of the impedance-transforming balun,showing physical dimensions, and a photograph of the balun used.

Fig. 11 :
Fig. 11: The relative permittivity (top) and loss tangent (bottom) of lunar soil as a function of density

Fig. 13 :Fig. 14 :
Fig. 13: Simulation results for a membrane antenna in free space.Top Panel: the |S 11 | parameter, Middle Panel: the power beam pattern in E-plane, Bottom Panel: the power beam pattern in H-plane.

Table 1 :
Dimensions of the membrane antenna