An Active Ribbon Dipole as an Array Element Prototype for the Lunar Very Low Frequency Radio Telescope

This work is concerned with a detailed study of an active antenna, which can serve as a prototype of a phased array antenna element for a future lunar very-low-frequency (VLF) radio telescope operating in the frequency range of 1–30 MHz. The antenna consisted of a ribbon symmetrical dipole and a low-noise preamplifier. A dipole 10 m long lay on a flat surface of lunar soil, consisting of a layer of regolith 10 m thick and solid bedrock. The dipole parameters were determined by full-wave simulation using the Altair Feko 2022 software. The preamplifier was a single-stage HEMT low-noise amplifier, whose parameters were determined using the Advanced Design System 2023 software. An active antenna was analyzed using a model created to calculate all electrical and noise parameters. Special attention was paid to the analysis of the antenna sensitivity in terms of the System Equivalent Flux Density (SEFD) and Sky Noise Dominance (SND), taking into account changes in the lunar ambient temperature from 100 K to 400 K. It was shown that the frequency dependences of many active antenna parameters, in particular, radiation efficiency, directivity, effective area, SND, and SEFD had noticeable oscillatory components. The radiation pattern of the antenna was also subject to cyclical changes that occur in sync with the changes in directivity. These properties of the active antenna, caused by the presence of two-layer soil, should be considered when developing future lunar VLF radio telescopes.


I. INTRODUCTION
Low-frequency (LF) radio astronomy studies electromagnetic radiation from extra-terrestrial sources at frequencies below 100 MHz, which allows it to obtain data on the universe that are not available in any other way. Although K. Jansky, the pioneer of radio astronomy, made his discoveries in this frequency range, the development of LF radio astronomy was for a long time constrained by the need to invest heavily in the construction of radio telescopes whose dimensions in this range reach thousands of meters. However, progress The associate editor coordinating the review of this manuscript and approving it for publication was Wanchen Yang .
in the fields of antenna technology, microelectronics, and digital technologies at the beginning of this century has made it possible to begin the development and construction of contemporary large new-generation LF radio telescopes. These include LOFAR [1], which has an operating range of MHz, and MWA [5], part of the operating range of which f = (80 − 300) MHz belongs to the field of low-frequency radio astronomy. Most of these have been put into operation and provide unique scientific results. These results could be significantly supplemented if it were possible to expand the range of operation of radio telescopes at frequencies f <10 MHz. However, this expansion is hindered by Earth's ionosphere, which does not transmit radio waves below f = (8 − 10) MHz. In addition, the presence of strong man-made and atmospheric RFI at frequencies below 30 MHz makes it very difficult to perform radio astronomical observations. These obstacles can be overcome if the LF radio telescope is taken out of the Earth's ionosphere and located in a place protected from terrestrial interference. The Moon's far side is the place closest to Earth.
Radio astronomy, which covers the frequency range below 30 MHz is commonly referred to as very low frequency (VLF) [6]. The scientific prospects that open up for radio astronomy and astrophysics after the creation of VLF radio telescopes on the Moon are covered in detail in the literature [6], [7], [8], [9], [10], so we will not dwell on them. These prospects have inspired researchers and engineers to create radio astronomical observatories on the Moon.
One of the earliest projects of the lunar VLF radio telescope was proposed in [11]. In the authors' opinion, this construction is extremely simple and inexpensive. It consists of a large array of short wires (dipoles) laid across the lunar surface, each of which is equipped with an amplifier and digitizer and connected to a common computer. Arrays of two configurations were considered: one was a square with 100 × 100 elements, occupying an area of 15 km ×15 km, and the second was T-shaped with arms of 30 km and 15 km, which contained 200 and 100 elements, respectively.
The European Space Agency (ESA) developed a project [12] of a VLFA (Very Low Frequency Array) radio telescope with an operating range of 500 kHz to 16 MHz for performing radio astronomical observations on the far side of the Moon. It is assumed that the VLFA will have a classic Y-shape, or a 3-arm logarithmic spiral shape. Each of the three arms holds approximately 100 elements that will be electrically short tubular dipoles, 4 m long and approximately 4 cm in diameter, spaced along the arms according to a power law.
In [13] a NASA-funded concept of a Radio Observatory on the Lunar Surface for Solar studies (ROLLS) was proposed. The ROLSS antenna array has three arms arranged in a Y-shape. Each arm is approximately 1000 m long and is made of thin polyimide tape (Kaptone-4), on which 16 identical dipole antennas are printed and distributed along the arm according to a logarithmic law. The length and width of the dipole were 14 m and 1 m. The signals from the antennas were transmitted to a central electronics package by transmission lines, printed on the same polyimide film. The array was operated in the frequency range of 1-10 MHz.
One more NASA-funded project, FARSIDE (Farside Array for Radio Science Investigations of the Dark ages and Exoplanets), is a concept to place a low radio frequency interferometric array on the farside of the Moon [14], [15], [16].
The proposed interferometer antenna consisted of two arrays, each with 128 dipoles. One of them is designed to cover the range of 100 kHz -2 MHz, and the other 1 -40 MHz. Dipoles have lengths of 100 m and 5 m, respectively. Each antenna had a low noise amplifier (LNA) that sent a signal to the Base Station via optical fibers as an analog signal.
One of the latest projects is FarView (A Lunar Far Side Radio Telescope to Explore The Cosmic Dark Ages) [17], [18], which is planned to be built on the lunar far side. It will be a low-frequency (5-40 MHz) radio observatory with a sparse array antenna of ∼100,000 elements covering an area of ∼120 km 2 . Each array element is a 10 m long dipole antenna. The innovations in FarView are the near-exclusive use of in situ resources and manufacturing to build the observatory, including antennas and power generation infrastructure. This project was funded by NASA Innovative Advanced Concepts (NIAC).
Proposals for the creation of the first VLF observatory on the far side of the Moon were also presented in [19] and [20]. Their difference from the previous ones is that they proposed, as a first step, to place a small-sized array of several elements (for example, five) on the Moon, made in the likeness of the well-proven array elements of groundbased low-frequency radio telescopes. The effectiveness of such a step is evidenced by test radio astronomy observations of solar bursts at frequencies below 10 MHz, and on some days (when the ionosphere allowed) up to 5 MHz and even up to 2 MHz [21]. These observations were performed using an inverted V-dipole 5.6 m in length, which is a 2-fold scaled array element of the GURT [4].
As can be seen from this short review, short electric dipoles equipped with preamplifiers are chosen as elements of antenna arrays in all lunar radio telescope projects mentioned here. Most developers attribute this choice to the high stability of the shape of the short dipole radiation pattern over a wide frequency range when it is located both in free space and above dielectric half-space. It is also noteworthy that the length of the dipoles varied from 4 m to 14 m for the same frequency range. In some projects, theoretical and experimental studies of the dipole parameters have been carried out, albeit under terrestrial conditions, as well as their electromagnetic modeling, taking into account the vacuum/regolith interface. However, regolith is only a sheet of loose superficial deposits covering the solid bedrock. Regolith is a fairly good dielectric, the parameters of which, according to various estimates, are in the following ranges: dielectric constant ε r = 1.7 − 4.4 and loss tangent of 0.003-0.04 [22], [23], [24], [25], [26]. Its thickness varies from approximately 1m to 20 m [26], [27], [28], [29] and its average value is approximately 4-12 m depending on the region, which is comparable to the wavelength at a frequency of 30 MHz and much less than that at a frequency of 1 MHz. Thus, the regolith is not as thick as it ignores the lower bedrock when estimating the parameters of an antenna on or near the lunar surface.
The recently published results [30], [31] of electromagnetic simulations of a short dipole located near two-layer lunar soil showed that the presence of a second regolith/bedrock interface leads to a noticeable frequency dependence of the dipole radiation pattern, as well as to distortions of the traditional frequency dependencies of important parameters such as the effective area and radiation efficiency. It is known that these parameters directly affect the sensitivity of the active antenna, which was either not estimated in the above projects or was estimated approximately without considering the influence of ambient temperature, which varies over a very wide range on the Moon's surface. Therefore, it is necessary to evaluate the parameters of the antenna, which can serve as a prototype element of the antenna array of the lunar VLF radio telescope, considering the two-layer structure of the soil and the large ambient temperature drops. This study is devoted to partially solving this problem.

II. ANTENNA DESIGN
We assume that the element of the antenna array of the future lunar VLF radio telescope will be an active antenna consisting of a symmetrical dipole and a low-noise amplifier.

A. DIPOLE
A convenient form of dipole implementation is a thin layer of metal printed on thin polyamide tape made from Kapton-4. It was shown in [32] that arrays of such dipoles could be easily laid on the soil surface by unfolding the tape using automatic rovers. In addition, the results of climatic tests of such a film are described in [13], namely, the impact of ambient temperature fluctuations and hard ultraviolet radiation, which showed the possibility of its application in lunar conditions. Based on the results of preliminary calculations, we chose a symmetrical ribbon dipole with a length 2L = 10 m and width w = 0.3048 m (12 inches). In the central part of the dipole, its arms are pointed and connected by a jumper a = 4 cm in length and 1 cm in width. The jumper in the middle is divided by a thin excitation gap to which the LNA input terminals are connected (Fig. 1). As shown in the figure, such a dipole shape makes it easy to combine it with the same dipole on a perpendicular tape, which may be a part of the array for receiving an electromagnetic wave of orthogonal polarization.
The tape with the dipole lies on the flat surface of lunar soil, which consists of a loose regolith layer and solid bedrock (Fig. 2). Such a two-layer model [33] of lunar soil has been successfully used to interpret the measurement data of a horizontal electric dipole field in the frequency range of 1-32 MHz that was collected on the Moon by Apollo 17 [34]. We assumed that the thickness of the regolith layer is d = 10 m, and its electrical parameters are ε r1 = 2.52 and tan δ 1 = 0.007. The bedrock on the Moon is represented by different rocks, among which basalts, anorthosites, and granites predominate, so its electrical parameters can vary widely ε r ≈ 4 − 16 and tan δ ≈ 0.005 − 0.1 [35], [36].   We have chosen for the 2nd medium ( Fig. 2) the values ε r2 = 5.2 and tan δ 2 = 0.01, which are similar to the parameters of granite.
The calculation of the electrical characteristics of the dipole was carried out by full-wave electromagnetic simulation in Altair Feko 2022 [37], which correctly takes into account the presence of a flat-layered medium. Figure 3 shows the frequency dependence of the dipole impedance Z = R + jX , from which it follows that in the frequency range of 1-35 MHz, the dipole resistance R varies from 6 to 616 , and the reactance X from -2147 to 195 , undergoing three resonances (X = 0) at frequencies of 10.7 MHz, 18.7 MHz, and 33.7 MHz. It is easy to verify that the first resonance corresponds to a half-wave dipole, the second to a full-wave dipole, and the third to a one-anda-half-wave dipole, if we take into account that the current wavelength along the dipole lying at the vacuum/regolith interface is (ε r1 + 1) 2 ≈ 1.32 times shorter than in VOLUME 11, 2023 free space. Fig. 4 shows the frequency dependencies of the dipole gain G 0 and directivity D 0 in the zenith direction [38], as well as its radiation efficiency η, considering the absorption of energy in the ground. Here, the oscillatory type of all three dependencies is striking, which was first noticed in [30] and [31], where the fundamental characteristics of a short electric dipole over a two-layer ground were studied. The reason for these oscillations can be explained using the ray approximation of electromagnetic wave propagation in a layered medium, which is effectively used to estimate lunar regolith parameters [26], [33]. According to this approach, the dipole radiation field in the upper half-space can be represented as the sum of three waves: a direct wave, a wave reflected from the vacuum/regolith interface, and a wave reflected from the regolith/bedrock interface. The last wave passes through the regolith layer twice before entering the upper half-space, causing its phase to change with the frequency. This wave, which interferes with the other two waves increases or decreases, depending on the frequency, the total wave amplitude that propagates in the zenith direction, which leads to oscillations in the dipole parameters frequency dependences (Fig. 4). It should be noted that not only are the mentioned parameters of the dipole subject to oscillations but also their radiation pattern that cyclically expands and contracts synchronously with the change in the directivity. . The dipole itself also contributes to the change in the radiation pattern, the electrical length of which increases with increasing frequency. Fig. 6 shows the normalized radiation patterns in the E-and H -planes at the same frequencies. It can be seen that the narrowing of the pattern with increasing frequency is more clearly manifested in the E-plane than in the H -plane and is more noticeable at the frequencies of the directivity maxima than at minimum frequencies. After a frequency of 31 MHz, there is a rapid increase in the side lobes of the dipole pattern, which then become the main ones, and the lobe level in the zenith direction at 35 MHz drops to -10.5 dB. Fig. 7 shows the frequency dependences of the dipole effective area A e and absorption area S abs , which are related as [39] where D m is the maximum dipole directivity, λ is wavelength in free space. These graphs show that the dominant dependence of these areas on the frequency of the 1 f 2 type was also superimposed by oscillations that correlate with the gain and directivity oscillations shown in Fig. 4.

B. PREAMPLIFIER
LNAs have been successfully used in antenna array elements of contemporary ground-based low-frequency radio telescopes [1], [2], [3], [4] to amplify the received signal and facilitate impedance matching of dipoles with terminal loads over a wide frequency range. Using an LNA in a lunar radio telescope helps to solve the same problems; however, the requirements for its parameters differ markedly from those on the ground because of changes in its operating conditions. The main changes consist of a noticeable reduction in the requirements for the linearity of the LNA [40], [41] because of the absence of intense interference on the far side of the Moon, in the expansion of the requirements for its stable operation in a wide range of ambient temperature changes (approximately from 100 K to 400 K [42]), as well as minimizing power consumption.
Because we do not know the system requirements for the LNA and therefore cannot offer its complete design, we consider only its front end, which largely determines the system sensitivity. Fig. 8 shows a circuit diagram of the preamplifier compiled considering these requirements. Its main element X1 is the Avago ATF-38143 low-noise HEMT transistor, which has a high gain and low power consumption. An RF transformer with a turn ratio of 2:1 at the input of the preamplifier improved its impedance matching with the dipole at low frequencies. The resistor R1=3.6 k , supplied to increase the stability factor of the amplifier, had almost no effect on its noise figure. The remaining circuit elements have the following values: R2=125 , R3=75 , C1. . . 4=0.1 uF, L1. . . 3=1 mH. The preamplifier supply voltage was 3 V, and the drain current was 5 mA. When a fiber-optic collection system is used in the array antenna, the LNA can be mounted on one arm of the dipole close to the drive gap. In such a case, this arm will be used as the grounded (''negative'') electrode of the LNA, and its ''positive'' input electrode is connected to the other arm of the dipole on the opposite side of the gap. The negligibly small dimensions of the LNA board in comparison with the dimensions of the arm will not affect the dipole parameters in any way. The design and study of the preamplifier were carried out using a circuit simulator of the PathWave Advanced Design System (ADS) software [43] using the original temperature-scalable nonlinear large-signal model of the ATF-38143 transistor from the vendor. This approach allows the determination of all electrical and noise parameters of the preamplifier in the frequency range from DC to the maximum frequency declared in the transistor datasheet, considering changes in ambient temperature.

III. ANALYSIS TECHNIQUE
The receiving active antenna under consideration can be analyzed using the technique proposed in [44]. It is based on the representation of an active antenna by a cascade connection of two two-terminal networks, the first of which corresponds to a dipole and the second to a preamplifier loaded on a transmission line with a characteristic impedance Z c . Scattering matrices S were used to describe the electrical parameters of these two-port networks, and correlation matrices of noise waves C were used to describe the noise parameters. The parameters of the first two-port network can be determined using the formulas obtained in [45], where the dipole radiation efficiency η and impedance Z obtained by the simulation in Feko should be substituted. The parameters of the second two-port network were determined by simulating the preamplifier in the ADS. Combining these two-port networks, we obtain a mathematical model of the active antenna as a whole, which makes it possible to obtain formulas for calculating all its parameters. We use some of these to evaluate the sensitivity of an active antenna according to the signal-tonoise criterion.
We assume that the antenna operates in the receiving mode and that the source of its excitation is a plane electromagnetic wave that carries a useful signal. The wave was incident from the (θ, ϕ) direction, its power flux density was S i , and its polarization was matched to that of the dipole. In this case, the power of the signal received by the dipole is where F(θ, ϕ) is the normalized dipole radiation pattern. The preamplifier transforms P 1 to power P 2 at the active antenna output where G P is the preamplifier operating power gain IMF is impedance mismatch factor G T is the transducer power gain of the preamplifier given by is the dipole input reflection coefficient S mn are preamplifier S-parameters. The antenna receives not only a useful signal but also external noise (due to the galactic and extragalactic background radiation), the intensity of which can be described by the following formula, which is valid for the considered frequency range: where I g and I eg are the intensities [W·Hz −1 ·m −2 ·sr −1 ] of galactic and extragalactic background radiation, respectively; Equation (8) was obtained in [46] based on the results of the study of the polar regions of the sky and corrected in [47] and [48] by increasing I g by 30%, which makes it possible to use it to estimate the average T B over the entire sky sphere.
According to Rayleigh-Jeans law, the intensity I f can be associated with the brightness temperature T B of the sky The noise power caused by receiving this radiation is given by where T ext is the external noise temperature of the active antenna at the dipole terminals An active antenna produces intrinsic noise, the sources of which are the preamplifier and dipole, together with the ground. Because the dipole is made of highly conductive metal, its noise can be neglected. Then the effective temperature of the internal (intrinsic) noise of the active antenna, referred to the dipole terminals, can be represented as the sum where T pre is the effective noise temperature of the preamplifier T gnd is the noise temperature induced on the dipole terminals by the ground C mn are preamp C-matrix elements; T 0 is the ambient temperature.
One of the main performances of a radio telescope is its fluctuation sensitivity, which is usually estimated by the minimum flux density that it can detect against the background of noise [4], [49] where f is the predetection bandwidth, τ is the post-detection integration time, n is the number of records averaged, SEFD is the system equivalent flux density, which for a single-polarized antenna is determined as [50] SND = T ext T int is the sky noise dominance [51] and T sys = T ext + T int is the system noise temperature of the receiving active antenna.
In the case of a crossed dipole, its SEFD can be calculated using the technique developed in [52] and [53]. 75230 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

IV. ANALYSIS RESULTS AND DISCUSSION
The technique described above combined with the use of Feko and ADS software enabled us to analyze the main parameters of the active antenna placed on a layered lunar soil. Fig. 9 shows the frequency dependences of the IMF (5) and three power gains of the preamplifier, G S21 = |S 21 | 2 , G P (4), and G T (6), corresponding to the three reflection coefficients S s seen looking toward the source S s = 0, S s = S * 11 , and S s = , respectively, whereas the reflection coefficient seen looking toward the load is zero. It can be observed that the preamplifier operating power gain G P remains constant over the entire frequency range under consideration and is equal to ∼27.2 dB, which is a rather large value for a single-stage circuit. The gain of the G S21 is also constant at ∼8.6 dB, whereas the G T varies with the frequency in sync with the IMF, dropping to a minimum of ∼0 dB at 3MHz and peaking at 19 dB at 19 MHz. The preamplifier has absolute stability; its stability factor has the smallest value of 1.45 per 35 MHz, which increases monotonically to ∼50 upon decreasing the frequency to 1 MHz.
In Fig.10 the frequency dependences of the external T ext and internal T int noise temperatures of the active antenna, referred to the dipole terminals are shown. The first of them practically does not depend on the ambient temperature T 0 , whereas the second is subject to its noticeable influence. In this regard, T int is shown in Fig. 10 for three values of ambient temperature: the standard T 0 = 290K, the minimum T 0 = 100K, to which the temperature on the Moon can drop at night, and T 0 = 400K, the maximum temperature on the lunar surface during the daytime.
Before discussing the behavior of the curves in Fig. 10, the ratio between the contributions to T int made by the preamplifier and the ground noise should be evaluated. These contributions are shown in Fig. 11 for the nighttime. This figure clearly shows that the ground noise temperature T gnd was almost constant over the entire frequency range under consideration. Because of the low dipole radiation efficiency,  T gnd is close to the ambient temperature T 0 = 100K (14), and barely noticeable T gnd fluctuations, synchronous with radiation efficiency fluctuations, remove it from T 0 at some frequencies by no more than 12K. In contrast, the effective noise temperature T pre of the preamplifier as part of an active antenna varies over a very wide range, from approximately 5 K to 1460 K, which is more than 24 dB. This behavior of T pre is caused by the strong frequency dependence of the dipole impedance Z (and its reflection coefficient ), which is connected to the preamplifier input. The preamplifier noise temperature riches minimum T min ≈ 5 K (Fig. 11), when the source connected to its input has an optimum reflection coefficient S opt ≈ 0.9. This temperature is constant over almost the entire frequency range and it increases to 8 K only at frequencies near 1 MHz. The mutual arrangement of the curve of change (f ) and optimal reflection coefficient S opt can be traced on the Smith chart (Fig. 12). It can be seen that the (f ) curve most closely approaches S opt near a frequency of 19 MHz, which corresponds to the T min in Fig. 11.
Returning to this figure, it should be noted that the ground noise temperature T gnd at night prevails over the effective preamplifier noise temperature T pre over most of the frequency range, and the relationship is reversed only below 8 MHz. From the point of view of reducing the internal noise of an active antenna, the most problematic are the frequencies 1-5 MHz, where T pre is large owing to a strong noise mismatch of the preamplifier with the dipole. The inclusion of transformer TF1 (Fig.8) with a turn ratio of 2:1 into the preamplifier made it possible to increase S opt from 0.7 to 0.9, thereby bringing it closer to (f ) at the lower frequencies of the range, which made it possible to reduce T pre by approximately 5 dB at 1 MHz. However, a further increase in the turn ratio is impractical because it leads to a noticeable decrease in the IMF and deterioration of the other parameters of the active antenna. As the ambient temperature increased, the internal noise temperature of the active antenna also increased; however, all the described behaviors remained the same, except that the intersection point of T pre and T gnd gradually shifted, and at T 0 = 400K it turned out to be near to 12 MHz. Fig.13 shows the frequency dependence of SND, which is an important indicator of the quality of an active antenna as an element of a radio telescope array. The larger the SND, the less the internal noise of the antenna affects the sensitivity of the radio telescope. In SND, as in other previously considered active antenna parameters, there is an oscillatory component caused by the presence of a two-layer ground. The acceptable value of SND is considered to be 6 dB [51], at which, to completely level out the influence of internal noise on the sensitivity, it is necessary to increase integration time by only ∼57% more than with a perfect noiseless preamplifier. Calculations have shown that the SND of the considered active antenna noticeably exceeds the permissible level in a significant part of the frequency range at any ambient temperature; and at T 0 = 100 − 300K it does not drop below the level of 6 dB, and only at an extremely large temperature T 0 = 400K does it ''fall short'' of the acceptable level is only 2-3 dB at the extreme frequencies of the range. Fig. 14 shows the frequency dependence of SEFD which allows us to estimate the fluctuation sensitivity of the studied active antenna (16). However, before discussing the graphs given here, we transform equation (17) by substituting S abs (1) and T B (9). After assuming SND ≫ 1 we obtain It follows that the SEFD of an active antenna with a perfect noiseless amplifier is completely determined by its directivity D m , the larger D m , the smaller the SEFD, therefore, the higher the sensitivity. For an antenna with D m = Const., the frequency dependence of the SEFD is the same as of the intensity I f (f ). An example of a similar antenna is a Hertzian dipole located near an interface with a homogeneous halfspace. Since its directivity is D m ≈ 4 and does not depend on the frequency, then the SEFD of this dipole with a noiseless  amplifier is determined as The frequency dependence of SEFD H is illustrated by dashed line 1 in Fig. 14, which is determined by the physical properties of the intensity I f (8) of the galactic and extragalactic noise radiation. This curve has a maximum at ∼3 MHz, after which it drops sharply with decreasing frequency and slowly decreased (approximately as 1 √ f ) with increasing frequency. Curves 2 (dash-dotted) and 3 (solid) in the same figure show the SEFD frequency dependences of the studied active antenna under the assumption that its preamplifier is noiseless and that the lunar soil is a homogeneous medium filled with regolith (curve 2) or a two-layer regolith/bedrock medium (curve 3). Curve 2 is close in shape to curve 1; however, it decreases faster with increasing frequency than curve 1 because of the increasing ribbon dipole directivity. The shape of curve 3 is additionally affected by the oscillations of the dipole directivity (Fig. 4) caused by the  presence of two-layer lunar soil. Fig. 14 clearly shows that curve 3 oscillates around curve 2, and the amplitude of these oscillations reaches approximately 40%.
The effect of diurnal changes in ambient temperature on the active antenna sensitivity is shown in Fig. 15. As expected (17), the ambient temperature T 0 has almost no effect on SEFD in most of the frequency range, where the SND of the antenna is quite high (> 10 dB), and only at the edges of the range, where the SND drops to 6 dB and below, this influence becomes noticeable. It should be noted that at night temperature T 0 = 100K the antenna sensitivity remains practically the same as that in the case of a noiseless amplifier. With an increase in the temperature to 400K, the SEFD increases by 700 kJy at 1 MHz and by approximately the same at frequencies of 30-35 MHz, which lie outside the operating frequency band of the antenna, where the dipole radiation pattern undergoes noticeable distortion.

V. CONCLUSION
An active antenna with a ribbon symmetrical dipole and low-noise preamplifier connected to its terminals was investigated. A dipole of 10 m long was printed on a thin polyamide tape 0.305 m wide, which lies on the flat surface of the lunar soil, consisting of a loose surface layer of 10 m thick regolith, and hard bedrock. The preamplifier was a single-stage HEMT low-noise amplifier with low power consumption, which was the first stage in front-end electronics.
The results of a detailed numerical analysis of the electrical and noise parameters of the active antenna in the frequency range of 1-35 MHz, such as the radiation efficiency, directivity, effective area, and effective noise temperature, are presented. It was found that the presence of a two-layer ground leads to the appearance of the frequency dependences of most of these parameters of noticeable oscillatory components, the amplitude of which can reach several dB. These non-uniform frequency responses lead to the appearance of spurious spectral effects, which are similar to the well-known interference of noise waveforms (standing waves) in mismatched transmission lines. This should be considered when studying broadband cosmic radio emissions, including the search for signals from cosmic dark ages. It may be necessary to correct the measured spectra using similar calculations and corresponding calibrations, for example, by galactic nonthermal radiation with a uniform power-law spectrum.
Variations in the noise temperature of an active antenna under the influence of ambient temperature, which varied from 100K to 400K during a lunar day, were studied. Particular attention is paid to the analysis of the fluctuation sensitivity of the active antenna, which is presented in terms of SEFD and SND.
It is shown that the studied active antenna has sufficiently high-quality performance in the frequency range of 1-30 MHz, in particular, SND > 6 dB, and SEFD which is close to the maximum possible, to serve as a prototype for designing elements of phased array antennas for lunar VLF radio telescopes.
The investigated design is a prototype, which is a preliminary and simplified version of a real device, although not yet ready for industrial production. It has already demonstrated the essential properties of later versions that will be made on its basis. Before developing a working version of an active antenna, it is necessary to clarify the thickness of the regolith layer at the construction site of the radio telescope, as well as to measure the electrical parameters of the regolith and bedrock. Most likely, it will also be necessary to develop a complete LNA scheme using the relevant parts. We hope that the technique and results of the studies performed in this work will be useful for the development of antenna array elements for future lunar VLF radio telescopes.