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A space-based decametric wavelength radio telescope concept

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Abstract

This paper reports a design study for a space-based decametric wavelength telescope. While not a new concept, this design study focused on many of the operational aspects that would be required for an actual mission. This design optimized the number of spacecraft to insure good visibility of approx. 80% of the radio galaxies– the primary science target for the mission. A 5,000 km lunar orbit was selected to guarantee minimal gravitational perturbations from Earth and lower radio interference. Optimal schemes for data downlink, spacecraft ranging, and power consumption were identified. An optimal mission duration of 1 year was chosen based on science goals, payload complexity, and other factors. Finally, preliminary simulations showing image reconstruction were conducted to confirm viability of the mission. This work is intended to show the viability and science benefits of conducting multi-spacecraft networked radio astronomy missions in the next few years.

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Acknowledgments

We thank S. Murray and K. Weiler for their guidance and helpful comments at an early stage of this concept development as well as R. MacDowall for illuminating conversations. Some of the science motivation for the RELIC concept was articulated in “Small Satellites: A Revolution in Space Science” study co-led by Charles Norton, Sergio Pellegrino, and Michael Johnson at the W. M. Keck Institute for Space Studies. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Copyright 2017. All rights reserved.

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Authors and Affiliations

  1. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, 91109, USA

    K. Belov, A. Branch, S. Broschart, J. Castillo-Rogez, S. Chien, L. Clare, R. Dengler, J. Gao, D. Garza, A. Hegedus, S. Hernandez, S. Herzig, T. Imken, H. Kim, S. Mandutianu, A. Romero-Wolf, S. Schaffer, M. Troesch, E. J. Wyatt & J. Lazio

  2. Climate and Space Sciences and Engineering Department, University of Michigan, Ann Arbor, MI, 48109-2143, USA

    A. Hegedus

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  1. K. Belov
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Appendices

Appendix A: RELIC HF antenna and front-end design

While the detailed description of the science data acquisition hardware is beyond the scope of this paper, it is nonetheless an integral part of the mission concept description and it is also responsible for generating the raw science data that are then transmitted by the daughter ships (which is much of the focus of this paper). Accordingly, we present here a brief description of how the science data acquisition hardware for RELIC might look.

Objectives

The objective of this is to characterize the antenna length and front-end impedance parameters that provide a background-noise-limited system for the RELIC antenna. The RELIC signals will be wide-band measurements across the 0.1-30 Mhz band. The overall desired performance is 1) that the antenna noise be greater than the amplifier noise, 2) stable gain in each sub-band, 3) smooth gain and phase variations across the band, 4) reducing too much variation of gain across the band so that dynamic range in not an issue. The scope of this document is to identify a solution for a high-impedance input design that primarily aims to meet point 1 but with points 2-4 in mind.

Assumptions

3.1 Antenna model

The band of interest for RELIC extends from 0.1–30 MHz. Below 1 MHz, the galactic noise is low but “shot noise” due to the plasma environment is dominant. The antenna models used for the initial assessment are 6-meter and 5-meter full length dipoles made of 0.6 cm (∼0.25”) diameter copper. The antennas are modeled using NEC2. The directivity, impedance (real and imaginary) along with the phase and group delay are shown in Fig. 21.

Fig. 21
figure 21

NEC2 models of a 6-meter and 5-meter full-length dipole. The model assumes the antenna is made of copper rod with 0.6 cm diameter floating in free space

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3.2 Background noise

The galactic noise is modeled according to the parametrization described in [9]. A plot of the average galactic noise temperature is shown in Fig. 22.

Fig. 22
figure 22

The galactic noise temperature from the parameterization in [9]

Full size image

The noise-voltage-squared spectrum at the antenna terminals due to galactic noise is given by \(V^{2}_{A,gal}= 4k_{B}T_{gal}R_{ant}\), where kB is Boltzmann’s constant and Rant is the real part of the antenna impedance. In addition to galactic noise, there is a “shot noise” contribution due to electrons in the plasma colliding with the antenna and inducing currents [65]. The noise-voltage-squared contribution as parameterized by [66] is given by:

$$ V^{2}_{A,QTN}= 5\times10^{-5}\frac{V^{2}}{Hz}\times\left( \frac{n_{e}}{cm^{-3}}\right)\times\left( \frac{T_{e}}{K}\right)\times\left( \frac{f}{\text{Hz}}\right)^{3}\times\left( \frac{L/2}{\text{m}}\right)^{-1}, $$
(A1)

where ne is the plasma frequency in electrons per cm3, Te is the electron plasma temperature in Kelvin, f is the frequency in Hz, and L is the full dipole length in meters. We assume ne = 5 cm− 3 and Te = 105 Kelvin. The background noise-voltage-squared contributions are shown for a modeled 6-meter (full length) and a 5-meter dipole made of 0.6 cm diameter copper rod in Fig. 23.

Fig. 23
figure 23

The noise-squared voltage at the antenna terminals for the plasma shot noise contribution and the galactic noise. The noise is modeled for a 6 m and 5m full-length dipole

Full size image

Analysis

The goal is to estimate the sources of noise at the first amplifier in the signal chain to ensure the noise is dominated by external backgrounds rather than by the amplifier itself. The external noise sources producing voltages at the antenna terminals with produce a voltage at the load according to

$$ V_{L}=\frac{Z_{L}}{Z_{A}+Z_{L}}V_{A}, $$
(A2)

where ZL is the complex impedance of the load and ZA is the antenna impedance. The noise due to the amplifier, at the load is given by \(V^{2}_{L,amp}=k_{B}T_{amp}R_{amp}\). We consider an operation amplifier (OpAmp) approach for producing a high-input impedance to the amplifier as seen from the terminals of the antenna.

OpAmps can be designed to have a high input impedance but modeling their noise is somewhat more involved. A modeling effort using an OpAmp was done for JPL?s Universal Space Transponder (UST) Jovian burst science application development. Figure 24 is an OPA656-based design by Robert Dengler for the Universal Space Transponder (UST) using 12.7 kΩ input impedance (set by R8 in Fig. 24).

Fig. 24
figure 24

Operational amplifier front end design by Bob Dengler for the universal space transponder

Full size image

For this application, we considered the OPA656 from Texas Instruments. The choice is driven by the noise characteristics \(V_{n}= 7\text {nV}/\sqrt {Hz}\), \(I_{n}= 1.3\text {fA}/\sqrt {Hz}\). The low current noise is particularly important for these high impedance applications. It is worth mentioning the e-POP radio receiver instrument on CASSIOPE also used OPA656 for its receiver with a 100MΩ input impedance [67].

Based on the Analog Devices Tutorial MT-049, adapted to the notation on our circuit diagram, the noise model is calculated according to:

$$\begin{array}{@{}rcl@{}} V_{L,amp}^{2}&=&{V_{n}^{2}}+{I_{n}^{2}} Z_{+}^{2}+{I_{n}^{2}} \left( \frac{R_{3} R_{4}}{R_{3}+R_{4}}\right)\\ &&+ 4kT_{0}\left( Re(Z_{+}) +R_{3}\left( \frac{R_{4}}{R_{3}+R_{4}}\right)^{2}+R_{4}\left( \frac{R_{3}}{R_{3}+R_{4}}\right)^{2} \right), \end{array} $$
(A3)

where Z+ is the lump impedance seen from the terminal labeled “ + ”, including the antenna impedance and T0 is the physical temperature of the resistors, taken to be room temperature T0 = 290 Kelvin. The last term in curly brackets is the Johnson noise of the system. The different noise terms, assuming R8 = 12.8, 50 and 100 kΩ, are shown below. The different noise contribution, for a 5-meter antenna, are shown in Fig. 25. In all cases V n is, by far, the dominant source of noise.

Fig. 25
figure 25

The operational amplifier noise assuming different input impedance values. The noise is dominated by the voltage term regardless of the impedance used in the range considered. These simulations are for the 5-meter antenna only

Full size image

Simulations were run to obtain the impedance as a function of frequency for 12.8 kΩ, 50 kΩ, and 100 kΩ, simply by changing R8 in the design. The impedance of the amplifier as seen by the terminals of the antenna, is shown in Fig. 26.

Fig. 26
figure 26

Simulations of the impedance seen by the antenna terminals looking into the front-end design in Fig. 24 for R8 equal to 12.8, 50, and 100 kΩ

Full size image

This OpAmp design has an impedance that is high at low frequencies and lower at high frequencies, which is the general desired direction for keeping the antenna noise above the amplifier noise across the band. The voltage at the load is given by:

$$ <{v_{L}^{2}}> =<{v_{A}^{2}}>\frac{|Z_{L} |^{2}}{|Z_{L}+Z_{A} |^{2}}, $$
(A4)

where ZL is the impedance shown in Fig. 26. The results for the antenna noise compared to the amplifier noise for the impedances considered here are shown in Fig. 27.

Fig. 27
figure 27

Results for the noise due to the antenna and the amplifier noise for the front-end design in Fig. 24 assuming values of R8 equal to 12.8, 50, 100 kΩ

Full size image

The results of the OpAmp approach indicate that the OpAmp has a higher antenna to amplifier noise ratio. The reason points to the impedance vs frequency of the OpAmp, which has a profile with high impedance at low frequencies and low impedance at higher frequencies. This is the general behavior needed for the antenna noise to dominate across the band. We also note that using an OPA656 impedance with R8 resistor value > 50 kΩ meets the desired design objectives laid out in the introduction. The antenna noise is above the amplifier noise with smooth behavior across the band that is not highly variable. The expected noise levels below 1 MHz can be as > 10 times higher than parts of the band above 1 MHz. However, frequencies below 1 MHz account for < 10% of the full band.

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Belov, K., Branch, A., Broschart, S. et al. A space-based decametric wavelength radio telescope concept. Exp Astron 46, 241–284 (2018). https://doi.org/10.1007/s10686-018-9601-6

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