Amateur Radio-Astronomy by Peter Bremer

This website shows how to build an amateur radio-astronomy system and its results.

1 Goal

The goal is to measure the Hydrogen line from sources in our galaxy.

2 Source signal

2.1 Hydrogen line

The Hydrogen line from sources in our galaxy radiates at 1420.406 MHz (wavelength 21.1 cm).

2.2 Doppler shift

2.2.1 Expected values

The relative speed of those hydrogen sources compared to our location in space is in the order of $\ \pm 5-200\;\frac{km}{s}$

This relative speed causes a Doppler shift of the observed radio-spectrum of hydrogen.

The speed of a radiowave is $300.000\;\frac{km}{s}$ . That means the speed of the observer $v_r$ and the source $v_s$ is much smaller than the speed of the wave.
According explanation on wikipedia in that case the formula for he shift in frequency is: $\Delta f=\frac{\Delta v}{c}f_0$
which means, as $c=\lambda_0f_0$ , $\Delta f=\frac{\Delta v}{\lambda_0}$ or $\Delta v=\lambda_0\Delta f$ .
Using the relative speeds of hydrogen sources to be observed, the expected Doppler shift range is $\Delta f=\frac{\Delta v}{\lambda_0}=\frac{\pm\;200\;\frac{km}{s}}{21.1\;cm}=\pm\;948\;\text{kHz}$
Meaning the Doppler range around the original spectrum of the hydrogen line of approximately ± 1 MHz is relevant for the measurements.

The other way around it can also be determined with those formulas what the relative speed of the source of the hydrogen spectrum is per 100 kHz Doppler shift:
$\Delta v=\lambda_0\Delta f=21.1\;cm\cdot 100\;\text{kHz}=21.1\cdot 10^{-2}\;m\cdot 100\cdot 10^3\;\frac{1}{s}= 21.1\;\frac{km}{s}$
A Doppler shift to higher frequencies than the original frequency of the source, indicates an object moving relatively towards the observer.

2.2.2 "Local" movements

2.2.2.1 Earth rotation

The earth rotates around its own axis at a latitude of 53° N/S at a speed of $0.28\;\frac{km}{s}$
as, with the circumfence of he earth being 40075 km, and rotating at 23 h 56 min about its own axis $\frac{40075\;km\cdot\cos(53^\circ )}{23.93\;\text{h}}=1007\;\frac{km}{h}=0.28\;\frac{km}{s}$
This means when looking east or west towards the horizon it could lead to an extra observable Doppler shift of $\frac{0.28\;\frac{km}{s}}{21.1\;\frac{km}{s}}\cdot100\;\text{kHz}=1.3\;\text{kHz}$

2.2.2.2 Earth circulation around the sun

Earth also moves through space around the sun at an average speed of $107226\;\frac{km}{h}=29.8\;\frac{km}{s}$ which could lead to an extra Doppler shift of $\frac{29.8\;\frac{km}{s}}{21.1\;\frac{km}{s}}\cdot100\;\text{kHz}=141\;\text{kHz}$
if the object is in the earth ecliptic plane due to movement of earth in that same ecliptic plane.
The earth circulates around the Sun with a velocity that varies between its maximum value of 30.29 km/s, a Doppler shift of 143.6 kHz, at its perihelion (2-5 January) and its minimum value of 29.27 km/s, a Doppler shift of 138.7 kHz, at its aphelion (4-6 July).

The spiral arms of our galaxy make an angle of 63° with the earth ecliptic plane while the earth makes a 23.5° angle with the ecliptic plane, leading to a relative speed of earth varying between $\cos(63^\circ+23.5^\circ)=0.06$ and $\cos(63^\circ-23.5^\circ)=0.77$ depending on the season. This means it could lead to an extra Doppler shift of 8.6 kHz - 108 kHz due to movement of earth in the ecliptic plane when observing objects in our galaxy.

3 System

The system consist of the following parts:

3.1 Antenna

3.1.1 Parabolic

For radio astronomy using a parabolic antenna is very common. For calculating the characteristics of a parabolic antenna the formulas on page 15.65 of the ARRL Antenna book, 24th edition, june 2019 can be used:

$\text{Aperture:}A=\pi\;r^2$

$\text{Gain:}\;G_{dB}=10\log_{10}\left(\eta\frac{4\pi}{\lambda^2}A\right)=10\log_{10}\left(\eta \left(\frac{2\pi r}{\lambda}\right)^2\right)$
$\text{Opening angle:}\;\psi=\frac{70\lambda}{D}$

with r the radius of the dish and D the diameter of the dish.

Based on an efficiency factor of 0.5, the characteristics as function of size are:

Diameter [cm]	Gain [dBi]	Opening angle (-3 dB) [°]
60	16.0	24.6
90	19.5	16.4
100	20.4	14.8
150	24.0	9.8
200	26.5	7.4
250	28.4	5.9
300	30.0	4.9
350	31.3	4.2
2500	48.4	0.6

The disadvantage of a parabolic antenna is its size, which does not make it easily transportable.

There exist some foldable parabolic antennas, e.g. from sub-lunar but they are relatively expensive and would need to be ordered from the US with extra tax and shipment costs:

FD6, 1.8 m with 1420 MHz feed: USD 1500
FD8, 2.4 m with 1420 MHz feed: USD 2000
SL-1 rotor: USD 700

Folded size of the parabolic antennas:

20.5 cm x 20.5 cm

x 1.35 m (for 1.8 m dish)
x 1.68 m (for 2.4 m dish)

3.1.2 Patch Yagi

The following articles on the website of astropeiler.de show some interesting alternatives as described in Introduction and Antenna Options (or directly in pdf: Hydrogen_1.pdf) and evaluated in
Observation Results with Different Antennas (or directly in pdf: Hydrogen_4.pdf).
The patch yagi antenna, as they call it, seems the most compact antenna with still a flexible design.

In table 1 of the evaluation document the SNR of the 7 element (5 directors) patch antenna as shown above is 22.2 dB, while for a 90 cm parabolic antenna it is 24.1 dB and for a 3 m parabolic antenna it is 27.2 dB.
The patch antenna as presented is better known as cigar antenna. It is basically a yagi antenna with discs instead of rods.
A half wave dipole antenna in free space has an impedance of 73 Ω. With a cigar antenna, it can be matched to 50 Ω when the connection is slightly off center.

For a normal Yagi, calculations can be done with the Yagi Uda Antenna Calculator, or more detailed with VHF/UHF Yagi Antenna Quick Designer from K7MEM
Filling in 1420.4 MHz with a thickness of parasetic elements of 1 mm and a electrically connected boom with a diameter of 10 mm gives the following results:

Number of elements Number of directors (=Number of elements - 2)	Boom length [mm]	Gain [dBi]	Opening angle (-3 dB) [°]
3	58	7.0	75.9
4	96	8.7	59.0
5	141	10.0	52.0
6	194	11.1	47.4
7	253	12.0	44.1
8	316	12.7	41.4
9	383	13.4	39.1
10	452	14.4	37.2
11	532	14.9	35.5
12	616	15.3	34.0
13	714	16.4	32.6
14	788	15.7	31.4
15	959	16.1	30.3
16	1000	16.4	29.3
17	1057	16.7	28.2
18	1123	16.9	27.5
19	1191	17.2	26.6
20	1301	17.4	26.0

The issue with this patch yagi antenna is that up to now I could not find any designs suitable for 1420 MHz and I do not have the knowledge and tools to design and make one myself.

3.1.3 Wifi Grid dish antenna

Another alternative is the Wi-Fi grid dish antenna alu 2.4 GHz, 24 dBi

The size when assembled is for the dish 100 x 60 cm and total depth over the feed beam and mount is 50 cm.

The main specifications (@ 2.4 GHz) from the manual are:

Gain: 24 dBi
Horizontal beamwidth: 8°
Vertical beamwidth: 12°

What the specifications will be @ 1420 MHz has to be determined.
Someone else indicated that the return loss on 1420 MHz is 5 dB.

To estimate the gain @ 1420 MHz, we assume it behaves as a parabolic antenna which has a gain of:
$G_{dB}=10\log_{10}\left(\eta\left(\frac{2\pi r}{\lambda}\right)^2\right)$
Both $\eta$ and $r$ are unknown, but we can rewrite te above formula as
$G_{dB}=10\log_{10}\left(\eta\left(\frac{2\pi r}{\lambda}\right)^2\right)= 10\log_{10}\left(\frac{\eta\left(2\pi r\right)^2}{\lambda^2}\right)$ , the $\eta\left(2\pi r\right)^2=k$ is wavelength independent, which leads to a simplified formula:

$G_{dB}=10\log_{10}\left(\frac{k}{\lambda^2}\right)$
For this grid dish antenna that means with known values for $\lambda$ and Gain: $k=\lambda_{2400\;\text{MHz}}^2 10^{\left(\frac{G_{2400\;\text{MHz}}}{10}\right)}$

That leads to a gain of this grid dish antenna for any other wavelength of:
${G_{dB}\left(\lambda\right)=10\log_{10}\left(\frac{\lambda_{2400\;\text{MHz}}^2 10^{\left(\frac{G_{2400\;\text{MHz}}}{10}\right)}}{\lambda^2}\right)=$
$10\log_{10}\left(\frac{\lambda_{2400\;\text{MHZ}}^2}{\lambda^2}10^{\left(\frac{G_{2400\;\text{MHz}}}{10}\right)}\right)=10\left(\log_{10}\left(\frac{\lambda_{2400\;\text{MHZ}}^2}{\lambda^2}\right)+\log_{10}\left( 10^{\left(\frac{G_{2400\;\text{MHz}}}{10}\right)}\right)\right)=$

$10\left(\log_{10}\left(\frac{\lambda_{2400\;\text{MHz}}^2}{\lambda^2}\right)+\frac{G_{2400\;\text{MHz}}}{10}\right)=G_{2400\;\text{MHz}}+10\log_{10}\left( \frac{\lambda_{2400\;\text{MHz}}^2}{\lambda^2}\right)$

With as final result:
$G_{dB}\left(\lambda\right)=G_{2400\;\text{MHz}}+20\log_{10}\left(\frac{\lambda_{2400\;\text{MHz} }}{\lambda}\right)$

For 1420 MHz that gives:

$\Delta G(1420\;\text{MHz})=20\log_{10}\left(\frac{\lambda_{2400\;\text{MHz}}}{\lambda_{1420\; \text{MHz}}}\right)=20 \log_{10} \left(\frac{1420\;\text{MHz}}{2400\;\text{MHz}}\right)=-4.6\;dB$

Meaning the return loss is estimated to be -4.6 dB and the gain 19.4 dBi

To estimate the opening angle of this grid dish antenna @ 1420 MHz, we assume it behaves as a parabolic antenna, which makes the opening angle linear with the wavelength:
$\psi = \frac{70 \lambda}{D}$
Which then gives the following estimates for the

Horizontal beamwidth: $8^\circ\cdot\frac{2400\;\text{MHz}}{1420\;\text{MHz}}= \boldsymbol{13.5^\circ}$
Vertical beamwidth: $12^\circ\cdot\frac{2400\;\text{MHz}}{1420\;\text{MHz}}= \boldsymbol{20.3^\circ}$

These figures are comparable with a parabolic antenna of 90 cm.

To get the same results with a disc yagi antenna would require more than 20 elements and a boom length of more than 1.30 m. The disc yagi will be less wide but still needs a heavy contra weight.

To be able to direct this antenna, an azimuth-elevation system has been constructed using scaffolding tube parts of 42 mm as available from the Gamma.

The rod in the direction of the feed behind the antenna provides balance, both in the horizontal plane and in the vertical plane.
Adjustment of the azimuth and elevation axes can be arranged via rotation at the T piece.
The couplings are a bit spacious on the T-piece, of course the screws have not been tightened there. I covered all three entrances of that T-piece with the soft part of Velcro that is available at Praxis for mounting mosquito nets to get it nicely fitting.
The coupling piece on the tube opposite to the antenna feed is not used as a coupling piece, but as a movable counterweight. After balancing the setup in the horizontal plane, I defined the location of the T-piece on the azimuth axis with two pieces of soft Velcro.
The arrangement in the foot is not ideal, but good enough for now.

3.2 Hydrogen line specific LNA

Nooelec SAWbird+ H1 - Premium SAW Filter & Cascaded Ultra-Low Noise Amplifier (LNA) Module for Hydrogen Line (21cm) Applications. 1420MHz Center Frequency

The SAWbird+ series contains 2 ultra-low-noise LNAs sandwiched around a custom-designed, high-performance SAW filter centered at the frequency of interest.
A spec sheet is available directly from this site.

Very high attenuation outside of the 65 MHz bandpass region
Centered near 1420 MHz,
Minimum of 40 dB of gain at the frequency of interest.
Nominal current draw is 120 mA.
Low noise figure of ~0.8 dB
EMI shield to separate the LNAs from external interference.
Maximum input signal 0 dBm

Measuring the one I have, including below mentioned DC Block, (images are clickable to enlarge them in a seperate window):

Measurement was done with a LiteVNA 64 which has a measurement range of 50 kHz to 6.3 GHz and the nanoVNA app on the PC to control it.
As the Sawbird+ has a maximum input signal of 0 dBm and the LiteVNA 64 has an output of +5 dBm maximum and an input of max +10 dBm, an attenuator of 10 dB + 30 dB = 40 dB was used between output port 1 of the LiteVNA 64 and the input of the Sawbird+. The LiteVNA 64 has been calibrated for the applicable frequency range including the attenuators and cables of the measurement system.

And to prevent 5 V DC to be passed to the next LNA from the wrong side, added a SMA In-Line DC Block from Nooelec:

50 kHz - 8 GHz
Maximum power 2W
Maximum blocking voltage 50V
Insertion loss of <0.3 dB below 6GHz and <0.8 dB below 8 GHz
Maximum VSWR is <1.2 below 6 GHz and <1.3 below 8 GHz

3.3 Cable

3.4 Wideband LNA

To get the small signal up to a level suitable for the SDR a Wideband LNA from RTL-SDR.com is used. It is based on the SPF5189Z 50MHz to 4000MHz, GaAs pHEMT Low Noise MMIC amplifier.

For 1420 MHz:

Gain 16 dB
Noise figure 0.7 dB
Operating Current 75 - 105 mA, nominal 90 mA @ 5 V
3 - 5 V bias tee powered (i.c. from RTL-SDR which provides 4.5 V)

3.5 SDR

As radio the RTL-SDR Blog V3, based on the R820T2 = R860 tuner and the RTL2832U demodulator.

<1 ppm temperature compensated oscillator (TCXO)
500 kHz — 1766 MHz
Sensitivity of approximately -80 dB
Noise figure of around 3.5 dB
Bandwdth of 2.4 MHz

The <1 PPM temperature compensated oscillator (TCXO) giving accurate tuning and almost zero temperature drift (2 ppm max. initial offset, 0.5-1 ppm temperature drift).
The stability of the oscillator is 1 ppm which is equivalent to a stability of around 1.4 kHz for the relevant frequency. Meaning rotation of the earth around its axis can not reliable be observed, but movement of the earth in its ecliptic plane, should be observable with the Doppler effect.

3.6 Signal processing

Signal processing will be done with a Raspberry Pi 4 Model B Rev 1.4, with a quad core ARMv7 Processor rev 3 (v7l), running Debian Raspbian GNU/Linux 11 (bullseye).

For signal processing the gnu-radio program will be used. It is a system in which advanced signal processing can be programmed graphically and processed real time. The graphical program is translated to python in the background; The actual signal processing is done in Python. A GNU Radio Wiki and Tutorial are available.

An example gnu-radio program for measurements around the 1420 MHz hydrogen line which will be used for further investigation is:

The associated grc file is available for download.