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#### twinsen

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« on: 18:31:17, 12 July, 2009 »
Hey guys well as a result of me having way too much spare time I have now been delving into the regime of interferometry and after many many hours research looking into botrh optical and radio interferometry have come to the conclusion that I still dont fully understand it but that it can be done on an amateur level.

This has already been sucessfully acomplished by a system called SIDI developed by a radio ham in slovenia see http://lea.hamradio.si/~s57uuu/astro/sidi1/index.htm I plan to now build a simmilar device to record the phase and time information to a computer for analysis. The first step is to build a reciever that is matched to a single local frequency in order to get adequate phase accuracy between two seperate antenna. The original plan was to make a setup that could work in the 10ghz region but this is complicated by having to synch the LNBs required to detect the microwave frequencies. This however will still be the end goal of my project however to begin with I will be observing in lower frequencies most likely the 1.4ghz band trying to detect the neutral hydrogen line.

Since this will be my first ever attempt at any kind of radio astronomy I will be tackling this goal in pieces, Lots of pieces

I will start off simply trying to recieve some kind of astronomical signal using the equipment and then try and further modify it for interferometric use.

1. Make/buy a simple directional antenna to operate at 1.4ghz, could perhaps mount on telescope stand for accurate pointing
2. Aquire a Low noise amplifier to amplify the signal at 1.4ghz for transmission down coaxial cable to the shed.
3. Build some kind of reciever, initially I am looking to modify a digital satelite tuner following the SIDI idea
4. I think that the signal will then need to be amplified further so a further amp is needed but this time at a lower base frequency.
5. Develop some kind of computer interface or just use a Data aquisition unit(DAQ) that are availiable to plug into your pc.
6. Develop some kind of data logging/analysis software.

I believe the key to geting good phase accuracy which is really the most important thing in interferometry is to make sure all frequency transformations are performed using phase locked oscillators all locked to a single crystal. This ensures that all the transformations are performed equally on both channels.
If this phase locking could be applied to modern commercial lnbs then it may be possible to mix two high frequency signals in the same kind of reciever setup as for the 1.4ghz signals.

Basically I could do with all the bloomin help I can get, electronics advice as well as any information regarding antenna design would be especially useful. This thread will be updated as I progress in the project,( I thought it would be better suited here than in projects area as this forum was looking rather spartan :).

Alex
Vixen GP - Celestron 102 f9.8  - Canon EF300f4

#### allyman

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« Reply #1 on: 18:54:25, 12 July, 2009 »
Alex,

Good luck with this venture for I'm sure there will be many pitfalls, especially with interferometry where phase shift can occur by just using the wrong length of cables. I'm sure there will be help and advice out there but perhaps listening to Jupiter or the Sun might be a more achievable start.

Graham.

#### Kellys_eye

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« Reply #2 on: 13:21:03, 13 July, 2009 »
Check out SDRs (software defined radios) for decent spectral analysis software.  A lot of this stuff is free.
Dave Gill

250/f4.5 newt, 150/f5 refractor, Mak 127, lots of bits'n'pieces mostly homebrewed.

#### Roger Banks

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« Reply #3 on: 15:28:11, 13 July, 2009 »
Alex
This is a BIG and complex task - not wishing to put you off or anything but there is that much phase shift naturally on the received signals that I question if you are going to actually detect anything. The lower in frequency you go the bigger the phasing and the bigger the antenna you will need.
Remember that amatuer radio enthusuasts can bounce their signals off the moons surface but to do so and to recieve a strong enough signal to detact requires a HUGE antenna array. Now at 1.4 GHz or about 20cm a single 10 element yagi would probalbly be about 1 meter long and give you about 12 dbi - way way short of what you will need. 2 will give you 15db, 4 = 18 and so on. I would doubt you will get sufficent gain at this frequency to make it possible without a garden dedicated to an antenna farm....
Go to 10GHz and you can start to use parabolic dishes and get useful gain but at 10 gigs the receive section is as much about prescision engineering that discreet components.....

#### twinsen

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« Reply #4 on: 17:56:08, 13 July, 2009 »
Yes at 10ghz the electronics is extrmely precise as is the engineering. I hope to be able to do away with the need to build a reciever at this frequency by using the superheterodyne idea converting a high frequency microwave frequency aka 10/4ghz down to a more manageable L band frequency from 950-2000mhz. I realise that gain will be a problem at low frequencies but though for initial testing of my reciever it would be wise to use a freqeuncy that would plug straight into my L band range.

I thought it may be possible to use a dish at 1.4ghz as well like these folk at nrao.http://www.nrao.edu/epo/amateur/N2I2.pdf

My first goal will be simply to detect the sun using a reciever then I can start working on building the sensitivity and interferometric parts.

Alex
Vixen GP - Celestron 102 f9.8  - Canon EF300f4

#### twinsen

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« Reply #5 on: 18:59:37, 18 July, 2009 »
I was wondering if anyone has any ideas on how to create a long wavelength 1.4ghz detector to attatch to a dish? The idea buzzing round in my head at the moment is to attatch a small patch antenna at the focal point of a 1.2m offset satellite dish. Im hoping this will give me sufficient gain to observe something even if it is just the sun. I can't help feeling 1.2m sounds too small but I think that is the most I can feasibly mount to my vixen gp.

Does anyone know how youd go about creating a 1.4ghz feedhorn or any other ways of actually collecting the signal focused by a parabolic dish?

Vixen GP - Celestron 102 f9.8  - Canon EF300f4

#### Roger Banks

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« Reply #6 on: 07:59:39, 20 July, 2009 »
A simple hald wave dipole at the focal point would be all that is needed. At 1.4GHz it will be 10.7 cm total width

#### twinsen

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« Reply #7 on: 03:09:07, 21 July, 2009 »
I kinda wanted to try the patch antenna as it is quite directional compared to a dipole which would more likely pick up ground noise as well. I thought about constructing a feedhorn for a half wave dipole like you suggest but at 21cm it will be pretty hefty so would probably upset the weight distribution of the antenna. Should be getting a few bits and pieces by the end of the week to start work putting it together.

Another problem Im having is im still unsure how Im going to be able to program the correlator using the quadrature(I/Q) component outputs of the tuner. These outputs give you the phase of the wave but do not have a frequency component, so it differs from standard analogue correlation techniques where the cross correlation gives you ...

The way it is meant to work(I think) if you have your incident signals of the form

$$Y_1=A_1\cos{(wt)} Y_2=A_2\cos{(wt-\phi{})}$$

In order to measure the phase usually you multiply the two together(cross corellation) then take a time average to get rid of the high frequency terms. If A1=A2=A where the signal amplitude is equal at both antenna

$$Y_1Y_2=A^2\cos{(wt)}cos{[w(t-\phi)]}=\frac{A^2}{2}[\cos{(2wt-w\phi)}+\cos{(w\phi)}] <Y_1Y_2>=\frac{A^2}{2}\cos{(w\phi)}$$

The problem I have at the moment is that my tuner gives me a downconverted low frequency output in quadrature phase form. This is such that an incoming wave of singal frequency.

$$Y=A\sin(wt+\phi)$$

can be expressed as a combination of sin and cosine terms with different amplitudes I and Q corresponding to the (inphase and quadrature(90degree phase change) components). As so..

$$Y=I\sin{(wt)}+Q\cos{(wt)}$$

The problem is the actual voltages which the tuner gives out are the amplitudes I/Q these do not contain information about the orinal frequency of the carrier wave. So I and Q are defined as.

$$I=A\sin{(\phi)} Q=A\cos{(\phi)}$$

If you try to correlate the same as before by taking two waves and multiplying together, you end up with this.

$$<Y_1Y_2>=\frac{I_1I_2}{2}+\frac{Q_1Q_2}{2} \therefore = \frac{A^2}{2}cos{(\phi)}$$

Clearly the angular frequency segment is missing??
Im not really how to develop this for a wider frequnecy range would the I/Q components be the sum of all the different I/Q components for the different frequency waves?
If anyone knows anything about working waves expressed in this I/Q form it would be very helpful. At the moment my design has kind of stopped at measurning the output of my tuner im still wondering how best to sample these two outputs. The SIDI project i mentioned used one bit comparator sampling on each I and Q channel though this seems rather limiting since if you cut down on your precision at the recoring stage it can never be regained. Then again it needs to be a balance between data quantity and sampling rate/number of samples.

Alex
Vixen GP - Celestron 102 f9.8  - Canon EF300f4

#### starf

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« Reply #8 on: 15:29:19, 21 July, 2009 »
from what i remember from simple harmonic motion, the displacement along axis x with regard to time (t) is

$$x(t)=x_{m}\cos(\omega t + \phi)$$

where

$$t$$ is time
$$(\omega t + \phi)$$ is the phase
$$x(t)$$ is displacement at time t
$$x_{m}$$ is the amplitude
$$\omega$$ is the angular frequency
$$\phi$$ is the phase constant or phase angle

to find $$\omega$$, the displacement $$x(t)$$ must return to its inital value after one period T of the motion; that is $$x(t)$$ must equal $$x(t + T)$$ for all t. if you put $$\phi = 0$$ into the above then you can write

$$x_{m}\cos \omega t = x_{m} cos \omega(t + T)$$

since the cosine function first repeats itself when its argument (the phase) has increased by $$2 \pi rad$$, the above gives us

$$\omega(t + T) = \omega t + 2\pi$$

or

$$\omega T=2\pi$$

and since $$T = \frac{1}{f}$$

$$\omega=\frac{2\pi}{T}=2\pi f$$

#### twinsen

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« Reply #9 on: 19:39:29, 21 July, 2009 »
Indeed what you say is true   but im not sure if the phase will change with time arg its confusing me now lol.
If the wave is travelling to the right along the x axis it can be expressed as

$$y=A\cos{(kx-wt+\phi)}$$

I suppose this means that the measured phase at a point x1 along x will depend on t and the speed of the wave and theres my missing frequency :)
so perhaps in my case with a wave travelling at c.

$$\phi=2\pi\frac{\lambda{}t}{c}$$

Does this make sense?? Is it right to use a travelling wave in measurning a signal like this?/ Really not too good at the maths here
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#### starf

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« Reply #10 on: 16:22:38, 22 July, 2009 »
The speed of a wave is related to the wave's wavelength and frequency by your equation, but it is set by the properties of the medium. if a wave passes through a medium such as air or water it must cause the particles of that medium to oscillate and for that to happen the medium must have both mass(for kinetic energy) and elasticity (for potential energy).

we know that the speed of wave $$v$$ is given by the ratio $$\frac{\Delta x}{\Delta t}$$. if you think of a sinusoidal wave with a point marked on a peak, that point retains its displacement y despite the wave moving. the phase in the equation must remain a constant. ie

$$kx-\omega t = \text{a constant}$$

now take the first derivative of this so

$$k\frac{dx}{dt}\quad - \quad\omega = 0$$

using

$$k=\frac{2\pi}{\lambda}$$ (by t=0 in y(x,t) = ym sin(kx-wt)

and

$$\omega = \frac{2\pi}{T}$$

we get

$$v = \frac{\omega}{k} = \frac{\lambda}{T} = \lambda f$$

#### twinsen

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« Reply #11 on: 15:16:57, 28 July, 2009 »
ha.. thanks for the help on this one starf..
Been reviewing my maths on the whiteboard and it seems that somehow i mistook a time delay $$\delta T$$ for an absolute phase shift. This small mistake has caused me 3 days of trouble :)

If in the original equation for correlation we should have.

$$Y_1=A_1\cos{(w(t-\delta{}T))}$$

this gives us as a final result.

$$R=\frac{V^2}{2}\cos{(w\delta{}T)}$$

If we say

$$\delta{}T=\frac{\delta{}x}{v} \delta{}\phi{}=k\delta{}x \therefore{} \delta{}T= \frac{\delta{}\phi{}}{kv} kv=w \therefore{} R=\frac{V^2}{2}\cos{(\delta{}\phi{})}$$

This gives us the result that I found for multiplying the I and Q components. SO all is good pretty much all I have to do to get my correlated output is multiply the 4 voltage outputs (I1,Q1,I2,Q2) as so.

$$R=\frac{I_1I_2+Q_1Q_2}{2}$$

The next stage is to find a cheapish satellite dish and a datalogger of some kind. I plan to digitize the information straight out the I and Q channels. At this stage the plan is to use a high speed adc pci device hopefully I can find one cheap enough. Since the information will be split between the two I/Q channels the overall phase resolution should I think be equal to $$\frac{2\pi{}}{2^{(n+1)}}$$ where the ADC has n bit resolution. The thing is as Roger said phase noise is easy to introduce and i think it may be pointless having very high resolution phase detection if most of the bits contain noise. Unfortunately most of the ADC pci cards have 12-16bit resolution which would give stupidly high amounts of data. Marko who built the SIDI interferometer mentioned earlier uses 1 bit sampling which gives him 90degree phase measurement. I had thought about using a sound card input as my adc but that would give me a very low bandwidth ~22khz. I seem to think a larger bandwidth => better sensitivity??#

Sorry for the f*ck up with the maths and hope it didnt confuse people too much.

Regards
Alex
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#### twinsen

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« Reply #12 on: 21:55:35, 05 August, 2009 »
Right so the project is moving on slowly but steadily still gathering the components.
I have just recieved courtesy of maplin a cheapo 1.8m solid steel dish, unfortunately it comes on the most primative mount possible(I had to actually bend the metal support rods to assemble it). I have sourced an adlink pci-9812(http://www.adlinktech.com/PD/web/PD_detail.php?cKind=&pid=33&seq=&id=&sid=) off ebay which set me back 300 smackers but should be up to the task of monitoring simple 2 dish interferometry signals. Its basically a high speed adc I am planning to run at a continuous rate of 10mhz on all 4 channels at 12bit resolution. As I havnt yet got any test program written I have no idea how many clock cycles it will take to process the data but im hoping my 1.8ghz opteron pc will cope. The general idea at this point in time is that the signals will be processed in real time so ~80mb/s, the correlated signals will be written to disk but this data write will be considerably slower since there is an integration function in the correlator which will slow the overall data output. I have 2x10k rpm sata dishs set up dedicated to the interferometer.

One quandry that im stuck on at the moment is impedance mismatching. This is because my salvaged sat tv tuners have 75ohm F connectors but my antenna will be 50 ohm to match the 50ohm low noise amplifier. Is it worth using a 50/75 balun to minimize reflection or do these not work at high? 1.4ghz frequency???

Will post some pics of the dish tommorow.

Alex
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