[amsat-bb] Re: HF Satellite Relay

Bob- W7LRD w7lrd at comcast.net
Tue Jun 29 21:51:21 PDT 2010

You gotta love this guy!  It takes me days to figure it out, but I always learn something! 

73 Bob W7LRD 

----- Original Message ----- 
From: "i8cvs" <domenico.i8cvs at tin.it> 
To: "Bob Bruninga" <bruninga at usna.edu>, "AMSAT-BB" <amsat-bb at amsat.org> 
Sent: Tuesday, June 29, 2010 6:52:57 PM 
Subject: [amsat-bb] Re: HF Satellite Relay 

----- Original Message ----- 
From: "Robert Bruninga" <bruninga at usna.edu> 
To: <amsat-bb at amsat.org> 
Sent: Monday, June 28, 2010 7:44 PM 
Subject: [amsat-bb] HF Satellite Relay 

> Heard today of a Passive HF relay satellite being proposed. 
> Wondered if Hams could relay off of it. 
> It's a 10m diameter sphere. 
> I assumed a 10m signal and 1000 Watts 
> And antenna gains at both ends of 10 dB. 
> Unless I made a dumb error, it looks impossible? 
> I get a received signal of -170 dBm 
> Compared to a good HF receiver of -122 dBm 
> So its 48 dB down in the noise. 
> Going to narrow band, could improve things, but the Doppler of 
> +/- 600 Hz would make that difficult. 
> Anyway, if someone else wants to double check the link budget 
> using the radar range equation, go for it. 
> The beauty of this system is that it is perfectly spherical, so 
> the reflection coefficient would be constant within 1 dB.  That 
> is the advantage over trying to use the ISS or other large 
> rocket body... They vary by 20 dB making communication by 
> reflection impossible. 
> Oh, and it would be in space for 30 years or more.  So with 
> something that reliable, it would be worth developing an amateur 
> capability to use it. 
> It is not designed for comms, but as a calibration sphere for 
> over the horizon radars that have LOTS more power and LOTS more 
> gain than we do. 
> Bob, Wb4APR 

Hi Bob, WB4APR 

I have assumed that the altitude of the Passive HF relay satellite over the 
earth is 1500 km and as we know the diameter of the sphere is 10 meters. 
Also I assumed that the reflectivity coefficient of the sphere is 50% 

The 28 MHz Round Trip Isotropic Attenuation using the concept of Radar 
Equation is as follows: 

          Pt x Gt x Ar x Sigma 
Pr = ------------------------------ 
           (4 x 3.14 x R^2)^2 

where : 

Pr = received power 

Pt = transmitted power = 1watt 

Gt = gain of a 28 MHz isotropic antenna = 1 in power ratio 

Ar = Aperture of the isotropic antenna at 28 MHz in square meters. 

R  = Radius of a sphere wich distance from the earth is 1500^3  i.e 
         the distance from the Passive HF relay satellite and the earth 
         expressed in meters. 

Sigma = Surface of the target in square meters i.e. of the Passive 
               HF relay satellite as seen as a radar target disc multiplied 
               by the reflectivity coefficient of 50% 


                 / 2                     2 
               /\                10.71 
 Ar  = ----------  =  ----------- = 9.13 square meters 
           4 x 3,14       4 x 3,14 

Sigma = 5^2 x 3.14 x 0.5 = 39.2 square meters 

                    1 x 1 x 9.13 x 39.2 
Pr = --------------------------------------- = 4.47 ^ -25 watt 
              (4 x 3.14 x 1500000^2) ^2 

Round trip attenuation = 10 log --------------- = 243.5 dB 
                                                        4.47^ -25 

Link budged calculation: 

Assuming that we are using a good HF receiver with a NF= 8 dB 
equivalent to 1539 kelvin we must consider in addition that the receiver 
sensitivity is limited by the external available noise power.For quiet,rural 
locations the galactic noise is the limiting factor and at 28 MHz the noise 
temperature is around 29.000 kelvin so that reducing the  Noise Figure 
belove 8 dB at 28 MHz do not improve too much the S/N ratio. 

With the above data the noise floor of this receiver for SSB into a 
bandwidth of 2500 Hz can be calculated as follows: 

Noise Floor = KTB = 1.38 x 10^-23 ( 1539 + 29.000 ) x 2500 = - 151dBW 
or - 121 dBm 

TX power 1000 watt.............................+30 dBW 
TX Antenna gain....................................+10 dBi 
Transmitted EIRP .................................+40 dBW 
Round trip attenuation 1500 km..........- 243.5 dB 
Received power Pr on isotropic 
antenna on the earth ..............................-203.5 dBW 
RX antenna gain....................................+  10 dB 
Available power at RX input............... - 193.5 dBW 
RX noise floor...................................... - 151 dBW 
Signal received with a S/N ratio.......... -  42.5 dB 

So according with Bob calculations the signal is 42.5 dB under the noise and 
so it is not detectable. 

Best 73" de 

i8CVS Domenico 

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