# How to find G/T of antenna if everything else is provided - Link budget

1. Oct 23, 2008

### spacedude25

Hello guys,

i got a task to design the ground station antenna. I need atleast to figure out G/T of the station. I looked at different link budget analysis, but could not find out how to calclate G/T of the antenna, or atleast how to assume this value. Usually G/T is given, but i got inverse task - to find G/T when everything else (well, almost everything) is provided. Satellite and channel parameters are given below:

Orbital altitude: 36 000 km
Inclination, Position: 0º, 30 º W
DL frequency: 20 GHz
UL frequency: 30 GHz
Polarization: UL: RHCP , DL: LHCP
Bandwidth, 3 channels: 143 MHz each
Modulation: QPSK
Minimum satellite EIRP: 54 dBW
Minimum SFD from satellite at ground stations: -100 dBW/m2
Maximum SFD from satellite at ground stations: -80 dBW/m2
Minimum satellite G/T: 6.7 dB/K

Can someone give a hint?

Thanks,

spacedude25

2. Oct 24, 2008

### marcusl

Welcome to PF, spacedude!

Are you asking how to back it out of what you have? I suppose you can do that by using the Friis transmission equation. Satcom books (even general books like Space Mission Analysis and Design, or Balanis's Antenna Theory) will cover this.

Usually you calculate G/T from the ground up. G comes from the shape and size of the antenna, and includes the effects of any aperture taper. T is the effective receive temperature. It takes into account the receiver noise figure, any feed losses, etc., and the background thermal noise. The latter would be 290K if you are pointed at the warm earth, but at low frequencies is closer to 10K when looking into the blackness of space. However at Ka band you are still within the atmospheric water absorption band, so the background noise temp will be somewhere around 150K and depends on the weather.

Books like Skolnik's Introduction to Radar Systems (3rd ed.) show you how to do the gain and noise temperature calculations, and also include curves of T_sky. It's covered more precisely in his Radar Handbook (2nd ed), which also shows how T_sky depends on the look angle (it is minimum when looking straight up and increases as you look through more of the atmosphere towards the horizon).

3. Oct 25, 2008

### schroder

In general, the minimum value of earth station G/T is the difference between the received carrier power density and the required carrier/thermal noise ratio. It is a very simple computation but you need to know the satellite EIRP per carrier as well as the occupied bandwidth and the required receive carrier/noise ratio based upon the bit error rate desired.

You provided a bandwidth of 143 Mhz per carrier, which I think is suspect. As far as I know, the widest transponder bandwidth on ka-band satellites is 54 Mhz. Maybe what you gave is the bandwidth for all 3 channels? The satellite EIRP of 54 dBw looks about right.
What we can do is demonstrate a typical calculation of a full transponder (54 Mhz bw) carrier utilizing the full transponder EIRP of 54 dBw. Maybe that will give you an idea of how to do a calculation for any carrier you want?

The ka-band path loss is easily calculated to be 210 dB at 20 Ghz. Atmospheric losses can be very considerable at ka and need to be factored in for worst case along with the implementation margin for link reliability, but we leave that for last!

So, 54 dBw – 210 dB path loss = -156 dBw received carrier density at earth station.
I will assume a standard modem C/N of 9.7 dB for QPSK. Convert that to C/N in dB-Hz by adding 10*Log bw: 9.7 + 77.3 = 87 dB-Hz C/N

Now the carrier/temp is computed by adding Boltzmann’s constant:
87 + (-228.6) = -141.6 dBw/k
So the minimum required earthstation G/T is: -141.6 – (-156) = 14.4 dB/k
This is a bare bones minimum which does not consider atmospheric losses, link implementation margin and intermod, among other things. It might be OK for a backyard VSAT terminal but for a reliable commercial operation you want to double that number.

4. Oct 25, 2008

### spacedude25

Thanks a lot for the answer. Presently we own several S, X and Ku band antennas for satellite communication, but we want to go for higher frequency bands, like Ka-band. Therefore, it is not a backup, it is something more or less new for us. The gain and size is exactly my problem, because, i have to design the antenna completley without any apriori knowledge of its size and therefore gain. I have no knoledge of ground station parameters except its available power. System noise temperature was not a big deal. I had frequency and commercial LNA and receivers parameters, so i could figure it out and got 265 K for clear sky conditions and about 1130 K for rainy and foggy weather for ground station. I also heard that at Ka-band the waveguide introduces a problem, but i could not really find what that problem is. Any idea? Are those simply return losses?

Thanks for the references, i found really good explanations in Skolnik's book for all that.

Cheers,

the Spacedude

5. Oct 25, 2008

### Pumblechook

Yes but don't want a thumping great fade margin... maybe more as an anti-jamming measuring so fussing over a few dB here and there hardly seems to matter.

6. Oct 25, 2008

### schroder

Just want to clarify, when I said to double that number, I meant to increase it by 3 dB, from 14.4 to 17.4. The system noise calcs look to be in the ballpark at around 1100 K worst case, or 30 dB. If you use G/T of 14.4 dB/K that means you need 45 dBI of antenna gain which can be done with a one meter dish at Ka. To implement with a G/T of 17.4 dB/K you will need to go up to about 1.5 m dish. Not much difference in price there but you will probably want the extra margin.
With Ka band waveguide, there is always the possibility of transmit harmonics getting into the receive path, similar to Ku only worse. So (assuming you will be transmitting) you probably want transmit reject filters in the receive waveguide at front end of LNA which reduces the G/T somewhat. Maybe that is the waveguide problem you mentioned?