Dish Gain & Surface Area ?

[moonbase]

Hi,

Would anybody please be able to clear up some confusion I have in the relationship between the gain of a dish and the active surface area.

I have a 1.5m dish and a 1.8m dish, both prime focus and the same make. The manufacturers figures for mid gain are 43.1db (1.5m) and 44.7db (1.8m) but the surface area of the 1.8m dish is considerably more so I would possibly have expected a higher mid gain figure.


On the subject of surface areas, would anyone please be able to provide the mathematical formula to calculate the surface area for a prime focus dish, I assume it is some type of derivative of the area of a circle but with a factor to allow for the curvature (got no pi on my keyboard).


Thx for any insight on the subject.



Rgds

 

[Channel Hopper]

The gain increase looks about right for the two dish sizes, the 1.8m being about 40% more area.

As for surface areas, only the two dimensional area is valid for any communication requirement, as the signal is derived from the aperture that observes the satellite. The effective area of a prime focus dish would therefore be D/2 x D/2 x 3.1415926 etc, minus the outer rim that isn't part of the parabola, the shadows caused by the feedarms, feed, LNB and any cable dangling in front of the dish.

If you did want to work out the total surface area you would need to look at the work of Archimedes and his calculations using the mathematics behind cross sections through cones (parallel to the slant edge), which can be found on the following link.

_http://docs.google.com/viewer?a=v&q=cache:ligSYIx17aIJ:www.shsu.edu/~mth_jaj/math467/tate_..._i8D5w&sig=AHIEtbQHQ6cNA1I9rs4Dxsk-A6LM3uQ8jQ

Every PC I've had has a calculator within the 'start/programmes/accessories' link, and can be set to 'scientific' which brings up the 'Pi' button

 

[moonbase]

.....As for surface areas, only the two dimensional area is valid for any communication requirement, as the signal is derived from the aperture that observes the satellite

Channel Hopper,

Thanks for the detailed reply.

Logic is telling me that the signal is reflected from the surface of the dish towards the focal point at which the LNB feedhorn is located and that the amount of signal reflected is dependent on the surface area available to reflect.

Hovever, as the parabolic profile for a prime focus dish is a direct mathematical derivative of the two dimensional aperture then I suppose that for any two dimensional circular window of surface area there is always the same fixed amount of reflector surface notwithstanding rimming loss and shadow loss, interesting concept nonetheless.


Rgds

 

[Channel Hopper]

As mentioned above, the illumination of the surface is the important part from the communications point of view, the three dimentional aspect is purely the requirement for a parabola to act as a collector of signal.


When flat plane antennas finally reach the same efficiency, the thoughts of Archimedes can finally be put to bed.

 

[ralphmagno]

hi,
i like all the big words.
the bigger the lens the more ants you can burn.
the reflector focus the rf energy to the focal point the lnb feed horn.
the antenna is about the size of a nail head located inside the lnb opening.
there is 120 bd loss from space to the dish.
there is about 55 db gain from the converter (lnb) and 42 to 47 db gain from the dish if one is using 1.20 cm to 3 meter dish.
ralph

 

[PaulR]

In rough figures, and taking only the dish itself, a 1.5m dish has a surface area of just under 1.8 sq m and a 1.8m dish is just over 2.5 sq m which is under twice the surface area. In order to get twice the surface area you would have to have a dish of just over 2.1m diameter!

And then we come to decibels. This is a logarithmic scale where a 10dB gain is an increase of 10 times and 20dB is 100 times. A mere doubling is only about 3 dB which, as we saw above, would need a 2.1m dish.

So 1.6dB gain looks about right.

 

[Lazarus]

the bigger the lens the more ants you can burn.

Brilliant summary!

 

[esto]

There's tons of formulas and examples if you Google "parabolic antenna gain formula".
Here's Wikipedia: _http://en.wikipedia.org/wiki/Parabolic_antenna#Gain
Here's another: _http://www.montgomerycollege.edu/Departments/cadtecgt/es100c/materials/Bern/parabolic antennas.pdf

 

[Huevos]

And if you want to compare the collector size in relative terms you don't even need to work out the area or use Pi. Just do: ((big-dish^2)/(small-dish^2)) = ((1.8^2)/(1.5^2)) = 1.44.

 

[Huevos]

In rough figures, and taking only the dish itself, a 1.5m dish has a surface area of just under 1.8 sq m and a 1.8m dish is just over 2.5 sq m which is under twice the surface area. In order to get twice the surface area you would have to have a dish of just over 2.1m diameter!

And then we come to decibels. This is a logarithmic scale where a 10dB gain is an increase of 10 times and 20dB is 100 times. A mere doubling is only about 3 dB which, as we saw above, would need a 2.1m dish.

That's true if you are measuring power , but most signal meters are measuring voltage (dBuV). When you are working in volts 3dB relates to a doubling of diameter of the dish, not the area. The theory behind this is power equals voltage squared divided by the resistance (W = V^2/R). If you calculate a doubling of power (area) you'll see the voltage only goes up by 1.4:

W = V^2/R
1W = ((1V x 1V)/1ohm)
2W = ((1.4V x 1.4V)/1ohm)

To double the voltage you need 4x the power (dish area) which equates to double the diameter:

4W = ((2V x 2V)/1ohm)

 

[samoloko]

Huevos

would you please tell us what receiver got better tuner (selectivity, sensitivity) DM500HD or Vu Duo

 

[Huevos]

would you please tell us what receiver got better tuner (selectivity, sensitivity) DM500HD or Vu Duo

The DM500HD is a clone so I can't say. The tuner in the Vu+ is top quality for sensitivity and selectivity. It struggles a bit to lock symbol rates below 2Mbps, but lots of receivers are like that. Apart from that it is excellent... but if I wanted a twin tuner receiver now I'd wait for the Ultimo. Lots of people are raving about the Clarke-Tech ET9000 but with the motherboard battery issue I personally would not consider one of those.

 

[samoloko]

thank you

I hear that a lot of people In my region raving about DM500HD tuner that Is why I asked

 

[Huevos]

I hear that a lot of people In my region raving about DM500HD tuner that Is why I asked

If I just wanted a single tuner receiver I'd go for the Vu+ Uno. It's got a top quality tuner, with blind scan, and the hardware is far superior.