# Re: todays math problem

• Subject: Re: [amsat-bb] todays math problem
• From: "Frederick M. Spinner" <fspinner@xxxxxxxxxxx>
• Date: Tue, 04 Feb 2003 17:02:24 +0000

```Doubling the diameter of a dish gives it four times the area.  The area is
directly proportional to gain.

If the efficiencies are the same (key point here),  four times the area is
6dB extra gain.

If an optimal dish is say 20dB and then you lose 50% of the signal to
inefficiency that gives you -3dB or 17 dB.
If the twice as big optimal dish is 26dB then you lose 50% (-3 dB) then your
at 23 dB.

23 dB - 17 dB = 6 dB.

The inefficiency isn't hurting the bigger dish more.

Oh okay Now, I see Jerry is talking about the aperature area doubling not
the diameter... I've just figured that out from the message.

So yes area doubling on a dish = 3 dB more gain regardless of efficiency.
Diameter doubling == area times four == 6 dB more gain.

In this case:

1959 sq/in / 791 sq/in = 2.47 x as large in area.   10 log(2.47) == 3.93 dB
more gain.

At S-band, however these are both well below established "minimum" dish
sizes (10 wavelengths or more are considered to be "well behaved dishes").
So contrary to what one might think, the bigger dish is likely to be more
efficient than the first, and if a dB were picked up that way it would be
possible to see an S-unit difference.  Couple that with less noise pickup
and it is probably worth upgrading to that dish.

But I doubt if it would be 7.5 dB better...

Fred W0FMS

>From: K5OE@aol.com
>To: w7lrd@juno.com, amsat-bb@AMSAT.Org
>Subject: Re: [amsat-bb] todays math problem
>Date: Tue, 04 Feb 2003 03:29:41 -0500
>
>Bob,
>One of the biggest factors in dish gain is the efficiency of illumination,
>but ignoring that complexity (since you didn't give us any specifics) and
>assuming a 50% efficient dish/feed combination in both cases, a convenient
>short-cut equation for "typical" dishes at 2.4 GHz is:
>Gain = Log10(0.256 * Area in sq in.)
>
>Thus:  791 sq in = 23 dBi and 1959 sq in = 27 dBi
>
>...for a delta of only 4 dB.  Roughly, each doubling of the dish aperture
>is worth 3 dB when all other variables are unchanged.
>
>73,
>Jerry, K5OE/G
>
>
>In a message dated 2/3/2003 9:49:50 PM Eastern Standard Time,
>w7lrd@juno.com writes:
>
> > Hello
> > Bob has two dishes, dish 1 is 1959 square inches. Dish 2 is 791 square
> > inches.  So dish 1 is about 2.5 times larger than dish 2.  Bob thinks
> > dish 1 should be 7.5 db better than dish 2, that's 2.5X3db,
> > or maybe a
> > little over one S unit. Is Bob right?
> >
> > 73...Bob...W7LRD
> > Seattle
>----
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