[TowerTalk] Funniest thing I've seen in weeks

[Jim Smith]

Sorry to have taken so long to respond to this.

I'm told, by many people who know a zillion times more about this stuff 
than I do, that increasing antenna gain doesn't improve received SNR 
under the following conditions:
  The received noise is greater than the internal noise of the receiver
  The noise has a uniform spatial distribution
    i.e. no stronger in one direction than any other
       
This doesn't seem to agree with my experience so I conducted the 
following thought experiment.

Assume the following:
  An omni directional antenna
  External (incoherent) noise has a uniform azimuthal distribution
    i.e. we're considering a 2 dimensional system here
  Noise power at the antenna terminals contributed by 1 degree of 
azimuth is 1 uW
  Signal power at the antenna terminals is 360 uW
   
Under these conditions the total noise power at the antenna terminals is 
1 uW x 360 deg = 360 uW, giving an SNR of 0 dB.

Now consider an idealized antenna with same gain as before but 
restricted to a 60 deg arc and no response whatsoever over the remaining 
300 deg.  The antenna is, of course, pointing at the signal source.

The only noise the antenna will pick up is that noise within the 60 deg arc
The noise power at the antenna terminals will now be 1 uW X 60 deg = 60 uW
The signal power at the antenna terminals will still be             360 uW
SNR is now 10 log 360/60 = 10 log 6 = 7.8 dB


Now consider an idealized antenna with 6 dB gain everywhere within a 60 
deg arc and no response whatsoever over the remaining 300 deg.  This is 
6 dB with respect to the previous antenna.

The noise power at the antenna terminals will now be 1 uW X 60 deg X 4 = 
240 uW
The signal power at the antenna terminals will now be       360 uW X 4 = 
1440 uW
SNR is now 10 log 1440/240 = 7.8 dB


Interestingly, the antenna gain cancels out.  i.e. with the same pattern 
a gain of 12 dB will still yield an SNR of 7.8 dB, just like everybody's 
been telling me.  So how come I can hear things on a yagi that I can't 
hear on a dipole at the same height?


If the antenna has 6 dB gain but responds over only a 30 deg arc then:
The noise power at the antenna terminals will now be 1 uW X 30 deg X 4 
=  120 uW
The signal power at the antenna terminals will now be       360 uW X 4 = 
1440 uW
SNR is now 10 log 1440/120 = 10.8 dB

So, more antenna gain but with the same pattern makes no difference to 
received SNR.

Narrower pattern, regardless of gain, will increase SNR.

So it would seem that the fact that a yagi at the same height as a 
dipole will hear signals that the dipole won't, not because of the 
yagi's gain but because it's pattern reduces the total noise power 
picked up by it.

I seem to be happy with this explanation provided by my highly idealized 
(but easy to deal with) model.  Don't know if anyone else is, though.

73 de Jim Smith   VE7FO


Jim Lux wrote:

>----- Original Message -----
>From: "Jim Smith" <jimsmith at shaw.ca>
>Cc: "towertalk reflector" <towertalk at contesting.com>
>Sent: Friday, July 30, 2004 1:46 AM
>Subject: Re: [TowerTalk] Funniest thing I've seen in weeks
>
>
>
>>If the received noise is uniformly distributed in azimuth I would think
>>that additional gain, presuming that it comes from a narrower azimuthal
>>pattern, would increase the SNR of the desired signal.
>>
>
>No... consider the noise as just another signal, so increased gain in a
>particular direction (of the signal) increases the noise AND the signal by
>the same amount.  SNR stays the same.
>-> Exceptions:
>1) VHF or higher where receiver noise dominates...
>2) Where the antenna is physically large enough that you can coherently
>combine two paths with the signal, while the noise is uncorrelated.  An
>array with antennas separated by LARGE distances (many wavelengths) might
>achieve this (imagine combining the receive signals from separate antennas
>in Los Angeles and San Francisco... the noise probably isn't identical)..
>The improvement in SNR is sqrt(Nantennas) in this case.  (What this really
>is is a way to make the original assumption (noise uniformly distributed in
>azimuth) not true any more)
>
>
>>If there is a lot of noise from one direction and the increased
>>directivity is such that there is now a null in the direction of the big
>>noise then the SNR of the desired signal would increase a lot.
>>
>
>Yes... and, consider that "noise" isn't usually what you're worried about..
>it's some other station(s), which come from a single (but different)
>direction
>
>>Am I on the right track here or totally out to lunch?
>>
>>73 de Jim Smith   VE7FO
>>
>>Tom Rauch wrote:
>>
>>
>>>This is actually pretty important, because MANY people think
>>>7dB of additional antenna gain improves the receiving and
>>>transmitting 7dB. The actual receiving change can be
>>>anything from zero to dozens of dB. If for example you have
>>>a 15 meter Yagi with 3dB of feedline loss and improve system
>>>gain 2dB by replacing the feedline, the receive S/N will
>>>remain the same.
>>>
>>>73 Tom
>>>
>>>
>>>_______________________________________________
>>>
>