[Elecraft] Re: K3: listening to both rcvrs - Reduced receiver noise floor

[Tayloe Dan-P26412]

>> So the reduction in SNR (assuming equal noise power) is
>> 3.01 dB, not 6 dB.

>That's the best case if the noise power is equal.  If the 
>"other" receiver has higher noise power (wider bandwidth, 
>more interfering signals, etc.) the S/N reduction is greater. 
>Even 3 dB reduction in S/N is a big hit if the DX Station 
>you're trying to hear is at or just below the noise level. 

>It would be a shame to turn a top performing radio into a 
>mid-pack device by mixing the audio - because of some old 
>wife's tail.  Let those who want mixing do it externally 
>so it doesn't impose a S/N penalty otherwise.

There seems to be a fundamental mis-understanding on how 
uncorrelated and correlated noise works.  If two receivers 
are listening to the exact same signal and use the same 
antenna, then the short answer is that summing the output 
from these two receivers together will produce the same signal 
at a level 6 dB higher with no signal to noise change. This 
assumes the receivers themselves are identical and do not 
contribute noise (more on this later), so the two receiver 
outputs will be identical.  Band noise from one receiver at 
any instant in time will look exactly like band noise from 
the second receiver.  The desired stations signal will look 
the same from both receivers.  The point is that magic is 
not involved, and that neither of these two receivers can 
tell the difference between band noise and the desired 
signal and thus will process both the desired station and 
the band noise the same.  

Thus, there would be no degradation or improvement in signal 
to noise ratio as long as we are talking about ideal receivers.

However, if the situation is a weak signal situation where 
the receiver noise floor is at least partially masking 
the desired signal, we have a different situation.  Band 
noise and stations on the band will both be correlated coming 
out of both receivers and thus get a 6 dB improvement.  On 
the other hand, the internal noise produced in each receiver 
is independent and thus uncorrelated.  While correlated 
signals add voltage wise (V + V = 2V or 6 dB gain), 
uncorrelated noise adds as the square root of the sum of the 
squares sqrt(V*V + V*V) = 1.4V or 3 dB gain.  

This means what when adding the output of two identical 
receivers, the band noise and the desired station signals 
will increase by 6 dB while the receiver noise contributions 
will increase by only 3 db.  You have in essence created a 
single composite receiver with a lower noise floor.  If you 
added just enough RF pre-amplification to overcome the signal 
splitting loss to N receivers, adding more and more receivers 
in parallel will produce a composite receiver that has a 
better and better noise floor.  This is in essence what the 
space telescope folks do.  They gang many dishes and many 
receivers together across a very large area to get an 
enhancement on the signal and space noise and a suppression of 
the effective receiver noise contribution.

Thus, if the noise floor of the receivers are the limit, 
listening to the same signal with two identical receivers 
will have the effected of reducing the receiver noise 
contribution by 3 db.  Conversely, that also means that if 
you are listening on 40m where the band noise is way higher 
than the receiver sensitivity, reducing the receiver noise 
contribution will be of no benefit.

- Dan Tayloe, N7VE