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

[Kok Chen]

On Nov 17, 2008, at 1:01 PM, Tayloe Dan-P26412 wrote:

> How can it hurt the SNR?

Because in split operation, you are adding the noise from two  
different bandpasses, yet you are only hearing the signal from the  
original single receiver.

Let receiver (1) hear s(t) + n1(t) and receiver (2) hear n2(t) .   
Remember that s(t) is outside the passband of the second receiver, so  
there is no s(t) component in receiver 2.

Sum the two receivers, and you get s(t) + n1(t) + n2(t).

Prob( (s+n1+n2)^2 ) = Prob(s^2 + n1^2 + n2^2 + n1.n2 + s.n1 + s.n2).   
If s, n1 and n2 are uncorrelated, then Prob(n1.n2) = Prob(s.n1) =  
Prob(s.n2) = 0.

Thus the output power of the summed signal is (s^2) + (n1^2) + (n2^2).

The original single receiver SNR is (s^2)/(n1^2). The summed receiver  
SNR is (s^2)/( (n1^2)+ (n2^2) )

73
Chen