No subject

noise, and all) evenly between two paths, which then ideally feed identical double balanced mixers (I'm thinking of a
hardware implementation, obviously) whose only difference is the quadrature phase of the LO. So both paths are seeing the
same SNR at that point. So my first guess would be that the relative phase of the LO to the input signal would only affect
the phase of the output from each path, but the noise content ( or modulation if there is any) would not be any different
between the two paths. I'm not aware that a single DBM used as a downconverting mixer shows any preference to the phase angle
of the input to the LO. 

Tom Holmes, N8ZM

-----Original Message-----
From: Lux, Jim <jim at luxfamily.com> 
Sent: Thursday, August 26, 2021 1:37 PM
To: Discussion of precise time and frequency measurement <time-nuts at lists.febo.com>
Subject: [time-nuts] uncertainty/SNR of IQ measurements

This is sort of tangential to measuring time, really more about 
measuring phase.

I'm looking for a simplified treatment of the uncertainty of I/Q 
measurements.  Say you've got some input signal with a given SNR and you 
run it into a I/Q demodulator - you get a series of I and Q measurements 
(which might, later, be turned into mag and phase).

If the phase of the input happens to be 45 degrees relative to the LO 
(and at the same frequency), then you get equal I and Q values, with 
(presumably) equal SNRs.

But if the phase is 0 degrees, is the SNR of the I term the same as the 
input (or perhaps, even, better), but what's the SNR of the Q term (or 
alternately, the sd or variance) - Does the noise power in the input 
divide evenly between the branches?  Is the contribution of the noise 
from the LO equally divided? So the I is "input + noise/2" and Q is 
"zero + noise/2"

If one looks at it as an ideal multiplier, you're multiplying some "cos 
(omega t) + input noise" times "cos (omega t) + LO noise" - so the noise 
in the output is input noise * LO + LO noise *input and a noise * noise 
term.

I'm looking for a sort of not super quantitative and analytical 
treatment that I can point folks to.
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