Back when I was taking an RFIC design course, I was pretty disappointed by the noise part of the class, specifically calculating the output-referred noise voltage, noise figure of an amplifier, etc. It seems like you should be able to apply basic circuit theory principles, such as Kirchhoff's Laws. However, I'm not really sure that you're allowed to do that, and I don't feel like my class went in-depth enough for me to understand.
Take Kirchhoff's Current Law. It's based on the idea that there can be no sources nor sinks of current in a circuit. The sum of all currents at a node should be zero (an equal amount of current leaves the node as enters it). The problem is that noise sources are random. So, the concept of current flowing "into" a node doesn't really make sense because whether it flows into or out of the node is random, and my impression is that a noise current source wouldn't have a direction/sign unlike a traditional current source.
Either... A) Is my understanding totally flawed? Do we assign signs to noise sources like everything else and apply regular circuit theory? (I doubt this is the correct answer.) Or... B) Does circuit theory need to be reformulated when dealing with noise sources? So, would the rules, like Kirchhoff's Laws, be different? If so, are there any resources that describe exactly how this works in a precise manner? I haven't been able to find anything satisfying, but maybe I'm not as good at Googling as I once thought.