Resources on Noise Circuits

Question

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.

Answer 1

Noise sources are not very different from AC sources. Most AC sources averaged over time are zero mean, yet we still analyze the circuit similar to DC. The difference is we need to consider the frequency of the signal. Get comfortable analyzing circuits in the frequency domain. Bode plots make things make more sense, since white noise sources have frequency content on every frequency but only on average.

Explaining how to analyze noise in circuits is too long for one post, but there is a good resource. A great source to learn how to analyze random sources is Noise Reduction Techniques by Henry W. Ott I've used the tequniques in this book to develop systems that measure nV and uV.

Source: http://www.hottconsultants.com/book.html

Answer 2

Here is example of a circuit: noisy sensor, noisy precision-gain stage, noisy low pass filter, and noisy ADC. Combined noise is 13 microVolts. The math uses RSS Root Sum Square. No current-noise sources are modeled.

Rsensor is 200 ohms, as you'd get from a strain gauge bridge.

OpAmp model is similar to OPA-211, with 62 ohms internal Rnoise (produces exactly 1nanovolt/rtHz noise density); has 101 ohms to Ground and 100,000 ohms Rfeedback, to produce 1,000x voltage gain.

Without the RC LPF, the opamp's frequency response (under a 60dB gain requirement) with F3dB near 100KHz, causes the noise(s) to peak near 50KHz: 460 uV total integrated noise for the sensor (remember that is 200 ohms); 325 uV total integrated noise for the 101 ohm Rg to ground; 257 uV total integrated noise for the 62 ohms internal to the opamp; Rfeedback and ADC input resistor are about 10uV each. RSSing all of these, WITHOUT THE RC LPF, the noise INTO the ADC is 620uV.

With the RC LPF enabled, the RSS greatly reduced, to 13 uV RMS. Of course, the bandwidth dropped, to dc -- 10Hz (16Kohm, and 1uF)