Based on which formula does Signal Chain Designer calculate the thermal noise?

Hi,

For noise analysis, the Signal Chain Designer injects equivalent noise sources for each noise contributor (i.e. resistors, amplifier voltage noise, amplifier current noise, etc.) in the circuit.  Then, we use small-signal analysis to determine the noise gain from each noise source to the output of an individual stage or the entire signal chain.  The referred-to-input (RTI) noise is calculated by dividing the referred-to-output (RTO) noise by the signal gain of the stage or signal chain.

The noise sources for resistors are simply voltage or current sources with thermal (4kTR) noise density.  The noise sources for amplifiers and references are composite noise sources that may include thermal noise, flicker noise, and shot noise, and are modeled to match the amplifier datasheet or characterization measurements.  The noise sources for ADCs are derived from the measured RMS noise and equivalent noise bandwidth, including the sampling, digital filtering, and aliasing.  Since these sources are based on measurements that include all noise types, we do not show separate thermal, flicker, shot, or kT/C noise contributors for amplifiers, references, or ADCs.

A few notes: 

* The signal gain used to determine the RTI noise is the maximum gain within the measurement region (typically the dc gain for DC-coupled signal chains).

* The sum of noise sources is determined by simple addition of correlated noise sources and root-sum-squared (RSS) addition of uncorrelated noise sources.

While we do not have detailed descriptions of the formulas because the tool uses generalized small-signal analysis to calculate the noise, there is more detail about the noise simulation in the help topics for the noise analysis:

To get an idea of how to individual noise contributors are affected by their position in the circuit, these videos might be helpful:

https://www.youtube.com/watch?v=W0vfALQ_n54

https://www.youtube.com/watch?v=ZaDK-Nqfp-U

When you are doing hand analysis, as shown in the videos, you typically assume both the noise source and the transfer function are constant across frequency.  i.e. I multiply 4 nV/rt(Hz) by a gain of 10.  Then at the end you integrate with an equivalent noise bandwidth to get a rough idea of the integrate noise.   The great thing about a computer is that it's happy to do lots of math, so can you a similar analysis, but at lots of frequencies.  So you can be more accurate in both variables - 1) your noise source can vary over frequency (for example because of 1/f noise) and 2) the transfer function acting on the noise source will vary over frequency.  The result is a graph of curves like Kerry showed above.  Which can then be integrated to get the rms noise: