Johnson and Shot noise the Frequency Term

[Master J]

I am a bit confused over the frequency term that appears in Johnson and Shot noise formulae. What is this term?

Is it bandwidth? Of what? In relation to say a photodiode, is it the range of frequencies being detected?

And how would this relate to say a DC circuit which no frequency terms at all?

 

[jsgruszynski]

Strictly it's the bandwidth of the detecting/analyzing system/circuit. This could also be the bandwidth of a desired signal since you must use the same bandwidth to detect the signal correctly.

There are cases when it's something a bit different when you have a internal device feedback loop that can see the full noise bandwidth even when the external system has a lower bandwidth - but for most purposes it's the above.

In terms of DC, DC does have frequency. In the words of a microwave engineer I knew who was presented with presentation about "DC testing": "Yes, but what frequency DC?" The guy presenting wasn't a microwave/RF guy so he didn't understand the question. You see for her, 30 MHz was DC. That's the cut-off of an HP 8510 network analyzer's "DC input" that she used. It's all relative.

And at some point in even a "DC" circuit you had to turn on the DC and then later turn off the DC so you minimally have a transfer AC component equal to 1/(time on). But even a DC source isn't perfectly constant - there is always some d/dt.

When you deal with low frequency noise, DC is also relative. Consider that 0.1 Hz is 10 seconds. So when you measure low frequency noise you have to sample (in this case) for say 100 seconds to get 5 point (Nyquist sampling). This is part of the "fun" of measuring noise. This "low frequency/long time" integration is especially common with 1/f noise measurement.