The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Design >> Analog Design >> How to understand "kTC" noise?
https://designers-guide.org/forum/YaBB.pl?num=1539867984

Message started by A Kumar R on Oct 18^th, 2018, 6:06am

Title: How to understand "kTC" noise?
Post by A Kumar R on Oct 18^th, 2018, 6:06am

Hi,

I have been going through noise fundamentals and while i was reading about "kTC" noise...they say it is independent of resistor. To some extant this is understandable because the resistor noise is white (meaning uniform across all frequencies) and only C has to play a role to band limit the noise.

what surprises me is that the final equation (you can find this in Razavi noise chapter also), which is sqrt(kT/C) when integrated from 0 to infinity, gives much less noise than you would otherwise get if you were to sum each noise voltage at each frequency in that 0 to infinity band.

i have understood the math of this, but, qualitatively not getting it.

one more thing, when a circuit gives complex impedance at its two ports, then the thermal noise is calculated by looking at the real part of this complex impedance.

my question is that the real part you would get is not physically present in the circuit wheras the noise will be generated from physical resistor right?

why is this so?

Thanks,
Kumar R

Title: Re: How to understand "kTC" noise?
Post by Maks on Oct 28^th, 2018, 5:16pm

This expression (kT/C - for thermal noise power on a capacitor) is exactly equal to (and derived from) the thermal noise power spectral density on a resistor (4ktRdf) integrated over infinite frequency range.

In a circuit, thermal noise can be generated not only by resistors (intended or parasitic), but by any other element containing a non-zero real part of the complex impedance - such as MOSFET (channel), diode, etc.

This fact - that the noise power spectral density is determined by the real part of the complex impedance - is following from a very general theorem in statistical physics (for systems in thermodynamic equilibrium), called FDT - Fluctuation Dissipation Theorem:

https://en.wikipedia.org/wiki/Fluctuation-dissipation_theorem