# Question about thermal noise.

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#### Alles Gute

##### Full Member level 2
bw*1.57 noise

When calculating the thermal noise of a resistor together with capacitor:
The noise density within the bandwidth of the RC filter is proportional to R, but that the bandwidth is inversely proportional to R, so that the total noise is KT/C independent of R.

But, a capacitor always has parasitic resistance, although it may be pretty small. Does that mean the thermal noise of a capacitor is always KT/C?

#### pixel

##### Advanced Member level 2
I am not sure that I have understood but:

Noise density er=√(4kTR) [V/√Hz]
Noise Equivalent BW NEB= (1.57*1/2πRC)

Output rms noise:
er*NEB ~1/√R

#### claudiocamera

##### Full Member level 4
The question must be improved in order to we have a better understanding, anyway I will try to guess the answer.

Termal noise is due only to resistive components, usually when studying RLC circuits we consider capacitors and inductors as ideal components, the Noise Power spectrum density due to a Resistor is Sn(w) = 2KTR, when the resitor is associated with a capacitor in paralell for instance the NPSD is in the output Sno(w) = Sn(w) * | H(w)|^2 , Where H(w) = 1/( jwRC + 1), It gives Sno(w) = 2KTR/(1+w^2*C^2*R^2) integrating it from - infinite to + infinite we found KT/C just because we have a R cancelation in the integral . It has nothing to do with the capacitor, Therefore there is not thermal noise in capacitor, since in the deduction the capacitor is ideal.

This results has a similar when you consider the available noise power density in a RLC circuit the results is KT/2 no matter resistors, capacitors and inductor values in the circuit.

#### jiaming_lee

##### Junior Member level 2
Alles Gute said:
When calculating the thermal noise of a resistor together with capacitor:
The noise density within the bandwidth of the RC filter is proportional to R, but that the bandwidth is inversely proportional to R, so that the total noise is KT/C independent of R.

But, a capacitor always has parasitic resistance, although it may be pretty small. Does that mean the thermal noise of a capacitor is always KT/C?

The parasitic resistance can be included, but it still does not influence the total noise KT/C. it only influence the very high frequency noise spectre

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