Hi, it should nothing happen with Johnson noise. In practical cases when You measure noises at very low frequencies (10Hz and lower) additional noise sources could be dominant in Your measurements. For example flicker noise which has power spectrum density inverse proportional to the frequency. It is also known as "1/f - noise". Another remark is: by regime when you connect your resistor to DC Voltage you have to measure current fluctuations (cause voltage across a resistor is controlled by voltage source) and by connecting your resistor to current source you have to measure voltage fluctuations.

Regards, S.

I don't know if I got your question well. But to be more precise, delf is not the frequency of interest, it is the bandwidth over which the noise is measured so it is a range not a single value. In case of just DC, this bandwidth is zero and we neglect the thermal noise. 

Hi Mohammed

You are right that delf is bandith. Sorry for that. But I don't think in case of DC thermal noise is zero. Normally V^2=4KbTR per unit band width.  My observation in literature people take V=sqrt(4KbTR)*sqrt(delf). Means they report  V in terms of nV/sqrt(Hz) in a given bandwidth. For DC people normally take bandwidth as 1Hz in order to report Johnson noise/thermal noise. But I am not sure whether that is correct.

Thanks

Ankur

 Hi Ankur,

I think it is a little bit tricky here, when you use a measurement instrument, the noise that you will measure will be due to the bandwidth of this measuring device. If you are able to measure only the low frequency component, or see it in the frequency domain, I agree with Sergey that the flicker noise will be dominant.

Talking about theory, I still convinced that the contribution of a single frequency to the thermal noise is zero. But if we assumed a non-perfect DC source, may be this is why they assume 1 Hz for analysis.

Best Regards,

Mohamed

Hi guys, as far as I understood from your discussion here, the Problem is in terminology which you use. DC signals in ideal world have meanining of constant value. So, mathematically thinking if you would have hypothetic Instrument which could provide you ideal DC voltage (or current) it means that this Instrument will control your voltage (or current) on your resistor, therefore as a result you will get 0 voltage (or current) fluctuations. (Mathematicaly: 0 frequency bandwidth results in 0 fluctuations ) In real world all processes take some finite Duration, therefore it is impossible to have ideal DC source of Signal. So, any DC source have some bandwidth. "DC" in real application world means device with "relatively" low bandwidth (let us say below 1MHz).When designer of Instrument writes Application note or Spec.sheet it is more convinient to give noise characteristics as a Power Spectrum Density (V^2/Hz or A^2/Hz). Cause it is simple for user to estimate amplitude of fluctuations in his application for certain bandwidth which was chosen by user. In some cases Producers specifiy only Standard Deviation of the fluctuations Signal at the Output of Instrument or device. Typically it is also written a bandwidth in which this quantity was measured. It is definitely less Information in comparison with Spectrum, but better than nothing...

In any measurement system you have a finite non-zero bandwidth, otherwise it could never change reading! You should be able to work out this measurement bandwidth and therefore calculate the Johnson noise. There is no reason to assume 1 Hz, it could be orders of magnitude more or less than this. Do not mix up bandwidth and figures expressed as densities where you need to multiply the density by the bandwidth to get a meaningful noise values. It is common to express noise as an RMS voltage density, V/Hz^0.5, to get RMS volts you need to multiply this figure by the square root of the bandwidth.

However, at low frequencies, other noise sources are very likely to dominate, the 1/f noise or pink noise is likely to be far higher especially if any type of semiconductors are involved in the measurement.