What is the Bandwidth in resistor thermal noise formula?

Hi all,

The formula for resistor's thermal noise (johnson noise) is:



My question is, How to decide what bandwidth should be used in this formula? For example, I am lighting up a LED with a 12V DC source through a resistor, what will be the bandwidth?

These are for RF signals , I suppose...

I agree, but I beleive any resistor connected to a Voltage source will have some degrees of thermal noise. If I want to be more clear about my question: I want to know what is the bandwidth in my given example, how to calculate it, is it 0 or not in the same source -> resistor -> LED example. I know the thermal noise plays no rule in this example but it for sure exist and I want to know it's value. The only thing stops me from calculating it, is that I do not know the Bandwidth in this case.

Please help!

Johnson noise is caused by random movement of charge carriers, most often electrons. For most practical purposes, it has an infinite bandwidth. To calculate its effect on circuit performance, we have to decide on the bandwidth of interest for the application.

Thats the point, how can one decide what is the bandwidth of an application?!

If it's for audio, the bandwidth of interest is 20kHz. But that's a very general statement. Specific audio systems may require different bandwidth specs. If it's for the video amplifier in analog TVs, the bandwidth is about 5MHz. If it's for a bandpass circuit with a centre frequency of 10MHz and the frequency of interest is from 9.7MHz to 10.3MHz, then the bandwidth of interest is 600kHz.

The bandwidth of the application has to be defined as in the above examples.

But may be the noise that is produced be "Shot noise", coz it is when current starts flowing....

When measuring noise you precede your instrument with a filter so you are sure over what bandwidth the noise in being measured. Take for instance a video circuit, it is specified to be flat to 5MHZ. so you hook your noise measuring set to it and actually measure a significant carrier at 8MHZ (clock breakthrough from some where). Its not in the band of interest so it should be filtered out, so you precede the noise measuring set with a 5MHZ low pass filter. An interesting bit of the video band is 4.4MHZ +- 1MHz, this is where the chrominance channel is on PAL TV, any noise in this band would show up badly on the coloured bits of a picture. So you precede the noise measuring set with a suitable filter ( "chroma filter"), else your wideband measurements won't tell you much about the noise in the colour area. Also for audio the filter is not only band- limited but also so weighted, as the ear is much more sensitive to the frequencies around 2Kz, then 20Hz or 20KHz.
As to your particular case, you have thermal noise generated by both the LED and resistor (in parallel) and shot noise due to the LED. Look at Wikipedia.org for explanations.
Frank