thanks godfreyl
could you tell me how can we effect of Bandwidth of voltmeter of this problem? and how we can find the min accuracy(in this example 1mV) that a voltmeter have to with a thermal noise?
Did you see that resistor noise depends on measurement bandwidth? Higher bandwidth has more noise.
If we measure the noise of the 100K resistor, we find:
Noise = 40uV between 0 and 1 MHz (bandwidth = 1MHz)
Noise = 40uV between 1 and 2 MHz (bandwidth = 1MHz)
Noise = 4uV between 0 and 10 KHz (bandwidth = 10KHz)
Noise = 4uV between 10 and 20 KHz (bandwidth = 10KHz)
Noise = 5.7uV between 0 and 20 KHz (bandwidth = 20KHz)
That's in fact answered in the quoted literature:
- it gives a formula for resistor noise
- it clarifies that resistor noise can't be reduced (it doesn't discuss cryogenic cooling)
Nevertheless, you can reduce the effect of resistor noise by omitting resistors, if applicable.
Resistors can have a certain amount of excessive noise with applied DC voltage, but "ideal" kT noise will be most likely dominant. In so far the quoted equation is giving the "practical" method.