# Noise power in conductor

by Rudibot
Tags: conductor, noise, power
 P: 10 The noise power in a conductor is given by P = k.t.B Does this mean the noise power is independant of the conductor length? Also, does this only apply for a conductor with no resistance? Thnks, Rudi
 P: 4,667 KTB is just the thermal power in a circuit at temperature T and bandwidth B, not considering any other sources of noise. KTB is about -114 dBm per MHz at 273 kelvin. It has nothing to do with conductor length. See http://en.wikipedia.org/wiki/Johnson...3Nyquist_noise Bob S
 P: 10 Thanks Bob, Sowhy do we need the relationship P = 4.k.t.R.B If we already know the power in the circuit?
P: 4,667

## Noise power in conductor

 Quote by Rudibot Thanks Bob, Sowhy do we need the relationship P = 4.k.t.R.B If we already know the power in the circuit?
Pn=4kTBR is the minimum NOISE power, so your signal-to-noise ratio is Ps/Pn for a signal power of Ps. The only way to reduce the noise power is to reduce T (temperature), B (bandwidth), or R (resistance).
Bob S
PF Patron
Emeritus
P: 6,203
 Quote by Rudibot Thanks Bob, Sowhy do we need the relationship P = 4.k.T.R.B If we already know the power in the circuit?
4 k T R B is the variance of the voltage (which you could call "the power" but of the voltage signal, "power" not being physical power, but "square of the signal").

BTW, if you look at the "current signal", then the "power" is 4 k T B / R

The physical power you can *extract* from a voltage source with voltage variance V2, and internal resistance R, is by connecting a load-resistor R to it.

The current flowing in the circuit is then sqrt(V2)/(2 R), and the power dissipated in the load resistor is then (I^2 R) or (sqrt(V2) / (2 R))^2 R = 4 k T R B / (4 R) = k T B.

(btw, that's with an un-physical ideal resistor with no noise as a load - in reality, the load resistor pumps just as much power back into the "source" resistor as the other way around, so that there is no net power flux if both resistors are at same temperature).
 P: 10 Thanks vanesch, so p=k*t*b is the real power. p=4*k*t*r*b is the signal power. But if the power is independent of conductor length, what is to stop me from cutting a conductor into *infininte* (read lots) of peices and getting lots of power?
PF Patron