Resistor Shot Noise

Created on 2013-11-01 02:21:00

In previous months I have been sharing some thoughts regarding noise in resistors.  However no discussion of noise would be complete without including the topic of “shot noise”.  Shot noise is quite simply the random fluctuation in current flow caused by the fact that electronic charge comes only in discrete steps, i.e. the charge of an electron. 

If we build a circuit and cause 1 mA of dc current to flow through a resistor, there will also be a small ac noise component superimposed. The magnitude of this noise current can be derived:

where q is the charge of an electron, or 1.6022e-19 coulombs

One immediate observation is that shot noise is independent of temperature where resistor noise is highly dependent upon temperature. Both are proportional to sqrt(BW), where BW is the measurement bandwidth of interest. There is also an interesting similarity in that shot noise if proportional to sqrt(Idc) while resistor noise is proportional to sqrt(R). 

In the above example where Idc = 1 mA and BW = 20 kHz, the associated shot noise is 2.53 nA (rms). This may seem like a negligibly small value (about -111.9 dB in comparison to the 1 mA dc component), but the designer must be careful to analyze how this affects a given circuit in relation to the intended signal levels. 

Shot noise tends to dominate the input noise current of bipolar op-amps.  Shot noise also contributes to the noise voltage developed across semiconductor junctions, for example in the familiar emitter coupled pair.  Indeed, deriving the equation for the noise voltage of an emitter coupled pair is surprisingly difficult.  Beware that many such published formulas are either over-simplified or just plain wrong.