# Shot noise

## What do you need to know to understand this topic?

• Only the basics of electricity
• Power Spectral Density (PSD)

## What is shot noise?

Current is made of electrons flowing in a certain direction. The amount of electrons flowing per unit of time is not precise, but instead it fluctuates through time. To that fluctuations around the mean value we call shot noise. It is considered only in devices in which electrons need to cross a barrier, such as diodes or transistors. The Power Spectral Density (PSD) of this noise is: $$\overline{i_n^2} = 2qI_{DC}$$ where $q$ is the electron charge (Coulomb) and $I_{DC}$ is the average current (A). This noise is proportional to current because more current means more electrons and more collisions, leading to more fluctuations. The PSD does not depend on the frequency because shot noise is white (equal power for all frequencies).

In order to find out how much noise power the device would generate in some circuit, multiply the PSD by the equivalent noise bandwidth of the system ($\Delta f$): $$v_n^2 = \overline{v_n^2}\Delta f = 2qI_{DC} \Delta f$$