# Flicker ($1/f$) noise

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

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

## What is flicker or $1/f$ noise?

It is not certain the source of this noise, but is often associated with imperfections in the conductivity medium, such as contacts between materials. The Power Spectral Density (PSD) of this noise depends on the type of device. For instance, for MOSFET transistors is: $$\overline{v_n^2} = \frac{K}{WLC_{ox}f},$$ where $K$ is a process and temperature dependent parameter, $W$ and $L$ are the width and length of the device, $C_{ox}$ is the oxide capacitance and $f$ is the frequency. This noise is emulated by a voltage source with equal power at the gate of the transistor. This noise is inversely proportional to $f$, being higher for lower frequencies. Because of this type of relation with frequency, it is called $1/f$ or pink noise .

In order to find out how much noise power the device would generate in some circuit, we have to integrate the noise along the bandwidth $BW$ of interest (probably the bandwidth of the system): $$v_n^2 = \int_0^{BW}\overline{v_n^2}\partial f$$

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