Noise ultimately limits the performance of all systems. For example, the maximum gain of an amplifier is limited to VDD/vn where VDD is the power-supply voltage and vn is the noise floor at the input of the amplifier. Gains higher than this limiting value will simply amplify noise to saturating power-supply values and leave no output dynamic range available for discerning input signals.

Since power is the product of voltage and current, low-power systems have low voltages and/or low current signal levels. Hence, they are more prone to the effects of small signals such as noise. A deep understanding of noise is essential in order to design architectures that are immune to it, in order to efficiently allocate power, area, and averaging-time resources to reduce it, and in order to exploit it. We will begin our study of noise in physical devices from a first-principles view of some of the fundamental concepts and mathematics behind it.

The mathematics of noise

We pretend that macroscopic current is the flow of a smooth continuous fluid. However, the current is actually made up of tiny microscopic discrete charged particles that flow in a semi-orderly fashion. The random disorderly portion of the charged-particle motion manifests itself in the macroscopic current as noise. Figure 7.1 reveals how macroscopic current is actually made up of tiny fluctuations around its mean value which constitute current noise.