In this chapter we will look into the question of extracting weak signals from noise. The subject is huge, and we will be able to cover only a few basic techniques. Even then, we will have to progress through fairly long preliminaries in disparate domains before we are ready to analyze significant experiments from the literature.

We will begin by examining the degree to which transistor amplifiers increase the noise in signals from resistive sources. To do so, we will first need to obtain noise models of bipolar transistors and JFETs. (MOSFETs are like JFETs except for a generally much higher level of flicker noise, so that we need not treat them separately.)

Nonlinear devices are essential in some of the signal-recovery techniques we will develop, and we will therefore study how they affect signals and noise. In doing so, we will learn the basics about modulation (shifting of signals in frequency) and about detection (recovery of the original signals in the case of lock-in detection). We will proceed in two stages: first discuss signal manipulation in the absence of noise, and then see how the signal-to-noise ratio is affected.

As an interesting topic in its own right, but also as a preparation for the experiments on correlations between photons and on optical beats presented in Exercises 13-12 and 13-13, we will discuss photomultipliers both as nonlinear devices for the detection of optical signals and as current amplifiers, and obtain their ...

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