Introduction to Random Signals and Noise

6

Noise in Networks and Systems

Many electrical circuits generate some kind of noise internally. The most well-known kind of noise is thermal noise produced by resistors. Besides this, several other kinds of noise sources can be identified, such as shot noise and partition noise in semiconductors. In this chapter we will describe the thermal noise generated by resistors, while shot noise is dealt with in Chapter 8. We shall show how internal noise sources can be transferred to the output terminals of a network, where the noise becomes observable to the outside world. For that purpose we shall consider the cascading of noisy circuits as well. In many practical situations, which we refer to in this chapter, a noise source can adequately be described on the basis of its power spectral density; this spectrum can be the result of a calculation or the result of a measurement as described in Section 5.4.

6.1 WHITE AND COLOURED NOISE

Realization of a wide-sense stationary noise process N(t) is called white noise when the power spectral density of N(t) has a constant value for all frequencies. Thus, it is a process for which

holds, with N₀ a real positive constant. By applying the inverse Fourier transform to this spectrum, the autocorrelation function of such a process is found to be

The ...