Linear Noisy Multiports

Abstract

Microwave and optical devices may all be described as multiports: signals are propagated into the device through input waveguides and emerge in output waveguides. If signal distortion is avoided, these devices are characterized as linear multiports. Of course, even linear multiports may distort a broadband signal by introducing frequency-dependent changes of the amplitudes and phases of the Fourier components of the signal. A linear multiport with loss does not only attenuate the signal, it also adds noise at thermal equilibrium. Linear multiports with gain amplify the signal, but also add noise in the process. In this chapter we study the basic noise properties of linear multiports. Linear multiports are described by an appropriate response matrix, which is a function of frequency, and a set of (Langevin) noise sources; there are N such sources for a multiport with N ports. Since the sources are generated by noise processes with a large number of degrees of freedom, they are usually Gaussian, according to the central limit theorem. Then, the correlation matrix of the noise sources, which is a function of frequency, is sufficient for their specification. In Sect. 4.7 we determined the noise sources for passive multi-ports at thermal equilibrium. Active multiports, such as amplifiers, contain noise sources that are determined by the physics of the amplifying process.