  Much has been written about the representation of noisy linear 2-ports. Here
we present a theory of noisy $N$-ports. We show how in the general case there
are $(2N)!/(N!)^2$ equivalent representations and give the transformations
relating them. We also discuss singular cases in which some of the
transformations are not possible as well as how to measure the noise properties
of an $N$-port. This work is motivated by the REACH experiment to observe the
global 21 cm signal for which modelling noise with exquisite precision is
essential for a reliable calibration.
