We analyse a lossy transmission line and the Johnson-Nyquist noise generated therein. A representation as a noisy two-port with a voltage and a current noise sources on one end of a noiseless two-port is given. An expression for the noise properties is given for an arbitrary temperature profile along the transmission line. Compatibility of the general expression found here with expectations for special cases calculable using thermodynamics is demonstrated.

Much has been written about the representation of noisy linear 2-ports. Here we present a theory of noisy Nports. 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.