Noise power

The theory of the noise voltage generated by a resistor was developed by Nyquist (1928), following experimental measurements by Johnson (1928). The phenomenon is therefore named after either, or both, of these researchers.

Suppose we have a long coaxial transmission line at temperature T. This line acts as a 1-D cavity for the propagation of electromagnetic waves at a velocity, v, where we will assume v ≃ c. We can then follow the analysis of Section 1.3.4 to obtain the number of available modes. If the transmission line is laid out along the z-axis, the electric and magnetic fields are restricted to the xy-plane, and boundary conditions require the electric field to be zero at the ends of the line, where z = 0 and z = L. Allowed modes along the transmission line are therefore restricted by a z-version of Eq. (1.33) to kz = πmz/L, for integer mz, and the 1-D nature of the problem implies that mz is the only such integer required to define a mode. There are still, however, two independent polarizations allowed (along the x- and y-axes), so we modify the above restriction on modes to k = 2πm/L, where we have dropped the z-subscript.