Interpreting anomalously low voltage noise in two-channel measurement systems

In this work we 1) analyze and give a theoretical explanation for the anomalously low cross-spectral density of voltage fluctuations that is observed when two thermal noise sources with matched intensities are coupled to the inputs of two-channel phase modulation (PM) or amplitude modulation (AM) noise measurement systems (NMS), 2) empirically evaluate spectral resolutions of different types of measurement systems, and 3) discuss noise measurement techniques involving cross-correlation signal processing. Our work shows that the statistical uncertainty, which sets the ultimate spectral resolution in the thermal noise limited regime, is approximately the same for both systems. However, in practical terms, the non-stationary nature of the noise, the temporal separation of calibration and measurement, and the difficulty of reproducing the calibrations for two measurements make it extremely difficult to resolve noise that is more than 10 dB below the noise floor in a single channel NMS. In a two-channel NMS, however, the calibrations of the two channels are carried out simultaneously, and one can take full advantage of a large number of averages and make reproducible noise measurements with resolution 10 dB below the noise floor of a single channel NMS.