Advanced interferometric phase and amplitude noise measurements

Abstract

The measurement of the close-to-the-carrier noise of two-port radio frequency and microwave devices is a relevant issue in time and frequency metrology and in some fields of electronics, physics, and optics. While phase noise is the main concern, amplitude noise is often of interest. Presently the highest sensitivity is achieved with the interferometric method, that consists of the amplification and synchronous detection of the noise sidebands after suppressing the carrier by vector subtraction of an equal signal. A substantial progress in understanding the flicker noise mechanism of the interferometer results in new schemes that improve by 20–30 dB the sensitivity at low Fourier frequencies. These schemes, based on two or three nested interferometers and vector detection of noise, also feature closed-loop carrier suppression control, simplified calibration, and intrinsically high immunity to mechanical vibrations. This article provides the complete theory and detailed design criteria, and reports on the implementation of a prototype working at the carrier frequency of 100 MHz. In real-time measurements, a background noise of −175 to −180 dBrad2/Hz has been obtained at f=1 Hz off the carrier; the white noise floor is limited by the thermal energy kBT0 referred to the carrier power P0 and by the noise figure of an amplifier. Exploiting correlation and averaging in similar conditions, the sensitivity exceeds −185 dBrad2/Hz at f=1 Hz; the white noise floor is limited by thermal uniformity rather than by the absolute temperature. A residual noise of −203 dBrad2/Hz at f=250 Hz off the carrier has been obtained, while the ultimate noise floor is still limited by the averaging capability of the correlator. This is equivalent to a signal-to-noise (S/N) ratio of 2×1020 with a frequency spacing of 2.5×10−6. All these results have been obtained in a relatively unclean electromagnetic environment, and without using a shielded chamber. Implementation and experiments at that sensitivity level require skill and tricks, for which a great effort is spent in the article. Applications include the measurement of the properties of materials and the observation of weak flicker-type physical phenomena, out of reach for other instruments. As an example, we measured the flicker noise of a by-step attenuator (−171 dBrad2/Hz at f=1 Hz) and of the ferrite noise of a reactive power divider (−173.7 dBrad2/Hz at f=1 Hz) without need of correlation. In addition, the real-time measurements can be exploited for the dynamical noise correction of ultrastable oscillators.