Cross-spectrum measurement of thermal-noise limited oscillators

Abstract

Abstract:Cross-spectrum analysis is a commonly-used technique for the detection of phase and amplitude noise of a signal in the presence of interfering noise. It extracts the desired correlated noise from two time series in the presence of uncorrelated interfering noise. Recently, we demonstrated that the phase-inversion (anti-correlation) effect due to AM noise leakage can cause complete or partial collapse of the cross-spectral function [1], [2]. In this paper, we discuss the newly discovered effect of anti-correlated thermal noise that originates from the common-mode power divider (splitter), an essential component in a cross-spectrum noise measurement system. We studied this effect for different power splitters and discuss its influence on the measurement of thermal-noise limited oscillators. An oscillator whose thermal noise is primarily set by the 50  source resistance is referred to as a thermally-limited oscillator. We provide theory, simulation and experimental results. In addition, we expand this study to reveal how the presence of ferrite-isolators and amplifiers at the output ports of the power splitters can affect the oscillator noise measurements. Finally, we discuss a possible solution to overcome this problem.

Cross-spectral collapse from anti-correlated thermal noise in power splitters

“…In spite of the discrepancy between the measurements and simulation, the relative differences in the measured thermal noise levels between 1-R and 3-R as well as between 3-R and 2-R power splitters are nearly the same as the simulated results. In [11], we demonstrated that if the power splitter is connected to a real 50 Ω load impedance, the simulation and experimental results agree well; we verified this for the AM noise measurements. The simulation results given in Table 1 for different types of power splitters were performed in the Advanced Design System (ADS) software.…”

“…For this simulation, the thermal noise contribution of the source, the power splitter and the load resistors are considered. A detailed description of the simulation can be found in [11]. Table 1 tabulates the results of thermal noise contribution of the individual component to the output cross-spectrum as a fraction of the noise from R s .…”

“…One cause of the noise under-estimation as explained in [8] can occur due to the anti-correlation (phase-inversion) collapse mainly from AM noise leakage. More recently, a different source of anticorrelation in a cross-spectrum measurement has been identified; its origin is from the common-mode power splitter [9]- [11]. Correlated thermal noise of the power splitter appears equally but in opposite phase in two channels of the cross-spectrum system.…”

Photonic microwave signals with zeptosecond-level absolute timing noise

“…Methods). Thermal noise is intrinsically rejected in the cross-correlation process 25 Improvements to the close-to-carrier phase noise could be obtained with better ultra-stable laser frequency stability. Longer or cryogenic reference cavities 26,27 with crystalline coatings 28 or spectral hole burning stabilization 29 could lower the phase noise limit by one order of magnitude.…”

Cross-Spectrum PM Noise Measurement, Thermal Energy, and Metamaterial Filters

“…In this conditions, the peak of {S yx } is close to zero, as predicted by Eq. (12). Off resonance, the resonator is open circuit (Γ = 1), hence its thermal noise does not appear in the signals x and y.…”