Microwave phase-noise influence on Josephson-junction array voltage standards

In this paper we analyze the influence of the microwave phase noise on the Josephson-junction array (JJA) reference voltage in order to investigate the limit of the contribution to the voltage fluctuations. In the framework of a simple model introduced for this purpose, we found that the spectrum of the fractional voltage fluctuations is equal to the spectrum of the fractional frequency fluctuations assuming a band-limited noise process. On the other hand, the standard deviation of the voltage across the JJA is not only related to the noise spectrum but also to the ratios between the bandwidths of the free-running oscillator, the control loop, and the voltage measuring system, three different measurement situations are considered by referring to different locking conditions of the Gunn oscillator. A value of σ_v/V(n)≃6×10^-12 is calculated for a fully phase-controlled Gunn oscillator, while the value σ_v/V(n)≃3×10^-10 is the approximate estimate for the case of a frequency-controlled Gunn oscillator, suggesting that the phase-controlled method of stabilization is best suited for direct comparisons of JJA voltage standards. An implementation of a phase-controlled microwave source is also presented