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Software-defined radio (SDR) provides stability, flexibility, and reconfigurability to radio frequency signal processing. Applied to oscillator characterization in the context of ultrastable clocks, stringent filtering requirements are defined by spurious signal or noise rejection needs. Since real-time radio frequency processing must be performed in a field-programmable array to meet timing constraints, we investigate optimization strategies to design filters meeting rejection characteristics while limiting the hardware resources required and keeping timing constraints within the targeted measurement bandwidths. The presented technique is applicable to scheduling any sequence of processing blocks characterized by a throughput, resource occupation and performance tabulated as a function of configuration characteristics, as is the case for filters with their coefficients and resolution yielding rejection and the number of multipliers.

This paper introduces the Ω counter, a frequency counter-i.e., a frequency-to-digital converter-based on the linear regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the Ω counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a system on chip, under test in our laboratory, and we compare the Ω counter to the traditional Π and Λ counters. The LR exhibits the optimum rejection of white phase noise, superior to that of the Π and Λ counters. White noise is the major practical problem of wideband digital electronics, both in the instrument internal circuits and in the fast processes, which we may want to measure. With a measurement time τ , the variance is proportional to 1/τ(2) for the Π counter, and to 1/τ(3) for both the Λ and Ω counters. However, the Ω counter has the smallest possible variance, 1.25 dB smaller than that of the Λ counter. The Ω counter finds a natural application in the measurement of the parabolic variance, described in the companion article in this Journal [vol. 63 no. 4 pp. 611-623, April 2016 (Special Issue on the 50th Anniversary of the Allan Variance), DOI 10.1109/TUFFC.2015.2499325].

This paper introduces the parabolic variance (PVAR), a wavelet variance similar to the Allan variance (AVAR), based on the linear regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the Ω frequency counter, which implements the LR estimate. The PVAR combines the advantages of AVAR and modified AVAR (MVAR). PVAR is good for long-term analysis because the wavelet spans over 2τ, the same as the AVAR wavelet, and good for short-term analysis because the response to white and flicker PM is 1/τ(3) and 1/τ(2), the same as the MVAR. After setting the theoretical framework, we study the degrees of freedom and the confidence interval for the most common noise types. Then, we focus on the detection of a weak noise process at the transition-or corner-where a faster process rolls off. This new perspective raises the question of which variance detects the weak process with the shortest data record. Our simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in all cases, exhibits the best ability to divide between fast noise phenomena (up to flicker FM), and is almost as good as AVAR for the detection of random walk and drift.

The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works., (© 2012 IEEE)

We present new results on a cryogenic solid-state maser frequency standard, which relies on the excitation of whispering gallery (WG) modes within a doped monocrystalline sapphire resonator (alpha-Al2O3). Included substitutively within the highest purity HEMEX-grade sapphire crystal lattice are Fe2+ impurities at a concentration of parts per million, an unavoidable result of the manufacturing process. Mass conversion of Fe2+ to Fe3+ ions was achieved by thermally annealing the sapphire in air. Above-threshold maser oscillation was then excited in the resonator at zero applied DC magnetic field by pumping high-Q WG modes coincident in frequency with the electron spin resonance (ESR) energy levels of the Fe3+ spin population. A 2 stage annealing process was undertaken for a sapphire resonator with exceptionally low Fe3+ concentration, resulting in an improvement of 6 orders of magnitude in output power for this particular crystal, and exceeding the previous best implementation of our scheme in another crystal by nearly 20 dB. This represents an output signal 7 orders of magnitude more powerful than a typical commercial hydrogen maser. At this power level, we estimate a limit on the frequency stability of order 1 x 10(-17)/square root(tau) due to the Schawlow-Townes fundamental thermal noise limit.

In this paper, we describe the implementation of a microwave cryogenic sapphire oscillator (CSO) at the Laboratoire de Physique et Métrologie des Oscillateurs. In our realization we solved the problem of the spurious modes by operating the sapphire resonator in an open cavity. The CSO compared to a hydrogen maser demonstrates a frequency stability better than 3 x 10(-14) at short term. Its long-term frequency instability of the order of 3 x 10(-12)/day is limited by a random walk process. A first attempt to use this reference oscillator to characterize other signal sources is presented.

We report new measurements of dielectric properties of Lanthanum gallium silicate (Langasite or LGS) conducted with the whispering-gallery mode technique at microwave frequencies and between 4.2 K and 300 K. The real part of the permittivity tensor of LGS presents two components having temperature coefficients of opposite sign. This unique property enables the design of a temperature compensated resonator that may be useful in building stable microwave oscillators or filters. We report also the first measurements of the two independent components of the imaginary part of the permittivity tensor. It appears LGS is a relatively high-loss dielectric material compared with sapphire or quartz.