The Allan Variance - challenges and opportunities

Abstract

The Allan variance has historically been estimated using heterodyne measurement systems, which have low noise and preserve the carrier phase information needed for long-term stability. The single-sideband phase noise has traditionally been estimated using phase detectors that suppress the carrier to achieve even lower noise. The recent development of the direct-digital phase noise measurement technique makes it possible to estimate both statistics accurately and simultaneously from the same time series of the phase. Our comparison of the 3 techniques has revealed several challenges to the accurate estimation of the Allan variance including undesired aliasing, biased estimators, and spurious signal generation. Investigation of these difficulties has led to several opportunities to improve Allan variance estimation, including the ability to estimate the instrumentation noise floor during a measurement and the existence of an optimum measurement bandwidth. In the end, this has led to faster, easier, more reliable, and more accurate measurement methods.

Simplified Three-Cornered-Hat Technique for Frequency Stability Measurements

“…As this is linear in i , the number of cycles i elapsed at time t i can be found by allowing i to be real and solving (25) to find (26) which is of the form that we desire. Therefore, by inserting time-tags according to (25) one adds an additional source to those existing multichannel DMTD systems with a freerunning reference oscillator.…”

“…Therefore, by inserting time-tags according to (25) one adds an additional source to those existing multichannel DMTD systems with a freerunning reference oscillator.…”

“…We next consider the more practical case of measurements of the Allan variance [24], [25], which is equal to half the variance of the difference between consecutive average frequency measurements. Using the overlapping form as given by Riley [21], we simulate four random processes, each the sum of white phase noise (white PM), white frequency noise (white FM), and random-walk frequency noise (RW FM) processes, using the method of Kasdin and Walter [26].…”

Direct-digital time-domain oscillator stability measurement

“…Another approach to determine the short-term phase noise spectrum is the phase detector (PLL method) [6]. This homodyne approach operates as follows: the oscillator under investigation is mixed with the reference oscillator.…”

“…This approach does not require calibrated analog mixers or filters and can cover a wide phase-noise spectrum. However the accuracy is limited by the ADCs' quantization noise and the poor resolution of the arc-tangent function around the zero-crossing [6].…”