On temporal correlations in high-resolution frequency counting

We analyze noise properties of time series of frequency data from different counting modes of a Keysight 53230A frequency counter. We use a 10MHz reference signal from a passive hydrogen maser connected via phase-stable Huber+Suhner Sucoflex 104 cables to the reference and input connectors of the counter. We find that the high resolution gap-free ("CONT") frequency counting process imposes long-term correlations in the output data, resulting in a modified Allan deviation MDEV similar to tau(-1/2)-characteristic of random walk phase noise. Equally important, the CONT mode results in a frequency bias. In contrast, the counter's undocumented raw continuous mode ("RCON") yields unbiased frequency stability estimates with white phase noise characteristics, MDEV similar to tau(3/2), and of a magnitude consistent with the counters 20 ps single-shot resolution. Furthermore, we demonstrate that a 100-point running average filter in conjunction with the RCON mode yields resolution enhanced frequency estimates with flicker phase noise characteristics, MDEV similar to tau(-1). For instance, the counter's built-in moving-average function can be used. The improved noise characteristics of the averaged RCON mode versus the CONT mode imply that the former mode yields frequency estimates with improved confidence for a given measurement time.