On temporal correlations in high-resolution frequency counting

TL;DR

This paper investigates the noise characteristics of high-resolution frequency counting modes, revealing that the undocumented raw continuous mode provides unbiased, white phase noise estimates, unlike the standard CONT mode which introduces long-term correlations and bias.

Contribution

It demonstrates that the raw continuous mode of a Keysight frequency counter offers more accurate and unbiased frequency stability measurements compared to the standard high-resolution mode.

Findings

CONT mode introduces long-term correlations and bias.

RCON mode provides unbiased, white phase noise estimates.

Averaging RCON mode improves resolution and noise characteristics.

Abstract

We analyze noise properties of time series of frequency data from different counting modes of a Keysight 53230A frequency counter. We use a 10 MHz 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 that is 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, and of a magnitude consistent with the counter's 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. 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.