A collapse of the cross-spectral function in phase noise metrology

Abstract

Cross-spectral analysis is a mathematical tool for extracting the power spectral density of a correlated signal from two time series in the presence of uncorrelated interfering signals. We demonstrate and explain a set of amplitude and phase conditions where the detection of the desired signal using cross-spectral analysis fails partially or entirely in the presence of a second uncorrelated signal. Not understanding when and how this effect occurs can lead to dramatic under-reporting of the desired signal. Theoretical, simulated and experimental demonstrations of this effect as well as mitigating methods are presented.

Pulsed Optically Pumped Rb clock

“…Curve (a) reports the phase noise measurement of the 100 MHz signal. Particular attention must be paid while measuring the 100 MHz output of ultra low noise OCXOs (such as the Pascall) with a commercial cross-correlation measurement benches, because they do not have a low enough phase noise reference [10] to ensure the right measurement resulting in phase noise measurements exhibiting numerous bump and roll-off (a discrepancy of about 10 dB has been observed). A dedicated bench based on the cross-correlation techniques [11] has then been developed to ensure the right measurement of the OCXO at 100 MHz and at 1.6 GHz (see [12] for more information).…”

Cross-spectral collapse from anti-correlated thermal noise in power splitters

“…3 is used for the phase noise measurement of this oscillator. A variable dc offset voltage was added at the input of the phase locked loop (PLL) integrator to reduce the device under test (DUT) AM noise thus minimizing the effect of anti-correlation collapse due to the AM noise leakage [8]. At first a Wilkinson power splitter (WPS) was chosen and the phase noise of the oscillator was measured with attenuator 'A' equal to 3 dB at the output of the oscillator.…”

“…Despite being commonly used, this technique is susceptible to experimental errors [5], [6]. One among many of these errors is caused either by positive or negative correlations resulting in over-estimation or under-estimation respectively of the oscillator noise [7], [8].…”

“…5 MHz quartz-crystal oscillator; it displays simultaneously the effect of both positive correlation above 10 kHz offset and negative correlation around 10 Hz offset. One cause of the noise under-estimation as explained in [8] can occur due to the anti-correlation (phase-inversion) collapse mainly from AM noise leakage. More recently, a different source of anticorrelation in a cross-spectrum measurement has been identified; its origin is from the common-mode power splitter [9]- [11].…”

A 1 MHz to 50 GHz direct down-conversion phase noise analyzer with cross-correlation

“…The frequency response of the analog PLL must be known or calibrated to correct the final measurement result. Furthermore an analog PLL achieves only a rather poor rejection of amplitude modulation to the phase output, an effect that has recently gained attention as a cause of cross-spectrum collapse [1].…”