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Phase noise measurements with a cryogenic power-splitter to minimize the cross-spectral collapse effect

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The cross-spectrum noise measurement technique enables enhanced resolution of spectral measurements. However, it has disadvantages, namely, increased complexity, inability of making real-time measurements, and bias due to the “cross-spectral collapse” (CSC) effect. The CSC can occur when the spectral density of a random process under investigation approaches the thermal noise of the power splitter. This effect can severely bias results due to a differential measurement between the investigated noise and the anti-correlated (phase-inverted) noise of the power splitter. In this paper, we report an accurate measurement of the phase noise of a thermally limited electronic oscillator operating at room temperature (300 K) without significant CSC bias. We mitigated the problem by cooling the power splitter to liquid helium temperature (4 K). We quantify errors of greater than 1 dB that occur when the thermal noise of the oscillator at room temperature is measured with the power splitter at temperatures above 77 K.
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... However, such rejection cannot be achieved in practice because of fundamental phenomena and artifacts. The thermal energy in the input power splitter [3]- [7] and impedance matching [8] first caught the attention of the scientific community. These and other problems were addressed in three international workshops [9]- [11]. ...
... Let us start with a review of key facts, based on References [3]- [7]. The phase noise is described in terms the power spectral density (PSD) of the random phase ϕ(t), and denoted with S ϕ (f ). ...
... Therefore, compensating for T s alone is a metrologically correct approach, and mitigates the problem. The brute force approach of putting the power splitter in a liquid-He cryostat [7] is not more effective because of the crosstalk. ...
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... However, such rejection cannot be achieved in practice because of fundamental phenomena and artifacts. The thermal energy in the input power splitter [3,4,5,6,7] and impedance matching [8] first caught the attention of the scientific community. These and other problems were addressed in three international workshops [9,10,11]. ...
... The measurement of sub-thermally limited oscillators is clearly a problem. The brute force approach of putting the power splitter in a liquid-He cryostat [7] does not solve the issue of the crosstalk. In our experiment, the crosstalk equivalent temperature is ςT c = −122 K. ...
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