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Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle

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Influence of Noise on Scattering-Parameter Measurements.

Dazhen Gu¹, Jeffrey A Jargon¹, Matthew J Ryan²

¹RF Technology Division, National Institute of Standards and Technology, Boulder, CO 80305 USA.

IEEE Transactions on Microwave Theory and Techniques

|January 13, 2022

Summary

We developed a model for noisy scattering-parameter (S-parameter) measurements using a vector network analyzer (VNA). Noise significantly impacts S-parameter accuracy, especially for small magnitudes, requiring careful statistical analysis.

Keywords:

Network analysis noise probability distribution random variable (RV)scattering parameter (S-parameter)uncertainty

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Area of Science:

Electrical Engineering
Metrology
Signal Processing

Background:

Scattering-parameter (S-parameter) measurements are crucial for characterizing electronic components.
Vector network analyzers (VNAs) are standard instruments for S-parameter measurements.
Understanding and quantifying measurement noise is essential for accurate results.

Purpose of the Study:

To present a general model for noisy S-parameter measurements using a VNA.
To statistically analyze the residual error introduced by noise in S-parameter measurements.
To validate the proposed noise model through experimental data.

Main Methods:

Development of a general mathematical model for noisy S-parameter measurements.
Statistical analysis of the residual error, treating it as a complex Gaussian quotient.
Derivation and discussion of relevant statistical quantities.
Experimental validation using a two-port VNA.

Main Results:

The residual error in S-parameter measurements due to noise can be modeled as a complex Gaussian quotient.
Statistical quantities characterizing the noise influence were derived.
Experimental results validated the proposed noise model.
Noise-induced uncertainty is often critical, particularly for small-magnitude S-parameters.

Conclusions:

The developed model accurately describes noise in VNA S-parameter measurements.
Statistical analysis provides a framework for understanding noise impact.
Accurate characterization of noise is vital for reliable S-parameter data, especially in sensitive applications.