Non-Ideal Lorentzians: Quantifying Shape Deviation from Ideal

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SUMMARY

The discussion focuses on quantifying the deviation of high-Q resonator transmissivity (S21) from an ideal Lorentzian shape, particularly under varying temperature conditions. The resonator exhibits distortion at elevated temperatures, prompting the need for a method to quantify this change. The concept of a "shape factor" is mentioned as a potential metric for this analysis, although its specific application in this context remains unclear. The participants seek established methodologies to accurately assess and visualize these deviations.

PREREQUISITES
  • Understanding of high-Q resonators and their characteristics
  • Familiarity with transmissivity measurements (S21 parameter)
  • Knowledge of Lorentzian functions and their applications in physics
  • Basic principles of temperature effects on material properties
NEXT STEPS
  • Research methods for quantifying shape deviations in resonance curves
  • Explore the concept of "shape factor" in atomic spectroscopy
  • Investigate temperature dependence effects on high-Q resonators
  • Learn about advanced data analysis techniques for resonance data visualization
USEFUL FOR

Physicists, electrical engineers, and researchers analyzing high-Q resonators and their temperature-dependent behaviors will benefit from this discussion.

f95toli
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"Non ideal" Lorentzians

I am not sure if this is a question about math, physics or electrical engineering...
Anyway, I am currently trying to analyze some measurement data. What I have is essentially the transmissivity (i.e. S21 using EE terminology) for a high-Q resonator (Q value about 10^6). Ideally a resonator of this type should have a shape that is very nearly Lorentzian. However, what we see is that the shape depends on the temperature and at elevated temperatures s clearly "distorted" , we believe there is a rather interesting reason for this temperature dependence (meaning it is worth looking into).
Now, I would like to somehow "quantify" this change to that I can plot it as a function of temperature.

Is there a generally accepted way to quantify how much the shape of a resonance deviates from an ideal Lorentzian?
I seem to remember seeing something similar, i.e. a "shape factor" (not the same thing as the shape factor in EE), being used in atomic spectroscopy but I can't find anything useful using Google schoolar.
 

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