- #1
curiously new
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- TL;DR Summary
- Searching for a noise floor figure to compare to op-amp noise floor (nV per square root Hertz).
I'd like approximate the noise floor of an ultrasonic air transducer starting from molecular vibrations.
Simply put, if I treat atmospheric air as an ideal gas and I confine each air molecule to exist in a volumetric cube with a square face ##A_\mathrm{face}##, then I approximate the number of air molecules that are abutted against a transducer's element with area ##A_\mathrm{T}## by $$n=\frac{A_\mathrm{T}}{A_\mathrm{face}} .$$ Now, if I assume the rough estimate that an air molecule travels on average at a velocity ##v##, then I can approximate the frequency of total collisions against the transducer's element by $$f=\frac{1}{6}\frac{1}{t}n=\frac{n}{6}\frac{v}{\sqrt{A_\mathrm{face}}}=\frac{1}{6}\frac{vA_\mathrm{T}}{A_\mathrm{face}^{3/2}} ,$$ where we divide by six because only a single side of each molecule's volumetric cube is abutted against the element.
Then, I can assume that this frequency varies as Gaussian whose standard deviation ##\sigma## is the square root of the frequency, which is the variation in the number of collisions. Then, I could say that my noise ##N## is given by $$N=\sqrt{f}$$ in units square root Hertz (##\sqrt{\text{Hz}}##).
So, I would like to compare this noise floor against the noise floor approximation of an op-amp, which are usually given in units ##\text{nV}/\sqrt{\text{Hz}}##. My task lies in understanding how to translate this frequency of collisions (in square root Hertz) into a comparable unit to the op-amp's noise floor. Should I consider the momentum energy transferred by each molecule upon the element to get a pressure that I can then use a transducer's conversion factor (usually ##\text{V}/\mu\text{bar}=\text{dB}##) to convert?
Simply put, if I treat atmospheric air as an ideal gas and I confine each air molecule to exist in a volumetric cube with a square face ##A_\mathrm{face}##, then I approximate the number of air molecules that are abutted against a transducer's element with area ##A_\mathrm{T}## by $$n=\frac{A_\mathrm{T}}{A_\mathrm{face}} .$$ Now, if I assume the rough estimate that an air molecule travels on average at a velocity ##v##, then I can approximate the frequency of total collisions against the transducer's element by $$f=\frac{1}{6}\frac{1}{t}n=\frac{n}{6}\frac{v}{\sqrt{A_\mathrm{face}}}=\frac{1}{6}\frac{vA_\mathrm{T}}{A_\mathrm{face}^{3/2}} ,$$ where we divide by six because only a single side of each molecule's volumetric cube is abutted against the element.
Then, I can assume that this frequency varies as Gaussian whose standard deviation ##\sigma## is the square root of the frequency, which is the variation in the number of collisions. Then, I could say that my noise ##N## is given by $$N=\sqrt{f}$$ in units square root Hertz (##\sqrt{\text{Hz}}##).
So, I would like to compare this noise floor against the noise floor approximation of an op-amp, which are usually given in units ##\text{nV}/\sqrt{\text{Hz}}##. My task lies in understanding how to translate this frequency of collisions (in square root Hertz) into a comparable unit to the op-amp's noise floor. Should I consider the momentum energy transferred by each molecule upon the element to get a pressure that I can then use a transducer's conversion factor (usually ##\text{V}/\mu\text{bar}=\text{dB}##) to convert?