Analytical figures of merit noise and s n ratio
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Analytical figures of merit, noise, and S/N ratio. Chemistry 243. Noise. A signal is only of analytical value if it can be definitively attributed to the species/system of interest in the presence of noise . Probably noise, or not very useful; a hint of a signal. Looks like a real signal.

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Analytical figures of merit noise and s n ratio

Analytical figures of merit, noise, and S/N ratio

Chemistry 243


Noise

Noise

  • A signal is only of analytical value if it can be definitively attributed to the species/system of interest in the presence of noise.

Probably noise, or not very useful;

a hint of a signal

Looks like a real signal


What is signal and noise

What is signal and noise?


Signal to noise ratio s n

Signal-to-noise ratio (S/N) is a measure of the quality of an instrumental measurement

Ratio of the mean of the analyte signal to the standard deviation of the noise signal

High value of S/N : easier to distinguish analyte signal from the noise signal

Signal-to-Noise Ratio (S/N)

Mostly

Signal

signal

Std. Dev.

Mostly

Noise

Rev. Sci. Inst., 1966, 37, 93-102.


Where does noise come from

Where does noise come from?

  • Chemical noise

    • Temperature, pressure, humidity, fumes, etc.

  • Instrumental noise


Detector and post detector noise

Detector and post-detector noise

  • Thermal (Johnson) noise

  • Shot noise

  • Flicker (1/f) noise

  • Environmental noise

  • Popcorn (burst) noise

  • Microphonic noise


Thermal johnson noise

Thermal (Johnson) noise

  • Random motions of charge carriers (electrons or holes) that accompany thermal motions of solid lattice of atoms.

  • Lead to thermal current fluctuations that create voltage fluctuations in the presence of a resistive element

    • Resistor, capacitor, etc.

nrms = root-mean-square noise voltage

k = Boltzman’s constant

T = temperature

R = resistance of element (W)

Df = bandwith (Hz) = 1/(3tr)

tr = rise time


Thermal johnson noise continued

Thermal (Johnson) noise continued

  • Dependent upon bandwidth (Df) but not f itself

    • white noise

  • Can be reduced by narrowing bandwidth

    • Slows instrument response time

    • More time required for measurement

  • Reduced by lowering T

    • Common to cool detectors

      • 298K77K lowers thermal noise by factor of ~2

N2(l): bp=77K

nrms = root-mean-square noise voltage

k = Boltzman’s constant

T = temperature

R = resistance of element (W)

Df = bandwith (Hz) = 1/(3tr)

tr = rise time


Shot noise

11 e-/s

10.5 e-/s

10 e-/s

Shot noise

  • Arises from statistical fluctuations in quantized behaviors

    • Electrons crossing junctions or surfaces

  • Independent of frequency

  • Example: current

irms = root-mean-square noise current

I = average direct current

e = electron charge

Df = bandwidth (Hz)


Flicker 1 f noise

Flicker (1/f) noise

  • Magnitude is inversely proportional to the frequency of the signal

  • Significant at frequencies lower than 100 Hz

    • Long-term drift

  • Origin is not well understood

    • Dependent upon materials and device shape

      • Metallic resistors have 10-fold less flicker noise than carbon-based resistors.

    • Referred to as “pink” noise—more red (low frequency) components


Environmental noise

Environmental noise

  • Comes from the surroundings

  • Biggest source is “antenna” effect of instrument cabling

J. Chem. Educ., 1968, 45, A533-542.


Noise contributions in different frequency regimes

Noise contributions in different frequency regimes

Frequency independent

Supposedly 1/f—mostly at low frequencies

Occurs at discrete frequencies


Enhancing signal to noise

Hardware methods

Grounding and shielding

Difference and Instrumentation Amplifiers

Analog Filtering

Lock-In Amplifiers

Modulation and Synchronous Demodulation

Software methods

Ensemble averaging

Boxcar averaging

Digital filtering

Correlation methods

Enhancing signal-to-noise


Grounding and shielding

Grounding and shielding

  • Surround circuits (most critical conductors) with conducting material that is connected to ground

    • Noise will be picked up by shield and not by circuit

  • Faraday cage

http://www.autom8.com/images_product/table_farady_benchtop.jpg

http://farm2.static.flickr.com/1227/578199978_17e8133c7c_o.jpg


Analog filtering

Analog filtering

  • Low pass filter removes high frequency noise

    • Thermal and shot noise

  • High pass filter removes low frequency noise

    • Drift and flicker noise

  • Narrow-band electronic filters

High freq removed.

Low freq preserved

(passed).

Example of low-pass filter


Lock in amplifiers

Lock-in amplifiers

  • Modulation

    • Translate low frequency signal (prone to 1/f noise) to a high frequency signal which can amplified and then filtered to remove 1/f noise

Mechanical chopper


Lock in amplifiers continued

Lock-in amplifierscontinued

  • Synchronous demodulation

    • Converts AC signal to DC signal synchronous with chopper—follows reference

  • Low-pass filtering

    • Back converts high frequency DC signal to return filtered, low frequency output.


Ensemble averaging to increase s n

Ensemble averaging to increase S/N

  • Averaging multiple data sets taken in succession

    • Divide sum of data sets by number of data sets

J. Chem. Educ., 1979, 56, 148-153.


Ensemble averaging continued

Ensemble averagingcontinued

  • Signal-to-noise improves with increasing number of data sets

N = rms noise

n = number of replicate scans

i = number of replicate scans

in other data set

# Scans, n Relative S/N

1 1

4 2

16 4

64 8


Boxcar averaging

Boxcar averaging

  • Smoothing irregularities and increasing S/N

  • Assumes signal varies slowly in time

  • Multiple points are averaged to give a single value

  • Often performed in real time

  • Detail is lost and utility limited for rapidly changing samples

  • Boxcar integrators commonly used in fast (pico- to microsecond) measurements using pulsed lasers.


Moving average smooth

Moving average smooth

  • Similar to a boxcar average, but changes in time


Downside of moving average smoothing

Downside of moving average smoothing


Digital filtering

Digital filtering

  • Fourier transform

    • Convert data from time- to frequency-domain, manipulate to remove higher frequency noise components, regenerate time-domain signal

  • Polynomial data smoothing

    • Moving average smooth

    • Least-squares polynomial smoothing


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