Lecture 4

Noise, signal/noise ratio,detection limit

Standard analytical terminology

Value (mean, average)

Standard deviation

Relative standard deviation(RSD)

Electronics

Signal

Noise

Signal-to-noise ratio (S/N)

RSDratioNS 1_/

A noisy set of data

Less noisy measurements. Signal is well visible.

Sine wave – a primitive model of a noisy experiment

Peak-to-peak noise = 3 s (approximately)

Noises:

Thermal BRTnoise ~temperature

resistance bandwidth

BInoise ~Shot (quantum)current

“Flicker”frequency

noise 1~

Environmental noise

A simple filter

What should I do to reduce the noise?

Removal of the amplifier noise by filtering

Boxcar averaging

Computer can help:

c = a + b Random numbers a and b

sc = ?22bac sss

c = a + a 22 222aaaac sssss

2aac

22

2 aac

sss

Naaac

...

Nss a

c

Nss a

c cscNS /

asNcNS /

NtmeasuremenoneNStsmeasuremenNNS )_(/)_(/

This N stands for word “noise”And this isnumber ofmeasurements

A: one measurement, S/N=4B: 100 measurements(scans), S/N= 40

concentration

intensity

Limit of quantitation (limit of determination)

Limit of detection (detection limit)

3s/slope

10s/slope

0

Limit of linearity