1.1 What is Noise?any ‘unwanted” part of the analytical signalalways some noise in a signal
1.2 Signal-to-noise ratio (S/N) for a set of data (replicate measurements)
for a temporal-varying signal
For meaningful measurements, S/N 3,
RSDsx
NS 1
S
Sx
NS
Ss
55
2.1 White Noise – amplitude invariant with respect to frequency Thermal Noise -voltage fluctuation due to random electron motions in the resistive elements
k: Boltzmann’s constantT: absolute temperatureR: resistancef: frequency bandwidth,
fkTRrms 4
r
f31
Hzfs
f
r
r
33 01.0
31
Shot Noise-current fluctuations due to random motion of electrons cross a junction (e.g., PN interface, space between anode/cathode)
I: average currente: charge of electron
fIeirms 2
2.2 Flicker Noise – amplitude varies with 1/f, drift in instruments
2.3 Environmental Noise
- different forms of noise that arise from the surroundings
- some occurs at known discrete frequencies
- some unpredictable, and difficult to correct (e.g., TV stations, computers, motors,etc)
2.4 Composite Noise Spectrum
Fig. 5-3 (p.113)
2.4 Composite Noise Spectrum
White Noise reduce f, temp, resistance, and I Flicker Noise make measurements at frequencies >100kHz Shielding & Grounding absorbing electromagnetic noise
But signal often at or near dc (low freq) often directly proportional to resistance often directly proportional to current often measured with transducers having very large f (fast response, PMT
f >107Hz)
3.1 Reducing f (white noise)3.1.1 Analog filtering: low-pass RC circuit
Fig. 5-5 (p.115)
High-frequency components rejected, and f reduced
A slow varying dc signal containing high frequencies with bandwidth extending over wide range
fRGCC 21
3.1.2 Digital filtering: Fourier transform/smooth
-It is easy to smooth/filter signal as well as noise. Make sure that the result is not distorted
- trade-off between resolution and noise. Need high point density to prevent losing information.
control in the frequency domain by manipulating pass function
Fig. 5-12 (p.121)
3.2Increasing f (flicker noise) We need to move f to >100kHz… How?
- Modulate: encode analytical signal at a high frequency, where 1/f noise is negligible- Amplify the signal at the modulation frequency, while reduce the noise.- demodulate the signal
Lock-in Amplifier
Chopper
Fig. 5-8 (p.117)3. Demodulate
2. Amplify modulated signal1. Modulate
3.3Signal Averaging
Total intensity of signal: increase linearly with the number (n) of replicate signals
Noise: increase as (n)1/2
S/N increase as (n)1/2
n
SSN
n
ixi
ii
1
2)(
ii
i
n NSn
NnnS
NS
n
iiin nSSS
1
ii
n
iinn NnnN
1
22
3.3.1 An Example for Signal Averaging
3.3.2 Signal Averaging For a Spectrum
Get S/N increased with n½
Need good synchronization for replicate scan
Fig. 5-10 (p.119)
3.3.3 Boxcar Averaging A approach for smoothing irregularities
A single –channel signal averagerselect a single delay time
integrated signal over selected gate time
average signal for n-replicate
repeat at new delay time
S/N increases with (averaging time)1/2
Fig. 5-11 (p.119)
3.3.3 Boxcar Averaging
select a single delay time
integrated signal over selected gate time
average signal for n-replicate
repeat at new delay time
Fig. 5-11 (p.119)