Noises and Interferences limit the sensitivity and resolution of the signals from the sensors

1
Noises and Interferences limit the sensitivity
and resolution of the signals from the sensors

• What are the tricks to fight against these
  unwanted signals?

2
Signal recovery techniques

• Amplitude Rectification and Phase Detection
• Lock-In Amplifiers
• Boxcar and Signal averagers
• Phase locked loops

3
AC vs DC methods of sensor probing

• In many cases signals from sensors are
  represented by relatively slowly changing signals
  (voltages, currents). The question is what is
  the best way to accurately measure these changing
  signals? (If the changes are not slow the answer
  is more obvious DC is ruled out)
• DC sensing
• Source of excitation is DC
• Bandwidth considerations
• fL 1/tacq where tacq is the acquisition time.
• fH 1/2tconv where tconv is the ADC conversion
  time
• Advantages simplicity, no sophisticated
  detection is needed
• Disadvantages parasitic DC signals which are
  hard to separate from useful signals and which
  can exceed the useful signal (T-EMF, offsets,
  drifts,etc), suffers from 1/f noise
• AC sensing
• Source is AC signal
• Advantages
• No influence on the signal from DC parasitics,
• Narrow-bandwidth signaling allows to minimize
  noise and coherent interference
• Allows to measure differential parameters and
  derivatives
• Can be used to measure even small DC signals (by
  using chopping)
• Disadvantages more complicated circuitry (but
  not always)

4
Example How to measure Coulomb blockade
oscillationsin Single-Electron Transistors?

• Conductance oscillates as a function of gate
  bias, Vg
• Signals MUST be small, because of the small scale
  of energies (eVdsltltEC1 meV), Vds100 mV
• What to choose for measurements
• AC or DC ?

5
DC measurement

• Conductance G (Vg)
• For small I and V
• Vds 100 mV
• Using IV-converter
• To measure DC Vout using DVM with averaging time
  of 60 conversions per sec
• Bandwidth estimation
• fL1/1sec 1 Hz
• fH 0.3146019 Hz for conversion time of 1/60
  sec
• BW18 Hz
• 1/f noise may be significant

6
AC measurement

• If we use AC excitation
• Signal at the output of the IV converter
• Then after rectification and Low Pass Filter
• How to do rectification
• Amplitude detection
• Phase detection

RF
7
Conversion from AC to DC

• Simplest and inaccurate use a diode
• Much better fill wave rectifier with opamps
• Whats missing?
• A low pass filter to get rid of ripple

8
Ripple in the rectifier

• For a sawtooth the factor from P-P to RMS is
  1/(2v3) (instead of 1/(2v2) for a sinewave)
• The frequency is doubled (thanks to full wave
  rectification), so Vripple(RMS)
• For 1 sec time constant and 60 Hz
  Vripple(RMS)VP 0.024
• For 1 sec time constant and 289 Hz
  Vripple(RMS)VP0.0005

9
Amplitude Detection in presence of Coherent
Interference
VOUT(t) abs(VS sin(wStf) VCI sin(wCItf2))
Signal
LPF removes high frequencies 2w
LPF
Signal CI

• Low-pass filter removes the ripple but does not
  remove rectified CI signal!
• fT2Hz (red)
• fT1Hz (blue)
• fT0.5Hz (magenta)
• fT0.25Hz (green)

Coherent Interference
10
Amplitude Detection in presence of Noise
Vexc(t) abs(VS sin(wStf) VNoise)
Signal
LPF
Signal Noise

• Low-pass filter removes the ripple but does not
  remove rectified NOISE signal!
• fT2Hz (red)
• fT1Hz (blue)
• fT0.5Hz (magenta)
• fT0.25Hz (green)

Noise
11
Amplitude detection summary

• If the SNR of the incoming signal is large AD can
  be safely used
• BUT
• Amplitude detector does not allow to recover
  signal in presence of noise or CI.
• The only possible improvement is to use a
  narrowband filter before detector so there is no
  CI or noise before signal is rectified
• If the envelope function of modulating signal
  changes sign, there is no way to figure it out
  using AD because unwanted signals are rectified
  as well
• Is there a way to fix that?

12
Phase Sensitive Rectifiers I (multiplication)

• Demodulation can be done by analog multiplier
• A reference signal (which is in-phase with
  transducer excitation)
• is multiplied with AC  signal from the QUT
• Multiplying with the reference
• Using trig identities
• As a result VZ is the desired signal multiplied
  by a scale factor
• Unique phase information (f1-f2 ) is used to
  decode the signal
• If Df0 (between the reference VR and the signal
  V0)
• After putting it through LPF

Vout
Vref Asin(wctf2)
Vout f (Vg)sin(wctf1)
Vref Asin(wctf2) f (Vg)sin(wctf1)
VZ A/2f (Vg)(cos(f1-f2 ) - cos(2wctf1f2)
VZ A/2f (Vg)(cos(0) - cos(2wctf1f2)
VZ Af (Vg)1/2
13
How phase detector rectifies a sinewave

• Output voltage after LPF is proportional to the
  Magnitude of the input signal
• Phase difference is between the reference and the
  signal we want to demodulate

14
Phase Sensitive Rectifiers II(flipping sign
technique)

• Switching gain technique
• Switch closed total gain is -1
• Switch opened total gain is 1
• Equivalent to multiplication of signal by the
  function SGN(t)
• Signal
• After multiplication by SGN
• Low-pass filter removes high-frequency components
  2f and higher
• The modulating signal is recovered
• Works for harmonics- one can use square wave
  modulation

15
Coherent Interference rejection in PSD
Signal
LPF
Signal CI
VoutVS?cos(Df)
Reference Signal (f0)

• Low-pass filter removes the ripples at parasitic
  frequencies
• fT2Hz (red)
• fT1Hz (blue)
• fT0.5Hz (magenta)
• fT0.25Hz (green)

Coherent Interference
16
Noise rejection in PSD
Signal
LPF
Signal Noise
VoutVS?cos(Df)

• Low-pass filter removes the traces of noise
• fT2Hz (red)
• fT1Hz (blue)
• fT0.5Hz (magenta)
• fT0.25Hz (green)

Noise
17
Comparing the results

• for acquisition time of 1 sec
• DC method BW 18Hz
• AC method with 300 ms time constant BW 0.8Hz
• SNR improvement for white noise in Vout
  measurement
• Far better in the presence of extra noises and
  interferences
• Amplitude rectification does not improve anything
  unless one puts the filter BEFORE rectifier
• Filtering the rectified signal in the amplitude
  detector only reduces ripple, but does NOT change
  the bandwidth for the signal recovery
• But very same filter used with phase detector
  will further improve the SNR by attenuating the
  noises

18
Example

• Signal from the sensor is a 10 nV sine wave at 10
  kHz. Too small to be used for control/monitoring.
  Amplification is needed!
• A very good low noise amplifier adds 5 nV/vHz
  of input noise.
• For the amplifier bandwidth of 100 kHz and the
  gain is 106, the output produces 10 mV of signal
  (10 nV x 106) and 1.6 V of broadband noise (5 nV/
  v Hz x v 100 kHz x 106). All you see is noise!
• Add a high quality band pass Q100 centered at 10
  kHz, bandwidth 100 Hz (10 kHz/Q). The noise
  after the BPF will be 50 mV (5 nV/ v Hz x v 100
  Hz x 106) and the signal will still be 10 mV.
• Using PSD the bandwidth can be squeezed by LPF
  down to 0.01 Hz In this case, the noise in the
  detection bandwidth will be only 0.5 mV (5 nV/ v
  Hz x v 0.01 Hz x 106)
• The SNR is now 20 thus sensor signal can be
  accurately measured.

19
What is measured using detectors (both AD and
PSD)?

• For sinewave test signals
• Average value of fully rectified sinewave is
• Once we get rid of ripples, we can end up with
  amplitude, A
• So for sinewave to get RMS from A is to multiply
  it by 0.707

20
What is a lock-in Amplifier?
21
Lock-In Amplifier Technique. How it works.
Carrier signal

• Time varying dependences can be measured
• Change in the sensor modulates the carrier signal
• PSD rectifies the signal
• After PSD the shape of the modulating curve is
  nicely recovered
• Note that amplitude rectifier will lose all the
  information about the signature of the modulating
  signal hidden in the phase
• Lock-in detection amounts to bandwidth narrowing
  again, with the bandwidth set by the
  post-detection low-pass filter

Green - original function Red filtered signal
after PSD
22
Lock-in applications. Small Light Intensity
measurements

• In many optical measurements the intensity of a
  beam of light reflected or passed through the
  sample is of interest. If the light beam is very
  weak then the electrical signal from the
  photo-detector is very weak and has to be
  amplified. A continuous optical beam will create
  a DC signal at the output of the photodetector
• High-gain DC amplification is difficult (drift,
  offset, noise). Also, stray light will also be
  amplified and appear at the output
• So conversion from DC to AC is needed. This can
  be achieved by chopping
• The most common technique is to pass the beam
  through a rotating disk that has holes or slots
  cut into it at regular intervals. As the disk
  rotates it "chops" the beam producing an on/off
  signal which when detected by a photodetector
  will appear as an AC signal
• The mechanical chopping of the light beam is very
  precisely controlled by the chopper and therefore
  the resultant AC signal due to the chopped light
  is at a known and stable frequency which can be
  monitored and amplified easily using an extra
  photodetector

Chopper
Sample (for transmission)
Laser
Signal PD
Beam splitter
Reference PD
23
Lock-In Amplifier application. Use of choppers
Sample is affected by external parameter

• Chopper replaces small DC signal from PD with AC
  signal by chopping the beam
• At the same time reference signal is created by
  chopping direct beam
• The signal from Signal PD is magnified with
  narrow-band amplifier
• Phase sensitive detector converts signal into DC
  with magnitude proportional to the magnitude of
  signal and phase shift between signal and
  reference
• DC signal is further magnified and filtered
• The functional dependence is recovered

24
Lock-In applications using AD630 demodulator
Poor mans lock-in
25
Dual channel Lock In amplifier
VR1
VC
VIN
2 phase LIA

• Very often both X and Y are of interest
• First PSD uses in-phase reference VL cos
  (wtQref)
• Second PSD uses out of phase (shifted by 90
  degrees reference)
• 1st PSD

26
Application of the lock-in technique to the
measurements of function derivatives

• There are many situations in science and
  engineering when the desired information is
  hidden in the derivative of the QUT response to
  external parameter (EP) rather then in its
  functional dependence
• How to measure the derivative?
• Applying a small modulating signal on top of the
  changing EP
• Dvmod V0cos(wt)
•  DVout(dVout/dvmod)Dvmod.
• Total signal is Vout f(EP)  DVout
• f(EP) is slowly changing signal, well below the
  bandwidth of the modulation signal
• After demodulation we get the derivative dV/dvmod
  V0

27
Example of derivative measurement using numerical
method

• IV measurement of nanoscale microstrips
• Conventional IV measurement shows straight line
  superimposed with noise
• With noisy signals numerical differentiation does
  not produce good results signal is sunk into
  noise

28
Measurement of I-V 1st derivative using lock-in
technique
Excitation voltage 0.1 V
Lock-in Amplifier SR830
Internal Oscillator Signal Exc Ref Signal
input
Division by 103
Microstrip
VDS
IV converter
Ramp generator

• Experimental setup
• Simple resistive divider is used
• to provide ramping VDS
• and a small AC signal of constant amplitude
  (100 mV) superimposed on
• Internal oscillator (built into lock-in) is used
  to provide both reference and excitation signals
• IV converter is used to magnify small current
• Signal is amplified and demodulated in lock-in
  amplifier
• When lock-in technique is used, clear feature on
  the dI/dV curve shows up

Instrumental
Numerical
29
Measurements of higher order derivatives
30
AC measurement techniques -II

• What to do if lock-in could not be used?
• Signal averagers
• Phase locked loops
• Frequency and time interval measurements

31
Limitations of Lock-in technique

• The best method to recover a signal from noise
  depends on the nature of the signal of interest
  and the required representation of the result
• Lock-in Amplifiers are extremely powerful signal
  recovery instruments if the signal can be made to
  be an amplitude modulated AC waveform, where the
  envelope of the modulation is the required output
• However, where this cannot be done, or where the
  rise/fall time of the signal exceeds the
  available bandwidth, or where the signal is short
  lived, other techniques are needed
• Why? Narrow bandwidth is bad for signals for
  which Fourier spectrum is not a single peak a
  significant portion of information is lost

32
Signal Averaging

• By repeating the experiment and averaging the
  results, SNR can be greatly improved
• Signal-to-Noise Improvement ratio (SNIR)vn
• Instruments available for averaging which must be
  synchronized with the source of pulses
• Digital Oscilloscopes
• Fast ADC capable of fast data transfer to the
  storage
• Boxcar Averagers
• Signal Averagers

SNRIN
ADC
Averager
SNROUT
Averager
Pulse Generator
QUT
Detector
Sync
33
Boxcar averager (aka boxcar integrator, gated
integrator)

• The Boxcar Averager uses analog electronics,
  supported by digital control, to monitor one
  discrete point in time on a repetitive signal.
• Gated Integrator circuit is the key. S1 sampling
  gate RC storage circuit
• Choice of RC V0 is close to V1 by the end of
  gating
• High frequency components are removed Equivalent
  noise bandwidth
• 1.57/(2pRC)
• It builds up an average of that point over many
  cycles before recording it as a value
• Two types of averaging. Note that outputs of
  averager (not gated integrator!) are shown.
  Outputs of the gated integrator look like pulses
  of almost equal height
• Linear (good for digital storage)
• Acquire a sample, pass it to averager, reset the
  charge stored in C. Note that each step is
  nothing but a stored voltage across C by the end
  of gating time.
• Exponential (analog storage) RCltltR2C2
• Acquire a sample, pass it to the exp
  averager(2nd), reset the the charge stored in C
  of the first integrator
• After averaging is finished the reset is done to
  null the averager storage (analog or digital)

Note that the steps Are not of the same height.
For exp integrator the output is reaching the
height of single step in linear integration
method only by the end of the averaging cycle
34
Use of Boxcars

• Two modes of operation
• Static gate pulse recovery
• Waveform recovery.
• The groups of gated signal corresponding to fixed
  delay are averaged, then delay is incremented,
  and process is repeated for a new delay.
• Usually the gate interval is shorter compared to
  static pulse recovery
• The number of datapoints representing the signal
  is m
• In either case make sure your bandwidth is
  adequate!

35
Some useful info about boxcars

• Boxcar are the best for averaging a single point
  in time repetitively.
• Example the amplitude of one peak of a
  spectrum, from a repetitively swept
  monochromator, could be averaged easily and
  recorded as a function of time using a Boxcar
  system.
• This technology can also give good time
  resolution, with better than 1 ns being possible.

36
Signal Averagers vs Boxcar

• The Signal Averager uses digital techniques to
  record all of the waveform on each cycle. This
  makes it much more time efficient than Boxcar
  systems. Nonetheless the time taken to do the
  summation does limit the maximum data throughput
  unless a dedicated hardware averager is included
• In the case of Gaussian noise, the improvement in
  signal-to-noise ratio gained from this process is
  approximately equal to the square root of the
  number of summed cycles. Hence averaging 100
  records of an identical event will improve the
  signal-to-noise ratio by 10 times.
• Signal Averagers can provide maximum time
  resolutions of a similar level, but are better
  suited to waveform recovery and to monitoring
  short lived phenomena due to their better time
  efficiency.

37
Phase Locked loop basics

• PLL is a frequency selective circuit designed to
  synchronized with the incoming signal and
  maintain synchronization inspite of noise or
  variations in the incoming signal frequency
• Consists of phase detector (PD), loop filter and
  a VCO (voltage-controlled oscillator)
• VCO generates a free standing frequency if no
  input is applied
• If input frequency changes an error voltage
  develops to adjust the frequency which will then
  minimize the phase shift
• VE can be used as output to detect changes in
  input frequency
• VCO frequency can be used to recover signal
  buried in the noise and for frequency synthesis

38
Frequency multiplier locked to the reference

• Inserting frequency divider in PLL feedback is
  similar to inserting voltage divider in feedback
  loop of op-amp voltage swing increases for
  op-amp, frequency swing increases for PLL
• Phase detector converts phase to voltage
• VCO converts voltage to time derivative of the
  phase (frequency)
• Fixed input voltage error produces a linearly
  rising phase error at the VCO output
• Generated frequency is 60 Hz 102461440 Hz.
  This results in 7.5 measurements/sec (4096 pulses
  per ramp)

39
FM demodulator using PLL

• Change in input frequency leads to change in VE,
  VE in turn will adjust the local oscillator
  frequency
• Popular chip 4046 is used (contains buffers, PC
  and VCO)
• VE is used as an output for frequency
  demodulation
• Input is 1 MHz10kHz
• For VCO, free standing frequency is set to 1MHz
  (by choosing 100pF cap)
• The bandwidth for a LPF (connected after phase
  comparator PC1) is set to 10 KHz

40
Frequency and Period Measurements

• Input signal is converted into pulses
• 1 second pulse comes from divided oscillator
• The signal starts BCD (binary coded decimal)
  counter
• Result is latched and displayed
• Counter is reset between counting intervals
• Limitations  it is hard to accurately measure
  frequencies close to 1/Tgate.
• Example with a gate time of 1 sec 10 Hz will be
  read as 9,10, or 11, whereas 1 MHz can be
  measured in the same setup with 1ppm resolution.

41
Phase Locked loop basics

• PLL is a frequency selective circuit designed to
  synchronized with the incoming signal at f0 and
  maintain synchronization inspite of noise or
  variations in the incoming signal frequency
• Consists of phase detector (PD), loop filter and
  a VCO (voltage-controlled oscillator)
• VCO generates a free standing frequency if no
  input is applied
• If input frequency changes an error voltage
  develops to adjust the frequency which will then
  minimize the phase shift
• VCtrl can be used as output to detect changes in
  input frequency
• VCO frequency can be used to recover signal
  buried in the noise and for frequency synthesis

42
Frequency multiplier locked to the reference

• Inserting frequency divider in PLL feedback is
  similar to inserting voltage divider in feedback
  loop of op-amp voltage swing increases for
  op-amp, frequency swing increases for PLL
• Phase detector converts phase to voltage
• VCO converts voltage to time derivative of the
  phase (frequency)
• Fixed input voltage error produces a linearly
  rising phase error at the VCO output
• Generated frequency is 60 Hz 102461440 Hz.
  This results in 7.5 measurements/sec (4096 pulses
  per ramp)

43
FM demodulator using PLL

• Input is 1 MHz10kHz how to detect it?
• Change in input frequency leads to change in VE,
  VE in turn will adjust the local oscillator
  frequency
• Chip 4046 is used (contains buffers, PC (phase
  comparator) and VCO)
• For VCO, free standing frequency is set to 1MHz
  (by choosing 100pF cap)
• PC gives 0 after filter if f in 1 MHz
• vo is used as an output of FM demodulator
• The bandwidth for a LPF (connected after phase
  comparator PC1) is set to 10 KHz
• The output signal is free from noise, because of
  the squeezed bandwidth

44
Summary for signal recovery

• Always try to minimize the bandwidth to improve
  SNR
• Noisy signals could be recovered by carefully
  choosing the appropriate instrumentation
• If the information from the sensor is encoded in
  the magnitude of the signal and probing signal is
  a sinewave or, more generally, a waveform where
  most of the power is concentrated within first
  few harm onical components (meander, symmetrical
  triangular, wave, clipped sinewave, etc), then
  use lock-in amplifiers for signal recovery
• If the signals of interest are repetitive, but
  have broad spectrum (e.g., pulses with duty cycle
  Dt/T0ltlt1 (where T0 is a period and Dt is a pulse
  length), use boxcar averagers ofr signal
  averagers
• If the information is encoded in the frequency
  change around the carrier (tone modulation, FM )
  or there is a need to create a signal with rigid
  phase attachment to some standard, then use Phase
  Locked Loops