Biomedical Instrumentation

1
Biomedical Instrumentation

• Signals and Noise
• Chapter 5 in
• Introduction to Biomedical Equipment Technology
• By Joseph Carr and John Brown

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Types of Signals

• Signals can be represented in time or frequency
  domain

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Types of Time Domain Signals

• Static unchanging over long period of time
  essentially a DC signal
• Quasistatic nearly unchanging where the signal
  changes so slowly that it appears static
• Periodic Signal Signal that repeats itself on
  a regular basis ie sine or triangle wave
• Repetitive Signal quasi periodic but not
  precisely periodic because f(t) / f(t T) where
  t time and T period ie is ECG or arterial
  pressure wave
• Transient Signal one time event which is very
  short compared to period of waveform

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Types of Signals

• A. Static non-changing signal
• B. Quasi Static practically non-changing signal
• C. Periodic cyclic pattern where one cycle is
  exactly the same as the next cycle
• D. Repetitive shape of the cycle is similar but
  not identical (many BME signals ECG, blood
  pressure)
• E. Single-Event Transient one burst of activity
• F. Repetitive Transient or Quasi Transient a
  few bursts of activity

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Fourier Series

• All continuous periodic signals can be
  represented as a collection of harmonics of
  fundamental sine waves summed linearly.
• These frequencies make up the Fourier Series
• Definition
• Fourier
• Inverse Fourier

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Eg. v Vm sin(2?t)

• v instantaneous amplitude of sin wave
• Vm Peak amplitude of sine wave
• ? angular frequency 2p f
• T time (sec)
• Fourier Series found using many frequency
  selective filters or using digital signal
  processing algorithm known as FFT Fast Fourier
  Transform

Time (sec) 1 sec
Sine Wave in time domain f(t) sin(2?3t)
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Every Signal can be described as a series of
sinusoids
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Signal with DC Component
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Time vs Frequency Relationship

• Signals that are infinitely continuous in the
  frequency domain (nyquist pulse) are finite in
  the time domain
• Signals that are infinitely continuous in the
  time domain are finite in the frequency domain
• Mathematically, you cannot have a finite time and
  frequency limited signal

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Time vs Frequency
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Spectrum Bandwidth

• Spectrum
• range of frequencies contained in signal
• Absolute bandwidth
• width of spectrum
• Effective bandwidth
• Often just bandwidth
• Narrow band of frequencies containing most of the
  energy
• Used by Engineers to gain the practical bandwidth
  of a signal
• DC Component
• Component of zero frequency

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Biomedical Examples of Signals

• ECG vs Blood Pressure
• Pressure Waveform has a slow rise time then ECG
  thus need less harmonics to represent the signal
• Pressure waveform can be represented in with 25
  harmonics whereas ECG needs 70-80 harmonics

ECG
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Biomedical Examples of Signals

• Square wave theoretically has infinite number of
  harmonics however approximately 100 harmonics
  approximates signal well

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Odd or Even Function
Even function when f(t) f(-t)
Odd function f(t) f(-t)
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Analog to Digital Conversion

• Digital Computers cannot accept Analog Signal so
  you need to perform and Analog to digital
  Conversion (A/D conversion)
• Sampled signals are not precisely the same as
  original.
• The better the sampling frequency the better the
  representation of the signal

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• Two types of error with digitalization.
• Sampling Error
• Quantization Error

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Sampling Rate

• Sample Rate must follow Nyquists theorem.
• Sample rate must be at least 2 times the maximum
  frequency.

19
Quantization Error

• When you digitize the signal you do so with
  levels based on the number of bits in your DAC
  (data acquisition board)
• Example is of a 4 bit 24 or 16 level board
• Most boards are at least 12 bits or 212 4096
  levels
• The staircase effect is call the quantization
  noise or digitization noise

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Quantization Noise

• Quantization noise difference from where analog
  signal actually is to where the digitization
  records the signal

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Quantization Noise
20 levels
Red magnitude Black timing interval
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4 levels
Red magnitude Black timing interval
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Nyquist Sampling Theorem Error in Signals
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1 Sec
1 Sec
10 samples / 1 sec 10 Hertz
30 samples / 1 sec 30 Hertz
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Spectral Information Sampling when Fs gt 2Fm

• Sampling is a form of amplitude modulation
• Spectral Information appears not only around
  fundamental frequency of carrier but also at
  harmonic spaced at intervals Fs (Sampling
  Frequency)

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Spectral Information Sampling when Fs lt 2Fm

• Aliasing occurs when Fslt 2Fm where you begin to
  see overlapping in frequency domain.

27

• Problem if you try to filter the signal you will
  not get the original signal
• Solution use a LPF with a cutoff frequency to
  pass only maximum frequencies in waveform Fm not
  Fs
• Set sampling Frequency Fs gt2Fm
• Shows how very fast sampled frequency if sampled
  incorrectly can be a slower frequency signal

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Noise

• Every electronic component has noise
• thermal noise
• shot noise
• distribution noise (or partition noise)

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Thermal Noise

• Thermal noise due to agitation of electrons
• Present in all electronic devices and
  transmission media
• Cannot be eliminated
• Function of temperature
• Particularly significant for satellite
  communication

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thermal noise

• thermal noise is caused by the thermal motion of
  the charge carriers as a result the random
  electromotive force appears between the ends of
  resistor

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Johnson Noise, or Thermal Noise, or Thermal
Agitation Noise

• Also referred to as white noise because of
  gaussian spectral density.
• where
• Vn noise Voltage (V)
• k Boltzmans constant
• Boltzmans constant 1.38 x 10 -23Joules/?Kelvin
• T temperature in ?Kelvin
• R resistance in ohms (?)
• B Bandwidth in Hertz (Hz)

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Eg. of Thermal Noise

• Given R 1Kohm
• Given B 2 KHz to 3 KHz 1 KHz
• Assume T 290K (room Temperature)
• Vn2 4KTRB units V2
• Vn2 (4) (1.38 x 10 23J/K) (290K) (1 Kohm)
  (1KHz)
• 1.6 x 10-14 V2
• Vn 1.26 x10 7 V 0.126 uV

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Eg of Thermal Noise

• Vn 4 (R/1Kohm) ½ units nV/(Hz)1/2
• Given R 1 MW find noise
• Vn 4 (1 x 106 / 1x 103) ½ units nV/ (Hz) ½
• 126 nV/ (Hz) ½
• Given BW 1000 Hz find Vn with units of V
• Vn 126 nV/ (Hz) ½ (1000 Hz)1/2 400 nV
  0.4 uV

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Shot noise

• Shot noise appears because the current through
  the electron tube (diode, triode etc.) consists
  of the separate pulses caused by the
  discontinuous electrons
• This effect is similar to the specific sound when
  the buckshot is poured out on the floor and the
  separate blows unite into the continuous noise

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Shot Noise

• Shot Noise noise from DC current flowing in any
  conductor
• where
• In noise current (amps)
• q elementary electric charge
• 1.6 x 10-19 Coulombs
• I Current (amp)
• B Bandwidth in Hertz (Hz)

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Eg Shot Noise

• Given I 10 mA
• Given B 100 Hz to 1200 Hz 1100 Hz
• In2 2q I B
• 2 (1.6 x 10 19Coulomb) ( 10 X10 3A)(1100 Hz)
• 3.52 x10 18 A2
• In (3.52 x1018 A2) ½ 1.88 nA

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Noise cont

• Flicker Noise also known as Pink Noise or 1/f
  noise is the lower frequency lt 1000Hz phenomenon
  and is due to manufacturing defects
• A wide class of electronic devices demonstrate so
  called flicker effect or wobble (trembling), its
  intensity depends on frequency as 1/f?, ?1, in
  the wide band of frequencies
• For example, flicker effect in the electron tubes
  is caused by the electron emission from some
  separate spots of the cathode surface, these
  spots slowly vary in time at the frequencies of
  about 1 kHz the level of this noise can be some
  orders higher then thermal noise.

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distribution noise

• Distribution noise (or partition noise) appears
  in the multi-electrode devices because the
  distribution of the charge carriers between the
  electrodes bear the statistical features

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Signal to Noise Ratio SNR

• SNR Signal/ Noise
• Minimum signal level detectable at the output of
  an amplifier is the level that appears above
  noise.

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Signal to Noise Ratio SNR

• Noise Power Pn
• Pn kTB, where
• Pn noise power in watts
• k Boltzmans constant
• Boltzmans constant 1.38 x 10 -23Joules/?Kelvin
• T temperature in ?Kelvin
• B Bandwidth in Hertz (Hz)

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Internal and External Noise

• Internal Noise
• External Noise
• Total Noise Calculation

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Internal Noise

• Internal Noise Caused by thermal currents in
  semiconductor material resistances and is the
  difference between output noise level and input
  noise level

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External Noise

• External Noise Noise produced by signal sources
  also called source noise cause by thermal
  agitation currents in signal source

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External Noise

• Total Noise Calculation square root of sum of
  squares Vne (Vn2(InRs)2) ½ necessary because
  otherwise positive and negative noise would
  cancel and mathematically show less noise that
  what is actually present

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Noise Factor

• Noise Factor ratio of noise from real
  resistance to thermal noise of an ideal resistor

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Noise Factor

• Fn Pno/Pni evaluated at T 290oK (room
  temperature) where
• Pno noise power output and
• Pni noise power input

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Noise Factor

• Pni kTBG where
• G Gain
• T Standard Room temperature 290oK
• K Boltzmanns Constant 1.38 x10-23J/oK
• B Bandwidth (Hz)

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Noise Factor

• Pno kTBG ?N where
• ?N noise added to system by network or
  amplifier

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Noise Figure

• Noise Figure Measure of how close is an
  amplifier to an ideal amplifier
• NF 10 log (Fn) where
• NF Noise Figure (dB)
• Fn noise factor (previous slide)

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Noise Figure

• Friis Noise Equation Use when you have a
  cascade of amplifiers where the signal and noise
  are amplified at each stage and each component
  introduces its own noise.
• Use Friis Noise Equation to calculated total
  Noise
• Where FN total noise
• Fn noise factor at stage n
• G(n-1) Gain at stage n-1

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• Example Given a 2 stage amplifier where A1 has a
  gain of 10 and a noise factor of 12 and A2 has a
  gain of 5 and a noise factor of 6.
• Note that the book has a typo in equation 5-27
  where Gn should be G(n-1)

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Noise Reduction Strategies

1. Keep source resistance and amplifier input
   resistance low (High resistance with increase
   thermal noise)
2. Keep Bandwidth at a minimum but make sure you
   satisfy Nyquists Sampling Theory
3. Prevent external noise with proper ground,
   shielding, filtering
4. Use low noise at input stage (Friis Equation)
5. For some semiconductor circuits use the lowest DC
   power supply

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Feedback Control Derivation
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Use of Feedback to reduce Noise
Vn Noise
Vin
V1G1
Vo
V1
V2
V2G2
S
G1
G2
S
B Vo
?
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Use of Feedback to reduce Noise
Vn Noise
Vin
V1G1
Vo
V1
V2
V2G2
S
G1
G2
S
B Vo
?
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Use of Feedback to reduce Noise
Derivation

• Thus Vn is reduced by Gain G1
• Note Book forgot V in equation 5-35

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Noise Reduction by Signal Averaging

• Un processed SNR Sn 20 log (Vin/Vn)
• Processed SNR Ave Sn 20 log (Vin/Vn/ N1/2)
• Where
• SNR Sn unprocessed SNR
• SNR Ave Sn time averaged SNR
• N repetitions of signals
• Vin Voltage of Signal
• Vn Voltage of Noise
• Processing Gain Ave Sn Sn in dB

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Noise Reduction by Signal Averaging

• Ex EEG signal of 5 uV with 100 uV of random
  noise
• Find the unprocessed SNR, processed SNR with 1000
  repetitions and the processing Gain

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Noise Reduction by Signal Averaging

• Unprocessed SNR
• Sn 20 log (Vin/Vn) 20 log (5uV/100uV) -26dB
• Processing SNR
• Ave Sn 20 log (Vin/Vn/N1/2)
• 20 log (5u/100u / (1000)1/2) 4 dB
• Processing gain 4 (- 26) 30 dB

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Review

• Types of Signals (Static, Quasi Static, Periodic,
  Repetitive, Single-Event Transient, Quasi
  Transient)
• Time vs Frequency
• Fourier
• Bandwidth
• Alaising
• Sampled signals Quantization, Sampling and
  Aliasing

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Review

• NoiseJohnson, Shot, Friis Noise
• Noise Factor vs Noise Figure
• Reduction of Noise via
• 5 different Strategies keep resistor values low,
  low BW, proper grounding, keep 1st stage
  amplifier low (Friis Equation), semiconductor
  circuits use the lowest DC power supply
• Feedback
• Signal Averaging

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Homework

• Read Chapter 6
• Chapter 3 Problems 16, 17, 21
• Chapter 4 Questions and Problems 5, 18, 19,
  21, 22
• Chapter 5 Homework Problems 4, 6, 7, 8, 10, 11,
  12, 13