05-11-2016, 10:16 AM
1464949680-Instrumentationchapter5ElectrodesSensorsTransducers.ppt (Size: 1.14 MB / Downloads: 58)
Types of Signals
Signals can be represented in time or frequency domain
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
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
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 =
Eg. v = Vm sin(2ωt)
v = instantaneous amplitude of sin wave
Vm = Peak amplitude of sine wave
ω = angular frequency = 2π f
T = time (sec)
Fourier Series found using many frequency selective filters or using digital signal processing algorithm known as FFT = Fast Fourier Transform
Every Signal can be described as a series of sinusoids
Signal with DC Component
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
Time vs Frequency
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
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
Biomedical Examples of Signals
Square wave theoretically has infinite number of harmonics however approximately 100 harmonics approximates signal well
Odd or Even Function
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
Two types of error with digitalization.
Sampling Error
Quantization Error
Sampling Rate
Sample Rate must follow Nyquist’s theorem.
Sample rate must be at least 2 times the maximum frequency.
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
Quantization Noise
Quantization noise = difference from where analog signal actually is to where the digitization records the signal
Quantization Noise
Nyquist Sampling Theorem Error in Signals
Spectral Information: Sampling when Fs > 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)
Spectral Information: Sampling when Fs < 2Fm
Aliasing occurs when Fs< 2Fm where you begin to see overlapping in frequency domain.
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 >=2Fm
Shows how very fast sampled frequency if sampled incorrectly can be a slower frequency signal
Noise
Every electronic component has noise
thermal noise
shot noise
distribution noise (or partition noise)
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
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;
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 = Boltzman’s constant
Boltzman’s constant = 1.38 x 10 -23Joules/Kelvin
T = temperature in Kelvin
R = resistance in ohms (Ώ)
B = Bandwidth in Hertz (Hz)
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
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
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;
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)
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 x10–18 A2) ½ = 1.88 nA
Noise cont
Flicker Noise also known as Pink Noise or 1/f noise is the lower frequency < 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.
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;
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.
Signal to Noise Ratio = SNR
Noise Power Pn
Pn = kTB, where
Pn =noise power in watts
k = Boltzman’s constant
Boltzman’s constant = 1.38 x 10 -23Joules/Kelvin
T = temperature in Kelvin
B = Bandwidth in Hertz (Hz)
Internal and External Noise
Internal Noise
External Noise
Total Noise Calculation
Internal Noise
Internal Noise: Caused by thermal currents in semiconductor material resistances and is the difference between output noise level and input noise level
External Noise
External Noise: Noise produced by signal sources also called source noise; cause by thermal agitation currents in signal source
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
Noise Factor
Noise Factor = ratio of noise from real resistance to thermal noise of an ideal resistor
Noise Factor
Fn = Pno/Pni evaluated at T = 290oK (room temperature) where
Pno = noise power output and
Pni = noise power input
Noise Factor
Pni =kTBG where
G = Gain;
T = Standard Room temperature = 290oK
K = Boltzmann’s Constant = 1.38 x10-23J/oK
B = Bandwidth (Hz)
Noise Factor
Pno = kTBG + ΔN where
ΔN = noise added to system by network or amplifier
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)
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
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)
Noise Reduction Strategies
Keep source resistance and amplifier input resistance low (High resistance with increase thermal noise)
Keep Bandwidth at a minimum but make sure you satisfy Nyquist’s Sampling Theory
Prevent external noise with proper ground, shielding, filtering
Use low noise at input stage (Friis Equation)
For some semiconductor circuits use the lowest DC power supply
Feedback Control Derivation
Use of Feedback to reduce Noise
Use of Feedback to reduce Noise
Use of Feedback to reduce Noise
Thus Vn is reduced by Gain G1
Note Book forgot V in equation 5-35
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
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
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
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
Review
Noise:Johnson, 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