Instrumentation: Elements of the data acquisition system

Instrumentation: Elements of the data acquisition system
Dr. Hussein EZZEDDINE

Course outline Introduction Elements of the data acquisition system
Sensor Instrumental amplifier Analog filter Sample and Hold circuits (S/H) Analog to Digital Converters (ADC) Digital to Analog Converters (DAC) Hardware /Software Links with Computer Applications

What is Data Acquisition System (DAS)?
I. Introduction What is Data Acquisition System (DAS)? Definition: Data acquisition (DAQ) is the process by which physical phenomena from the real world are transformed into electrical signals that are measured and converted into a digital format for processing, analysis, and storage by a computer. Data acquisition system is designed not only to acquire data, but also to act on it as well. ! Main companies working on DAQ : National Instruments (Labview)  NI DAYS in Beirut ! Texas Instruments Mathworks (matlab) : Data aquisition Toolbox

Block diagram of a data acquisition system :
Introduction Block diagram of a data acquisition system : Noise Filter Amp Physical Process Sensor ADC Converter Process PC comp and data storage DAC Converter Actuator

Introduction Data acquisition covers many different domains : Measurements techniques : sensors, metrology… Analog electronics : amplification, filtering Signal processing : sampling and quantification, Analog to digital conversion (ADC) and digital to analog conversion (ADC) Programming : Hardware/ Software links with a computer

II.1. The sensor (or transducer)
Elements of the data acquisition system II.1. The sensor (or transducer) Definition Categories Characteristics How to choose the suitable sensor

Elements of the data acquisition system
Examples : Biomedical system Ultrasound Transducer

Automotive Sensors Oxygen Sensor Airflow Sensor Water Temperature Oil Pressure Accelerometer CO Sensor

Elements of the data acquisition system II.1. The sensor (or transducer) a) Definition : A sensor is a device that converts a physical phenomenon into an electrical signal. Sensor physical quantity* Electric signal Temperature (°C) Speed (m/s) Pressure (Pa) …. Voltage (V) Current (A) Charge (C) … Noise * Also called Stimulus or Measurand

Elements of the data acquisition system II.1. The sensor (or transducer) Definition of noise : Noise is related to physical quantities which affect the operation of the sensor or the precision of the measurement, example : vibrations, humidity, electric supply , EM perturbations (EMC), … The designer (you !) of a data acquisition system should minimize the influence of these undesired noise or predict a compensation system !

Elements of the data acquisition system II.1. The sensor (or transducer) Actuator : An actuator is used to generate a physical phenomenon when an electric signal is applied on it. example : motor, Source of light,… Electric signal physical phenomenon Actuator

Elements of the data acquisition system II.1. The sensor (or transducer) Example : Actuator / Sensor

II.1. The sensor (or transducer) b) Categories of sensors : Active sensor : - An active sensor requires an external source of excitation. Resistor-based sensors. Thermistors, LDR and strain gages are examples of active sensors, because a current must be passed through them and the corresponding voltage measured in order to determine the resistance value. Passive sensor (or self-generating) : - Generate its own electrical output signal without requiring external voltages or currents. - Examples of passive sensors are thermocouples and photodiodes.

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Transfer Function The transfer function shows the functional relationship between physical input signal and electrical output signal. To obtain the transfer function, a sensor or instrument is calibrated by applying a number of KNOWN (use of a reference sensor or standards ) physical inputs and recording the response of the system That’s why the Transfer Function is also called calibration curve

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Sensitivity : Factor of proportionality between the physical input X and the signal output Y of the sensor : S help to estimate the value of the output of the sensor, then choose the most suitable sensor to the DAS.

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Range : interval of measured values of the physical quantity. The larger the range of a sensor, the more its usage in DAS. The sensor could give false results or be damaged if the value of the physical quantity is not inside the range !!! Piezoelectric accelerometer (shock sensor) Range : 2500 à g Thermocouple T28XX Range : à 260 ° C 9.8 ms-2

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Precision : the smallest variation of the physical quantity that can be measured by the sensor. Digital sensor : given by the least significant digit displayed on the screen Analog sensor : estimated to half the smallest division.

Elements of the data acquisition system II.1. The sensor (or transducer) Output x Input y c) Important factors in a sensor Ideal response Error of linearity : difference between the real response of the sensor and the ideal one given by its average sensitivity Error of linearity Real response Note : Sensors should have the most linear response for easier processing (amplification, filtering, …). For non-linear sensors, it’s required to build a conditioning circuit (specific electronic circuit) to get a linear output.

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Response time : is the time taken by the sensor to stabilize its output after an instantaneous variation of the physical quantity. Time The most frequent case : Exponential response of the form : The rise time is generally estimated to nearly 5τ Note : Lower response time => reduced Measurement time (real-time acquisition)

Elements of the data acquisition system II.1. The sensor (or transducer) c) Important factors in a sensor Bandwidth : a sensor acts as a lowpass filter. The bandwidth (at -3 dB) corresponds to frequencies not attenuated by this filter. For physical quantities varying at a frequency higher than the bandwidth, the sensor can not follow the high variations, then, attenuate the output. Fourier Transform of the time exponential response : The -3 dB cutoff frequency is given by :

Elements of the data acquisition system II.1. The sensor (or transducer) d) How to choose a sensor • boundaries values for the physical quantity : • Frequency and speed of variation of the physical quantity : • Required precision for the measurement : • Required linearity, … Range Bandwidth and response time Precision

Elements of the data acquisition system II.1. The sensor (or transducer) d) How to choose a sensor Other parameters to take into account : • Price • Lifetime • Size and weight (must match with other components of the DAS) • Consumption of electricity (must match with other components of the DAS) • impact of the sensor on other elements of the DAS The designer of a DAS (you) must take into account all these constraints for choosing the most suitable sensor for its application !

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors The word piezo comes from the Greek word piezein, meaning to press or squeeze. Piezoelectricity refers to the generation of electricity or of electric polarity in dielectric crystals when subjected to mechanical stress and conversely, the generation of stress in such crystals in response to an applied voltage. Quartz is the most known piezoelectric material. It’s used mainly in electronic oscillators + + + + + - - - - - - - Applications : Accelerometer (Wii, cars, …), measure of pressure, shock (Airbag)…

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors Upper and lower faces of the Quartz are charging with opposite signs when a force is applied. A voltage (capacitance effect) is created, and related to the strength of the applied force. Theory and Modeling The basic theory behind piezoelectricity is based on the electrical dipole. At the molecular level, the structure of a piezoelectric material is typically an ionic bonded crystal. At rest, the dipoles formed by the positive and negative ions cancel each other due to the symmetry of the crystal structure, and an electric field is not observed. When stressed, the crystal deforms, symmetry is lost, and a net dipole moment is created. This dipole moment forms an electric field across the crystal that is proportional to the pressure applied

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors If a reciprocating force is applied, an ac voltage is seen across the terminals of the device. Piezoelectric sensors are not suited for static or dc applications because the electrical charge produced decays with time due to the internal impedance of the sensor and the input impedance of the signal conditioning circuits. However, they are well suited for dynamic or AC applications.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors Piezoelectric sensors are used as tactile sensors : Touch Sensors: detect and measure contact forces at defined points. A touch sensor typically is a threshold device or a binary sensor, namely – touch or no touch. Good tactile sensors can be designed with piezoelectric films , such as polyvinylidene fluoride (PVDF ) used in active or passive modes.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors The upper and the bottom films are PVDF. The bottom piezoelectric film is driven by an AC voltage from an oscillator. This excitation signal results in mechanical contractions of the film that are coupled to the compression film and, in turn, to the upper piezoelectric film, which acts as a receiver. Since piezoelectricity is a reversible phenomenon, the upper film produces alternating voltage upon being subjected to mechanical vibrations from the compression film. These oscillations are amplified and fed into a synchronous demodulator.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors The demodulator is sensitive to both the amplitude and the phase of the received signal. When compressing force F is applied to the upper film, mechanical coupling between the three-layer assembly changes. This affects the amplitude and the phase of the received signal. These changes are recognized by the demodulator and appear at its output as a variable voltage. Size of the sensor : If the 25-μm PVDF films are laminated with a 40-μm silicone rubber compression film, the thickness of an entire assembly (including protective layers) does not exceed 200 μm.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Piezoelectric sensors Detection of breathing rate of a sleeping child, where minute movements of a body resulted from respiration had to be monitored in order to detect cessation of breathing. A body of a normally breathing child slightly shifts with each inhale and exhale due to a moving diaphragm. This results in a displacement of the body’s center of gravity that is detected by the PVDF film sensor. Piezoelectric Film Respiration Sensor

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Other technologies for tactile sensors : Capacitive Sensors : The capacitive sensors are popular in touch screen panels that typically are made of glass or a clear polymer coated with a transparent conductor such as indium tin oxide (ITO) that combines electrical conductivity and optical clarity.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Other technologies for tactile sensors : Capacitive Sensors : we can distinguish between a light and a strong touch since they don’t induce the same capacitance value ! No touch light touch strong touch

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors rotation Linear Potentiometer position sensors

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors Contact Capacitive displacement sensor : Cylindrical capacitor Parallel Plate capacitor

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors Non-contact capacitive sensors

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors Hall effect sensor Hall effect sensor Two magnets fixed to the wheel wheel

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors Optical encoder For more precision: 8 bits -> 256 pulse per turn ! Also used to measure absolute angle position Wheel Front view of the disk

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors Piezoelectric wheel revolution sensor Shaft Conditioning Electronics Vout Piezoelectric detector Vp Extension

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Position, displacement and motion sensors How can you get a digital display for the rotation speed ?

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Temperature sensors 1. Thermocouples : Seebeck effect = when two metallic conductors (A and B) are coupled at a junction, a voltage, proportional to the temperature of the junction, appears between conductors A and B. Advantage : Thermocouples are very precise (±0.1°C) and can handle very high temperature (up to 1400 °C) Disadvantage :they deliver a low voltage and is non linear Most popular : Type K thermocouple

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Temperature sensors 2. Resistive Devices : Thermistors , RTD (resistive temperature devices : are devices that change their electrical resistance in relation to their temperature. Thermistors are available in two different types: positive temperature coefficient (PTC) and negative temperature coefficient (NTC). PTC devices exhibit an increase in resistance as temperature rises, while NTC devices exhibit a decrease in resistance when temperature increases.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Temperature sensors 2. Resistive Devices : Thermistors , RTD (resistive temperature devices : Most popular : PT100 platinum resistance thermometers offer excellent accuracy over a wide temperature range (from –200 to +850 °C) has a resistance of 100 ohms at 0 °C and ohms at 100 °C Disadvantage : Not linear over a wide range of temperature Need a DC supply

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Temperature sensors 3. Silicon sensors: The most widely used today : popular Ics : LM35, LM19, … - Provide typical accuracies of ±¼°C at room temperature and ±¾°C over a full −55°C to 150°C temperature range. - Low cost … Principle :

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Temperature sensors 4. Infrared (IR) pyrometry All objects emit infrared energy provided their temperature is above absolute zero (0 Kelvin). There is a direct correlation between the infrared energy an object emits and its temperature : Wien's law IR sensors measure the infrared energy emitted from an object in the 4–20 micron wavelength and convert the reading to a voltage.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Flow sensors Ultrasonic Flowmeter :  Flow Measurement from Outside a Pipe Use doppler effect to measure the velocity of a liquid When the source moves, its frequency change Low frequency High frequency

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Flow sensors For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Flow sensors When the medium moves (there is a flow), the frequency change : Δf = f0 – fR is proportionnal to the variations of the velocity of the liquid Δv f0 fR When the fluid moves faster, the frequency shift increases linearly. The transmitter processes signals from the transmitted wave and its reflections to determine the flow rate.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Flow sensors

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Level sensors The most common application for level sensing is tank measurement and control operations. A number of level sensing technologies are currently available, including : Hydrostatic pressure, Ultrasonic, RF capacitance, magnetorestrictive-based, radar measurement systems.

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Level sensors Ultrasonic Ultrasonic level sensors emit sound waves, and the liquid surface reflects the sound waves back to the source. The transit time is proportional to the distance between the liquid surface and the transmitter. These sensors are ideal for noncontact level sensing of very viscous fluids such as heavy oil, …

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Level sensors Ultrasonic The RX will receive 2 pulses : - Reflection at the surface of the liquid - Reflection at the tank wall

Elements of the data acquisition system II.1. The sensor (or transducer) e) Examples of sensors Level sensors Ultrasonic We can deduce : Velocity of US waves in air : 340 m/s Velocity of US waves in the liquid. Example : for water : ≈1500 m/s

II.2. The instrumentation (or instrumentational) amplifier
Elements of the data acquisition system II.2. The instrumentation (or instrumentational) amplifier Role Review : OpAmp Differential Amplifier (Diff Amp) Instrumentation Amplifier Isolation amplifier

a) Role : Amplify the analog electric signal at the output of the sensor, which has usually a very weak amplitude, and contains noise ! noise Ampli Sensor The amplifier should amplify the signal without amplifying parasitic coming from noise !

b) Review on OpAmps : +Vcc + G0 - VS = G0 * (V+- V-) V+ -Vcc V- With G0 very high (G0 ~ 105 ) In open loop :

Consequently, the output is stable
Elements of the data acquisition system OpAmps are never used in open loop to realize a linear amplifier. In fact, the gain is very high such that saturation occurs for a very weak difference in input voltage (for example noise, …). Moreover, this gain varies with temperature and voltage supply (VCC), which make it difficult to obtain a stable output voltage. In closed-loop : Add of a feedback on the inverting input Gain depends on resistor values of the circuit Consequently, the output is stable

The most known OpAmps linear amplifiers :

c) Differential amplifier (Diff Amp): Used to amplify the difference between two input voltages Difference in input voltage Output voltage : V+ V- AD is the differential gain Ideally, AD is supposed constant, independent of the amplitude and the frequency of the input signals

Interest of differential amplification Differential amplification eliminates parasitic which are common to the two inputs Engineers usually try to get a differential voltage at the output of a sensor

Examples of parasitic eliminated by the differential amplifier : EM waves Sensor V+ V- Ampli VS VD + - Leakage current (ground potential) Non-linearity of the amplifier In practice, other parameters affect the output of the amplifier, such as : The frequency of signals Input and output impedances Linearity These parasitic are not completely eliminated

Common mode voltage : For a differential amplifier, we define the common mode voltage Vc as the voltage common to both inputs VA and VB and which doesn’t contain an information. Thus : The voltage measured by the sensor (intelligence or information signal) is the differential voltage : VD = V+ − V- Expression of the output voltage of the amplifier when taking into account the common mode voltage : With : Ad differential gain Ac common mode gain Response in differential mode (ideal) Response in common mode (parasitic)

Find us Elements of the data acquisition system
Ex 1 : Differential amplifier Find us For an ideal amplifier : us = 0 mV

Ex 2 : Differential amplifier Find us For an ideal amplifier : us = 10*(-20 mV) = -200 mV

Ex 3 : Differential amplifier Find us For an ideal amplifier : us = 10*(-20 mV) = -200 mV Conclusion : the common mode voltage could introduce high error to the response of a differential amplifier

For evaluating the capability of a differential amplifier to eliminate (reject) the common mode voltage, we define a factor called the : In dB : For the previous example : 46 dB is relatively low (the output voltage was dependent of the common voltage for the previous example) in practice, a CMRR value greater than 80 dB is required The greater the CMRR, the better is the amplifier

Basic structure for a differential amplifier Prove that :

If R2 = R4 and R1 = R3, then : But : AD = R4/R3 and AC = 0 CMRR = +∞ Example :

In practice, because of tolerances, the resistors are not exactly equal and AC ≠ 0 : Example : Find Ad , AC and the CMRR ?

Numerical Example : Conclusion : CMRR increases when the tolerances on resistors decrease

Using an IC Diff Amp with minimum tolerance on resistors would be a solution ! But, when we connect the amplifier to the source, the internal resistance of the generator and the resistance of the cable connecting the source to the amplifier will introduce parasitic resistor ԑR1 : ԐR1 UE+

Example : INA 106 (Burr-Brown) CMRR given by the data sheet : CMRR = 100 dB Find CMRR ? Response : CMRR # 87 dB (instead of 100 dB given by the data sheet)

d) Instrumentation amplifier We have seen previously that the internal resistance of the generator and the resistance of the cable connecting the source to the amplifier will introduce resistor mismatch, which decrease the CMRR To solve this problem, we need to design a differential amplifier with a high input impedance Such an amplifier is called Instrumentation amplifier An Instrumentation amplifier is used to amplify a differential voltage coming from sources with high impedance

Basic structure for an instrumentation amplifier The follower’s high input impedance makes negligible source’s resistances r1 and r2

Programmable Gain Instrumentation Amplifier (PGIA) : Widely used in practice Main designers : Analog devices, Texas Instruments, … Symbol : RG is a variable resistor used for tuning the value of the gain

Structure of a PGIA : If R = R’ , R2 = R4, and R1 = R3, then show that : The gain is controlled by RG

Examples : Differential amplifier Differential amplifier Unbalanced Wheatstone bridge : Differential amplifier

Thermocouple : To increase the value of voltage generated, several thermocouples may be connected in series to form a thermopile as shown in the following figure: Use of an OpAmp (non-inverting) because the input voltage is not differential

e) Isolation amplifier : Isolation amplifiers are used in circuits where we have a high risk of excessive common mode voltage (>2kV). Isolation amplifiers have a CMRR > 160 dB Input circuit Ampli The isolation separates grounds of input circuit and Ampli, then, cancel difference in ground potential between them Isolation amplifiers can be of mainly 3 types : - Transformer isolation (mutual inductance) : used at low frequency (<20kHz) and high voltage (>10kV), - Optical isolation (carry the input signal using optical couplers) : used at high frequency (>100kHz) and low voltage (<1kV), - capacitive isolation (a capacitor used to carry the input signal) : low frequency and low voltage

II.3. The analog filter Definition Review on passive filters
Active filters Comparison active filters/ passive filters Synthesis of higher order filters (cascading)

Definition : Filters are widely used in electronic circuits. They are particularly present in telecommunications systems (RF filters) Role of filters : eliminate parasitic signals which interfere with the information signal (intelligence). Parasitic signals are usually called noise. Note : Noise may come from multiple sources : External noise : come from the medium of propagation (cable, wireless, …) Internal noise : generated by passive (resistor) and active (transistor, OpAmp, …) components of the circuit itself Interference between different information signals : that’s why we use different frequencies for uplink and downlink signals, example : satellite link

Transfer function of a filter : A filter can be modeled by an LTI ( Linear Time Invariant) system characterized by his impulse response h(t) : X(t) : input signal y(t) : output signal h(t) : impulse response X(p) = TL (x(t)) Y(p) = TL (y(t)) H(p) = TL (h(t)) : Transfer function

Frequency response : For σ = 0 : H(jω) is called the frequency response of the filter, it’s obtained by taking the Fourrier Transform of the impulse response h(t) H(jω) = FT (h(t)) Complex form Magnitude in dB :

Attenuation Function : used sometimes instead of the transfer function H(p)

Types of filters : ideal filters Lowpass Highpass |H(f)| f fc |H(f)| f fc Bandpass Bandstop |H(f)| f f2 |H(f)| f f2 f1 f1

Real filter : In practice, it’s not possible to realize a Rectangular function (because the impulse response in this case is not causal) : H(f) H(f) Selectivity = slope of the transition between the passband and the stopband fc f fc f Ideal lowpass filter Real lowpass filter Higher selectivity => better filter (filter closer to the ideal)

Specifications of filters : (objective) Lowpass Amax : maximal ripple in the passband Amin : minimal attenuation in the stopband Highpass

Specifications of filters : (objective) Bandpass Bandstop

Steps to synthesize a filter 1 – Calculate the expression of H(P) which satisfies given specifications : We can show that a filter is physically realizable (causal, BIBO stable, …) if it’s transfer function H(p) is a rational function with real and positives coefficients : Roots of N(p) are known as « transmission zeroes » Roots of D(p) are known as « poles » Order of the filter n = order of D(p) Better selectivity but more complex polynomials to realize (compromise between performance and complexity) Higher order

Steps to synthesize a filter 1 – Calculate the expression of H(P) which satisfies given specifications : In practice, There are usual approximations for H(p) : Butterworth, Chebychev, and quasi-elliptic functions are the most known The choice between these functions depends on the specifications imposed on the designer For a given order n : Butterworth : presents the maximal flatness in the passband Chebychev : has better selectivity than Butterworth but presents ripples in the passband Quasi-elliptic : it’s a Chebychev function with transmission zeroes on the frequency axis

Steps to synthesize a filter 1 – Calculate the expression of H(P) which satisfies given specifications : Example : 2nd order Lowpass filter (n = 2) The passband of a Butterworth filter is defined at – 3dB (half-power) The passband of a Chebychev filter is taken at equal-ripple amplitude Normalized frequency

Steps to synthesize a filter 1 – Calculate the expression of H(P) which satisfies given specifications : Example : 2nd order Lowpass filter (n = 2) The transmission zero improve the selectivity near the passband ! Normalized frequency

Steps to synthesize a filter 2 – Design the filter realizing the desired transfer function : The technology to choose for realizing a filter will depend on many parameters such as : the operating frequency, the quality factor (losses), the price, the size and weight, …. The most known technologies are : Passive filters using lumped elements RLC Resonating filters : EM cavities, pizoelectric, Surfac acoustic wave (SAW) filter; … Active filters (using OpAmps) Digital filters : DSP, FPGA, Microcontroller circuits, …

Review on passive filters 1st order Lowpass filter : R vin C vout Cutoff frequency : Bode plot Cutoff frequency Slope : stopband passband

2nd order Bandpass filter : Time domain : Phasor :

With : |Z| is minimal when :

is minimal is maximal Quality factor

ω Higher Q => better selectivity Losses « R » are due to losses in the inductor (winding)

if f0 < 1MHz L should have high value Since, The inductor becomes bulky (mass, size) and introduces much losses In instrumentation, measured signals have in general low frequencies ( f < 1 MHz ), so, they can’t be filtered by traditional LC passive filters (since inductors would be bulky) ! To solve this problem, we use active filters !

Active filters Actives filters are realized using resistors, capacitors, and OpAmps. Active filters have a gain > 1 (0 dB), thus, they achieve filtering and amplification at the same time ! These filters are widely used in data acquisition systems when the frequency is < 1 MHz

1st order Lowpass filter : (inverting) 1st order highpass filter : (inverting)

1st order Lowpass filter : (non-inverting) 1st order highpass filter : (non-inverting)

2nd order lowpass filter : Sallen – Key structure :

Frequency response : Roll-off = -40 dB / dec = 2*roll-of of a first order filter Higher order => better selectivity

Comparison Active filter / Passive filter Active filter Passive filter Frequency domain F < 1 MHz F > 1 MHz DC Supply Quality factor Q Impedance matching Zin infinity and Zout =0 Load the circuit Function achieved Filtering + Amplification Only filtering

Synthesis of higher-order filters : For a filter, the selectivity increases when the order n is higher as follows : Selectivity = -n*20 dB/decade For better performance, we prefer working with higher order filters, but be careful about the size and weight of the filter ! Compromise : Selectivity / Compactness For synthesizing a higher order active filter (n > 3), we will cascade 1st and 2nd order filters ! The transfer function of the higher order filter is then the product of transfer functions of cascaded filters constituting this filter :

Coefficients ai and bi depend on the transfer function to be realized : Butterworth, Tchebychev, Bessel, … Tables for these coefficients can be calculated…

Tchebychev with a ripple ԑ = 0.5 dB
Butterworth Tchebychev with a ripple ԑ = 0.5 dB These coefficients are given for a prototype Lowpass filter (ωc = 1 rd/s) !! To obtain the desired filter at the desired cutoff frequency, we make a frequency transformation (see tutorial…)

II.4. Analog to digital Converter (ADC) and digital to analog converter (DAC) Introduction Sample and Hold circuit ADC DAC

Introduction In order to transform the analog signal at the output of the filter into binary data (digital signal), we need a Sample/Hold (S/H) circuit followed by an analog to digital converter (ADC) . The Sample/Hold (S/H) circuit transform the continuous variations of the signal amplitude into a signal with a limited number of levels. The Analog to Digital Converter (ADC) affects a binary code for each amplitude of the signal at the output of the S/H circuit. Sensor Amplifier filter Sample / Hold circuit ADC

S/H Circuit 1- Definition of sampling : Sampling consists on taking the value of the analog signal at each sampling period (Ts) : The sampling frequency is :

Nyquist–Shannon sampling theorem : With Fmax : The maximal frequency in the frequency spectrum of the analog signal Proof :

Example 1 : Fmax Spectrum of the analog signal Spectrum of the sampled signal fS 2*fS Spectrum of the sampled signal after filtering fS 2*fS

Example 2 : Spectrum of the analog signal fS/2 fS Spectrum of the sampled signal fS/2 fS 2*fS Spectrum of the sampled signal after filtering fS/2 fS 2*fS

2- Definition of holding : Holding is done by keeping constant the value of the sampled signal during the sampling period TS Sample / hold x(t) xSH (t) Ideal case : Holding is essential since it maintains constant the value of x(t) during the conversion time of the ADC (see tutorial)

Phase of memorization of the value of x(t)
Elements of the data acquisition system 3- Real S/H circuit Ts X(t) XSH(t) 2.Ts 3.Ts Phase of memorization of the value of x(t) Time for which we maintain constant the value of x(t). This time should be greater than the conversion time of the ADC : value of x(t) converted by the ADC

Equivalent circuit (closed switch)
Elements of the data acquisition system 4- Basic structure of a S/H circuit Basic elements - Switch (transistor) + control signal - Capacitor (memorization of the sample) - 2 buffer stages (OpAmps) Resistance of the closed switch + output resistance of A1  very weak R  Fast charging  memorization (sampling) input resistance of A2  very high R  Slow discharging  holding A1 A2 X(t) Ron très faible => Tau(charge) très faible => ok car Tsample est faible et on s’approche d’un échantillonneur idéal ! Rch très élevé => Tau(décharge) très grande => le condensateur se décharge très lentement => valeur de la tension maintenue presque constante ! XSH(t) Control signal of the switch Equivalent circuit (closed switch)

ADC : n is called resolution of the ADC n-bits ADC xSH (t) 010101… The ADC will affect to different amplitude values of xSH(t) a binary code of n bits corresponding to a numerical value N N is the value of the quantization level associated with the value of xSH(t0) at a given instant t0 Rule : a voltage xSH(t0) is associated to the number N if : N.q xSH (t0) (N+1).q Where q is called voltage resolution : With FS (full scale) is the voltage range of xSH(t) : difference between the highest and lowest values of xSH (t)

ADC : Example : FS = 10V Note : - For a unipolar ADC : xSH (t) [0 ; FS] - For a bipolar ADC : xSH (t) [-FS/2 ; FS/2]

Study in details for n = 2 :
Elements of the data acquisition system ADC : Study in details for n = 2 : Unipolar ADC x(t) V Quantization levels N Binary code 7.5=3q 3 11 5=2q 2 10 2.5=q 1 01 00 t (s) t (s) t (s)

Study in details for n = 2 :
Elements of the data acquisition system ADC : Study in details for n = 2 : Unipolar ADC x(t) V Quantization levels N Binary code 2.5=q 1 01 t (s) 00 t (s) t (s) -2.5=-q -1 11 -5=-2q -2 10 Two's complement

Review on digital electronics….
Elements of the data acquisition system ADC : Review on digital electronics…. For positive numbers

Review on digital electronics….
Elements of the data acquisition system ADC : Review on digital electronics…. For negative numbers : Two's complement The MSB defines the sign : MSB = 1 for negative numbers MSB = 0 for positive numbers Note : to obtain the Two's complement of a binary code : 1) We inverse all bits 2) We add 1

Default linear quantization (american) :
Elements of the data acquisition system ADC : Default linear quantization (american) : Decision that the quantization level = N.q if N.q X(t) (N+1). q Example of a variable voltage X(t) : X(t) N.q q t 2q 3q 4q 5q 6q 7q Instantaneous error (): X(t) – N.q The Instantaneous error can attain a maximal value of q (voltage resolution )

Default linear quantization (american) :
Elements of the data acquisition system ADC : Default linear quantization (american) : Transfer function of the American ADC : Relation between N and X(t) Bipolar ? X(t) Instantaneous error (): X(t) – N.q The quantization error is in the range : 0 < ε < q X(t)

Centered linear quantization (European) :
Elements of the data acquisition system ADC : Centered linear quantization (European) : Decision that the quantization level = N.q if (N-1/2).q X(t) (N+1/2).q X(t) N.q q/2 t q 2q 3q 4q 5q 6q 7q Erreur instantanée (): Ve – Ve,quantifiée Instantaneous error (): X(t) – N.q

Centered linear quantization (European) :
Elements of the data acquisition system ADC : Centered linear quantization (European) : Transfer function of the European ADC : Relation between N and X(t) Bipolar ? X(t) Instantaneous error (): X(t) – N.q The quantization error is in the range : -q/2 < ε < q/2 X(t)

ADC : Quantization noise : Centered linear quantization (European) : Decision that the quantization level = N.q if (N-1/2).q X(t) (N+1/2).q We can consider that we have a noise voltage Vnoise is added to X(t) whose value is equal to the quantization error X(t) + Vnoise = N.q where -q/ Vnoise q/2 This noise is Random ! It’s power (average of the square value) is : V2noise = Pnoise = q2/12 Note.1 : For the American quantization, we will obtain : V2noise = q2/3 Note.2 : The quantization noise is the most important noise in ADC (higher than thermal noise, …)

Signal to Noise Ratio : SNR
Elements of the data acquisition system ADC : Signal to Noise Ratio : SNR The Signal to Noise Ratio (SNR) for an ADC is defined for a sinusoidal full scale input voltage X(t) by the ratio of the RMS value of the signal XRMS over the RMS value of noise Vnoise,RMS Derivation :

Signal to Noise Ration : SNR
Elements of the data acquisition system ADC : Signal to Noise Ration : SNR Usually, we express the SNR in dB : This value is the maximal value of SNR (only due to quantization error) The SNR of an ADC increases when resolution (n) increases An additional bit to the ADC bring 6 dB to the SNR Note. 1: This formula of SNR is only available for a sinusoidal full scale input voltage X(t) Note. 2: a good acquisition card has an ADC of at least 16 bits SNRdb~98 dB theoretical

Example of an Audio (sound) card
Elements of the data acquisition system ADC : Example of an Audio (sound) card Copyright Creative

ADC : Conversion errors Offset error Output Code 111 110 101 100 011 010 001 000 1 2 3 4 5 6 7 Input Voltage (*q) Ideal transfer characteristic Actual transfer characteristic Shift between the ideal and the real transfer functions This error is equal to the value of the inout voltage when the output digital code is 0 (code 000) Affects all codes by the same amount of error -> Can be easily compensated For this example : offset ≈ 2.q

ADC : Conversion errors Gain Error Deviation in the line passing through centers of quantization levels Error due essentially to offset in the reference voltage value of the ADC (reference voltage presented later)

ADC : Conversion errors Consequences Offset error , gain error, and other types of errors : linearity, differential error…, are accumulated at the output of the ADC. To each binary code, the total error is equal to the difference between the edge (ideal) and the actual point These errors introduce random inaccuracy to the binary data, consequently, they decrease the SNR !!

ADC circuits and Techniques
Elements of the data acquisition system ADC : ADC circuits and Techniques Many techniques and circuits exist to implement ADC. Each Technique has advantages and drawbacks. The main characteristics we look for in an ADC are : Accuracy Cost Time of response … Depending on these characteristics, we choose the circuit or technology of implementation for the ADC :

DAC : Principle : Digital to analog conversion (DAC) consists on transforming a binary data (0 and 1) into an analog signal (voltage, current). The analog voltage vout take 2n different values : Vout = N.q = (bn-1 . 2n-1 + bn-2 . 2n-2 + … + b b0).q With Eref is the reference voltage applied to the DAC for generating the analog voltage at the output (Vout)

DAC : Principle : Transfer function : Example : n = 3 bits Vout Analog output voltage Binary input data

DAC : Principle : The analog voltage at the output of the DAC (Vout) presents some discontinuities, in order to reduce these discontinuities, we use a Lowpass filter, called a smoothing filter. Binary code Analog voltage at the output of the DAC Analog voltage filtered by the smoothing filter Vout Vout(filtred)

DAC : Techniques and circuits : 1st technique : Binary-Weighted Resistors Principle: Summation using OPAmps Use of switches controlled by bits b0 to bn-1 Use of binary-weighted resistors by factor 2 and supplied by Eref Vs = ?

DAC : Techniques and circuits : 1st technique : Binary-Weighted Resistors Drawbacks: necessity of precise values of resistors over a wide range of resistor values (from R to 128.R for a 8-bits ADC) Solution : use of sub-DAC of 4-bits to reduce the range of resistor values (from R to 8R), then, summation of the outputs of sub-DAC’s . Example for n = 8 bits :

DAC : Techniques and circuits : 1st technique : Binary-Weighted Resistors Vs = ?

DAC : Techniques and circuits : 2nd technique : R-2R resistor ladder network Principle: Similar to the previous one but we use only 2 values of resistors : R and 2R Vs = ?

DAC : Techniques and circuits : 2nd technique : R-2R resistor ladder network To find Vout, we use Thevenin :

Instrumentation: Elements of the data acquisition system

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Instrumentation: Elements of the data acquisition system

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