Sistemas de Aquisição de Dados

Sistemas de Aquisição de Dados

Mestrado Integrado em Eng. Física Tecnológica 2020/21

Aula 2

Sistemas de Aquisição de Dados MEFT 2020/21

Data Acquisition: “Sampling the World”

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Data acquisition is the process of sampling signals that measure real world physical conditions and converting the resulting samples into digital numeric values that can be manipulated by a computer.


Very Simple DAQ System

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Record/Measuring Temperature

Sample Rate= 1 Sample per Second


Another Example: “Gamma Particle”

The components of data acquisition system include: •Sensors that convert physical parameters to electrical signals. •Signal conditioning circuitry to convert sensor signals into a form that can be converted to digital values. •Analog-to-digital converters, which convert conditioned sensor signals to digital values.


Extreme Example:CERN CMS Detector

5

CMS Collision Analisys

DAQ SYSTEM

Sistemas de Aquisição de Dados MEFT 2020/21 6

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Tokamak ITER CODAC

7


Typical Components of Small Data Acquisition Systems

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5.1 A/D ConversionVoltage measurement during data acquisition relies on a processknown as analog-to-digital conversion (often abbreviated as A/D or A-to-D). An analog input board contains an A/D converter and supportcircuitry (Figure 5-1), which conditions and digitizes the incomingvoltage. The following list summarizes the individual circuit stages andoperation of a typical complete A/D circuit. Specialized analog inputboards may depart from this description, with multiple A/D convert-ers, large FIFO buffers, circular buffers, triggering, or other features.

• Signal conditioning (optional)

- Sensor excitation

- Filtering

- Input protection

• Multiplexer (selects a channel on multi-input A/D boards)

• Programmable instrumentation amplifier (applies gain)

• A/D converter (digitizes the signal)

• FIFO buffer (temporarily stores measurement data)

• Control circuitry (retrieves data from FIFO buffer)

Figure 5-1. Typical A/D converter and associated circuitry

5.1.1 A/D Resolution and SpeedThree of the most important specifications involved in choosing ananalog input board are A/D converter resolution, accuracy, and speed.These specifications and other A/D characteristics are interrelated,because higher performance in one area may come at the expense ofperformance in other areas. For example, high speed and high resolu-tion are usually mutually exclusive to some degree, and achieving both

- SECTION 5

InputProtection Multiplexer

InstrumentationAmplifier

ChannelSelect

GainSelect

CTRLControl

A/DConversion

Data

Data

Bus

A...

FIFO

Signal Conditioning: •Protection •Amplification (Unipolar/Differential) •Isolation •Filtering •Multiplexing (MUX) •Sampling and Hold (S&H)

Sensors


Example of Analog Circuits (Signal Conditioning)

9

Refer to “Electronic Instrumentation” Course

BufferDifference

Adder

Measure Resistance

Differentiator Integrator


Signal Conditioning IIInstrumentation amplifier

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Use: Precise measurements and Low Noise Input Circuit to ADC High Input Impedance High Common Mode Rejection (CMRR) Low Offset Output Voltage


Simple, Robust and very

stable. No power needed

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Signal Conditioning IIIInput filters (passive)

Sistemas de Aquisição de Dados MEFT 2020/21 12

Example: Sallen-Key Low Pass Filter Note: Switch “Rx” <->“Cx” and get a

“High Pass Filter”

Signal Conditioning IIIInput filters (passive)


The Data Converter Interface

13

Introduction

Boris MurmannStanford UniversityStanford University

[email protected]

Copyright © 2012 by Boris Murmann

B. Murmann 1EE315B - Chapter 1

Motivation (1)

This course

A/DSignal

This course

Digital Processing

A/D

D/A

Signal Conditioning

Signal

Analog Media and

Transducers D/A g

Conditioning

Sensors, Actuators, Antennas, Storage Media, ...



Data Converters

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Overview

• We'll fist look at these building blocks from a functional, "black box" perspective– Refine later and look at implementations


p

Uniform Sampling and Quantization

• Most common way of performing A/D conversionconversion– Sample signal uniformly in time– Quantize signal uniformly in

lit damplitude

• Key questions– How much "noise" is added dueHow much noise is added due

to amplitude quantization?– How can we reconstruct the

signal back into analog form?signal back into analog form?– How fast do we need to sample?

• Must avoid "aliasing"


A/D Conversion

D/A Conversion


The Data Conversion Problem

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Sampling, Reconstruction, Quantization

Boris MurmannStanford UniversityStanford University

[email protected] © 2012 by Boris Murmann


The Data Conversion Problem

• Real world signalsg– Continuous time, continuous amplitude

• Digital abstractionDi t ti di t lit d– Discrete time, discrete amplitude

• Two problems– How to discretize in time and amplitudeHow to discretize in time and amplitude

• A/D conversion– How to "undescretize" in time and amplitude

• D/A conversion


• D/A conversion

• Real world signals – Continuous time, continuous amplitude

• Digital abstraction – Discrete time, discrete amplitude

• Two problems – How to discretise in time and amplitude ? A/D conversion – How to "undescretise" in time and amplitude D/A conversion


ADC: “Double Discretisation"

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FUNDAMENTALS OF SAMPLED DATA SYSTEMS

2.2 SAMPLING THEORY

2.23

SECTION 2.2: SAMPLING THEORY

Walt Kester

This section discusses the basics of sampling theory. A block diagram of a typical real-

time sampled data system is shown in Figure 2.25. Prior to the actual analog-to-digital

conversion, the analog signal usually passes through some sort of signal conditioning

circuitry which performs such functions as amplification, attenuation, and filtering. The

lowpass/bandpass filter is required to remove unwanted signals outside the bandwidth of

interest and prevent aliasing.

Figure 2.25: Sampled Data System

The system shown in Figure 2.25 is a real-time system, i.e., the signal to the ADC is

continuously sampled at a rate equal to fs, and the ADC presents a new sample to the

DSP at this rate. In order to maintain real-time operation, the DSP must perform all its

required computation within the sampling interval, 1/fs, and present an output sample to

the DAC before arrival of the next sample from the ADC. An example of a typical DSP

function would be a digital filter.

In the case of FFT analysis, a block of data is first transferred to the DSP memory. The

FFT is calculated at the same time a new block of data is transferred into the memory, in

order to maintain real-time operation. The DSP must calculate the FFT during the data

transfer interval so it will be ready to process the next block of data.

Note that the DAC is required only if the DSP data must be converted back into an

analog signal (as would be the case in a voiceband or audio application, for example).

There are many applications where the signal remains entirely in digital format after the

initial A/D conversion. Similarly, there are applications where the DSP is solely

responsible for generating the signal to the DAC. If a DAC is used, it must be followed

by an analog anti-imaging filter to remove the image frequencies. Finally, there are

LPF

OR

BPF

N-BIT

ADCDSP

N-BIT

DAC

LPF

OR

BPF

fa

t

fs fs

AMPLITUDE

QUANTIZATIONDISCRETE

TIME SAMPLING

fa

1

fs

ts=1

fs

ts=


ADC Uniform Sampling and Quantization

17

Overview

• We'll fist look at these building blocks from a functional, "black box" perspective– Refine later and look at implementations


p

Uniform Sampling and Quantization

• Most common way of performing A/D conversionconversion– Sample signal uniformly in time– Quantize signal uniformly in

lit damplitude

• Key questions– How much "noise" is added dueHow much noise is added due

to amplitude quantization?– How can we reconstruct the

signal back into analog form?signal back into analog form?– How fast do we need to sample?

• Must avoid "aliasing"


• Most common way of performing A/D conversion: – Sample signal uniformly in time – Quantize signal uniformly in amplitude

• Key questions 1– How much "noise" is added due to amplitude quantization? 2– How can we reconstruct the signal back into analog form?

3– How fast do we need to sample? Must avoid "aliasing"


What is Aliasing ?

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fsig=101kHz

fsig=899 kHz

fsig=1101 kHz

All sampled signals are equal!


How to describe time discretisation using Math? “Dirac Pulses”

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X

Dirac CombSignal

=

f(t) �T =n=⇥�

n=�⇥�(t� n · T ) fa(t)

fa(t) = �T · f(t)

f(t0) =� ⇥

�⇥f(t)�(t� t0)dtBy definition of Delta “function”

“Sampled” signal (continuous time)

Sampled Signal

X =


With analog signals when we know the spectrum we use the “Fourier Transform”

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FT Properties:

1) If f(t) is Real F (�w) = F �(w) (Symmetry of FT)

f1(t) ⇤ f2(t) TF�⌅F1(w) · F2(w)

(Inverse) f1(t) · f2(t) TF�⌅12�

F1(w) ⇤ F2(w)

F (w) =� ⇥

�⇥f(t)e�iwtdt� f(t) =

12�

� ⇥

�⇥F (w)eiwtdw

2) Convolution FT

g(t) = f1(t) ⇥ f2(t) ⇤� ⇥

�⇥f1(�)f1(t� �)d�


Fourier Transform of the Sampled Signal

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fa(t) = �T · f(t) TF⇤⌅12⇥

TF{�T }(w) ⇥ F (w)

Fa(w) =n=⇥�

n=�⇥�(w � n · WT ) ⇤ F (w) =

⇥ ⇥

�⇥

n=⇥�

n=�⇥�(⇥ � n · WT ) · F (w � ⇥)d⇥

Fa(w) =n=⇥�

n=�⇥F (w � n · WT )

w

|F (w)|

WT�WT wWT�WT

......* =

2WT

|Fa(W )|


Discrete-time Fourier transform DTFT & DFT

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X2⇡(w) =1X

n=�1x[n]e�iwn w normalised frequency

in radians per sampleDTFT

DFT

Pick a arbitrary number of samples (N), and sample X(w)

xN [n] ⌘1X

m=�1x[n�mN ]

Xk =1X

n=�1x[n]e�i2⇡ kn

N for k = 0, . . . , N � 1

=X

N

xN [n]e�i2⇡ knN

Xk ⌘N�1X

n=0

x[n]e�i knN x[n] ⌘ 1

N

N�1X

k=0

X[k]eiknN , k, n 2 Z


Frequency AliasingThe frequencies

fsig and N· fs ± fsig (N integer), are indistinguishable in the discrete time domain


Nyquist–Shannon sampling theorem

A real signal with a frequency range DC(0Hz) -> Fmax must be sampled at a minimum frequency Fsamp ≥ 2⋅Fmax

The frequency spectrum is “periodized” by the timed sampling process, and it can overlap: (period WT=2π/Tsampling) - “ALIASING”

In a more general way, for real signals with frequency spectrum limited to an bandwidth ∆F= Fmax - Fmin , the minimum sampling frequency, is n: Fa ≥ 2⋅ ∆F

To avoid “ALIASING” for signals with an unknown frequency spectrum we need to eliminate frequency components ≥ Fsamp / 2 by Analog Filters before sampling

Jim CampbelL Portrait of a Portrait of Harry Nyquist (2000)

12 x 16 (192) LEDs


Sampling Baseband bandwidth signals. (Bandwidth equals the upper frequency)

• In order to prevent aliasing, we need fsig,max< fsamp /2

• The half of sampling rate fNyq= fs 2 is called the Nyquist rate.

• Two possibilities:

• Sample fast enough to cover all spectral components, including "parasitic" ones outside band of interest. (eg. harmonics)

• Limit fsig,max through filtering, e.g. Anti-Alias


Ideal Brick Wall Anti-Alias Filter

• But there are no Ideal Filters…


Practical Anti-Alias Filters


Anti-Aliasing Analog Filters

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Signal with unknown Spectrum Bandwidth

Correctly Sampled signal

PRATICAL ANALOG! Filter

ADC

LP Filter

|F (w)|

A=1

A=0

Ideal Filter

fs/2fs/2


Bibliography

• Analog-to-Digital Conversion, Second Edition, Marcel J.M. Pelgrom, Springer 2013

• Data Conversion Handbook, Chapter 2 Analog Devices Inc., 2004

• http://www.analog.com/library/analogDialogue/archives/39-06/data_conversion_handbook.html

• Data Acquisition and Control Handbook, A Guide to Hardware and Software for Computer-Based Measurement and Control , Keithley http://tinyurl.com/q6okgxs

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