Digital Data Acquisition Today

Today



Digital Data Acquisition

 Theory & Practice

Terminology pinpoint

 “probe”:

external part of sensor or transducer, usually handheld

 “sensor”:

element of the transducer directly affected by the measurand

 “transducer”:

device that provides an output quantity having a relationship with the quantity of the measurand

 “measurement instrument”:

device intended to be used to make measurements, standalone or in conjunction with any other device

 “measurement system”:

complete set of measuring instruments and any other equipment needed to carry out specified measurement

 “measurement chain”:

series of element of measuring systems that constitutes the path from the input to the output

Why digital?

 Low noise sensitivity

 High accuracy at low cost

 Automatic computation made easier

 Lossless data manipulation, recording, transmissition and reproduction possible

Digital Data Acquisition

The big issue with digital conversion:

a continuous value is made discrete

 In amplitude (Y axis issues)

 Resolution

 Saturation

 In time (X axis issues)

 Aliasing

 Leakage

 Frequency resolution

Digital Data Acquisition

Analog Digital conversion:

-

quantization:

-A continuous value is compared with a series of fixed, discrete intervals (states)

-

encoding:

-The interval mean value is converted into a digital, usually binary, chain of elements

Digital Data Acquisition

Binary representation:

 Data type length = N bit

 Binary encoding = O / 1

Having only two states possible per element allows for very robust handling and trasmission systems since the diffence between states can be high and electronics is simple and cheap.

Digital Data Acquisition

DIGITAL RESOLUTION

Having N bit data length  2^N different states 3 bit  2³ =8 different states (1 byte = 8 bit)

Digital Data Acquisition

8 bit  2⁸ =256 states 10 bit  2¹⁰ =1024 states 12 bit  2¹² =4096 states 14 bit  2¹⁴ =16384 states 16 bit  2¹⁶ =65536 states

AD converter transfer function is not linear: output = 2^N states

input = continuous value

Digital Data Acquisition

input

output

Resolution = minimum variation of the input quantity that can be detected by the AD converter.

It is equal to the value of the least significant bit (the smallest one)

LSB=“least significant bit”

1 LSB = FS / 2

Digital Data Acquisition

Resolution depends on both the full scale input of DAQ converter and bit length of data field

Es: FS=10 V N=3 bit LSB=1.25 V FS=10 V N=8 bit LSB=39 mV FS=10 V N=12 bit LSB=2.44mV

n

FS resolution FS

2

min max





Digital Data Acquisition

Digital Data Acquisition

Signal 3 bit 5 bit

Resolution is an uncertainty contributor:

with a uniform distribution of LSB/2 half width

If signal amplitude is A « FS

relative uncertainty goes up 

eg: FS = 10 V A=0.9 V N=8 bit u(V)=39 mV

Workaround:

amplify A to reduce relative uncertainty

Digital Data Acquisition

Input amplification: used to amplify input signal, usually with and adjustable gain G before the AD conversion to adapt the converter full scale input to the signal expected from the transducer

Relative uncertainty coming from resolution is minimized in this way

A(t)

T G A/D

Digital Data Acquisition

SIGNAL SAMPLING

FREQUENCY ISSUES (X axis issues)

Digital Data Acquisition

SAMPLING:

Conversion of a time continuous value into a chain of values

V

(t_i , V_i) i=1,... N t

t V

Digital Data Acquisition

Both V amplitude and it’s time coordinates are discrete values depending on ADC capabilities and configuration SAMPLING TIME t_C = t_i - t_i-1

SAMPLING FREQUENCY f_C = 1 / t_C

t V

t_i-1 t_i t_i+1

Digital Data Acquisition

With sampling frequency can be used to represent a signal without altering it?

t V

t V

both OK, but somehow different

Digital Data Acquisition

If sampling frequency is too low a problem with frequency representation can occurr: we have “aliasing”

t V

Sampling signal is no longer recognizible, ad its frequency seems lower than the original one.

Digital Data Acquisition

The issue of aliasing is related to the ratio between sampling frequency f_S and signal frequency f_A

f_S < 2 f_A  “aliasing” occurs

f_S > 2 f_A

f_S = 2 f_A

f_S < 2 f_A

Digital Data Acquisition

f_C = f_S

Singular condition

It’s easier to look at the issue by considering the frequency domain...

f original signal

f apparent signal

f_C

f_C/2 2f_C

45°

Digital Data Acquisition

Nyquist-Shannon theorem:

if a continuous signal with a top limited bandwith contains only

components with frequency up to f

therefore a coherent

representation could be achieved bu a sampling frequency f

> 2 f

Digital Data Acquisition

f

= 1 / t

f

= 1 / T

being f

> 2f

 ^t

^{< T}

^{/ 2}

We require at least two samples for each half period...

Digital Data Acquisition

Aliasing can be interpreted as a leftward translation in the frequency domain,

therefore can lead to misinterpretations

Digital Data Acquisition

To avoid aliasing:

- a higher sampling frequency can be required - a lowpass filter can be inserted before ADC anti-aliasing filter:

a lowpass filter has a cutoff frequency equal to nyquist frequency

f f_S / 2

Digital Data Acquisition

DAQ Boards are defined by:

 Maximum sampling frequency (or minimum s.time)

 Input channels available (number and setup)

 ADC resolution (in bit)

 Input range (Full scale input and minimum value)

Eg: NI USB-6009

 48 kS/s

 4 Differential / 8 Single-Ended

 14 bit differential / 13 single-ended

 ±20V, ±10V, ±5V, ±4V, ±2.5V, ±1.25V, ±1V

Digital Data Acquisition

Acquisition task itself has different properties:



Sampling frequency



Observation time



Input range Eg:



150 Hz



5 s



±4V

Digital Data Acquisition

All other relevant properties are connected with these and ADC resolution