isat 300 computer-based instrumentation (part 2) sampling and a/d converters 11/14/01

ISAT 300

Computer-Based Instrumentation (part 2)

Sampling and A/D Converters

11/14/01

Sampling (In the context of polling)

•Filter input first

Sampling (In the context of polling)

•Then sample

Sampling of Time-Varying Signals (Measurands)

• When using a computerized data acquisition system, measurements are only made at a discrete set of times, not continuously.

• For example, a temperature or voltage reading (called a sample) may be taken every 0.1 s or every 2 min, and no information is taken for the time periods in between the samples.

Sampling of Time-Varying Signals (Measurands)

a) time-varying signal

(e.g., voltage)

b) signal being sampled

c) the sampled points

(dots)

d) signal can be reconstructed by connecting the dots

Sampling of Time-Varying Signals (Measurands)

• The rate at which measurements are made is known as the sampling rate, expressed in samples/sec or Hz.

• Incorrect selection of the sampling rate can lead to misleading results.

The problem of aliasing

10 Hz inputsampled at11 Hz

Outputlooks like1 Hz !

The problem of aliasing (continued)

10 Hz inputsampled at9 Hz

Outputlooks like1 Hz

The problem of aliasing (continued)

10 Hz inputsampled at8 Hz

Outputlooks like2 Hz

The problem of aliasing (continued)

10 Hz inputsampled at12 Hz

Outputlooks like2 Hz

The alias frequency

10 Hz inputsampled at11 Hz

Outputlooks like1 Hz

actualsamplealias fff

When does aliasing happen?

10 Hz inputsampled at11 Hz

Outputlooks like1 Hz

actualsample f2f

Another pathology

10 Hz inputsampled at5 Hz

Outputlooks like0 Hz (dc)

N

ff actual

sample

Beware if

Avoiding aliasing

To avoid aliasing, sample your signal at greater than twice the maximum frequency of interest. This is a minimum -- 10 X the maximum frequency of interest would be better.

Another way to state this rule is the Nyquist criterion:

see""can you frequency maximum 2

ff s

N

The A/D converter--produces binary numbers

A one-bit A/D converter

Vin

Vin > 5 V output = on “1”

Vin < 5 V output = off “0”

InputOutput

A two-bit (unipolar) A/D converter

10.0 V

7.5 V

5.0 V

2.5 V

0 V0d

1d

2d

3d

N = 2

•Output has 2N possible values (error on page 78?)

Input Output

• Range?

• Span?

A two-bit (unipolar) A/D converter

10.0 V

7.5 V

5.0 V

2.5 V

0 V0d

1d

2d

3d

N = 2

(Vru - Vrl) / 2N

•How big is each input bin?

Input Output

Input resolution error = Quantization error

10.0 V

7.5 V

5.0 V

2.5 V

0 V0d

1d

2d

3d

N = 2

0.5 (Vru - Vrl) / 2N

Sampling and A/D Conversion

a) An analog signal has been sampled and then converted to digital (2’s complement).

b) This quantization results in error.

Saturation

10.0 V

7.5 V

5.0 V

2.5 V

0 V0d

1d

2d

3d

N = 2

Vin = 12 V

Input

Output

A two-bit (bipolar) A/D converter

5.0 V

2.5 V

0.0 V

- 2.5 V

- 5.0 V

0d

1d

-1d

-2d

N = 2

0.5 (Vru - Vrl) / 2N

Input Output (2’s complement)

Choosing an A/D converter--resolution

National Instrumentsmodel 16E-4

National Instrumentsmodel 16XE-50

12 bits

16 bits

Choosing an A/D converter--speed

National Instrumentsmodel 16E-4

National Instrumentsmodel 16XE-50

500 kS/s

20 kS/s

(kiloSamples/second)

Choosing an A/D converter--input range

National Instrumentsmodel 16E-4

National Instrumentsmodel 16XE-50

10 V

10 V

Calculating the digital output

• To estimate the digital output of an A/D converter, see page 81.• E.g., for a simple binary A/D converter:

N

rlru

rlinO VV

VVD 2int

Vin = analog input voltageVru = upper value of input rangeVrl = lower value of input rangeN = number of bitsDo = digital output (as a decimal number!)

Calculating the digital output

N

rlru

rlinO VV

VVD 2int

Example: 8-bit, simple binary A/D converter

Range is 0 to 5V. Input is 3.15V. Find output.

V145.3256

V 5161

0001101016128.161int256V 5

V 15.3int

V 5

2562 that so 8

bd

N

O

rlru

D

VV

N