25/09/2014

1

EMC 201 – Measurement and instrumentation

Chapter 4 – Computerized data acquisition systems

Chapter 4 – Computerized data acquisition systems

Outcomes:

At the end of this topic, you should be able to:

1. Represent numbers in computer system

2. Demonstrate basic analog-to-digital conversion

3. Estimate quantization error for in A/D converter

4.1 Introduction

• Computer significantly enhance the process of data acquisition, largely because of their versatility and speed

• Computer manage the acquisition of data from multiple sensors, save the data, manipulate and display the data and make use of the results to perform control

Figure 4.1 Computerized data-acquisition system.

• A multiplexer (or mux) is a device that selects one of several analog or digital input signals and forwards the selected input into a single line.

• A multiplexer is also called a data selector.

http://en.wikipedia.org/wiki/Multiplexer

• A data acquisition system is a system that records the input from one or more sensors.

DAQ unit

Software – Vee programming

4.1 Introduction

25/09/2014

2

• In digital signal transmission, the information in the transducer signal is converted to a series of voltage pulses, called bits, which transmit the information in digital code.

• If the voltage of the pulse exceeds a certain level, the pulse is “on”

• If the voltage is below another level, the pulse is “off”

4.2.3 Representing numbers in computer systems

• Computer represents numbers in base 2 (binary)

• Information is stored in bistable devices called flip-flops, which have possible states, “on” and “off”

• A series of flip-flops are required to represent a number

E.g., 1001 → 9 (base 10)

• Each of flip-flops represents a “bit” of the number

1001

• Computer breaks long binary numbers up into segment of 8 bits, which is know as bytes

• 1 byte = 8 bits = 256 patterns

• Bit, like an atom, the smallest unit of storage

• A bit stores just a 0 or 1

• "In the computer it's all 0's and 1's" ... bits

• One byte = grouping of 8 bits

• e.g. 01011010

• One byte can store one letter, e.g. 'A' or 'x'

4.2.3 Representing numbers in computer systems

See Examples 4.1 and 4.2

• Negative numbers are commonly represented inside computers by a technique known as 2’s complement

• Normal: 4 bits

0000 → 1111 = 0 → 15

• 2’s complement: 4 bits:

0000 → 0111 = 0 → 7

1000 → 1111 = -8 → -1

25/09/2014

3

• 2’s complement technique

–Positive number always starts with 0 (MSB)

–Negative number always starts with 1 (MSB)

• General procedure:

1. Convert the integer to binary as if it were positive

2. Invert all of the bits – change 0’s to 1’s and 1’s to 0’s

3. Add 1 LSB to the final result

• Floating-point numbers are handled by keeping separate track of the two parts of the number, the mantissa and exponent

This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8) = 13.625 in Decimal

http://www.mathsisfun.com/binary-number-system.html

Example: 10.1

The "10" means 2 in decimal,

The ".1" means half,

So "10.1" in binary is 2.5 in decimal

• For communication purpose, the binary codes are used to represent specific characters

• For example, American Code for Information Interchange (ASCII)

• 8 bits code used to represent 256 characters

• ASCII are used to transfer information and not useful for arithmetic operations.

4.3.2 Basics of analog-to-digital converters

• Analog signal is a continuous signal representing physical measurement.

• Digital signal is a discrete time signal generated by digital modulation to represent an analog signal.

• The analog-to-digital (A/D) converter (ADC) is the device to convert the analog transducer signals into the digital code

• The actual digital coding scheme used to represent an analog signal (e.g. voltage) is well defined in a particular situation, but not universal

• The digital representation is a code that related to the analog transducer output but does not describe the output exactly.

25/09/2014

4

• Example:

Bulb 1: on when Vs > 5.0 V

Bulb 2: on when Vs – V1 > 2.5 V

Source Bulb 1 Bulb 2 Digital

representation

V < 2.5 off off 00

2.5 ≤ V < 5.0 off on 01

5.0 ≤ V < 7.5 on off 10

7.5 ≤ V on on 11

• The output of ADC has 2N possible values where N is the number of bits used to represent the digital output.

• Examples:

1 bit has 2 (21) output states

2 bits has 4 (22) output states

8 bits has 256 (28) output states

• Three primary characteristics of an ADC

1. Number of bits

2. Input range

3. Conversion speed

• Number of bits – the greater the number of bits the greater the number of possible states leads to the higher accuracy of the digital output representing the analog output

• Input range – the range of analog input voltages over which the converter will produce a representative digital output

• Input voltages outside the range will not produce a meaningful output → saturation

– Mistake in input range selection

– Cannot be estimate through error analysis

– Input voltage must be ensured within the usable range

• Unipolar input range – responds to either “+” or “-” input,

E.g. 0 → 5 V, or 0 → -10 V

• Bipolar input range – responds to both “+” and “-” input

E.g. ± 5 V, or ± 10 V

25/09/2014

5

Unipolar single-slope integrating converter

• Fixed reference voltage is used to charge an integrator at a constant rate

• The integrator output voltage will increase linearly with time

• A digital clock (counter) is started at the same time that charging is begun

• The integrator output voltage is compared continuously with the analog input voltage using a comparator

• When the integrator voltage exceeds the analog input, the counter is stopped and the count of the digital clock is the digital output

• See example 4.4: Unipolar single-slope integrating converter

Figure 4.5 Ramp A/D converter process.

• Bipolar converters use one of two common codes

–offset binary • Like simple binary except that for bipolar converters,

the output code of zero corresponds to the lower end of the input range instead of an input of zero

–2’s complement binary • Starts with a binary number on 2N/2 at the lower end of

the range, has a value of zero in the center of the input range, and rises to 2N/2 -1 at the upper end of the range

Decimal representation -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Offset binary system 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

2’s complement binary system 1000 1001 1010 1011 1100 1101 1110 1111 0000 0001 0010 0011 0100 0101 0110 0111

Vrl Vru 2N/2 - 1 2N/2

Figure 4.7 Formulas to estimate A/D converter digital output.

4.3.2 Basics of analog-to-digital converters

• See Examples 4.5 and 4.6

25/09/2014

6

• ADC subjected to number of errors

• Systematic errors: linearity, zero and sensitivity (gain) errors

–Also subjected to thermal-stability effect

• Random errors: resolution error (uncertainty), also know as quantizing error.

𝑄𝑢𝑎𝑛𝑡𝑖𝑧𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟 = ± 0.5 𝐿𝑆𝐵

Translated into input units

𝐼𝑛𝑝𝑢𝑡 𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑒𝑟𝑟𝑜𝑟 = ±0.5𝑉𝑟𝑢 − 𝑉𝑟𝑙

2𝑁 𝑣𝑜𝑙𝑡𝑠 4.1

• If the input signal is varying rapidly, ADC will cause an error due to aperture time – the time required to convert the input signal

• To minimize this error, an additional device (sample-and-hold device) is needed to read the input value very rapidly (1.5µs or less) and hold for the conversion

4.3.3 Practical of analog-to-digital converters

• See Example 4.8

Figure 4.8 Graphical description of the method of successive approximations for a 4-bit A/D converter. Based on Franco (2002).

• Interval-halving technique is employed in successive-approximations converter.

• A series of known analog voltages are created and compared to the analog input voltage

• In the 1st trial, a voltage interval of one-half the input span is compared with the input voltage

• The comparison determines whether the input voltage is in the upper or lower half of the input range

25/09/2014

7

• If the input voltage is in the upper half of the range, the LSB is set to 1; else it is set to 0

• This process is repeated with an interval half the width of the interval used in the 1st trial to determine the second MSB and so forth until the LSB is determined.

• For N-bit converter, only N comparisons have to be made

4.3.4 Digital-to-analog converters

• Some devices operate on the basis of an analog input voltage – computer digital signals must be converted to analog signals.

• For analog device with simply on-off operation, a digitally controlled relays can be used

• If the analog device requires proportional control, a digital-to-analog converter (D/A converter or DAC) is needed.

• The resulting analog output voltage will be proportional to the digital input number.

• A/D converter is specified by

1. number of input bits,

2. the analog output range

3. the conversion speed

4. number of digital codes

Figure 4.12 Digital-to-analog converter. (Based on Turner, 1988.)

Problems 4.30

An 8-bit digital-to-analog converter has an output range of 0 to 5 V. Estimate the analog voltage output if the input is simple binary and has the decimal value of 30.

Learning points

1. What is LSB? What is MSB?

2. What is the difference between ‘bit’ and byte’?

3. Representation of negative number using 2’s-complement binary technique

4. Estimate A/D converter digital output

5. Simulation of successive approximation converter for A/D conversion

25/09/2014

8

Tutorials

• Problems (Chapter 4, pages 109 - 111)

4.6, 4.10, 4.12, 4.17, 4.22,

4.24, 4.31, 4.32, 4.34