This document discusses analog control systems used with programmable logic controllers (PLCs) and programmable automation controllers (PACs). It describes how analog signals have continuous values between on and off, unlike discrete signals. It then explains that PLCs and PACs use analog input/output modules to interface with field devices that have continuously varying signals, such as temperature sensors, pressure sensors, motors etc. The document provides details on analog signal processing, including analog to digital conversion using ADCs and digital to analog conversion using DACs. It discusses key specifications for analog I/O modules such as resolution, conversion time and settling time.

1. Analog Control

2. Supplemental material
Chapter 12 & 13

3. 3
 Discrete signals only have two states; ON
or OFF.
 Analog signals have an infinite number of
states. It can be totally ON, totally OFF or
anything in-between.
 PLC’s/PAC’s use analog I/O modules in
applications where the field device signals
are continuously varying.
Overview

4. Analog Signal
Continuous Signal
Time
MeasuredorCommandSignal

5. Analog I/O Devices
 Flow meters
 Humidity
transducers
 Load cells
 Potentiometers
 Pressure sensors
 Temperature
sensors
 Vibration
transducers
 I/P valves
 Motor controllers
 Fans/Blowers
 Heaters
 Chart recorders
 Actuators
 Analog meters

6. Analog Input ProcessProcess
Transducer Transmitter ADC
0000000000000000
15 0
Physical
Signal
Low level
Voltage or
Current
Amplified E or I
compatible with
analog input module
Analog
Input
Module
Toprocessor
Computer or PLC or PAC
Storage register

7. 7
Most common
 4 to 20mA
 0 to 10Vdc
 ±10Vdc
Less common
 0 to 1Vdc
 0 to 5Vdc
 1 to 5Vdc
 ±5Vdc
Analog Input Rates

8. Analog Output
Process
DAC
Analog
Output
Module
0000000000000000
11 0
Transducer
From
Processor
Storage register
in processor
Voltage or
current output
Analog
Signal
From water
reservoir
To water
supply
I/P Valve
Pump

9. 9
Most common
 4 to 20mA
 0 to 10Vdc
 ±10Vdc
Less common
 10 to 50mA
 0 to 5Vdc
 ±2.5Vdc
 ±5Vdc
Analog Output Rates

10. 10
 Analog signals are encoded by
representing them in a binary word, as a
binary number.
 The binary number corresponds to the
value of the analog signal at a given
instant in time.
Analog Signals

11. 11
 Analog input signals are represented in
digital format through the process of
sampling the continuous analog waveform
at regular intervals of time and then
performing an analog to digital
conversion.
 If the sample rate is twice the rate of the
analog signal change, the signal can be
exactly reproduced.
Sampling

12. 12
 The process of assigning a discrete binary
number to each sample introduces an
error known as quantization error.
 Quantization is an unavoidable error
resulting from the difference between the
actual value of the analog sample and the
nearest value encoded by one of the
binary numbers.
Sampling

13. Sampling
http://www.videomaker.com/article/14524/

14. Sampling
http://www.music-production-school.com/pro_tools_software_article.shtml

15. 15
 Analog to Digital Converter (ADC)
 ADC’s are used to interface analog input
signals with digital circuits, PLC’s, PAC’s or
computers.
 ADC’s are essentially a quantizing process,
whereby an analog signal is represented
by discrete states. These states can be
assigned appropriate codes such as
straight binary, BCD, gray code or binary
two’s compliment.
Analog to Digital
Conversion

16. 16
 Assume:
 A straight binary count.
 3-bit output
 Input of: 0Vdc to 1Vdc
 1 𝑏𝑖𝑡 𝐿𝑆𝐵 =
𝐹.𝑆.
2 𝑛
 Where:
 F.S. = Full scale input of the ADC
 n = number of output bits.
3-Bit ACD
D2 D1 D0
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

17. 3-bit ADCDigitalBinaryOutputCount
Ideally QuantizedAnalog Input Volage
3-Bit ADC Analog Voltage Input vs. Digital Bianry Output Count
000
100
011
010
001
111
110
101
1/8 7/83/45/81/23/81/40 1.0 F.S.
1 LSB
NominalQuantized
Value ½ LSB

18. 3-Bit ADC
Input vs. Output
Analog Input
for a 1VDC F.S.
ADC
Analog Input
for a 10VDC
F.S. ADC
Binary Digital
Output
0 0.00 000
1/8 1.25 001
1/4 2.50 010
3/8 3.75 011
1/2 5.00 100
5/8 6.25 101
3/4 7.50 110
7/8 8.75 111

19. 19
 By the previous graph and table the
following should be noted:
 The 3-bit ADC has 2n output states where ‘n’ is
the number of output bits.
 The value of input voltage required to change
the output by 1-LSB is obtained by:
3-Bit ADC
1 𝑏𝑖𝑡 𝐿𝑆𝐵 =
𝐹.𝑆.
2 𝑛 ±
1
2
𝐿𝑆𝐵

20. 20
 Analog input values shown represent the center
point of the analog values for each output word,
with transition points ±½ LSB from the center
points. The quantizing error or uncertainty is thus
½ LSB.
 The MSB (1002) output corresponds to ½ V on
the input which is half of the F.S. input range.
The largest output word (1112) corresponds to
7/8 V and F.S.
3-Bit ADC
𝑉𝑜 𝑚𝑎𝑥𝑜𝑢𝑡 = 𝐹. 𝑆 − 1 𝐿𝑆𝐵
or
1 𝑉𝑑𝑐 −
1
8
𝑉𝑑𝑐 =
7
8
𝑉𝑑𝑐

21. 21
 An ADC requires a certain length of time,
called conversion time, to change an
analog signal into the corresponding
digital signal.
 If the analog signal changes during the
conversion time the converter output may
be in error. To prevent this a sample and
hold circuit is used.
Sampling Concepts

22. Simplified Sample
and Hold
Input
Voltage
A1 A2
Electronic
Switch
Switch
Driver
C
Output
Voltage
Common
Sample
Control

23. 23
 Conversion Time
 The total time required to completely convert
an analog input current or voltage to a digital
output. The time is affected by the propagation
delay in the various circuits. It may be
specified as a number of conversions per
second.
 This is one of the most important specifications
to be considered when selecting an ADC.
Converters having more output bits usually
require more time.
ADC Characteristics

24. 24
 Resolution
 The amount of input voltage required to
increment the output by one LSB. The
resolution is determined by the number of
output bits. It is specified in terms of the
number of output bits or as one part per
number of output states. As an example: the
resolution of an 8-bit converter is specified as
either 8-bits or 1 out of 256
1
28 =
1
256
ADC Characteristics

25. 25
 Digital to Analog Converter (DAC)
 Digital systems can be used to transmit analog
signals. This is accomplished by using a DAC
whereby a given digital signal is transformed
into its equivalent analog signal.
 Three categories
 Current output
 Voltage output
 Multiplying type
Digital to Analog
Converter (DAC)

26. 26
 The DAC process can be viewed as finding
the equivalent weight of and object (less
then one unit) with weights in
geometrically proportional units, such as
1/8, 1/4 and 1/2. By using these weights in
various combinations, 8 different
measurements ranging from zero units to
7/8 units can be obtained.
Concept & Transfer
Function

27. 27
 Assume:
 A straight binary count.
 3-Bit output
 Output of: 0Vdc to 1Vdc
 Where:
 F.S. = Full scale input of
DAC
 n = Number of output
bits.
3-Bit DAC
D2 D1 D0
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

28. 3-Bit DAC Output
Voltage vs. Binary
3-Bit DAC Output Voltage vs. Binary Count
0
1/8
1/4
3/8
1/2
5/8
3/4
7/8
1
000 001 010 011 100 101 110 111
Binary Input Count
OutputVoltageChange

29. 3-Bit DAC Input vs.
OUtput
Binary Digital
Input
Analog Output
for a 1VDC F.S.
DAC
Analog Output
for a 10VDC
F.S. DAC
000 0 0.00
001 1/8 1.25
010 1/4 2.50
011 3/8 3.75
100 1/2 5.00
101 5/8 6.25
110 3/4 7.50
111 7/8 8.75

30. 30
 By the previous graph and table the
following should be noted:
 The 3-Bit DAC has eight 2 𝑛 = 8 possible input
combinations 𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑛𝑝𝑢𝑡 𝑏𝑖𝑡𝑠 , ranging
from 0002 𝑡𝑜 1112.
 If the F.S. analog voltage is 1Vdc, the smallest
unit 𝐿𝑆𝐵 001 is equivalent to
1
8
𝑉. No voltage or
step smaller can be identified by this DAC
(resolution).
3-Bit DAC

31. 31
 The MSB 𝑏𝑖𝑛𝑎𝑟𝑦 100 has the equivalent
value equal to
1
2
𝑉 𝑜𝑟 50% 𝐹. 𝑆.
 For the maximum input signal 𝑏𝑖𝑛𝑎𝑟𝑦 111 ,
the analog is
7
8
𝑉, which is
1
8
𝑉 less than
the F.S. value. Therefore:
𝑉𝑜 𝑚𝑎𝑥𝑜𝑢𝑡 = 𝐹. 𝑆. −𝐸𝑞𝑢𝑖𝑣. 𝑉 𝑓𝑜𝑟 1 𝐿𝑆𝐵
Where:
𝑉𝑜 𝑚𝑎𝑥𝑜𝑢𝑡 = 𝑡ℎ𝑒 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑎𝑛𝑎𝑙𝑜𝑔 𝑜𝑢𝑡𝑝𝑢𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
𝐹. 𝑆. = 𝐹𝑢𝑙𝑙 𝑠𝑐𝑎𝑙𝑒 𝑜𝑢𝑡𝑝𝑢𝑡 𝑟𝑎𝑡𝑖𝑛𝑔 𝑜𝑓 𝑡ℎ𝑒 𝐷𝐴𝐶
3-Bit DAC

32. 32
 Settling Time
 The time required, after a code transition, for
the DAC output to reach its final value within
specified limits, (usually ±1/2 LSB). The
settling time of a voltage output DAC is longer
then that of a current output type due to the
extra circuitry to transform current to voltage.
DAC Specifications

33. 33
 The smallest incremental change in output
voltage/current of a DAC.
In the previous example, for a 3-bit DAC
with an output voltage range of 0Vdc to
10Vdc, the resolution is:
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 =
𝐹. 𝑆.
2 𝑛
or
1.25𝑉𝑑𝑐 =
10𝑉𝑑𝑐
23
Resolution