6655_lab_manual_2.pdf

Optoisolator
Fuel Input
Setpoint
+
Temp
Control
-
+
Flow
Control
Valve
Process IN
Process
Flow
Sensor
Process OUT
Temp
Sensor
Introduction
To get the most out of this lab manual it is recommended that students follow
the following process:
1.
2.
3.
4.
Review a PowerPoint presentation about the lab activity.
Observe the lab outcome using LabVIEW
Build, troubleshoot and test the circuit using Multisim
Hardwire, troubleshoot and test the circuit using real devices and
components
5. Compare measurements obtained in Multisim with the hardwired ones
6. Solve a problem applying learned concepts
The LabVIEW files can be open with version 7.1. The Multisim files can be open
with version 7 or higher and are available to instructors. It is recommended that
students create the circuit for each lab in Multisim so they can get proficient in
the use of this software.
This material is based upon work supported by the National Science
Foundation under Grant No. 0411330.
Any opinions, findings and conclusions or recommendations expressed
in this material are those of the author and do not necessarily reflect the
views of the National Science Foundation (NSF).
TABLE OF CONTENTS
Page
LAB 1 – WHEATSTONE BRIDGE …………………………………..…...
4
LAB 2 – SIGNAL CONDITIONING CIRCUIT …………………………… 16
LAB 3 – DIGITAL TO ANALOG CONVERTER (DAC) ……………….. 29
LAB 4 – ANALOG TO DIGITAL CONVERTER (ADC) ……………….. 45
LAB 5 – TEMPERATURE SENSOR …………………………………….. 64
LAB 6 – SCR CIRCUIT ……………………………………………………. 77
LAB 7 – THE INTEGRAL CONTROLLER ……………………………… 89
LAB 8 – DERIVATIVE CONTROLLER …………………………………. 105
LAB 9 – PID CONTROLLER …………………………………………….. 121
LAB 10 – CLOSED-LOOP SYSTEM ………………………………..….. 145
MATERIALS FOR TECH 167 – LAB EXPERIMENTS ……………….. 161
4
LAB 1 – WHEATSTONE BRIDGE
Objectives
1. Build, test, and troubleshoot an application of the Wheatstone bridge to convert
resistance changes to voltage changes using Multisim.
2. Hardwire the Wheatstone bridge of objective 1 and compare the measurements of the
hardwire circuit with the measurements obtained using Multisim.
Preliminary Information
Basically, the Wheatstone bridge is made up of two voltage dividers powered by a dualpower supply or a single source (see figure 1-1). Among the junctions of the voltage
dividers, a galvanometer (a very sensitive current meter) has been connected with the
purpose of monitoring the current flow from one voltage divider to the other.
IL
I1
R1
R3
I3
G
V
I2
R2
Figure 1-1
R4
I4
When DC current doesn’t flow through the galvanometer, we say that the Wheatstone
bridge is balanced and the following is achieved:
I1 R1 = I3 R3
I2 R2 = I4 R4
I1 = I2
I3 = I4
(1)
(2)
(3)
(4)
Replacing equations 3 and 4 in equation 2:
I1 R2 = I3 R4
(5)
Finding I1 in equations 1 and 5:
I1 =
I3 R3
R1
(6)
I1 =
I3 R4
R2
(7)
5
Equating equations 6 and 7:
I3 R3 I3 R4
=
R1
R2
(8)
Eliminating the term I3 and ordering equation 8, we have:
R 1 R3
=
R2 R4
In conclusion, when the Wheatstone bridge is balanced, the following relationship is
established:
R1 R3
=
R2 R4
(9)
The Wheatstone bridge has multiple applications; initially it was used to find the unknown
value of a resistance by means of some modifications to figure 1-1.
R1
V
R3
G
R2
50%
Figure 1-2
Rx
Assuming the values of R1 and R3 are known, and R2 has been replaced by a potentiometer,
we will connect the unknown resistance whose value we want to find in the R4 position (in
this case we will call it Rx).
To find the unknown value, Rx; we follow the following procedure:
1. We vary the potentiometer R2 until the galvanometer shows zero current. In this
condition, we say that the Wheatstone bridge is balanced and we apply equation 9.
2. The R4 label is replaced by Rx in equation 9 and we find the value of Rx.
R1 R3
=
R2 RX
(10)
6
RX =
R2 R3
R1
(11)
With equation 11 determine the value of the unknown resistance.
Notes:
1. The potentiometer and the unknown resistance Rx can be located in any part of
the voltage dividers, being careful to replace them appropriately in equation 9.
2. The values of the known resistances can be the same or different.
The Wheatstone bridge is widely used in electronic instrumentation by substituting one or
more resistances with sensors. When the resistances of the sensors change, we obtain an
output that is proportional to this variation. At the output of the Wheatstone bridge, instead
of the galvanometer, we can connect an amplifier circuit that will allow us to activate a
control system.
Problem Statement
Build a circuit that converts resistance changes to voltage changes. We need to drive a 10
kΩ load and we have only a dual supply of ± 10 V. In addition, we want a gain of 2.2. One
of the resistances is an RTD (Resistance Temperature Detector) that has a nominal
resistance of 150 Ω at 25 °C. Due to product specifications two resistances in the
Wheatstone Bridge (R1 & R2) should be 2.2 kΩ and 1 kΩ.
a. Design the appropriate circuit. Don’t forget to design the interface circuit too.
b. Test the circuit under different RTD values (this is what will happen when the
temperature changes).
Given the design requirements, and the block diagram, the schematic diagram for the circuit
design is shown in Figures 1-3 and 1-4 respectively.
Buffer
Wheatstone
Bridge
Subtractor
Av = 1
Amplifier
Av = 2.2
Buffer
Figure 1-3. Block Diagram
To the
Load
7
VEE
-10V
4
2
U1
741
3
R3
6
7 1 5
VCC
5%
1.0k Ω
R4
10V
VEE
-10V
VCC
2
R6
10V
4
R11
5%
330 Ω
R2
5%
2.2k Ω
2
5%
1.0k Ω
U2
741
3
6
7 1 5
V2
3
R5
5%
1.0k Ω
5%
2.2k Ω
VEE
-10V
4 100nF
IC=0V
U3
741
7 1 5
4
R7
6
C2
VCC 100nF
IC=0V
10V
5%
1.0k Ω
2
U4
741
3
R8
5%
1.0k Ω
6
7 1 5
VCC
10V
VCC
V1
R1
R12
5%
1.0k Ω
VEE
C1
-10V
10V
XMM1
R10
V1
50%
VL = Av (V2 - V1) XMM3
XMM2
V2
VL
5%
1.0k Ω
500Ω
Key=A
Figure 1-4. Schematic Diagram
Circuit analysis
Basically, the Wheatstone bridge is made up of two voltage dividers (R2 - R1 and R11R10) and powered by a single power supply (VCC).
The resistances can have different values, however one of them (in this case R10) is a
variable resistance that simulates the RTD and allows balancing the circuit.
The Wheatstone bridge is balanced when:
R2 R11
=
(1)
R1 R10
Taking into consideration that two of the resistances should have 2.2 kΩ and 1 kΩ, we will
locate them in the positions of R2 and R1 respectively.
V1 = V2
then:
R9
5%
10k Ω
8
The RTD is essentially a temperature dependent resistor with a positive temperature
coefficient. Its value increases when the temperature increases and vice versa.
Potentiometer R10 will simulate the behavior of the RTD.
According to the specifications of the laboratory, at a 25º C temperature the RTD has a
resistance of 150 Ω. This specification will be our reference point for the Wheatstone
bridge. With this resistance value, we calculate the value of R11 using equation (1) in the
following way:
R11 =
(R2 * R10)
R1
R11 =
(2.2 KΩ * 150 Ω)
= 330 Ω .
1 KΩ
Since the reference point is 150 Ω, R10 should be greater than 150 Ω. We’ll use a 500 Ω
potentiometer.
Varying R10, to simulate the temperature variations, the circuit becomes unbalanced,
producing small voltage variations (between points V1 and V2 of the Bridge). These voltage
variations will be amplified by the 741s circuits to activate the 10K Ω load.
U1 and U2 are voltage followers (buffers), it is designed to prevent loading of V1 & V2 by
the following amplifier stage. U3 is a differential amplifier with unity gain and its output is
the potential difference between V1 and V2. The voltage gain of the differential amplifier is
R3
R5
giving by the ratio
or by
R4
R6
Since the voltage gain should be 1, then R3 = R5 and R4 = R6. This can be easily
accomplished by selecting R4 = R6 = 1 kΩ and R3 = R5 = 1 kΩ.
U4 is an amplifier with gain of 2.2 according to the problem requirements. The gain of this
circuit depends on the ratio R12/R7, thus R12 should be 2.2 times greater than R7.
Therefore, if we select R7 = 1 kΩ, then R12 should be 2.2 kΩ.
Notes:
a. Use a linear potentiometer in Multisim and in the hardwired circuit.
b. Choose the potentiometer with a 1% increment in Multisim.
c. Select Vout = VCC – 2 V
If VCC = 10V then Vout,max = 10V – 2 V = 8 V
Therefore, never exceed Vout = 8 V when using VCC = 10V.
9
Procedure/Tasks Using Multisim
1. Build the circuit indicated in Figure 1-4 in Multisim.
2. Adjust R10 (by pressing the A or SHIFT-A keys) until V2 is approximately equal to V1.
When this happens, VL should be approximately equal to 0. Is this correct? Explain.
Make V2 > V1 or V2<V1 and observe the voltage at the load (R9). Complete the following
table with three values of V2 > V1 and three values of V2 < V1.
V1
V2
VL
3. Replace the three 741 ICs by a single quad op-amp such as the LM324AJ. Note that the
LM324AJ has four sections A, B, C and D. Each section shows up on the screen with its
own power supply terminals, pin 4 (+V) and pin 11 (– V). You only need to connect the
respective power supplies to any section: pin 4 should be connected to VCC and pin 11
should be connected to ground.
4. Adjust R10 (by pressing the A or SHIFT-A keys) until V2 is approximately equal to V1.
When this happens, VL should be approximately equal to 0. Is this correct? Explain.
10
5. Make V2 > V1 or V2<V1 and observe the voltage at the load (R9). Complete the
following table with three values of V2 > V1 and three values of V2<V1. Use the same
values you did in step 3.
V1
V2
VL
6. Comparing your answers in steps 5 and 6 with your answers in steps 2 and 3, can you
use a single LM324AJ instead of three 741 ICs?
Questions
1. Is it possible to use a single supply? Why or why not?
2. How can you determine the maximum potential difference between V1 and V2 to
prevent the circuit reaching saturation voltages?
3. If R4 opens, how can you determine the voltage load (VL)? Hint: refer to the
appropriate equation.
4. If the voltage gain is 3.3 instead of 2.2, what modification(s) would you do to the
circuit?
11
Procedure/Tasks – Hardwired Circuit
Now that you are familiar with the Wheatstone bridge using Multisim it’s time to hardwire
the circuit shown in Figure 1-3 using real components. However, before continuing, you are
going to indicate the list of components and the equipment that you need to complete this
task.
List of components
Item #
Equipment
Component Description
Reference
Designators
Quantity
12
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such
a checklist will enable you to minimize errors in the circuit assembly, prevent malfunction,
and consequently reduce damage to components. This checklist should always be used, but
it is not limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For
example, it is not uncommon for IC manufacturers to use different pinouts
between DIP8 and SOIC8 packages for the same part. Sometimes a circuit
designer will layout a schematic using the pinout of a SOIC part and the
person doing the wiring of the circuit might use a DIP part. The consequence
of this is an incorrectly wired breadboard resulting in faulty circuit operation
and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin.
This is especially important when there is high speed digital or high load current
circuit combined with sensitive analog circuit (such as a Wheatstone bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a
tantalum bypass capacitor of 10 - 33μF should be used between power and ground
points where the power supply leads connected to the breadboard. Make sure the
polarity of the capacitor is correct and that its working voltage (WV) is at least 1.5
times the maximum voltage used in the circuit. e.g., the working voltage rating of a
capacitor is 10V; the supply voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback
resistors should be routed from the amplifier’s output pin directly to the input pin.
This helps to reduce the possible amplifier’s feedback loop pick up and amplifies the
unwanted noise.
13
•
All component leads should be kept as short as possible. Additionally, signal paths
from one IC to another should be kept as short as possible to minimize noise pickup.
If a signal path must be long for whatever the reason, ensure it is routed away from
other signal paths to reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all
ground buses and power buses should be terminated at one point. That is, you should
not be able to trace a loop from the ground or power supply connection to the
breadboard to all component connections and then back to the power or ground
source.
•
If it is possible, separate analog and digital power supplies and grounds from one
another. These should be routed back and terminated at the single power and ground
termination point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g.,
LMC555 over a TTL 555), unless the design calls for the high current capacities of
TTL.
The later lab experiments also include this checklist for your reference.
1. Adjust R10 potentiometer until V2 is approximately equal to V1. When this happens,
VL should be approximately equal to 0. Is this correct? Explain.
2. Make V2 > V1 or V2<V1 and observe the voltage at the load (R9). Complete the
following table with three values of V2 > V1 and three values of V2<V1. Try to match
the values you used in Multisim.
V1
V2
VL
14
Questions
1. Are the measurement obtained in the hardwired circuit similar to those obtained in
Multisim? Explain any difference.
2. What difficulties did you encounter in hardwiring the Wheatstone bridge?
Conclusions
After completing the Wheatstone bridge both in Multisim and hardwiring, what are your
conclusions?
15
Advanced Design
If you want to earn extra credit, try the following design.
You are a manufacturing engineer working for an injection molding company. Your
supervisor requests that you design and implement a circuit to measure temperature. The
objective is to measure the environmental temperature in the injection molding machine area
to determine how much it varies over the course of a day. He says these temperature
measurements will vary widely, because he wants to measure ambient air temperature as
well as surface temperature on the outside of the molds being used in the injection molding
machines during the molding process.
Knowns:
1. The temperature range your supervisor wants to measure has large range: anywhere
from room temperature which is ~ 20°C to ~150°C (the maximum surface temp of a
plastic mold during the molding process).
2. Your boss wants to measure to an accuracy of +/-1.0°C. This implies an ideal
resolution of ~0.1°C. (Usually, we want the resolution to be better than the accuracy
we need to measure. Cumulative errors in the sensor & circuit design as well as the
implementation must add up to be less than the desired accuracy in order to meet
performance requirements.)
3. Because of the possible high temperatures measurement, the Wheatstone Bridge
circuit has to be located some distance away from the temperature sensor
4. The environment is an electrically noisy environment, due to large industrial
machines being used.
5. Types of temperature sensors available for implementation: RTD, thermistor, and
thermocouple (TC).
6. Because the environment has a widely varying temperature, use of a stable reference
temperature is not practical.
Unknowns:
1. What kind of circuit is needed for the Wheatstone bridge?
2. What are the component values needed in the circuit?
3. Which temperature sensor is best for this application?
4. How would you properly interface the temperature sensor to the circuit?
16
LAB 2 – SIGNAL CONDITIONING CIRCUIT
Objectives
1. Build, test, and troubleshoot an analog signal conditioning circuit using Multisim.
2. Design an analog signal conditioning circuit to provide a range of desired output
voltages in respond to a certain range of input voltages.
3. Hardwire the analog signal conditioning circuit of objective 1 and compare the
measurements of the hardwired circuit with the measurements obtained in Multisim.
Preliminary Information
The signal conditioning circuit is an electronic circuit that converts signals provided by a
sensor to useful electric signals. These electric signals must meet specific criteria so that
they are correctly interpreted and processed by the rest of the system’s circuitry. The use of
Op-amps allows signal conditioning circuits to be more compact and precise in their
implementations.
Non usable
Electrical
Signal
Physical
Magnitude
Process to
control
Sensor
Signal
Conditioning
Usable
Electrical
Signal
Figure 2-1. Signal conditioning is important in a system of process control.
Signal conditioning carries out one or several of the following actions:
1. Change voltage levels so that they are compatible with the following circuitry.
2. Convert current to voltage. Some sensors, such as the NTC (Negative Temperature
Coefficient) and the PTC (Positive Temperature Coefficient) RTD (Resistance
Temperature Dependent) convert the variations of the process to control resistance
variations. Signal conditioning circuits provide the necessary current that converts a
resistance variation to an appropriate voltage.
3. Linearize and compensate sensor’s non-linear variations. This linearization is the
conversion of non-linear signals into linear signals by using Taylor series.
4. Convert the analog signal to digital signal. The signal conditioning circuit ensures
the analog signal is at levels that are compatible with the analog to digital conversion
17
circuitry. After having transformed the analog signals into digital, we can store their
numerical representations on a memory, process them with an application program,
display them on a monitor, send them through the Internet to another place, or print
them.
5. Convert the analog signal to current signal. It is an industry standard that the control
range is normalized from 4mA to 20mA dc. The minimum value of 4mA is defined as
"zero active" because it offers the advantage of being able to detect an interruption of
the connection between the sensor and the signal conditioning circuit. When the signal
conditioning provides 0 mA at its output, it will be an indication that the sensor is
defective or some other faulty circuit.
6. Eliminate undesired signals such as noise. The elimination of the undesired noise is
carried out with analog filters (i.e., RC, RLC, etc.) or in more challenging applications
with digital filtering.
7. Isolate the sensor. The signal conditioning circuit should isolate the sensor electrically
when the sensed signal contains high voltage pulses that can affect the measurements
and the subsequent circuitry of the system.
8. Multiplex different signals. Multiplexing consists of measuring several signals with a
single measurement device. This is feasible when the signals to measure change slowly,
such as when measuring temperature.
Optoisolator
In some applications, it is not necessary to process the entire range of the sensed signals
through an analog-to-digital converter. Some applications might require only that the sensor
acts as a switch. Therefore, the signal conditioning circuit in this case would consist of an
Op-amp comparator that acts as an analog-to-digital converter of one bit.
The other applications process a complex waveform from a sensor. Therefore, it might be
preferable to capture the energy of the waveform for later processing. In this case, the
signal conditioning circuit consists of a rectifier and a filter.
18
Problem Statement
Build a circuit that converts an input voltage of – 1 V to + 2.2 V to an output voltage of 0 to
5 V. We have a dual supply of ± 12 V available and we need to drive a 10 kΩ load. Test
your designs under different input voltages and verify that your output voltages are within ±
5% of the calculated ones.
Solution
The input voltage (– 1 V to + 2.2 V) is the independent variable while the output
voltage (0 to 5V) is the dependent variable.
By plotting the independent variable (x axis) and the dependent variable (y axis), we have:
y
5
final point
m
0
initial point
x
-1
2.2
Connect the intersection points, we find that the graph is a straight line, then:
y = mx + b
(1)
equation of the straight line.
y1 - y0
x1 - x 0
(2)
slope of the straight line.
where:
m=
Replace values in the slope of the straight line, we have:
m=
5-0
= 1.56
2.2 - (-1)
To find the value of the constant (b), in the equation of the straight line we replace the
variables (x, y) for the coordinates of the initial point (–1, 0) or the coordinates of the final
point (2.2, 5), through this linear equation:
y = mx + b
equation of the straight line
Use coordinates of the initial point (–1, 0)
0 = 1.56(–1) + b
b = 1.56
Use coordinates of the final point
5 = 1.56(2.2) + b
b = 1.56
(2.2, 5)
The result is the same; however, it is simpler to use the initial point as seen above.
19
Replacing the variables and the constant of the linear equation for equivalent electronic
terms we’ll have:
y = Vout
m = Av = 1.56
x = Vin
b = Voffset = 1.56
Vout
5
Av
0
-1
2.2
Vin
The constant of the equation can be called any name; in this case we’ll call it Voffset.
Then:
Vout = Av (Vin) + Voffset
(4)
Equation (4) indicates that we should use a circuit whose block diagram is:
Voffset = 1.56
Av = 1.56
Vin
Summing
Amplifier
To the
Load
Replacing values in equation (4), we have:
Vout = Av(Vin) + Voffset
(4)
Vout = 1.56 (Vin) + 1.56
Vout = 1.56 (Vin + 1)
(5)
Equation (5) provides a second possible solution; the block diagram is the following:
1V
Summing
Amplifier
Av = 1.56
Vin
To the
Load
The third possible solution comes from the previous circuit whose simplification is:
– 1V
Vin
+
-
Differential
Amp
Av = 1.56
To the
Load
20
Note: In all the solutions, it is recommended to use an op-amp voltage follower
between Vin and the input of the circuit. The purpose is to maintain impedance
matching and prevent excessive loading of previous circuit stages.
The design of the problem statement will be accomplished by using solution 2. Figure 2-2
shows the implementation of equation 5.
VCC
12V
R1
7
Voffset
3
50%
5kΩ
Key=B
2
XMM1
1
Figure 2-2
5
U1
741
6
R3
4
VEE
-12V
R4
VEE
-12V
2
R2
Vin
3
50%
R6
6
741
7
5kΩ
Key=A
4
2
U2
1
5
XMM2
5%
1k Ω
VEE
-12V
5%
1k Ω
4
5%
R8
5.6k Ω
5%
1k Ω
VEE
C1
-12V
3
R5
5%
1k Ω
100nF
IC=0V
U3
6
741
7
1
VCC
12V
5%
3.6k Ω
R7
5
4
2
3
C2
100nF
IC=0V
R10
5%
2.2k Ω
U4
741
7
1
6
VL
5
VCC
XMM312V
12V
VCC
R9
5%
10k Ω
Circuit analysis
Op-amps U1 and U2 are configured as voltage followers. It is always a good practice to
use a voltage follower or buffer between the input signal and the next stage. This
ensures the stability of the circuit. U3 is a summing amp with Av = 1. The gain depends of
the relationship between resistors R3/R4 or R3/R6. Since the gain of the circuit is unity then
R3 = R4 = R6; in this case we select 1 kΩ for each resistor.
U4 provides the circuit gain which is determined by the ratio between resistors R8/R7.
According to equation 5, Av = 1.56 then R8 must be 1.56 times greater than R7.
Assuming R7 = 3.6 kΩ, then the value of R8 would be 5.61 kΩ but we choose the closer
standard value of 5.6 kΩ.
Notice in Figure 2-2 that we are using Voffset = –1 V (in this case due to components
limitations it is –1.001 V).
21
Procedure/Tasks Using Multisim
1. Build the circuit indicated in Figure 2-2 using Multisim (Select 2% increments for all
the potentiometers).
2. Adjust R1 (by pressing the B or SHIFT-B keys) until Voffset is approximately
equal to + 1 V.
3. Adjust R2 (by pressing the A or SHIFT-A keys) until the input voltage (Vin) is
approximately equal to – 1 V. When this happens, the output voltage or VL should be
approximately equal to 0.
4. Adjust R2 (by pressing the A or SHIFT-A keys) until the input voltage (Vin) is
approximately equal to + 2.2 V. When this happens, the output voltage or VL should
be approximately equal to + 5 V. What you have completed in steps 3 and 4 is to
vary the input voltage, Vin from the given input range of –1 V to + 2.2 V. The
output voltage range should be 0 to + 5 V. Is this correct? Explain any discrepancies.
5. Vary the input voltage, Vin from –1V to + 2.2 V. Adjust Vin to the values indicated
on Table 2-1 and record the obtained output voltages, VL.
Table 2-1. Output voltage versus input voltage using Multisim
Vin
VL
–1V
0
0.5 V
1V
1.5 V
+ 2.2 V
6. Replace the four 741 ICs by a single quad op-amp such as the LM324AJ. Note that
the LM324AJ has four sections A, B, C and D. Each section will have its own power
supply terminals pin 4 (+V) and pin 11 (– V). You only need to connect the
respective power supplies to any section: pin 4 should be connected to VCC and pin
11 should be connected to ground.
22
7. Repeat step 5 and complete Table 2-2.
Table 2-2. Output voltage versus input voltage using a Quad op-amp using
Multisim
Vin
VL
–1V
0
0.5 V
1V
1.5 V
+ 2.2 V
8. Compare Tables 2-1 and 2-2. Are they about the same? Describe any discrepancies
and explain the possible causes.
Questions
1. Implement equation 5 by using solution 1 (Amplifier and Summer).
2. Design a circuit that converts input voltages of –1.5 V to + 3.5 V to output voltages of 0
to 8 V. We have a dual supply of ± 12 V available and we need to drive a 10 kΩ load.
23
Procedure/Tasks – Hardwired Circuit
Now, you are familiar with the signal conditioning circuit using Multisim and it’s time to
hardwire the circuit shown in Figure 2-1 using real components. Repeat what you did in Lab
1, that is, going through a checklist of components and the equipment that you need to
complete this task. This will reduce the careless errors and damaging to components.
List of components
Item #
Equipment
Component Description
Reference
Designators
Quantity
24
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such
a checklist will enable you to minimize errors in the circuit assembly, prevent malfunction,
and consequently reduce damage to components. This checklist should always be used, but
it is not limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For
example, it is not uncommon for IC manufacturers to use different pinouts
between DIP8 and SOIC8 packages for the same part. Sometimes a circuit
designer will layout a schematic using the pinout of a SOIC part and the
person doing the wiring of the circuit might use a DIP part. The consequence
of this is an incorrectly wired breadboard resulting in faulty circuit operation
and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin.
This is especially important when there is high speed digital or high load current
circuit combined with sensitive analog circuit (such as a Wheatstone bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a
tantalum bypass capacitor of 10 - 33μF should be used between power and ground
points where the power supply leads connected to the breadboard. Make sure the
polarity of the capacitor is correct and that its working voltage (WV) is at least 1.5
times the maximum voltage used in the circuit. e.g., the working voltage rating of a
capacitor is 10V; the supply voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback
resistors should be routed from the amplifier’s output pin directly to the input pin.
25
This helps to reduce the possible amplifier’s feedback loop pick up and amplifies the
unwanted noise.
•
All component leads should be kept as short as possible. Additionally, signal paths
from one IC to another should be kept as short as possible to minimize noise pickup.
If a signal path must be long for whatever the reason, ensure it is routed away from
other signal paths to reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all
ground buses and power buses should be terminated at one point. That is, you should
not be able to trace a loop from the ground or power supply connection to the
breadboard to all component connections and then back to the power or ground
source.
•
If it is possible, separate analog and digital power supplies and grounds from one
another. These should be routed back and terminated at the single power and ground
termination point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g.,
LMC555 over a TTL 555), unless the design calls for the high current capacities of
TTL.
The QJ49E Wheatstone
Resistance Bridge is a
highly stable, precision
Wheatstone Bridge for the
precision measurement of
meters, components,
windings and other
instruments.
26
Hardwired Circuit Procedure
1. Adjust R1 potentiometer until Voffset is approximately equal to +1 V.
2. Adjust R2 potentiometer until the input voltage (Vin) is approximately equal to –1 V.
When this happens, the output voltage or VL should be approximately equal to 0.
3. Adjust R2 until the input voltage (Vin) is approximately equal to + 2.2 V. When this
happens, the output voltage or VL should be approximately equal to + 5 V. What you
have done in steps 1 and 2 is to vary the input voltage, Vin, from the given input range
of –1 V to + 2.2 V. The output voltage range should be 0 to + 5 V. Is this correct?
Explain any discrepancies.
4. Vary the input voltage, Vin, from –1V to + 2.2 V. Adjust Vin to the values indicated on
Table 2-3 and record the obtained output voltages, VL.
Table 2-3. Output voltage versus input voltage in the hardwire circuit
Vin
–1V
0
0.5 V
1V
1.5 V
+ 2.2 V
VL
27
Questions
1. Compare the results of Tables 2-1 and 2-3. Are they about the same? Describe any
discrepancies and explain what could be the possible causes.
2. What difficulties have you encountered in hardwiring the signal conditioning circuit?
Conclusions
After completing the signal conditioning circuit both in Multisim and hardwire, what are
your conclusions?
28
Advanced Design
If you want to earn extra credit, try the following design.
You work in a failure analysis laboratory whose sole goal is to protect the end users’ safety
from defect components and investigate the failures. Your manager (the VP of R&D) has
given you the task of designing a circuit that can take an unconditioned output signal from
an accelerometer sensor and convert it into a reliable signal that can be analyzed in
LabVIEW. The accelerometer is used in a drop test fixture to measure the impact forces on
DUTs (Device Under Test). Because the accelerometer is in an abusive environment (i.e.,
being dropped all the time), it has minimal internal circuitry. This minimal circuitry can
only put out a relatively small bipolar voltage (as a function of impact forces). The output
signal must be interfaced to a data acquisition card in a PC that can only accommodate 0 to
5V signal inputs.
Knowns:
1. The accelerometer signal output is in the range of – 2.5V to +3.2V.
2. The accelerometer’s output impedance is ~1.5KΩ
3. The signal conditioning circuit output must be 0V to 5 V (because the data acquisition
card requires this input signal level to function properly)
4. The input impedance of the data acquisition card is high enough that circuit loading
should not be a concern.
5. The circuit will be located in an electrically noisy environment (hydraulic actuators are
driven to power the drop test fixture).
Unknowns:
1. What is the circuit configuration needed to properly interface the accelerometer output
to the data acquisition card input?
2. What are the component values needed to properly implement the circuit design?
3. How do we deal with the electrically noisy environment? (Hint: this will be addressed
by choosing the proper circuit configuration and careful routing of the wires from the
accelerometer to the signal conditioning circuit.)
29
LAB 3 – DIGITAL TO ANALOG CONVERTER (DAC)
Objectives
1. Learn how to design a DAC circuit that converts digital input signals to expected
corresponding analog voltage levels.
2. Build, test, and troubleshoot a DAC circuit using Multisim.
3. Hardwire the DAC circuit of objective 1 and compare the measurements of the
hardwired circuit with the measurements obtained using Multisim.
Preliminary Information
Digital to Analog Converters or DACs are used to convert digital values, represented by a
binary or BCD format, into a corresponding analog voltage level. The binary or BCD value
to be converted is usually inputted into the DAC in a parallel fashion with each bit from
LSB to MSB having its own corresponding digital input.
A DAC’s resolution, or smallest representative analog voltage, corresponds to the number
of bits it can accommodate and the reference voltage used. While 8-bit (28 = 256 analog
value) DACs are usually commonplace in industry, DACs can range from simple 6-bit (64
analog value) configurations up to 20-bit (1048576 analog value) configurations.
Typical DACs are available in either current output (IDAC) or voltage output (VDAC)
configurations. While the voltage output VDACs are more convenient to implement, they
tend to be slower and more expensive than their current output counterparts (refer to figure
3-1 for a VDAC example).
Therefore, for high-speed applications, circuit designers usually choose current output
IDACs and then use a high-speed op-amp to provide the I-V conversion at the output of the
DAC. For some low cost applications, an IDAC with a simple RC filter on its output is often
enough to meet certain non-demanding, high-input impedance applications.
30
All resistors are 330 ohm
The switches are actuated by
the keyboard numbers 0-7
S0 S1 S2 S3 S4 S5 S6 S7
X7
X6
X5
X4
X3
X2
X1
V1
5V
R9
XMM1
50%
D0 D1 D2 D3 D4 D5 D6 D7
+
VDAC
5kΩ
Key=R
A1
VDAC
Figure 3-1. VDAC implementation (Note the value of Vout with the LSB
set high, i.e., S0 closed).
X0
31
Problem Statement
Design an 8-bit DAC circuit that is capable of driving a 1K Ω load. Use a reference voltage
between 3 VDC to 5 VDC. The circuit should be designed such that it provides a positive
voltage (unipolar) output.
Solution
To ensure that we can drive a 1K Ω load without excessively loading the DAC output, the
most prudent approach would be to use an IDAC with an op-amp to provide the I-V
conversion and load driving capability. Because we desire an unipolar signal output from
the DAC both the –Vref input and –Iout output are tied to ground. Refer to figure 3-2 below
for a schematic on one solution for this circuit design.
The Digital-to-Analog
Converter Card is intended
for use with the Intelligent
Motherboard for the RS232
Serial Port Extension
System, and is an addition to
the other plug-in cards in
this range. The D-to-A
(Digital-to-Analog)
Converter transforms a
binary number, presented to
it via the system data bus
from the Intelligent
Motherboard, into an analog
voltage output. This output
from the D-to-A Converter
Card could then be used to
control analog equipment,
such as the volume of an
automated mixing desk or
the control of lighting, and
even motors and actuators.
etc.
Digital-to-Analog Converter Card
32
All resistors are 330 ohm
The switches are actuated by
the keyboard numbers 0-7
S0 S1 S2 S3 S4 S5 S6 S7
X7
X6
X5
X4
X3
X2
X1
X0
V1
5V
R9
XMM1
D0 D1 D2 D3 D4 D5 D6 D7
50%
IDAC
5kΩ
Key=R
R10
1kΩ
5%
VEE
-15V
U1
VCC
R11
1kΩ
5%
15V
Figure 3-2 – Example of IDAC design implementation in Multisim with I-V drive
capability for 1K Ω load. (note indicator order is MSB (X7) → LSB (X0), left to right ).
33
Circuit analysis
Referring to figure 3-2, we see a reference voltage of 5V (V1) with R9 setting the reference
current into the IDAC. Switches S0 – S7 enable setting of the binary value input into the
IDAC, with S0 representing the LSB and S7 representing the MSB.
On the output of the IDAC we have a general purpose op-amp (e.g., 741) configured
with +/– 15V bipolar voltage supplies. These voltage supplies must be greater than the
reference voltage to ensure full 0 – 5V output compliance (+/– 10V or +10V/–5V would
have also been adequate).
The op-amp’s feedback resistor (R10) is chosen to give the proper scaling of the desired
output voltage as a function of the IDAC’s output current.
Note that the inverting input of the op-amp is supplied by the +Iout output of the IDAC but
the Vout of the op-amp is positive based on the design requirements. One might expect a
negative voltage at the output of the 741, however, the +Iout pin of the IDAC actually sinks
current rather than sources it. Therefore, the voltage drop across U1’s feedback resistor is
positive to negative with respect to the op-amp’s output. R11 is the load resistance as
identified in the circuit design requirements.
Mathematical analysis of the DAC circuit is as follows:
•
When designing a DAC circuit, one of the important things to understand is the
resolution capability of the DAC being used. As mentioned previously, DAC
resolution is a function of both the number of bits being accommodated by the DAC and
the Vref being used.
Equation #1: DAC resolution = Vref / 2
Where:
n
Vref = the DAC reference voltage
n = # of bits accommodated by the DAC (e.g., 8-bit DAC)
Note: upon observation of equation #1, it is clear that the DAC resolution could be
improved by either increasing the number of bits employed or decreasing the
reference voltage. However, increasing the number of bits increases cost and
conversion time and decreasing the reference voltage makes the conversion
more sensitive to errors on noise.
Therefore, in the circuits of figure 3-1 & 3-2:
8
Resolution = 5V / 2 = 19.5 mV
This means that the smallest analog voltage step size that can be represented by the
DAC with a Vref = 5V is 19.5 mV.
34
•
To determine Vout for any binary value input:
n
Equation #2: Vout = Vref (N / 2 )
Where:
Vout is the DAC’s output voltage
(after I–V conversion with an IDAC or the Vout of a VDAC)
Vref = the DAC reference voltage
N = is the decimal equivalent to the binary input value
n = # of bits accommodated by the DAC (e.g., 8-bit DAC)
Therefore:
If we close the switch for only the LSB (S0 in figure 3-1, binary value = 00000001) we
should see approximately 20 mV at the output, because: 5V (1/256) = 19.5 mV
With all 8 switches closed (i.e., binary value = 11111111) we should see approximately
8
5V (255 / 2 ) = 4.98V at the output (this is illustrated in figure 3-2)
Procedure/Tasks Using Multisim
1. Build the circuit indicated in figure 3-2 using Multisim. Choose 1% increment for the
potentiometer (R9)
2. Adjust R9 (by pressing the r or SHIFT-r keys) until Vout is approximately equal to
4.98V with S0 – S7 all closed.
3. If R9 is properly adjusted for the correct Iref, Vout should equal 4.98V with S0 – S7 all
closed and Vout should equal approximately 0V with S0 – S7 all open.
Note: Vout will actually be on the order of μV with S0 – S7 open due to offset voltage
and bias currents of the op-amp. However, considering the DAC’s resolution of
20mV, this Vout value is essentially zero.
35
4. Using Multisim and equation #2 complete the following Table 3 –1 of DAC Vout
values for given binary input values.
Table 3 –1
S7 – S0 Input
(Binary)
Input
(Dec)
Input
(Hex)
Vout
Calculated
Vout
Measured
00000000
00000001
00000010
00000100
00001000
00010000
00100000
01000000
10000000
11000000
11100000
11110000
11111111
Questions
1. When the binary input value was increasing, did you notice a pattern in the corresponding
Vout values? What form did this pattern of Vout values take? Was it linear, or non-linear?
36
2. Based on the results cited in question 1, explain the reason for the observed Vout value
pattern?
3. Replace R10 with a 10 KΩ resistor and note the Vout values for binary inputs of
00000001 and 11111111. How does the R10 resistor value change affect Vout? Why?
4. Set U1’s VCC to +5V and VEE to ground and note the Vout values for binary inputs of
00000001 and 11111111. How do these circuit parameter changes affect Vout? Why?
Procedure/Tasks – Hardwired Circuit
Now, you have tested the circuit to satisfy the problem statement using Multisim, it is time
to hardwire the circuit shown in Figure 3-2 with real components. We will use the
DAC0800 LCN DIP IC and whose schematic diagram is depicted in Figure 3-3.
37
All resistors are 330 ohm
LSB
MSB
S7 S6 S5 S4 S3 S2 S1 S0
X7
X6
X5
X4
X3
X2
X1
X0
V1
5V
R9
20%
MSB
5 6 7 8
14
9 10 11 12
R10
LSB
+
+
4
1.0kOhm_5
DAC 0800 LCN
5kOhm
Key = r
15
3
16 13
1
VEE
-15V
2
2
0.01uF
3
VEE
-15V
VCC
15V
Vout
4
U1
6
7
741
VCC
15V
Figure 3-3. Schematic diagram of an IDAC using the DAC0800LCN DIP IC.
+
4.973
V
DC 10MOhm
R11
1.0kOhm_5
38
Follow the same steps as you did in the previous labs, you are going to indicate the list of
components and the equipment that you need to complete this task.
List of components
Item #
1
Component Description
National DAC0800 (or equivalent)
Equipment List
Reference
Designators
Quantity
A1
1
39
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such a
checklist will enable you to minimize errors in the circuit assembly, prevent malfunction, and
consequently reduce damage to components. This checklist should always be used, but it is not
limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For example, it
is not uncommon for IC manufacturers to use different pinouts between DIP8 and
SOIC8 packages for the same part. Sometimes a circuit designer will layout a
schematic using the pinout of a SOIC part and the person doing the wiring of the
circuit might use a DIP part. The consequence of this is an incorrectly wired
breadboard resulting in faulty circuit operation and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin. This is
especially important when there is high speed digital or high load current circuit
combined with sensitive analog circuit (such as a Wheatstone bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a tantalum
bypass capacitor of 10 - 33μF should be used between power and ground points where the
power supply leads connected to the breadboard. Make sure the polarity of the capacitor
is correct and that its working voltage (WV) is at least 1.5 times the maximum voltage
used in the circuit. e.g., the working voltage rating of a capacitor is 10V; the supply
voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback resistors
should be routed from the amplifier’s output pin directly to the input pin. This helps to
reduce the possible amplifier’s feedback loop pick up and amplifies the unwanted noise.
40
•
All component leads should be kept as short as possible. Additionally, signal paths from one
IC to another should be kept as short as possible to minimize noise pickup. If a signal path
must be long for whatever the reason, ensure it is routed away from other signal paths to
reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all ground
buses and power buses should be terminated at one point. That is, you should not be able to
trace a loop from the ground or power supply connection to the breadboard to all component
connections and then back to the power or ground source.
•
If it is possible, separate analog and digital power supplies and grounds from one another.
These should be routed back and terminated at the single power and ground termination
point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g., LMC555 over a
TTL 555), unless the design calls for the high current capacities of TTL.
0101001
CD Transport
PCM
1010010
Digital volume
Modulator ASIC
Switching
Amp
Low Pass
Filter
Analog
Amplified PWM
DIGITAL AMPLIFICATION
The main difference is that digital-to-analog conversion is performed after
amplification. The digital amplifier transforms input PCM (pulse code modulation)
signal into another digital format called PWM (Pulse Width Modulation), which then
amplifies it in the digital domain. The PWM amplification stage is a type of switching
circuit, and is therefore not influenced by nonlinearity and transistor noise.
The final stage of audio production in the signal path is a simple passive low-pass
filter. The low-pass filter transforms PWM digital signal into analog power signal,
which can directly drive a loudspeaker.
41
Hardwired Circuit Procedure
1. Build the circuit indicated in figure 3-3 using a breadboard and actual components.
2. Adjust R9 until Vout is approximately equal to 4.98V with S7 – S0 switches all closed.
3. If R9 is properly adjusted for the correct Iref, Vout should equal 4.98V with S7 – S0 switches
all closed and Vout should equal approximately 0V with S7 – S0 switches all open.
Note: Vout will actually be on the order of μV with S7 – S0 switches open due to offset
voltage and bias currents of the op-amp. However, considering the DAC’s resolution
of 20mV, this Vout value is essentially zero.
4. Using hardwired circuit measurements and equation #2, complete the following Table 3-2 of
DAC Vout values for given binary input values.
Table 3-2
S7 – S0 Input
(Binary)
00000000
00000001
00000010
00000100
00001000
00010000
00100000
01000000
10000000
11000000
11100000
11110000
11111111
Input
(Dec)
Input
(Hex)
Vout
Calculated
Vout
Measured
42
Questions
1. Compare the results of Tables 3-1 and 3-2. Are they about the same? Describe any
discrepancies and explain what could be the possible causes.
2. Replace R10 with a 10 KΩ resistor and note the Vout values for binary inputs of 00000001
and 11111111. How does the R10 resistor value change affect Vout? Did you obtain the same
results in Multisim?
3. Set U1’s VCC to +5V and VEE to ground and note the Vout values for binary inputs of
00000001 and 11111111. How do these circuit parameter changes affect Vout? Does the
circuit work as expected? How do the results obtained with the hardwired circuit compare to
those obtained with Multisim?
43
Conclusions
After completing the DAC circuit implementation in both Multisim and hardwiring, what are
your conclusions? What similarities do they hardwired circuit and the circuit simulation share?
What major differences did you notice between the two?
Advanced Design
If you want to earn extra credit, try the following design issue.
Your supervisor informs you that the department is having problems with an expensive piece of
test equipment and she wants you to investigate. You find the piece of equipment in question is a
multi-channel, modular data logger that uses multiple data acquisition cards. Manufacturing
engineers using the unit say that its 12-bit multi-channel DAC card is unreliable and producing
questionable results. Using what you now know about DACs, how would you go about resolving
this issue?
Knowns:
1. The manufacturing engineers complaining about the “bad DAC board” have not taken
measurements to verify its alleged performance issues. Their complaints stem from the fact
that fixtures apparently function correctly, although the DAC board produces results that
imply otherwise.
44
2. Because the equipment cost is quite expensive, outright replacement of the equipment is out
of the question.
3. The data logger repair cycle time is about three months due to a shortage of replacement
parts. This situation poses a very important company need: checking and calibrating
production test fixtures.
4. Your supervisor does not care how you resolve the problem as long as it is completed in a
timely manner that does not cost too much money. (i.e., you cannot purchase new DAC
boards)
5. You have the data sheets on the 12–bit DAC data acquisition card. Therefore, you know how
to set its Vref levels, and its current output gain settings (which are similar to those in the
circuit in figure 3-2).
6. The data logger is used to check fixtures that run on +/– 12V power supplies with digital
logic levels of 0 – 5V
7. Required resolution for the test fixture application must be a minimum of 5 mV to meet
performance requirements.
8. DAC board measurements show Vout to be equal to 3 mV with a binary input of
000000000001 and 11.99V with a binary input of 111111111111.
9. You must show the manufacturing engineers proof of your findings, i.e., calculations
showing the DAC is either functioning properly or not and offer a solution to their problems.
Unknowns:
1. How do you confirm whether or not the DAC board is functioning correctly?
2. If the DAC board is malfunctioning, can you design a temporary solution using a 12-bit DAC
and associated components, knowing what you did with DACs and this particular
application? (Hint: refer to digital circuit textbooks and manufacturer’s DAC data sheets and
application notes for other in insights).
3. If you do not have enough information to design a work around solution for the issue, what
other information is required and why is it needed?
45
LAB 4 – ANALOG TO DIGITAL CONVERTER (ADC)
Objectives
1. Learn how to design an ADC circuit that converts analog input signals to corresponding
binary output values.
2. Build, test, and troubleshoot an ADC circuit using Multisim.
3. Hardwire the ADC circuit of objective 1 and compare the measurements of the hardwired
circuit with the measurements obtained using Multisim.
Preliminary Information
In many applications, ADCs and DACs are used together to provide a digital interface to an
analog world. One such example is the entertainment industry. The music industry uses analog
to digital conversion (ADC) techniques to record musicians playing in a studio (analog signal
source) and this analog signal is encoded into a digital format which is then stored in compact
disks (CD) and sold to the consumer. The consumer then takes his/her compact disk and plays it
in a CD player.
The CD player uses digital to analog conversion (DAC) techniques to decode the digital signal
and reconstitute the original recorded sounds of the musicians into an analog format. This analog
signal in the audio band (20 Hz to 20 kHz) is then amplified and used to drive speakers. This
same analogy also applies to the film industry, which now stores and distributes its movies on
DVD (Digital Video Disk).
Analog to Digital Converters or ADCs are used to convert analog signals into corresponding
digital signals. The digital signal generated in this fashion is a binary representation of the
original analog signal’s amplitude.
At a very fundamental level, ADCs determine the digital representation of an analog input signal
by comparing it to a given reference voltage. The resulting digital value represents the proportion
between the analog input signal and the reference voltage.
Using an example, if Vin = 2.5V and Vref = 5V for an 8-bit ADC we would expect to see a
binary value of 10000000 at the ADC output. Why?
Because 2.5 / 5V = 50% and 50% of 28 = 256 = 10000000. We will cover this
in more detail in the circuit analysis section below.
Many ADC techniques are currently employed in industry; however, we will provide a brief
overview of only the techniques that are most widely used.
46
1. Parallel converter or Flash converter – uses many comparators connected in parallel,
each with a different reference voltage. The outputs of these comparators are then input
into a priority encoder. This encoder provides a binary output based on which comparator
outputs are high and which are low.
The number of bits the flash ADC accommodates determines the number of comparators
8
used. e.g., an 8-bit flash ADC would require 2 – 1 = 255 comparators to implement the
8-bits. Therefore, while flash ADCs are the fastest converters, but they are limited in the
number of bits they can accommodate.
Generally, flash converters are limited to 4-bit up through 10-bit digital output
resolutions.
2. Dual-Slope converter – this type of converter uses an op-amp integrator, comparator,
digital control circuits, and digital clock circuits, along with a counter to generate the
binary or BCD value from an analog source signal.
The fundamental idea is to switch the integrator input in a synchronized fashion between
the analog signal to be converted and a known reference voltage (a negative voltage).
This enables both charging and discharging of the integration capacitor at a constant rate.
When the integration capacitor charges to a specific level, it triggers the comparator. The
comparator then triggers both discharging of the integrator capacitor and a counter that is
used to count during the capacitor’s discharge cycle.
The value of the count is the amplitude of the analog input signal. This count value is
then converted to a binary or BCD value and made available at the latch outputs of the
ADC. Although the part count and circuit complexity for the dual-slope converter is
much less than that of the flash converter, the dual-slope converter is considerably slower
due to the charge and discharge times required for its integrating capacitor.
3. Successive-Approximation converter – this type of converter employs the use of a
DAC and a successive approximation register (SAR), along with control logic circuits,
latch and output drivers to perform its ADC operations.
Initially, all binary or BCD bits in the successive approximation register are set to zero.
Once the conversion starts, the MSB is set to “1” and the bits (e.g., 10000000 for an 8-bit
converter) are then fed, in a parallel fashion, into the DAC input, where the binary or
BCD value is converted by the DAC into a reference voltage.
This reference voltage is then fed into a comparator input where it is compared with the
analog input signal. If the analog input signal is greater than the DAC derived reference
voltage, the MSB is left as a “1” in the SAR; otherwise, it is set to “0”. Then, this new
binary value is shifted out to the DAC where a new reference voltage is generated and
compared with the analog input signal.
47
This function essentially provides a means of performing a binary search on the analog
input voltage level. This cycle continues until all binary bit values, from the MSB to the
LSB, in the SAR have been set accordingly. Finally, the value is shifted out from the
SAR into latch and output drivers to be made available outside of the ADC.
Most of the off-the-shelf ADC ICs incorporate the SAR type converter.
Problem Statement
Design an 8-bit ADC circuit that utilizes LEDs to indicate its binary output value. Use a
reference voltage of 2.5V to 5 VDC. Design the circuit such that it will continually update its
binary output for a changing analog input signal. Design the circuit to accommodate positive
voltage (unipolar) operation only.
Solution
The implementation of the above design requirements is relatively straightforward considering
the unipolar operating requirement. To enable the device to operate in a unipolar fashion, the
positive Vref must be tied to the 2.5 to 5V reference as described above and negative Vref must
be tied to ground.
Additionally, setting the ADC to constantly update based on a changing analog input signal
requires an external clock to toggle the ADC’s SOC (Start of Conversion) pin. Additionally, the
ADC’s OE (Output Enable) pin must be pulled high to ensure constant updating of the binary
output value.
Refer to figures 4-1 & 4-2 below for a schematic of such implementation.
48
X7 X6 X5 X4 X3 X2 X1 X0
A1
R1
VIN
0%
V1
5 V 1kΩ
Key=A
1K
D1
R2
VREFP
VREFN
100%
1kΩ
Key=B
1K
XMM1
D0
D2
D3
D4
XMM2
SOC
D5
OE
D6
V2
2kHz
5V
D7
EOC
ADC
Figure 4-1. ADC output with the analog input voltage equal to approximately 0V and +Vref = 5V
49
X7 X6 X5 X4 X3 X2 X1 X0
A1
R1
VIN
100%
V1
5 V 1kΩ
Key=A
1K
D1
R2
100%
1kΩ
Key=B
1K
XMM1
D0
VREFP
D2
VREFN
D3
D4
XMM2
SOC
D5
OE
D6
V2
2kHz
5V
D7
EOC
ADC
Figure 4-2. ADC output with the analog input voltage equal to the reference voltage of 5V and +Vref = 5V.
50
Circuit analysis
Referring to figures 4-1 & 4-2, we see an adjustable reference voltage available to +Vref
(VREFP in the schematic) via voltage supply V1 and potentiometer R2. The varying analog
input signal is also derived from V1 using potentiometer R1 to provide signal variation to
the VIN input of the ADC.
Additionally, we note –Vref (VREFN) pulled to ground to enable the unipolar output
operation. The SOC (Start of Conversion) pin is tied to a square wave signal generator to
provide the necessary clock source to ensure continual updating of the ADC.
Note, when designing such a continually updating (i.e., free-running) ADC application, care
must be taken to ensure the SOC clock frequency provides enough time to allow the
converter to complete the conversion process in its entirety.
Failure to do so will result in erroneous conversion in the binary output values. In this case,
a clock frequency of 2 KHz provides a period of 500 μs, which is more than enough time for
a worst case ADC conversion cycle (e.g., the National Semiconductor ADC0804 requires
a worst case conversion time of 114 μs).
The OE pin of the ADC is pulled to ground to ensure the binary outputs are constantly
updated as conversions are completed. Data output pins are tied to indicators per the
problem definition requirements.
Chip ADC0804
51
Mathematical analysis of the ADC circuit is as follows:
The following parameters are important when characterizing the performance of an ADC
circuit design:
1) An ADC’s % resolution can be defined in either of the following ways:
n
Equation #1: ADC % resolution = [1 / (2 )] x 100%
Or
Equation #2: ADC % resolution = (Step Size / Vref) x 100%
2) An ADC’s Step Size is defined as the smallest possible voltage representation of the
ADC or the voltage that is equivalent to its LSB value:
n
Equation #3: ADC step size = Vref / (2 )
Where: ADC % resolution represents % of Vref
Vref = the ADC reference voltage
n = # of bits accommodated by the ADC
(e.g., 8-bit ADC = 256 values)
Note: Observing equations #1 & 2, it is clear that the ADC resolution could be improved
by either increasing the number of bits employed or decreasing the reference
voltage. However, increasing number of bits increases cost and conversion time and
decreasing the reference voltage makes the conversion more sensitive to errors due
to noise.
Therefore, in the circuits of figure 4-1 & 4-2:
8
Step size = 5V / (2 ) = 19.53 mV
% Resolution = [19.53mV / 5V] x 100% = 0.3906%
Or
8
% Resolution = [1 / (2 )] x 100% = 0.3906%
This means that the smallest analog voltage step size that can be represented by the ADC
with a Vref = 5V is 19.53 mV and that this step size is 0.3906% of Vref (or Full Scale
Voltage)
52
To determine the binary value for a given Vin:
n
Equation #4: ADC decimal number output = INT [(Vin / Vref) 2 ]
Then convert the ADC decimal number to binary to obtain binary equivalent of Vin
Where: Vin is the ADC analog input voltage to be converted
Vref = the ADC reference voltage
n = # of bits accommodated by the ADC (e.g., 8-bit ADC)
INT indicates taking the integer of the calculated value by truncating the
calculated quantity in [ ]
Referring to figure 4-1:
8
ADC decimal number output = INT [ (5μV / 5V) 2 ] = INT [0.000256] = 010
010 = 000000002
Referring to figure 4-2:
8
ADC decimal number output = INT [ (5V / 5V) 2 ] = INT [256] = 25610
8
7
6
5
4
3
2
1
0
25610 = 1 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2
25610 = 1000000002
8
However, because the ADC is limited to a maximum value represented by 8-bits or 2 –1, its
full-scale output will show the following:
7
6
5
4
3
2
1
0
25510 = 1 x 2 + 1 x 2 + 1 x 2 + 1 x 2 + 1 x 2 + 1 x 2 + 1 x 2 + 1 x 2 = 111111112
This value is represented in the circuit simulation in figure 5-2
As an additional example, assume Vin = 2.5V, then we would expect to see the following at
the ADC output:
8
ADC decimal number output = INT [ (2.5V / 5V) 2 ] = INT [128] = 12810
7
6
5
4
3
2
1
0
25610 = 1 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 + 0 x 2 = 100000002
53
Procedure/Tasks Using Multisim
1. Build the circuit indicated in figures 4-1 & 4-2 using Multisim. Choose 0.1% increment
for potentiometers R1 & R2 and set adjustment keys as shown.
2. Adjust R1 (by pressing the A or SHIFT-A keys) until VIN (Vin) is equal to 5V
3. Adjust R2 (by pressing the B or SHIFT-B keys) until VREFP (Vref) is equal to 5V
4. Using Multisim and equation #4 complete the following table of ADC binary output
values for given voltage input values.
Table 4-1
Vin (R1 setting as
indicated by U1)
0V
0.020V
0.040V
0.080V
0.160V
0.320V
0.640V
1.280V
2.500V
3.750V
4.375V
4.680V
5.000V
Binary Output
Calculated
Binary Output
Indicated (X7 – X0)
54
Questions
1. As the Vin value was increasing, did you notice a pattern in the corresponding binary
output values? What form did this pattern of binary values take? Was it linear, or nonlinear?
2. Based on the results cited in question 1, explain the reason for the observed binary
output value pattern.
3. Set R2 such that VREFP is set to 2.500V as indicated on U2. If you were to vary Vin
over the same voltage range as in Table 4-1, what would the binary output values
indicate for each Vin value? Why?
4. If Vin exceeded Vref in a real ADC IC, would it actually damage the IC? If not, what
would the binary output values be for a given Vin that was larger than Vref? Refer to the
data sheet of the National Semiconductor ADC0804 IC and check the absolute
maximum ratings & electrical characteristics section to reinforce your understanding.
55
Procedure/Tasks – Hardwired Circuit
Now that you have tested the circuit to satisfy the problem statement using Multisim, it is
time to hardwire the circuit depicted in Figures 4-1 & 4-2 using real components. As you did
in the previous labs, you are going to indicate the list of components and the equipment that
you need to complete this task. Refer to figure 4-3 below for a schematic of the hardwired
circuit.
List of components
Item
#
1
Component Description
National ADC0804 (or equivalent)
Equipment List
Reference
Designators
Quantity
A1
1
56
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such
a checklist will enable you to minimize errors in the circuit assembly, prevent malfunction,
and consequently reduce damage to components. This checklist should always be used, but
it is not limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For
example, it is not uncommon for IC manufacturers to use different pinouts
between DIP8 and SOIC8 packages for the same part. Sometimes a circuit
designer will layout a schematic using the pinout of a SOIC part and the
person doing the wiring of the circuit might use a DIP part. The consequence
of this is an incorrectly wired breadboard resulting in faulty circuit operation
and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin.
This is especially important when there is high speed digital or high load current
circuit combined with sensitive analog circuit (such as a Wheatstone bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a
tantalum bypass capacitor of 10 - 33μF should be used between power and ground
points where the power supply leads connected to the breadboard. Make sure the
polarity of the capacitor is correct and that its working voltage (WV) is at least 1.5
times the maximum voltage used in the circuit. e.g., the working voltage rating of a
capacitor is 10V; the supply voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback
resistors should be routed from the amplifier’s output pin directly to the input pin.
This helps to reduce the possible amplifier’s feedback loop pick up and amplifies the
unwanted noise.
57
•
All component leads should be kept as short as possible. Additionally, signal paths
from one IC to another should be kept as short as possible to minimize noise pickup.
If a signal path must be long for whatever the reason, ensure it is routed away from
other signal paths to reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all
ground buses and power buses should be terminated at one point. That is, you should
not be able to trace a loop from the ground or power supply connection to the
breadboard to all component connections and then back to the power or ground
source.
•
If it is possible, separate analog and digital power supplies and grounds from one
another. These should be routed back and terminated at the single power and ground
termination point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g.,
LMC555 over a TTL 555), unless the design calls for the high current capacities of
TTL.
58
VCC
5V
R9
C1
10uF-POL
10kOhm
C2
150pF
VCC
5V
R10
50%
10 K
1
2
20
19
3
4
18
17
5
6
16
15
7
14
8
9
13
12
10
11
ADC0804
R1
R2
R3
R4
R5
R6
X7
X6
X5
X4
X3
X2
All resistors are 220 ohms
Figure 4-3. ADC0804
R7
X1
R8
X0
59
Hardwired Circuit Procedure
1. Build the circuit indicated in figure 4-3 using a breadboard and actual components. Refer to
the National ADC0804 data sheet for pin function descriptions.
2. Adjust R10 until Vin (pin 6) is equal to 0V.
3. Using equation #4 and hardwired circuit measurements complete the following table of ADC
binary output values for given voltage input values.
Table 4-2
Vin (R10 setting)
Binary Output
Calculated
Binary Output
Indicated
X7 → X0
0V
0.020V
0.040V
0.080V
0.160V
0.320V
0.640V
1.280V
2.500V
3.750V
4.375V
4.680V
5.000V
60
Questions
1. Compare the results of Tables 4-1 and 4-2. Are they about the same? Describe any
discrepancies and explain what could be the possible causes.
2. Add another 10K potentiometer to the circuit of figure 4-3 such that the wiper is connected to
pin 9 (Vref / 2). Connect the potentiometer’s remaining pins to VCC & ground. The new
potentiometer should now be connected in a manner similar to R2 in figures 4-1 & 4-2.
Adjust the potentiometer such that 1.25V is applied to pin 9 of the ADC0804. Repeat the
measurements performed for Table 4-2. How do these results compare the results in Table
4-1, question #3 in the Multisim section?
61
3. Review ADC literature (textbooks, data sheets, applications notes, etc.), then name and
describe three kinds of errors often associated with ADC operations.
Conclusions
After completing the ADC circuit implementation in both Multisim and hardwiring, what are
your conclusions? What similarities do the hardwired circuit and the circuit simulation share?
What major differences did you notice between the two?
62
Advanced Design
If you want to earn extra credit, try the following design issue.
Reviewing the extra credit problem from Lab 3 – Digital to Analog Converters, we had the
following scenario:
Your supervisor informs you that the department is having problems with an expensive piece of
test equipment and she wants you to investigate. You find the piece of equipment in question is a
multi-channel, modular data logger that uses multiple data acquisition cards. Manufacturing
engineers said that its 12-bit multi-channel DAC card was unreliable and produced questionable
results. Using what you now know about DACs, how would you go about resolving this issue?
Knowns:
1. The manufacturing engineers complaining about the “bad DAC board” have not taken
measurements to verify its alleged performance issues. Their complaints stem from the fact
that fixtures apparently function correctly, although the DAC board produces results that
imply otherwise.
2. Because the equipment cost is quite expensive, the instant replacement of the equipment is
out of the question.
3. The data logger repair cycle time is about three months due to a shortage of replacement
parts and it fills a very important function: checking and calibrating production test fixtures.
4. Your supervisor does not care how you resolve the problem as long as it is completed in a
timely manner that does not cost too much. (i.e., you cannot purchase new DAC boards)
5. You have the data sheets on the 12-bit DAC data acquisition card. Therefore, you know how
to set its Vref levels, and its current output gain settings (which are similar to those in the
circuit in figure 4-2).
6. The data logger is used to check fixtures that run on +/– 12V power supplies with digital
logic levels of 0 – 5V
7. Required resolution for the test fixture application must be a minimum of 5 mV to meet
performance requirements.
8. DAC board measurements show Vout to be equal to 3 mV with a binary input of
000000000001 (12 bits) and 11.99V with a binary input of 111111111111 (12 bits).
9. You must show the manufacturing engineers proof of your findings, i.e., calculations
showing the DAC is either functioning properly or not and offer a solution to their problem.
63
Unknowns:
1. How do you confirm whether or not the DAC board is functioning correctly?
2. If the DAC board is malfunctioning, can you design a temporary solution using a 12-bit DAC
and associated components, knowing what you do about DACs and this particular
application? (Hint: refer to digital circuit textbooks and manufacturer’s DAC data sheets and
application notes for other insights.)
3. If you do not have enough information to design a work around solution for the issue, what
other information is required and why is it needed?
Based on what you have learned from this ADC lab, how could you use an ADC to solve this
DAC issue? Draw a schematic of any proposed circuit design solution you might have in mind
and describe how the circuit functions. Explain how your circuit design would solve the problem.
64
LAB 5 – TEMPERATURE SENSOR
Objectives
1. Build, test, and troubleshoot a temperature sensor circuit using Multisim.
2. Design a temperature sensor circuit that detects temperatures higher than the specified value.
3. Hardwire the temperature sensor circuit of objective 1 and compare the measurements of the
hardwired circuit with the measurements obtained in Multisim.
Preliminary Information
Sensor circuits, in some applications, may use a comparator circuit. As its name indicates, a
comparator compares the voltage applied to one input of the op-amp with a known voltage or
reference voltage (VREF) applied to the other input terminal.
In its simpler form, a comparator is an open loop configured op-amp, with two analog input
terminals and a digital output. The output can be a positive or negative saturation voltage
depending on the polarity and how big the applied input voltage is. In practice, the op-amp
comparator is usually used with some form of positive feedback with hysteresis to ensure proper
output signal saturation. However, for the purposes of this lab we will rely on the more
simplified open loop configuration, but you should be aware of the uses of positive feedback and
hysteresis in actual industry applications.
Vi
Input
Voltage
R2
100kOhm_5%
7 1 5 U1
3
VREF
2
LM741CH
4
V1
15V
6 Vo
V2
15V
R1
100kOhm_5%
Figure 5-1. Op-Amp comparator with VREF in the inverting input and dual power supply
configuration
In the circuit of figure 5-1, we observe that the reference voltage (VREF) is the voltage drop
across resistor R1. Resistors R1 and R2 are in series with the power source V1 (15V) and as
such they form a voltage divider.
65
Since the two resistors are equal (100 kΩ each), the reference voltage will be half of 15V or
7.5V.
In the circuit of figure 5-1, you can verify that:
When Vi > VREF
Vo = + Vsat = + 13 V
When Vi < VREF
Vo = – Vsat = – 13 V
Note: The condition of Vi = VREF is not stable.
Figure 5-2 shows the op-amp comparator with the reference voltage present in the non-inverting
input and the input voltage is applied to the inverting input.
VREF
Vi
Input
Voltage
V1
15V
R2
100kOhm_5%
7 1 5 U1
3
2
LM741CH
6
4
Vo
V2
15V
R1
100kOhm_5%
Figure 5-2. Op-Amp comparator with VREF in the non-inverting input and dual power
supply configuration
In the circuit of figure 5-2, the results are the opposite of the comparator with VREF in the
inverting input of figure 5-1; this means:
When Vi > VREF
Vo = – Vsat = – 13 V
When Vi < VREF
Vo = + Vsat = + 13 V
66
Establishment of the Reference Voltage
To establish VREF, we only need to modify the values of R1 and R2 of the op-amp comparator,
applying the rule of the voltage divider as follows:
R2
100kOhm_5%
VREF =
V1(R1)
R 1 + R2
(1)
VREF
V1
15V
R1
100kOhm_5%
Figure 5-3
To apply the rule of the voltage divider (equation 1) we choose the value of one resistor and
we calculate the value of the other.
Example:
Calculate the values of R1 and R2 for a reference voltage equal to 3.5 V. The source voltage is
15V.
Solution.
Using the circuit of figure 5-3 and assuming R1 = 10KΩ, we find the value of R2 in equation 1.
VREF =
V1(R1)
R1 + R2
R1 + R2 =
V1(R1)
VREF
(1)
⇒
R2 =
V1(R1)
- R1
VREF
Replacing values
R2 =
15V(10K)
- 10K = 32.857 KΩ
3.5V
Then R2 = 33KΩ (commercial value).
To obtain an exact reference voltage, replace resistor R2 by a potentiometer and adjust it
until you obtain the desired voltage.
67
Op-amp Comparator with Single Source
When a single source is used, the output voltage will be zero or positive as shown in Figure 3-4.
R2
100kOhm_5%
7 1 5 U1
3
Vi
Input
Voltage
2
VREF
LM741CH
4
Figure 5-4.
Op-amp Comparator with
VREF in the inverting input
and single source.
R1
100kOhm_5%
Since VREF is connected to the inverting input:
When Vi > VREF
Vo = + Vsat = + 13 V
When Vi < VREF
Vo = 0 V
On the other hand, if VREF is connected to the non-inverting input:
When Vi > VREF
Vo = 0 V
When Vi < VREF
Vo = + Vsat
6
V1
15V
68
Problem Statement
A sensor provides temperature sensitivity of 200 μV/°C. Design a circuit that activates an alarm
when the temperature reaches 300 °C. Use a single 10 V supply, if possible. The alarm could be
any type, visual- or sound-based.
Solution
We need to determine the reference voltage, Vref. According to the problem statement, the
sensor provides 200 μV/°C and the temperature that we need to detect is 300 °C. Thus,
Vref = 300 °C * 200 μV/°C = 60 mV
With this information we can design the respective circuit that is in Figure 5-5.
XMM1
VCC
10V
VCC
R5
100kΩ
10V
4
3
U1A
2
Vref
R1
5kΩ
Key=B
10V
LM324AJ
11
50%
VCC
R4
1kΩ
1
LED1
XMM2
11
9
R6
U1C
4
100kΩ
10
5
R2
50%
5kΩ
Key=A
Vin
U1B
6
7
LM324AJ
11
R3
8
LM324AJ
10kΩ
4
Q1
2N3904
C2
VCC 100nF
IC=0V
10V
Figure 5-5. Temperature sensor
Circuit analysis
To simplify the design we are going to use the quad op-amp LM324AJ. Notice that we are using
three sections out of the four that this IC has. Each section has its own power supply terminals
(pins 4 and 11); however, we need to connect the power supplies to one section only as shown in
U1C in Figure 5-5. At this point you should be quite familiar with some portions of the
temperature sensor depicted in Figure 5-5. It is appropriate then that you are able to answer the
following questions.
69
Question 1. What type of configuration are U1A and U1B?
Question 2. What is the purpose of U1A and U1B?
Question 3. Is U1C an inverting or a non-inverting comparator? Why?
Question 4. What is the purpose of capacitor C2?
Vref is obtained by varying potentiometer R1. Potentiometer R2 is used to simulate the voltage
that would be supplied by a temperature sensor. This voltage is proportional to the temperature
being measured by the temperature sensor
Transistor Q1 and its associated components provide the current that will activate the LED. The
LED can be activated directly from the U1C op-amp; however, it is a good design practice to
isolate the load from the op-amp for stability purposes. In this circuit we need a single source
power supply because there is no need to have negative voltages at the output. We are using an
NPN transistor so we just need positive voltage at the base.
70
Procedure/Tasks Using Multisim
1. Build the circuit indicated in Figure 5-5 using Multisim. Choose 2% increment for the
potentiometers
2. Adjust R1 (by pressing the B or SHIFT-B keys) until Vref is approximately equal 60 mV.
3. Adjust R2 (by pressing the A or SHIFT-A keys) until the input voltage (Vin) is
approximately equal to 60 mV. When this happens, the LED should be ON. Is this correct?
4. Leaving Vref at approximately 60 mV, adjust Vin (by adjusting potentiometer R2) to the
values indicated on Table 5-1 and record if the LED is ON or OFF.
Table 5-1. LED status versus input voltage using Multisim
Vref (mV)
Vin (mV)
60
20
60
40
60
60
60
80
60
120
60
140
LED
71
Questions
1. Under what conditions the LED is ON or OFF?
2. If Vref = 100 mV and Vin = 90 mV, is the LED ON or OFF? Why?
3. Replace the Q1 transistor by a PNP transistor such as the 2N3906 using Multisim. Test your
answer and the transistor and its associated components.
In most process applications the
temperature sensor is inserted
into a thermowell or protection
tube. This protects the sensor
from its environment and
facilitates easy removal and
replacement. These assemblies
generally consist of a head,
nipple-union-nipple and
thermowell. Smart industrial
thermocouples and RTDs are
available in virtually any
calibration and resistance
temperature coefficient.
Industrial Assemblies
72
Procedure/Tasks – Hardwired Circuit
Now that you have tested the circuit to satisfy the problem statement using Multisim, it’s time to
hardwire the circuit depicted in Figure 5-5 using real components. However, as you did in Labs 1
and 2, before continuing you are going to generate the list of components and the equipment that
you need to complete this task.
List of components
Item #
Equipment
Component Description
Reference
Designators
Quantity
73
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such a
checklist will enable you to minimize errors in the circuit assembly, prevent malfunction, and
consequently reduce damage to components. This checklist should always be used, but it is not
limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For example, it
is not uncommon for IC manufacturers to use different pinouts between DIP8 and
SOIC8 packages for the same part. Sometimes a circuit designer will layout a
schematic using the pinout of a SOIC part and the person doing the wiring of the
circuit might use a DIP part. The consequence of this is an incorrectly wired
breadboard resulting in faulty circuit operation and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin. This is
especially important when there is high speed digital or high load current circuit
combined with sensitive analog circuit (such as a Wheatstone bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a tantalum
bypass capacitor of 10 - 33μF should be used between power and ground points where the
power supply leads connected to the breadboard. Make sure the polarity of the capacitor
is correct and that its working voltage (WV) is at least 1.5 times the maximum voltage
used in the circuit. e.g., the working voltage rating of a capacitor is 10V; the supply
voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback resistors
should be routed from the amplifier’s output pin directly to the input pin. This helps to
reduce the possible amplifier’s feedback loop pick up and amplifies the unwanted noise.
•
All component leads should be kept as short as possible. Additionally, signal paths from
one IC to another should be kept as short as possible to minimize noise pickup. If a signal
74
path must be long for whatever the reason, ensure it is routed away from other signal
paths to reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all
ground buses and power buses should be terminated at one point. That is, you should not
be able to trace a loop from the ground or power supply connection to the breadboard to
all component connections and then back to the power or ground source.
•
If it is possible, separate analog and digital power supplies and grounds from one another.
These should be routed back and terminated at the single power and ground termination
point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g., LMC555
over a TTL 555), unless the design calls for the high current capacities of TTL.
Hardwired Circuit Procedure
1. Adjust R1 potentiometer until Vref is approximately equal to 60 mV.
2. Adjust R2 potentiometer until the input voltage (Vin) is approximately equal to 60 mV. What
is the condition of the LED?
3.
Leaving Vref at approximately 57 mV, adjust Vin (by adjusting potentiometer R2) to the
values indicated on Table 5-2 and record if the LED is ON or OFF.
Table 5-2. LED status versus input voltage in the hardwire circuit
Vref (mV)
Vin (mV)
60
20
60
40
60
60
60
80
60
120
60
140
LED
75
Questions
1. Compare the results of Tables 5-1 and 5-2. Are they about the same? Describe any
discrepancies and explain what could be the possible causes.
2. If Vref = 100 mV and Vin = 90 mV, is the LED ON or OFF? Did you get the same result in
Multisim?
3. Replace the Q1 transistor by a PNP transistor such as the 2N3906 as you did using Multisim.
Does the circuit work as expected?
Conclusions
After completing the temperature sensor circuit both in Multisim and hardwire, what are your
conclusions?
76
Advanced Design
If you want to earn extra credit, try the following design.
You work for a product manufacturing company that uses a JIT (Just-In-Time) inventory system.
One of the workstations requires the use of 15 ball bearings during its assembly procedure for
each product. Because these ball bearings are small and difficult to handle, the company has built
an automated ball bearing dispenser machine for operators to use. This machine works great,
except for the fact that it is a completely enclosed container (to hold the ball bearing inventory
and keep it clean). As a result, there is no way to see when the ball bearing inventory is low.
Because ball bearing shortages have stopped the line numerous times, your supervisor has tasked
you to design a level sensing circuit that sets off an alarm when the ball bearing inventory gets
low.
Knowns:
1. The environment is electrically noisy, due to the large number of automated assembly
machines being used.
2. Your supervisor does not care how you implement the design, as long as it can reliably detect
when the level of ball bearings has gotten below a desired inventory level.
3. Your supervisor wants this detection implementation to be relatively simple so that it can be
placed to detect different levels of ball bearing inventory at different workstations.
Unknowns:
1. What kind of sensor do we use to detect the ball bearing level?
2. What kind of circuit do we need to detect the sensor output and trip an alarm? (Hint: look at
the temperature sensing circuit design in figure 5-5. How should this design be modified for
this application?)
3. What kind of components do we need to implement this circuit design?
4. How do we deal with the electrically noisy manufacturing environment and how does it
affect our circuit design? (Hint: look at the temperature sensing circuit design in figure 5-5.
How should this design be modified for this application?)
5. Who thought it was a good idea to design a product that needed 15 ball bearings, and why?
(This is a rhetorical question).
77
LAB 6 – SCR CIRCUIT
Objectives
1. Build, test, and troubleshoot an SCR circuit using Multisim.
2. Hardwire the SCR circuit of objective 1 and compare the measurements of the hardwired
circuit with the measurements obtained using Multisim.
Preliminary Information
The Thyristor is a device of four layers (PNPN). There are several devices of four layer
construction; in this case we will discuss three of them: the SCR, the TRIAC and the DIAC.
Silicon Controlled Rectifier (SCR).
The SCR is used to control high power because its junctions can be manufactured to pass current
in the hundreds of amperes and to withstand high reverse bias of several hundred volts.
The combination of high reverse voltage and high current handling is impossible for a power
transistor. An SCR can be considered as two interconnected transistors as follows:
Anode
Anode
Gate
Gate
Cathode
P
N
P
N
Cathode
SCR
Symbol
Anode
Anode
Equivalence with
four layers
Gate
N
P
P
N
P
N
Cathode
Equivalence with
two transistors
Gate
Cathode
Equivalence with
two transistors
78
For current analysis of an SCR we use a discrete transistor circuit model. This model provides a
view of an SCR with its equivalent transistor circuit connected to a load RL. Using this circuit
we will calculate the value of IL
From the figure we have:
Anode
IL = IC2 + IB2
(1)
IB2 = IC1
(2)
IB1 = IC2
(3)
IC1 = hFE1(IB1)
(4)
IC2 = hFE2 IC1
(5)
Substituting IC1 in equation 4 with equation 2:
IC1
IC2
Q1
IB1
Cathode
(6)
Substituting IC1 & IB2 in equation 1 with equations 5 and 6:
IL = hFE2 IB2 + hFE1 IB1
IB2
Q2
By definition:
IB2 = hFE1(IB1)
RL
IL
SCR - equivalence with
two transistors
(7)
Substituting IB2 in equation 7 with equation 6:
IL = hFE2 hFE1 IB1 + hFE1 IB1
(8)
Factoring, we have:
IL = hFE1 IB1 (hFE2 + 1)
(9)
Considering that:
hFE2 >> 1 then (hFE2 + 1) ≅ hFE2
(10)
Substituting (hFE2 + 1) in equation 9 with equation 10:
IL ≅ hFE1 hFE2 IB1
Formas físicas del SCR.
(11)
According to equation 11, a small IB1 current applied to the SCR’s gate will produce a big
current, IL.
79
The SCR remains off until an external current is applied at the gate. Once it triggered, the SCR
will remain on even if we remove the signal at the gate. The SCR will switch off only when the
current it passes falls below a value called the holding current or the voltage applied between the
anode and the cathode is removed or reversed in polarity.
The SCR is usually used as a high power diode rectifier that can be controlled by a relatively
small signal at its gate. This implementation is used to rectify AC, thus creating a pulsed DC
current, and control the availability of this DC current.
THE TRIAC
It can be considered as two SCRs with a single gate.
Anode 2
Anode 2
Gate
Gate
Anode 1
Anode 1
TRIAC Symbol
Equivalence of the TRIAC
with two SCRs
The TRIAC can be activated (triggered) with positive or negative pulses applied to the gate.
A small gate current is usually able to control a high load current, for example: 20 mA of gate
current can control 25 Amp of current in the load.
RL
50%
R
TRIAC
DIAC
C
AC Supply
Load
Trigger circuit
Thyristor
This schematic shows the
components of a thyristor circuit
(In this case it is a TRIAC) that
controls the amount of current
applied to the load (RL).
80
RL
50%
R
TRIAC
Supply AC
DIAC
C
When an alternating voltage is applied to the
circuit, current flows through resistor R and
charges the capacitor. As the applied voltage
increases, the charge in the capacitor
increases too. Meanwhile, the TRIAC
remains off.
When the voltage across the capacitor is
greater than the breakover voltage of the
DIAC, the capacitor discharges through the
DIAC producing a pulse current that triggers
the TRIAC.
Once the TRIAC is activated, it remains on and a high current flows through the load RL. On the
other hand, the voltage between the terminals of the RC network is limited by the voltage
between the anode and cathode of the TRIAC which is about 1 volt.
This situation continues until the half cycle of the AC source ends. At that point the applied
voltage is about zero and the current through the TRIAC drops below the "holding current",
turning the TRIAC off.
The AC source then enters the following half cycle, the capacitor starts charging again (in the
opposite direction) and the cycle repeats.
With appropriate RC values, the output can be varied from zero until near the maximum power
by adjusting the potentiometer.
The DIAC is a bidirectional diode connected at the SCR or TRIAC’s gate
when using alternating current. The DIAC has the following property: for
small applied voltages there is no current flow, but if the applied voltage is
increased above a value called breakover voltage, the device begins to conduct.
The breakover voltage is around 30 V.
DIAC Symbol
Among the more common applications of
the TRIAC are lamp dimmers and motor
speed controllers.
Physical shapes of TRIACS
81
Problem Statement
Build an SCR or TRIAC circuit that controls the power across a lamp which constitutes the load.
For safety reasons use a power transformer that provides a secondary voltage of 12.6 VAC. You
should be able to vary a potentiometer to control how much power is going to the load.
Solution
The appropriate circuit is shown in Figure 6-1.
XSC1
Voltage across the Load
G
T
A
B
X1
Key = Space
XSC2
12V_10W
J1
T1
TS_PQ4_12
G
R2
4.7kΩ
XMM1
T
A
B
V1
120 Vrms
60 Hz
0Deg
R1
50%
Voltage across the SCR
D2
100kΩ
Key=A
C1
220nF
IC=0V
D1
2N5064
1N4001GP
Figure 6-1. SCR circuit
Circuit analysis
Because we are using a low AC voltage for safety reasons, transformer T1 reduces the 120 VAC
to about 12 VAC. R1 and C1 determine the time constant; in other words, how fast or how slow
the capacitor charges. In this case, the time is varied by R1. R2 is added as a limiting resistor in
the event that R1 is inadvertently adjusted to 0 Ω. Notice that instead of a DIAC we are using a
diode. A DIAC needs a voltage greater than 30 V to conduct. Therefore, with the input voltage
being only 12 VAC, a DIAC will not work. In addition, an SCR cannot withstand negative
voltages at its gate; therefore, a diode allows only the positive alternations to be applied to the
gate and prevents the negative alternations from reaching the gate.
The lamp X1 constitutes the load. By varying the time constant through R1 you will notice how
the duty cycle of the lamp will also vary. You can view the waveforms with oscilloscopes in
Multisim. Oscilloscope XSC1 measures the voltage across the load (X1) and oscilloscope XSC2
measures the voltage across the SCR (D1).
82
Procedure/Tasks Using Multisim
1. Build the circuit in Figure 6-1 using Multisim. Make sure that you use two oscilloscopes, one
to observe the signal at the load (X1) and the other to observe the signal at the SCR (D1). In
addition, ensure that X1 is a 12 V lamp.
2. Adjust R1 (by pressing the A or SHIFT-A keys) and observe the waveforms at the load and
at the SCR. In addition, observe the duty cycle of the lamp and see how it corresponds to the
SCR waveforms.
3. You should notice then that R1 controls how much voltage is applied to the lamp (load).
Figure 6-2 shows an example of the voltage that you should observe across the load and
across the SCR.
voltage across the load
voltage across the SCR
Figure 6-2. Waveforms across the load and across the SCR.
By observing the waveforms in Figure 6-2, it can be seen that when the SCR is conducting
the voltage across the SCR is about zero. Additionally, when the voltage across the load is
zero, the SCR is off and the corresponding portion of the applied voltage appears across the
SCR.
4. Build the circuit depicted in Figure 6-3. Notice that we are using a higher VAC and we can
use the DIAC (D2). In this case, make sure that X1 is a 120 V lamp because the applied
voltage is 120 VAC. D3 ensures that the capacitor charges during the positive alternations
only, because the SCR’s gate cannot receive negative voltages.
83
XSC1
Voltage across the Load
A
B
X1
F1
2_AMP
120V_100W
D3
1N4002GP
XSC2
G
T
R2
4.7kOhm
V1
120 V
60 Hz
0Deg
G
T
A
20%
B
R1
D2
Key = A
100kOhm
C1
0.22uF
D1
2N5064
Voltage across the SCR
1N5758
Figure 6-3. SCR circuit with a DIAC and a higher input voltage.
5. Repeat steps 2 and 3. Do you observe the same behaviors and waveforms as in the circuit of
Figure 6-1? Describe any difference and explain the reasons.
84
XSC1
G
T
Voltage across the Load
A
F1
2_AMP
B
X1
XSC2
120V_100W
G
T
R2
4.7kOhm
V1
120 V
60 Hz
0Deg
A
50%
B
R1
D2
Key = A
1MOhm
C1
0.22uF
D1
2N5444
Voltage across the TRIAC
1N5758
Figure 6-4. TRIAC circuit.
6. Now, build the circuit indicated in Figure 6-4 using a TRIAC instead of an SCR.
7. By activating the circuit, observing the waveforms, and the lamp behavior what are your
conclusions of the circuit in Figure 6-4 respect the one in Figure 6-3?
85
Questions
1. What would happen if you use a 12-V lamp in the circuit of Figure 6-3?
2. Can you replace the SCR by a TRIAC in Figure 6-3? Explain
3. Assuming that the breakover voltage of DIAC D2 is 30 V in Figure 6-3 and the voltage
across the capacitor reaches – 30 V (negative voltage), Is this possible? Why?
4. Why is the reason that the circuit in Figure 6-4 does not need diode D3 as in Figure 6-3?
86
Procedure/Tasks – Hardwired Circuit
You are going to hardwire one of the circuits that you built and analyzed using Multisim. This
time you are going to hardwire the circuit shown in Figure 6-1. As you did in previous labs,
before continuing you are going to indicate the list of components and the equipment that you
need to complete this task.
List of components
Item #
Equipment List
Component Description
Reference
Designators
Quantity
87
1. Hardwire the circuit shown in Figure 6-1. If you don’t have access to an oscilloscope, then
disregard it in this part. You will observe the circuit behavior by looking at the lamp
brightness. If you do not have an oscilloscope, then skip step 2 and go to step 3.
2. When taking the measurements in the hardwired circuit, connect the oscilloscope to measure
the voltage across the load only. DO NOT attempt to use a dual-trace oscilloscope to
measure the voltage across the load and the voltage across the SCR (D1). What you can do is
connect the oscilloscope as XSC1 in Figure 6-1 to observe the waveform at the load. Then,
disconnect the oscilloscope and connect it the way XSC2 is connected in Figure 6-1 to
observe the waveform across the SCR.
3. Adjust R1 and observe the lamp’s brightness. If you have an oscilloscope, observe the
waveform across the load first. Then connect the oscilloscope across the SCR and observe
the waveforms across it.
4. What do you observe with the lamp’s brightness as you vary the R1 potentiometer?
5. Do you observe the same results when you use Multisim? Describe any discrepancies.
Questions
1. Can we substitute the lamp by a resistor?
2. What would happen if diode D2 is reversed?
88
3. What would happen if diode D2 opens?
4. What would happen if diode D2 shorts?
5. What difficulties have you encountered in hardwiring the SCR circuit of Figure 6-1?
Conclusions
After completing the SCR circuit both in Multisim and hardwire, what are your conclusions?
89
LAB 7 – THE INTEGRAL CONTROLLER
Objectives
1. Build, test, and analyze an integral controller circuit using Multisim.
2. Predict the expected output waveform of an inverting integral controller given a specific
input waveform and then verify it using Multisim.
3. Design a non-inverting integral controller given a certain time constant and voltage supplies
using Multisim.
Preliminary Information
Read “Controllers with Multisim” to gain an understanding about process control and how to
simulate controllers using Multisim.
The integral controller monitors the average error over a period of time. If an offset error exists,
the integral unit will, during the time that error exists, accumulate the value of the error and
output a correction signal whose rate of change (slope or dv/dt) is equal to the magnitude of the
accumulated error signal..
An integral unit is usually used together with a proportional unit and the two units are designated
as a PI controller (Proportional Integral).
Let’s assume that he signal shown in Figure 7-1 is applied to an integral controller.
+ 2V
0
1
5
ms
10
8
–4V
Figure 7-1. Input waveform applied to an Integral Controller
The block of an integral controller is depicted in Figure 7-2 and its corresponding output
equation is as shown in equation 1.
Vin
Vout = ∫ Vin
(1)
Integral
Controller
Vout
Figure 7-2. Block diagram of an integral controller.
90
To integrate the input signal, we will divide it in four functions that we call: f1(x), f2(x), f3(x),
and f4(x) as indicated in Figure 7-3.
Then: Vin = f1(x) + f2(x) + f3(x) + f4(x)
(2)
Observing the graph of the input signal, each function is defined in the following way:
f1(x) : y = 0 , 0 < x < 1
(3)
f2(x) : y = 2 , 1 < x < 5
(4)
f3(x) : y = - 4 , 5 < x < 8
(5)
f4(x) : y = 0 ,
(6)
8<x
3
2
1
0
–1
–2
–3
–4
5
8
f4
f1
1
1
5
8
f3
∞
∫ Vin = ∫ f1 (x) dx + ∫ f 2 (x) dx + ∫ f 3 (x) dx + ∫ f 4 (x)dx
0
5
Figure 7-3. Input signal divided into
four segments for analysis purposes.
Integrating both members of equation 2:
1
f2
(7)
8
Replacing equations 1, 3, 4, 5, and 6 in equation 7 and integrating each term, we have:
∫ Vin = Vout
1
1
(8)
∫ f1 (x) = ∫ 0 dx = [ 0 ]0 = 0
0
0
5
5
1
(9)
∫ f 2 (x) = ∫ 2 dx = [ 2x + C ]1
1
1
8
8
5
(10)
∫ f 3 (x) = ∫ - 4 dx = [ - 4x + C ]5
5
5
∞
∞
8
∫ f 4 (x) = ∫ 0 dx = [ 0 + C ]8
8
8
∞ =C
(11)
(12)
91
Output Waveform
To graph the output waveform, we will proceed to find the intersection points of equations: 9,
10, 11 and 12.
1
Step 1: Finding the points for equation 9:
∫ f1 (x) dx = [ 0 ]0 = 0
1
0
The result of equation 9 is zero, thus the graph is a straight line with a slope of zero (parallel to
the x axis), starting at the initial point (0, 0) until the final point (1,0) because this it is the
distance that covers the function f1(x). See line “a” in Figure 7-7.
5
Step 2: Finding the points for equation 10:
∫ f 2 (x) dx = [ 2x + C ]1
5
1
Calculation of C constant. See figure 7-4.
1. The value of x is similar to the
common point where the previous
function ends and the following
function begins. In this case it is 1.
2. To solve for the integration constant
(C) we must take the function we are
integrating and set it equal to the y
value endpoint calculated from the
previous interval. In this case it is
zero.
For: 2x + C and solving for C:
C=–2
2(1) + C = 0
3
2
1
0
–1
–2
–3
–4
f2
f4
f1
1
5
8
f3
Figure 7-4. Graph to find the C constant
value from equation 10.
Evaluating equation 10 with the minimum x value (1) and maximum x value (5):
5
5
1
1
∫ f 2 (x) = ∫ 2 dx = [ 2x + C ]1
For x = 1
For x = 5
5
[2x + C]x=1
Replacing values: 2(1) + (– 2) = 0
∫f
[2x + C]x=5
Replacing values: 2(5) + (– 2) = 8
∫f
The points for the graph of equation 10 are:
See line “b” in Figure 7-7.
2
2
( x )dx = 0
( x )dx = 8
Initial point: (1, 0)
Final point: (5, 8)
92
8
Step 3: Finding the points for equation 11:
∫ f 3 (x) dx = [ - 4x + C ]5
8
5
Calculation of C constant. See
figure 7-5.
1. The value of x is 5
2. Solving for C in f2(x) we take the
function we are integrating and set
it equal to the y value endpoint
calculated from the previous
interval. In interval f2 this value
was 8.
3
2
1
0
–1
–2
–3
–4
For: – 4x + C and replacing values:
– 4(5) + C = 8
f2
f4
f1
1
5
8
f3
Figure 7-5. Graph to find the C
constant value from equation 11.
C = 28
Evaluating equation 11 with the minimum x value (5) and maximum x value (8):
8
8
5
5
∫ f 3 (x)dx = ∫ - 4 dx = [ - 4x + C ]5
For x = 5
8
[– 4x + C]x=5
Replacing values: – 4(5) + 28 = 8
For x = 8
∫ f 3 (x) = 8
– 4x + C
Replacing values: – 4(8) + 28 = – 4
∫f
3
(x) = – 4
The points for the graph of equation 11 are:
Initial point: (5, 8)
Final point: (8, – 4)
See line “c” in Figure 7-7.
93
∞
Step 4: Finding the points for equation 12:
∫ f 4 (x)dx = [ 0 ]8
∞ =C
8
But
C = 0x + C
Calculation of C constant. See figure 7-6.
1. The value of x is 8
2. Solving for C in f3(x) we take the
function we are integrating and
set it equal to the y value
endpoint calculated from the
previous interval. In interval f3
this value was – 4.
3
2
1
0
–1
–2
–3
–4
f2
f4
f1
1
5
8
f3
For: 0x + C and replacing values
0(8) + C = – 4
C=–4
Figura 7-6. Graph to find the C
constant value from equation 12.
The graph is a straight line with a zero slope (parallel to the x axis), starting from the point
(8, – 4) towards infinity.
See line “d” in Figure 7-7.
Note:
This wave form (red) is the result of
using an integral controller with
non-inverted output.
Figure 7-7. Output of a noninverting controller
8
7
6
5
4
3
2
1
0
–1
–2
–3
–4
b
c
f2
f1
a 1
f4
5
8
f3
d
94
For an inverting integral controller, the output waveform (red line) is the one that is indicated in
the adjacent graph.
Figure 7-8. Output of an
inverting controller
4
3
2
1
0
–1
–2
–3
–4
–5
–6
–7
–8
d
f2
f4
f1
a 1
5
8
c
b
f3
95
Problem Statement
The input signal shown in Figure 7-1 is available. This figure is shown on page 1 but it’s
repeated here for convenience. Draw the expected output indicating its amplitude. The Integral
Controller has a time constant RC = 1 ms and uses a supply of ± 12 V.
+ 2V
0
1
5
ms
10
8
–4V
Figure 7-1. Input waveform applied to an Integral Controller
We assign points at the beginning of each segment as shown in Figure 7-9. These points are t0, t1,
t2, t3 and t4.
t0
+ 2V
0
t1
t2
1
t3
5
8
t4
ms
10
–4V
Figure 7-9. Input waveform divided by times
Expected Output Waveform
The equation of an integrator with a constant error input is:
Vo =
− Vin t
+C
RC
(13)
The procedure is as follows:
(a)
For time t0 to t1 and using equation 13 we have:
Vin = 0 V; t = t1 – t0 = 1 – 0 = 1 ms; RC = 1 ms; C = 0.
C is the previous Vo. Since the previous or initial Vo is not given we assume it is 0.
96
Vo =
(b)
− Vin t
− (0)(1ms)
+C =
+ 0 = 0 Segment “a” in Figure 7-8.
RC
1 ms
For time t1 to t2 and using equation 13 we have:
Vin = 2 V; t = t2 – t1 = 5 – 1 = 4 ms; RC = 1 ms; C = 0.
C is equal to 0 because the calculated previous Vo is 0.
Vo =
(c)
− Vin t
− (2V)(4ms)
+C =
+ 0 = −8V Segment “b” in Figure 7-8.
RC
1 ms
For time t2 to t3 and using equation 13 we have:
Vin = - 4 V; t = t3 – t2 = 8 – 5 = 3 ms; RC = 1 ms; C = – 8 V.
C is equal to – 8 V because the calculated previous Vo is – 8 V.
Vo =
(d)
− Vin t
− (−4V)(3ms)
+C =
+ (−8) = +4V Segment “c” in Figure 7-8.
RC
1 ms
For time t3 to t4 and using equation 13 we have:
Vin = 0 V; t = t4 – t3 = 10 – 8 = 2 ms; RC = 1 ms; C = + 4 V.
C is equal to + 4 V because the calculated previous Vo is + 4 V.
Vo =
− Vin t
− (0V)(2ms)
+C =
+ 4V = +4V Segment “d” in Figure 7-8.
RC
1 ms
97
Procedure/Tasks Using Multisim
1. Build the circuit shown in Figure 7-10 using Multisim.
1
Integrator
V2
1000V/V
0
3
0
Figure 7-10. Inverting Integrator controller
The Integrator block is the Voltage Integrator block in Multisim.
Voltage Integrator Block
In Multisim, you can have an inverting integrator or a non-inverting integrator as indicated in
Figure 7-11. In this case we are using an inverting integrator.
A1
Non-inverting Input
Non-inverting Output
Inverting Input
Inverting Output
1 V/V 0 V
Figure 7-11. Integrator block in Multisim
For the inverting integrator we can use the non-inverting input and the inverting output or the
inverting input and the non-inverting output. In either case both the input and output terminals
that are not used must be grounded. In this lab we’ll use the non-inverting input and the inverting
output.
The output equation of an integrator was indicated previously in equation 13 and repeated here
for convenience:
Vo =
− Vin t
+C
RC
If we make
(13)
1
= K then we have:
RC
98
Vo = – Vin t K + C
(14)
According to the problem statement RC = 1 ms; thus, K = 1/RC = 1/0.001 s = 1000 (1000 V/V in
the Integrator Block).
In addition, the supply is ± 12 V. This means that the saturation voltage is ± 10 V (2 V less than
the supply voltages).
The way we change the Gain (K) and the saturation voltage is by double-clicking the Integrator
block. When you do this, you’ll observe the following window:
The Gain of 1000 is changed in Gain (K).
– Vsat is the same as the “Output voltage lower limit (VL)”
+ Vsat is the same as the “Output voltage upper limit (VU)”
The initial voltage (Vinitial) is set in “Output initial condition (VOIC)”
The error signal source (V2) is called a Piecewise Linear Voltage (PWL) which produces the
type of waveform such as the one needed in this lab experiment.
99
When you double-click V2 you’ll observe the following window:
To produce the needed waveform, enter the following values:
Time
Voltage
Description
0
0
At 0 s, the voltage is 0
1e–3
0
At 1 ms, the voltage is still 0
1.001e–3
2
At 1.001 ms, the voltage jumps to 2 V
5e–3
2
At 5 ms, the voltage is still 2 V
5.001e–3
–4
At 5.001 ms, the voltage goes to – 4 V
8e–3
–4
At 8 ms, the voltage is still – 4 V
8.001e–3
0
At 8.001 ms, the voltage goes to 0 V
10e–3
0
At 10 ms, the voltage remains at 0 V
100
Circuit Operation
DO NOT turn on the power switch. In this lab experiment you are going to use the Transient
Analysis:
Simulate
Analyses
Transient Analysis
Make sure that you enter the following parameters:
Click on the Analysis Parameters tab. The Start time is set to 0 sec and the end time is set to 0.01
sec (10 msec).
Click on the Output variables tab.
Add nodes 1 (input) and 3
(output).
Note: These numbers can be
different in your circuit
depending on the order that the
components have been
selected, so make sure that you
add the proper nodes.
101
Next, click on Simulate. You should observe the waveforms depicted in Figure 7-12. The red
waveform is the input and the blue waveform is the output.
C
t1
D
t2
t3
t4
A
B
Figure 7-12. Waveforms of the Inverting Integral Controller using Multisim
Questions
1. Does the output waveform obtained in Multisim match the calculated one? Explain any
discrepancies.
2. Rearrange the circuit so that we use the non-inverting output and verify its behavior. What do
you observe in the output waveform?
102
3. Change RC to 0.5 ms and compare the measured output waveform with the calculated one.
Explain why the output waveform is distorted.
4. The input waveform illustrated in Figure 7-13 is applied to an inverting integrator with:
RC = 2 ms and a supply of ± 15 V.
4V
1V
0
1
5
8
10
12 ms
0
–2V
Figure 7-13. Input waveform for question 4.
a. Draw the expected output waveform below the input signal in Figure 7-13 indicating its
amplitude.
b. Draw the appropriate circuit using Multisim and observe the output waveform. Does the
observed output waveform match the one you drew in step 4a? Explain any
discrepancies.
103
5. The input waveform shown in Figure 7-14 is applied to a non-inverting integrator with:
RC = 5 ms and a supply of ± 18 V.
4V
0
2
6
14
18
20 ms
2V
0
–4V
Figure 7-14. Input waveform for question 5.
a. Draw the expected output waveform below the input signal in Figure 7-14 indicating its
amplitude.
b. Draw the appropriate circuit using Multisim and observe the output waveform. Does the
observed output waveform match the one you drew in step 5a? Explain any
discrepancies.
Conclusions. What are your conclusions regarding the Integrator Controller using Multisim?
104
Advanced Design
If you want to earn extra credit, try the following design.
The input waveform shown in Figure 7-1 is applied to a Proportional-Integral (PI) controller.
The integral controller has an RC constant of 1 ms and a supply of ± 16 V and the proportional
controller has a gain of –1. Test your solution using Multisim and compare your output
waveform with the one obtained in Multisim. For your convenience, Figure 7-1 is shown below.
+ 2V
0
–4V
1
5
8
ms
10
105
LAB 8 – DERIVATIVE CONTROLLER
Objectives
1. Build, test, and analyze an inverting derivative controller using Multisim.
2. Predict the expected output waveform of an inverting derivative controller given a specific
input waveform and verify it using Multisim.
3. Design a non-inverting derivative controller given a certain time constant and voltage
supplies using Multisim.
Preliminary Information
Read “Controllers with Multisim” to gain an understanding of process control and how to
simulate controllers using Multisim.
The Derivative Controller delivers a signal proportional to the rate of change (dv/dt) of the error
signal. When the controlled variable coincides with the reference point (set point), the derivative
signal is zero; conversely, when the value of the controlled variable changes, the derivative
signal is large. The result is a quick controller response to load changes.
Next, we will mathematically analyze the Derivative Controller when we apply the signal shown
in figure 8-1.
+ 2V
0
1
5
8
ms
10
–4V
Figure 8-1. Signal applied to the input of the Derivative Controller.
The Derivative Controller's block is shown in figure 8-2 and equation 1 is its corresponding
output equation.
Vout =
d
Vin
dt
(1)
Vin
Derivative
Controller
Vout
Figure 8-2. Block Diagram of a Derivative Controller
106
For the analysis, we will divide the input signal in four functions that we will call: f1(x), f2(x),
f3(x), and f4(x) as indicated in Figure 8-3.
Then: Vin = f1(x) + f2(x) + f3(x) + f4(x)
(2)
Each one of these four functions is based on the graph of figure 8-3, in the following way:
f1(x) : y = 0 , 0 < x < 1
(3)
f2(x) : y = 2 ,
1<x<5
(4)
f3(x) : y = – 4 , 5 < x < 8
(5)
f4(x) : y = 0 ,
(6)
8<x
3
2
1
0
–1
–2
–3
–4
f2
f4
f1
1
5
8
f3
Figure 8-3. Input signal divided into four segments
for analysis purposes.
Deriving both sides of equation 2:
d
d
d
d
d
Vin = f1 ( x ) + f 2 ( x ) + f 3 ( x ) + f 4 ( x )
dt
dt
dt
dt
dt
(7)
Deriving equations 3, 4, 5, 6 separately, we have:
d
d
f1 ( x ) = 0 = 0
dt
dt
(8)
d
d
f 2 (x) = 2 = 0
dt
dt
(9)
d
d
f 3 (x) = − 4 = 0
dt
dt
(10)
d
d
f 4 (x) = 0 = 0
dt
dt
(11)
Replacing equations 8, 9, 10 and 11 in equations 7 and 1, we have:
Vout =
d
Vin = 0 + 0 + 0 + 0 = 0
dt
(12)
107
Equation 12 indicates that the function results in a straight line with zero slope that is coincident
with the x axis. The graph of equation 12 is indicated in figure 8-4.
Figure 8-4. The blue line shows the output
waveform based on equation 12
3
2
1
0
–1
–2
–3
–4
1
5
8
Observing figure 8-3, notice that at the junction points of functions f1 and f2 (where x = 1), f2 and
f3 (where x = 5), f3 and f4 (where x = 8); there is discontinuity of the total function because there
are two values in the y-axis for a single value in the x-axis. For example:
For x = 1
we have
y=0
y=2
For x = 5
we have
y=2
y=–4
For x = 8
we have
y=–4
y=0
Multisim works only with continuous functions; therefore, to resolve the discontinuity issue of
the total function we should modify the waveform slightly, in the following way:
Figure 8-5. Waveform drawn with
exaggeration to show the
modifications in relationship to the
original signal of figure 8-3. The
functions are only indicated in the
discontinuity points.
3
2
1
0
–1
–2
–3
–4
g1
1
5
g2
8
g3
In figure 8-5, we have increased the x-axis by the thousandth between the end and beginning of
the following function. This incremental increase should be the possible minimum so that the
original signal does not change.
108
Now, we will analyze the output of the Derivative Controller at the intersection points of the
functions that we call g1(x), g2(x), g3(x). We will find the derivative of each of these new
functions in the following way:
(x2, y2)
Deriving the function g1(x).
(1.001, 2)
2
g1(x)
Figure 8-6. Enlarged view of the function
g1(x) with the initial and final points.
y = mx + b
(1)
(1, 0)
equation of the straight line
Applying equation 1 to the function g1(x), we have: g1(x) = mx + b
y − y1
m= 2
x 2 − x1
(3)
(x1, y1)
(2)
definition of the slope of a straight line
Substituting the values of figure 8-6 in equation 3, we have:
m=
2 − 0 = 2000
1.001 − 1
2000
Substituting equation 4 for m in equation 2:
g1(x) = 2000x + b
(1.001, 2000)
(4)
(5)
≈
Differentiating both sides of equation 5:
(1, 0)
d
d
g1 ( x ) =
(2000x + b)
dx
dx
(6)
d
g1 ( x ) = 2000
dx
(7)
Figure 8-7. Graph of the
derivative of function g1(x)
Note: It is not necessary to find the value of the constant b, because the derivative of a
constant is zero.
The graph of equation 7 is a straight line with a positive slope of 2000. Remember that every
number can be thought of as having some arbitrary unit value for its denominator. Therefore, to
graph equation 7 we should start from the initial point (1, 0), a unit in the horizontal axis, and
end 2000 units up to the vertical axis because the slope is positive.
Note: The word unit, for the layout of the straight line should be understood in the following
way: if we agree that the distance 2000 is equal to two centimeters, then the unit will
be 1/2000 = 0.0005 cm = 0.005 mm
109
Deriving function g2(x)
2
Figure 8-8. Enlarged view of the function g2(x)
with the initial and final points.
(5, 2)
g2(x)
–4
y = mx + b
(1)
(3)
(x2, y2)
(5.001, –4)
equation of the
straight line
Applying equation 1 to the function g2(x), we have: g2(x) = mx + b
y − y1
m= 2
x 2 − x1
(x1, y1)
(2)
definition of the slope of a straight line
Substituting the values of figure 8-8 in equation 3, we have:
m = − 4 − 2 = − 6000
5.001 − 5
(4)
Substituting equation 4 for m in equation 2:
g2(x) = –6000x + b
(5)
Differentiating both sides of equation 5:
d
d
g 2 (x) =
(−6000x + b)
dx
dx
(6)
d
g 2 ( x ) = −6000
dx
(7)
Since the second member of equation 7 has a negative sign, it corresponds to a straight line with
a negative slope. In this case, we should start from the initial point (5, 0), a unit in the horizontal
axis, and end 6000 units down to the vertical axis, as shown in figure 8-9.
(5, 0)
2
≈
Figure 8-9. Graph of the
derivative of the function g2(x)
(5.001, –6000)
–6000
110
Deriving the function g3(x)
Figure 8-10. Enlarged view of the
function g3(x) with the initial and final
points.
2
(x2, y2)
(1)
(x1, y1)
–4
To derive the function g3(x), we will
proceed in the same way as we did for
the functions: g1(x) and g2(x).
y = mx + b
(8.001, 0)
equation of the straight line
Applying equation 1 to the function g3(x), we have: g3(x) = mx + b
y − y1
m= 2
x 2 − x1
(3)
g3(x)
(8, – 4)
(2)
definition of the slope of a straight line
Substituting the values of figure 8-10 in equation 3, we have:
m=
0 − (−4)
= 4000
8.001 − 8
(4)
Substituting equation 4 for m in equation 2:
g3(x) = 4000x + b
(5)
Differentiating both members of equation 5:
d
d
g 3 (x) =
(4000x + b)
dx
dx
(6)
d
g 3 ( x ) = 4000
dx
(7)
The graph of equation 7 is a straight line with a positive slope that starts from the initial point
(8, 0) in the horizontal axis and ends 4000 units up to the vertical axis, as indicated in figure
8-11.
4000
(8.001, 4000)
≈
Figure 8-11. Graph of the derivative
of the function g3(x)
(8, – 0)
–4
111
The final graph of the output of the Derivative Controller is the sum of figures: 8-4, 8-7, 8-9
and 8-11.
4000
2000
≈
≈
2
1
–4
5
8
≈
– 6000
Figure 8-12. The blue waveform is the output of the Derivative Controller using the noninverting output. The red waveform corresponds to the input signal
The peaks demonstrate the behavior of the quick response of the Derivative Controller to the
changes of the input signal.
6000
≈
2
1
–4
– 2000
5
8
≈
≈
– 4000
In a real circuit, the maximum value of the peaks is limited by the +Vcc and – Vcc applied to the
Derivative Controller.
112
Problem Statement
Figure 8-14 is the intended input signal. Notice that this is the same input signal that you used in
the Integral Controller in Lab 7. As you did with the integral controller, you need to draw the
expected output indicating its amplitude.
The Derivative Controller has a time constant RC = 0.5 ms and uses a supply of ± 12 V.
We assign points at the beginning of each segment as shown in Figure 8-14. These points are:
t0, t1, t2, t3 and t4.
t0
+ 2V
0
t1
t2
1
t3
5
8
t4
ms
10
–4V
Figure 8-14. Input waveform applied to a Derivative Controller
Expected Output Waveform
The output equation of an inverting derivative controller is:
Vo = −RC
dVin
dt
(8-1)
A close inspection of Figure 8-14 and using equation 8-1 we notice that the derivative controller
will react every time the input signal changes direction.
For example, at 1 ms (t1) the input signal goes from low to high. In this case, the output signal
will go from 0 to – Vsat almost instantaneously as shown at point A in Figure 8-15. At 5 ms (t2)
the input signal goes from high to low. At this point, the output signal will go from 0 to + Vsat
almost instantaneously as shown at point B in Figure 8-15, and so on.
113
t0
+ 2V
0
t1
t2
t3
1
5
t4
ms
10
8
–4V
B
+ Vsat = 10V
0
– Vsat = –10V
A
C
Figure 8-15. Output waveform of an Inverting Derivative Controller
With this controller the saturation voltage is ± 10 V (typically, it is 2 V less than the supply
voltages).
Procedure/Tasks Using Multisim
1. Build the circuit shown in Figure 8-16 using Multisim.
1
Voltage_Differentiator
V1
d/dt
0.0005 V/V 0 V
0
3
0
Figure 8-16. Inverting Derivative Controller
The Derivative block is the Voltage Differentiator block in Multisim.
114
Voltage Differentiator Block
In Multisim you can have an inverting differentiator or a non-inverting differentiator as indicated
in Figure 8-17. In this case, we are using an inverting differentiator.
Non-inverting Output
Non-inverting Input
d/dt
Inverting Input
Inverting Output
0.0005 V/V 0 V
Figure 8-17. Differentiator block in Multisim
For the inverting differentiator we can use the non-inverting input and the inverting output or the
inverting input and the non-inverting output. In either case, the unused input and output must be
grounded. In this laboratory experiment, we’ll use the non-inverting input and the inverting
output.
The output equation of a differentiator was indicated previously in equation 8-1 and is repeated
here for convenience.
Vo = −RC
dVin
dt
(8-1)
If we make RC = K = Gain then we have:
Vo = −K
dVin
dt
(8-2)
According to the problem statement RC = 0.5 ms;
thus, K = 0.5 ms = 0.0005 (0.0005 V/V in the
Differentiator Block).
In addition, the supply is ± 12 V. This means that
the saturation voltage is ± 10 V (± 2 V of the
supply voltages).
The way we change this saturation voltage is by
double-clicking the Differentiator block. When
you do this, you will observe the following
window:
The Gain of 0.0005 is changed in Voltage Gain (E).
– Vsat is the same as the “Output Voltage Lower Limit (VL)”
+ Vsat is the same as the “Output Voltage Upper Limit (VU)”
115
Error signal source (V1) is called a Piecewise Linear Voltage (PWL). This signal source
produces the type of waveform needed in this lab experiment. This was described previously in
Lab 7 – Integrator Controller. Here, we are using the same input waveform.
Circuit Operation
DO NOT turn on the power switch. In this lab experiment, you are going to use the Transient
Analysis:
Simulate
Analyses
Transient Analysis
Make sure that you enter the following parameters:
Click on the Analysis Parameters
tab.
The Start time is set to 0 sec and the
End time is set to 0.01 sec (10 msec)
Click on the Output variables tab.
Add nodes 1 (input) and 3 (output).
Note: These numbers can be
different in your circuit depending
on the order that the components
have been selected. Therefore, make
sure that you add the proper nodes
for your circuit.
Next, click on Simulate. You should
observe the waveforms depicted in
Figure 8-18.
116
The red waveform is the input and the blue waveform is the output.
B
t1
t2
A
t3
t4
C
Figure 8-18. Waveforms of the Inverting Derivative Controller using Multisim
The red waveform is the input and the blue waveform is the output. In a differentiator, the output
reaches saturation every time the input signal goes from 0 to a positive direction or to a negative
direction. Since we are using the inverting output, we notice the following:
At t1 the input changes from 0 to + 2 V. The output reaches negative saturation, –10 V in this
case (Point A).
At t2 the input changes from + 2 V to – 4 V (negative direction). The output reaches positive
saturation, + 10 V in this case (Point B).
At t3 the input changes from – 4 V to 0 V (positive direction). The output reaches negative
saturation, – 10 V in this case (Point C).
Questions
1. Does the output waveform obtained in Multisim match the calculated one? Explain any
discrepancies.
117
2. Rearrange the circuit so that we use the non-inverting output and verify its behavior. What do
you observe in the output waveform?
3. Change RC to 2 ms and compare the measured output waveform with the calculated one.
What changes (if any) do you observe on the output waveform?
4. The input waveform illustrated in Figure 8-19 is applied to an inverting differentiator with
RC = 2 ms and a supply of ± 15 V.
4V
1V
0
1
5
8
10
12 ms
0
–2V
Figure 8-19. Input waveform for question 4.
a. Draw the expected output waveform below the input signal in Figure 8-19 indicating its
amplitude.
118
b. Draw the appropriate circuit using Multisim and observe the output waveform. Does the
observed output waveform match the one you drew in step 4a? Explain any
discrepancies.
5. The input waveform shown in Figure 8-20 is applied to a non-inverting differentiator with
RC = 5 ms and a supply of ± 18 V.
4V
0
2
6
14
18
20 ms
2V
0
–4V
Figure 8-20. Input waveform for question 5.
a. Draw the expected output waveform below the input signal in Figure 8-20 indicating its
amplitude.
119
b. Draw the appropriate circuit using Multisim and observe the output waveform. Does the
observed output waveform match the one you drew in step 5a? Explain any
discrepancies.
Conclusions
What are your conclusions regarding the Derivative Controller using Multisim?
120
Advanced Design
If you want to earn extra credit, try the following design.
The input waveform shown in Figure 8-14 is applied to a Proportional-Derivative (PD)
controller. The derivative controller has an RC constant of 1 ms and a supply of ± 16 V and the
proportional controller has a gain of –1. Test your solution using Multisim and compare your
output waveform with the one obtained in Multisim. For your convenience, Figure 8-14 is shown
below.
+ 2V
0
–4V
1
5
8
ms
10
121
LAB 9 – PID CONTROLLER
Objectives
1. Build, test, and analyze a Proportional-Integral-Derivative (PID) controller using Multisim.
2. Predict the expected output waveform of a PID controller given a specific input waveform
and then verify it using Multisim.
3. Design a non-inverting PID controller given a certain time constant and voltage supplies
using Multisim.
Preliminary Information
The ON/OFF Controller, also called All/Nothing, works satisfactorily when the process has a
slow reaction speed and has a minimum delay time.
When a quick response to the changes in the dependent variables or a precise control of the
controlled variable is required, the control ON/OFF is not the best choice.
For example, in a production process employing the continuous use of heat, the valve of the final
control should be located in some position in between fully open or fully closed to maintain the
temperature at a given reference point or set point. The controller that executes this task is
known as a Proportional Controller.
This Proportional Controller provides a signal proportional to the error, the greater the error
the larger the error signal.
The Integral Controller provides a ramp waveform output in response to an accumulated error
over time such that the correction of the error is executed progressively.
The Derivative Controller reacts quickly to the changes in the process control due to the effect
of interferences or forces which cause the process to deviate from a desired set point.
The PID or Proportional-Integral-Derivative Controller combines the advantages and
disadvantages of each controller allowing correction of the error signal in the most efficient way.
122
Input signal
(error signal)
Time of error signal above the reference
axis or setpoint.
0
Reference axis or setpoint.
Time of error signal below the
reference axis or setpoint.
Output signal
of integral
controller
0
Output signal
of derivative
controller
0
Figure 9-1. Output signals of each Controller.
Next, we will analytically determine the output waveform of the PID Controller. We will take
into account the following considerations:
1. The three controllers
(Proportional,
Integral and
Derivative) will have
unity gain.
2. We will use circuits
with non-inverting
output to take
advantage of the
calculations carried
out in labs 7 and 8.
Proportional
Controller
Input
Integral
Controller
Summing
amplifier
Output
Derivative
Controller
Figure 9-2. Connection
of the PID Controller.
3. We will connect the controllers as shown in figure 9-2.
The summing amplifier will be a circuit with unity gain and non-inverting output. The
output of the summing amplifier will be the combined actions of the three controllers.
123
4. The controllers will have a supply of +Vcc = +12V and –Vcc = –12V. Since in the internal
circuitry there is a loss of two volts, the maximum positive voltage or +Vsat will be +10V
and the maximum negative voltage or –Vsat will be –10V. This implies that the peaks of
the output of the Derivative Controller will be limited to +10V to –10V.
5. The input signal is equal to the output of the Proportional Controller because we are using a
circuit with unity gain and non-inverting output as seen in figure 9-3.
Summary of the controllers' waveforms.
f2
+2
0
The following
summarizes the
waveforms taken from
the preliminary
information of
laboratories 7 and 8.
–4
1
5
8
f1
f4
Output of the
Proportional
Controller
f3
+8
Output of the
Integral
Controller
0
–4
+10
Output of the
Derivative
Controller
0
–10
Figure 9-3. Output signals of each
controller for analysis purposes.
124
Waveform of the Proportional Controller
For this analysis, we will use a circuit with unity gain and non-inverting output. Therefore, the
output signal of the Proportional Controller will be identical to the input signal. With these
explanations, we will proceed to the input signal and its mathematical definition of Lab 7.
Observing the graph of figure 9-4, each
function is defined in the following way:
3
f2
2
f4
1
f1(x) : y = 0 ,
0<x<1
0
f2(x) : y = 2 ,
1<x<5
–1
f1
1
5
8
–2
f3(x) : y = – 4 , 5 < x < 8
–3
f4(x) : y = 0 ,
–4
8<x
f3
Figure 9-4. Output of the proportional
Controller
Summary of the controllers’ functions
To find the output functions of the summing amplifier or output of the PID Controller, we
separately add the variables and the constants of the functions generated by each controller in
each interval. They are presented as follow:
Interval
0<x<1
Interval
1<x<5
Interval
5<x<8
y=0
y=
y=
y=0
y = 2x – 2
y = – 4x + 28
y=–4
Integral Controller
y=0
y=
y=
y=
Derivative Controller
2
0
Interval
x>8
–4
0
y=
0
0
Output function of
Proportional Controller
Summing Ouput or PID
Algebraically summing the output function of each controller results in the following:
125
Interval
0<x<1
Interval
1<x<5
Interval
5<x<8
y=0
y=
y=
y=0
y = 2x – 2
y = – 4x + 28
y=–4
Integral Controller
y=0
y=
y=
y=
Derivative Controller
y=0
y = 2x
2
0
Interval
x>8
–4
0
y = –4x + 24
y=
0
0
y = –4
Output function of
Proportional Controller
Summing Ouput or PID
Next, we evaluate these functions with the values of the intervals, to find the initial and final
points of their corresponding line.
Interval 0 < x < 1
The output function of the PID is: y = 0
For x = 0
For x = 1
y=0
y=0
(0, 0) initial point
(1, 0) final point
m line
Interval 1 < x < 5
The output function of the PID is: y = 2x
y = 2 (1) = 2
y = 2 (5) = 10
For x = 1
For x = 5
(1, 2) initial point
(5, 10) final point
n line
Interval 5 < x < 8
The output function of the PID is: y = – 4x + 24
For x = 5
For x = 8
y = – 4 (5) + 24 = 4
y = – 4 (8) + 24 = – 8
(5, 4) initial point
(8, – 8 ) final point
p line
Interval x > 8
The output function of the PID is: y = – 4
For x = 8
(8, – 4)
These coordinates are the initial point of a line parallel to the x-axis that we will call q.
126
We draw the lines in the calculated intervals that correspond to the partial graph of the PID
output.
12
(5, 10)
10
8
n
6
4
2
0
(5, 4)
(1, 2)
m
–2
–4
–6
–8
–10
–12
(1, 0)
5
p
8
(8, – 4)
q
(8, –8)
Figure 9-5. Partial drawing of the PID Controller output.
To complete the graph we should find the response of the PID Controller at the junctions of the
functions, they are at the points: 1, 5, 8 of the x-axis.
Recall in Lab 8 - Derivative controller, the discontinuity of the total controller output function.
For that reason, we decided to distort the input signal slightly into three new functions that we
designate as: g1(x), g2(x), and g3(x). These functions are defined as follows:
g1(x) = 2000x + b
g2(x) = –6000x + b
g3(x) = 4000x + b
The output functions of the Derivative Controller are:
d
d
g1 (x) =
(2000x + b) = 2000 ⇒ y = 2000
dx
dx
d
d
g (x) =
(−6000x + b) = −6000 ⇒ y = − 6000
2
dx
dx
d
d
g 3 (x) =
(4000x + b) = 4000 ⇒ y = 4000
dx
dx
127
At point 3 of the considerations outlined previously, we said the controllers have a supply of
+Vcc = +12V and –Vcc = –12V. However, due to the loss in the internal circuitry, the outputs
were limited to +Vsat = +10V and –Vsat = –10V. Therefore, the functions of the derivative
controller: g1(x), g2(x), and g3(x) will be redefined with these value limits in the following way:
y = 10
y = –10
y = 10
The output functions of the Integral Controller from the input signal function are:
∫ f 2 (x)dx = ∫ 2 dx = 2x + b
∫ f 3 (x)dx = ∫ − 4 dx = − 4x + b
∫ f 4 (x)dx = ∫ 0 dx = 0
We will evaluate each one of these functions to find their corresponding value of the b constant.
To accomplish this we will use the graph of figure 9-6 taken from Lab 7 that corresponds to the
output of the Integral Controller.
For ∫ f 2 (x)dx : y = 2x + b
(5, 8)
+8
Calculating b for coordinates (1, 0) of the junction of the
straight lines a and b
y = 2x + b ⇒ 0 = 2(1) + b ⇒ b = −2
Then
b
0
(1,0)
d
–4
Figure 9-6
y = 2x – 2
For ∫ f 3 (x)dx : y = − 4x + b
Calculating b for coordinates (5, 8) of the junction of the
straight lines b and c
y = −4x + b ⇒ 8 = − 4 (5) + b ⇒ b = 28
b
0
a
(1, 0)
Figure 9-6
y =0
(8, – 4)
(5, 8)
+8
–4
Then y = – 4x + 28
For ∫ f 4 (x)dx = ∫ 0 dx = 0 :
c
a
c
d
(8, –4)
128
Summarizing, the output functions of the Integral Controller with b constant are:
y = 2x – 2
y = – 4x + 28
y=0
Graph of the output response of the PID controller at points 1, 5, 8
In figure 9-7 below figure 9-5 is repeated with the addition of the output signal of the
Proportional Controller for analysis purposes.
2
0
Output of Proportional Controller
–4
10
8
6
4
2
m
0
–2
–4
–6
–8
Figure 9-7
n
1
5
p
8
q
Partial output of PID Controller
Junction of lines m, n
In figure 9-7 PID Controller output, we join line m at point (1, 0) to line n at point (1, 2) with an
additional line. Following point (1, 2) the output function of the Proportional Controller is y = 2.
At the point (1, 0) we will calculate the coordinates of the following points by adding the output
functions of the three controllers. They are:
y=
2
y = 2x – 2
y=
10
-----------------------y = 2x + 10
Output of the Proportional Controller
Output of the Integral Controller
Output of the Derivative Controller
Output of the summing amplifier or PID output
129
At the point (1,0). Replacing values for x = 1
the final point is: (1, 12)
y = 2x + 10 = 2 (1) + 10 = 12
The junction of the lines m and n will be obtained by drawing a line that we will call u whose
initial and final points are (1, 0) and (1, 12) respectively. In a real circuit, the maximum value of
the peaks is limited by the +Vcc and – Vcc applied to the PID Controller.
Junction of the lines n, p
In figure 9-7 PID Controller output, we join line n at point (5, 10) to line p at point (5, 4) with an
additional line. Following point (5, – 4) the output function of the Proportional Controller is
y=–4
At the point (5, 10) we will calculate the coordinates of the next point by adding the output
functions of the three controllers, in the following way:
y=
–4
y = – 4x + 28
y=
– 10
-----------------------y = – 4x + 14
Output of the Proportional Controller
Output of the Integral Controller
Output of the Derivative Controller
Output of the summing amplifier or PID controller
At the point (5, 10). Substituting x = 5 into the above equation gives the following:
y = – 4x + 14 = – 4 (5) + 14 = – 6
therefore, the following point is: (5, – 6)
The junction of lines n, p will be obtained by drawing a line that we’ll call v whose initial and
final points are (5, 10) and (5, – 6) respectively.
Junction of lines p, q
In figure 9-7 PID Controller output, we join line p at point (8, – 8) to line q at point (8, – 4) with
an additional line. Following point (8, – 4) the output function of the Proportional Controller is
y = 0.
Then, at the point (8, –8) we will calculate the coordinates of the next point by adding the output
functions of the three controllers, in the following way:
y=
0
y=
0
y=
10
-----------------------y=
10
Output of the Proportional Controller
Output of the Integral Controller
Output of the Derivative Controller
Output of the summing amplifier or PID controller
130
At the point (8, –8).
Therefore, the following point is: (8, 10)
y = 10
The junction of the lines p, q will be obtained by drawing a line that we’ll call w whose initial
and final points are (8, – 8) and (8, 10) respectively.
Adding calculated lines u, v, w to figure 9-5 results in the complete output response of the PID
Controller as shown in figure 9-8.
12
10
8
6
4
2
0
(1, 12)
(5, 10)
u
v
(1, 0)
–2
–4
–6
–8
(8, 10)
w
5
8
(5, – 6)
(8, – 8)
Figure 9-8. Output response of the PID Controller
using circuits with non-inverting outputs.
(8, 8)
8
6
4
2
–2
–4
–6
–8
–10
–12
(5, 6)
0
(1, 0)
v
5
w
8
u
(5, –10)
(1, –12)
(8, –10)
Figure 9-9. Output response of the PID
Controller using circuits with inverting outputs.
131
Problem Statement
A controller input error signal is shown in Figure 9-10. Notice that this is the same input signal
that was used in the Integral Controller and the Derivative Controller, Labs 7 and 8 respectively.
Design a PID Controller with the following specs:
Proportional controller: Gain = –1
Integral Controller: RC = 1 ms
Non-inverting Derivative Controller: RC = 0.5 ms
Summing Amplifier: Gain = –1
Voltage supply = ± 12 V
All three stages must be in parallel
+ 2V
0
1
5
8
ms
10
–4V
Figure 9-10. Input waveform applied to a PID Controller
Solution
According to the problem statement, the block diagram of the PID controller is as indicated in
Figure 9-11
Proportional
Controller
Gain = –1
Figure 9-11. Block
diagram of the PID
controller.
Integral
Controller
RC = 1 ms
Derivative
Controller
RC = 0.5 ms
Summing
Amp
Gain = –1
Vo
132
You are already familiar with the Integral Controller and the Derivative Controller. The
Proportional Controller is simply an inverting amplifier. The statement of the problem calls for a
gain of –1. The summer adds the outputs of the three controllers and has a gain of –1.
Figure 9-12 shows the input waveform, the outputs of the three controllers and the output of the
PID controller. The analysis of figure 9-12 is as follows.
Input signal
+2V
0
t0
t1
t2
t3
D
E
t4
– 4V
+4V
Proportional
Controller
Integral
Controller
0
– 2V
A
B
+4V
0
–10 V
PID
Output
D
E
G
D
A
C
B
8V
6V
0
C
B
+10V
0
G
A
– 8V
Derivative
Controller
F
C
F
E
G
I
J
A
C
– 4V
F
H
–12V
B
D
Figure 9-12. PID controller output
Since the gain of the proportional controller is –1 its output signal is the inverted equivalent of
the input signal. The output of the integral controller was determined in Lab 7 and the output of
the derivative controller was determined in Lab 8. For illustration purposes, we have established
reference points on each of the output signals of the three controllers. These reference points are
shown in order beginning from left to right. For example, let us start with the output from the
proportional controller. At time t1 we have two voltage levels: 0 V (point A) and –2 V (point B).
At time t2 we have again two voltage levels: –2 V (point C) and 4 V (point D). At time t3 we
133
have two voltage levels: + 4 V (point E) and 0 V (point F). At time t4 we have only one voltage
level: 0 V (point G).
Input signal
+2V
0
t0
t1
t2
t3
D
E
t4
– 4V
+4V
Proportional
Controller
Integral
Controller
0
– 2V
A
B
–10 V
PID
Output
E
G
D
A
C
B
8V
6V
0
D
B
+10V
0
C
A
– 8V
Derivative
Controller
G
C
+4V
0
F
F
E
G
I
J
A
C
– 4V
F
H
–12V
B
D
Figure 9-12. PID controller output
Follow the same procedure for the outputs of the Integral Controller and the Derivative
Controller. The output of the PID controller is calculated next.
PID Point A = Prop Point A + Integral Point A + Derivative Point A = 0 + 0 + 0 = 0 V
PID Point B = Prop Point B + Integral Point A + Derivative Point B = –2 + 0 + (–10) = –12 V
PID Point C = Prop Point B + Integral Point A + Derivative Point A = –2 + 0 + 0 = – 2 V
Note: The output of the Derivative controller goes to – 10 V at point B and then quickly
returns to 0 V at point A again.
PID Point D = Prop Point C + Integral Point B + Derivative Point C = - 2 + (– 8) + 0 = –10 V
PID Point E = Prop Point D + Integral Point B + Derivative Point D = + 4 + (– 8) + 10 = + 6 V
134
PID Point F = Prop Point D + Integral Point B + Derivative Point C = + 4 + (– 8) + 0 = – 4 V
Note: The output of the Derivative controller goes to + 10 V at point D and then quickly
returns to 0 V at point C again.
Input signal
+2V
0
t0
t1
t2
t3
D
E
t4
– 4V
+4V
Proportional
Controller
Integral
Controller
0
– 2V
A
B
+4V
0
–10 V
PID
Output
D
E
G
D
A
C
B
8V
6V
0
C
B
+10V
0
G
A
– 8V
Derivative
Controller
F
C
F
E
G
I
J
A
C
– 4V
F
H
–12V
B
D
Figure 9-12. PID controller output
PID Point G = Prop Point E + Integral Point C + Derivative Point E = + 4 + 4 + 0 = + 8 V
PID Point H = Prop Point F + Integral Point C + Derivative Point F = 0 + 4 –10 = – 6 V
PID Point I = Prop Point F + Integral Point C + Derivative Point E = 0 + 4 + 0 = + 4 V
Note: The output of the Derivative controller goes to –10 V at point F and then quickly returns
to 0 V at point E again.
PID Point J = Prop Point G + Integral Point D + Derivative Point G = 0 + 4 + 0 = + 4 V
135
Procedure/Tasks Using Multisim
1. Build the circuit shown in Figure 9-13 using Multisim.
Proportional
K
0
Summer
1 V/V
0V0V
1
C
Out
A
8
B
Integral
7
1 V/V
0V
2
V1
1000 V/V 0 V
6
0
0
Derivative
d/dt
0.0005 V/V 0 V
0
Figure 9-13. PID controller using Multisim
We discussed the Integrator controller and the Derivative controller in Labs 7 and 8 respectively.
As a review:
The output equation of an integrator is Vout = –V*t/RC + C.
Or Vout = – K * V * t + C, where K = Gain = 1/RC.
The design calls for RC = 1 ms; thus, K = 1/RC = 1/0.001 s = 1000 (1000 V/V in the Integrator
Block).
The Derivative block is the Voltage Differentiator block in Multisim.
The output equation of a Differentiator is Vout = –RC dVin/dt
Or Vout = –K * dVin/dt, where K = Gain = RC.
The design calls for RC = 0.5 ms; thus, K = 0.5 ms = 0.0005 (0.0005 V/V in the Differentiator
Block).
136
The proportional controller is simply an inverting amplifier. The statement of the problem calls
for a gain of –1. This is achieved by setting the gain to 1 V/V and using the signal from the
inverting output as shown in Figure 9-14. The inverting input and non-inverting output are
grounded.
Non-inverting Input
Proportional
Non-inverting Output
K
Inverting Output
Inverting Input
1 V/V
0V0V
Figure 9-14. Proportional block in Multisim
The PID output is obtained by summing the outputs of the three controllers: proportional,
integral and derivative. The function block that performs this sum is called a summer in
Multisim. Notice that the inputs to this summer block are nodes 1, 2 and 6 and the output is
obtained at node 8 (Out). The gain of this summer is 1 or 1 V/V.
The supply is ± 12 V. This means that the saturation voltage is ± 10 V (2 V less than the supply
voltages).
Circuit Operation
DO NOT turn on the power switch. In this lab experiment, you are going to use the Transient
Analysis:
Simulate
Analyses
Transient Analysis
Follow the procedure outlined in Labs 7
and 8 to setup the gain of the Integral block
and the Derivative block.
Set the gain of the Proportional block as
follows: double-click on the Proportional
block and click on the Value tab.
Set the Voltage Gain (E) to 1 V/V.
137
Now double-click on the summer block and click on the Value tab. Set the values as shown in
the figure below.
Using the procedure for Transient Analysis as indicated in labs 7 and 8 you will obtain the
following outputs for each controller and the PID output.
The PID input is the same as the error input signal used in labs 7 and 8.
V or A
PID Input
2 -1 -0 -–1 -–2 -–3 -–4
I
0
I
2.5m
I
5.0m
Time (S)
I
7.5m
I
10.0m
138
The output of the proportional controller is depicted below. Notice that the output is exactly the
opposite of the PID input
V or A
Proportional Output
2 -1 -0 -–1 -–2 -–3 -–4
I
I
0
2.5m
I
5.0m
Time (S)
I
7.5m
I
10.0m
The outputs of the Integral block and Derivative block are shown below. They are exactly the
same as you saw in labs 7 and 8.
V or A
Integrator Output
5.0 -2.5 -0 -–2.5 -–5.0 -–7.5 -–10.0
I
0
I
2.5m
I
5.0m
Time (S)
I
7.5m
I
10.0m
139
V or A
Derivative Output
10 -5 -0 -–5 -– 10
I
I
0
2.5m
I
5.0m
Time (S)
I
I
7.5m
10.0m
Finally, the outputs of the three controllers are added in the summer block. The resulting output
is depicted below.
V or A
PID Output
10.0 --
2.5 --
–5.0 --
–12.5
I
0
I
2.5m
I
5.0m
Time (S)
I
7.5m
I
10.0m
140
The addition of the controllers’ outputs and the PID output can be easily understood by
connecting a 4-channel oscilloscope as shown in figure 9-15.
XSC1
G
T
A
B
C
Proportional
K
0
1 V/V
0V0V
Summer
1
6
C
Out
A
8
B
Integral
7
V1
1000 V/V 0 V
1 V/V
0V
2
0
0
Derivative
d/dt
0.0005 V/V 0 V
0
Figure 9-15. PID controller outputs observed using an oscilloscope.
D
141
The three controllers’ outputs and the PID output will be as seen below.
The top signal is the proportional output, the second from the top signal is the integrator output,
and the third signal from the top is the derivative output. Finally, the bottom signal is the PID
output. A close inspection of the oscilloscope settings shows that the time base scale is 1 ms/Div
and the vertical scale has been set to 20 V/Div.
Questions
1. Does the output waveform of the PID controller obtained in Multisim match the calculated
one? Explain any discrepancies.
142
2. Change the gain of the summer to –1 in Figure 9-13. Draw the expected waveform in Figure
9-16 and compare it with the one obtained in Multisim.
Input signal
+2V
0
t0
t1
t2
t3
D
E
t4
– 4V
+4V
Proportional
Controller
Integral
Controller
0
– 2V
A
B
+4V
0
–10V
C
D
E
G
B
D
+10V
0
G
A
– 8V
Derivative
Controller
F
C
A
C
B
F
PID
Output
Figure 9-16. PID output with summer gain = –1.
143
Conclusions
What are your conclusions regarding the PID Controller using Multisim?
Advanced Design
If you want to earn extra credit, try the following design.
The input signal shown in Figure 9-10 is applied to a PID controller with the following specs:
Proportional controller: Gain = 2
Integral Controller: RC = 2 ms
Derivative Controller: RC = 1 ms
Voltage supply = ± 15 V
All three stages must be in parallel
a. Draw the expected PID output waveform in Figure 9-17.
144
b. Verify your design using Multisim.
Input signal
+2V
0
t0
t1
t2
– 4V
Proportional
Controller
Integral
Controller
Derivative
Controller
PID
Output
Figure 9-17.
t3
t4
145
LAB 10 – CLOSED–LOOP SYSTEM
Objectives
1. Build, test, and troubleshoot a closed-loop system using Multisim.
2. Design a closed-loop system to meet certain requirements.
3. Hardwire the closed-loop system of objective 1 and compare the behavior of the hardwired
circuit with the one obtained using Multisim.
Preliminary Information
Most industrial processes are analog, where we regulate one or more of the following variables:
position, speed, pressure, force, flow, power, level, temperature, tension or intensity. To
accomplish this, we use either individually or in a combination control technologies. For
example, a valve can regulate flow with mechanical, pneumatic, and/or electronic technology.
The type of regulation depends on the process. We know what values we should adjust in certain
circumstances. However, in some cases the process loses control because of process variations
such as an increase in production, appearance of interferences, equipment aging, changes in
temperature, and other factors.
The control of the shower head flow is a clear regulation example. To obtain warm water, we
open the hot water and cold water valves alternately until achieving the desired temperature; in
this case the temperature sensor is the user. If for some reason the water becomes very hot or
very cold, we will have to manipulate the hot water and cold water valves again until the desired
temperature is achieved.
This method of controlling the warm water through human intervention is referred to as an open
loop control and its block diagram is shown in figure 10-1.
Input
PROCESS
Output
Figure 10-1. Open-loop
control system.
The open-loop control system is a relatively quick and simple way of implementing a mean of
the process control. However, the accuracy of the system depends on the calibration carried
out by a human operator. This method, however, is not desirable when:
1. The regulation of the process is complex and it requires a high degree of involvement by a
human operator. Human control of complex processes often leads to errors due to fatigue,
distraction, and other human-based factors.
146
2. On occasion, a manual control might require a person with much expertise and/or training
and that individual is difficult to replace.
3. In large-scale production, the manual control is expensive because any mistake generates loss
on excessive waste of material or reduction in the quality of the product.
For the above considerations, among others, it is preferred to use the closed-loop system as
depicted in Figure 10-2.
Process IN
Setpoint
+
Controller
Actuator
Process
Sensor
Process OUT
Figure 10-2. Closed-loop control system.
Figure 10-2 shows the generic block diagram of a closed-loop control system where the variable
to be controlled or output signal is continually measured (sensed) and compared with a reference
value or set point. The difference between the controlled signal and set point is referred to as
error or system deviation.
The controller executes the necessary corrections on the actuator until the signal difference or
error signal is eliminated and the controlled variable equals the reference variable.
The closed-loop control system uses feedback to reduce the error of the system. The use of
feedback improves stability of the process even though external interferences and internal
variations of the parameters of the system are present.
In industry, two or more dependent or independent closed-loop control systems are usually
used to fine-tune the control of a process.
Figure 10-3 depicts a temperature control system. When the measured temperature deviates from
the set point, the temperature controller varies the position of the valve or actuator that regulates
the fuel input.
Fuel Input Process IN
Setpoint
+
-
Temperature
Controller
Valve
Process
Process OUT
Figure 10-3. Closed-loop temperature control.
Temperature
Sensor
147
This closed-loop system adequately provides all the controlled characteristics of the fuel
(pressure, viscosity and other characteristics) that keep fuel flow constant.
Those characteristics such as fuel pressure varies that changes the flow through the actuator.
With variable fuel pressure, the temperature of the system will also vary requiring the controller
to carry out the necessary changes to readjust the actuator.
The changes of fuel pressure are random and delays in the temperature sensing feedback loop
slow the correction signals generated by the controller. The continuous changes of pressure will
produce a continuous correction on the control valve that sometimes acts when it is no longer
necessary because the flow has returned to its normal condition. This results in a system
instability that must be accounted in the control system design.
One likely way of addressing this system instability could be the following:
We notice in this control system that temperature is regulated by the flow of fuel and the
fluctuations of this flow affect the temperature of the process. As a means of possibly improving
performance of the system one might consider sensing the flow of the fuel rather than the change
in temperature. Due to thermodynamics concerns, temperature changes and the ability to sense
such changes is slower than the ability to measure changes in pressure. However, because there
is a correlation between fuel pressure variation and temperature changes we can anticipate what a
temperature change will be based on fuel pressure variations. This will enable us to adjust the
valve to compensate for the variations in fuel pressure before the fuel flow variations affect the
controlled temperature.
In this case, we say that the temperature sensor is controlling the primary variable and the flow
sensor is controlling the secondary variable. In this way, there are two feedback loops in the
process control system as shown in figure 10-4.
Fuel Input
Setpoint
+
Temp
Control
-
+
Flow
Control
Process IN
Process
Valve
Temp
Sensor
Flow
Sensor
Process OUT
Figure 10-4. Dual closed-loop control.
The output signal of the temperature controller acts as reference point for the flow control. The
second controller will quickly correct the flow variations due to the random interferences of the
fuel and maintain the capacity of the system to control the temperature along with the primary
controller at all times.
In a process where two or more variables are controlled, one variable dependent on
another, it is said that the control system is a cascade control.
148
Dead band
To clarify the dead band concept, we will refer to the ON/OFF controller that is used to control
the temperature of such processes as ovens in the plastic industry and others.
The controller turns on or off the heating element so that the temperature increases or decreases
respectively. This is often accomplished by means of an electromechanical relay or a thyristor, in
the following way:
1. When the temperature measured by the sensor is below the Set point, the controller activates
the relay or the thyristor and the heating element is on.
2. When the temperature measured by the sensor is above the Set point, the controller disables
the relay or the thyristor and the heating element is off.
Figure 10-5 shows graphically the two described steps.
ON
Heater
OFF
Setpoint
Figure 10-5. The heating element is activated or disabled due to slight temperature
variations.
In figure 10-5, when the temperature is slightly higher than the set point (for example 0.1 ºC) the
controller disables the heating element and when the temperature is slightly smaller than the set
point (example 0.1 ºC) the controller will activate the heating element.
The result of this will be the controller continually turning on or off the heating element thereby
causing the deterioration of the relay contacts. To avoid this problem, a “dead band” circuit is
added to the ON/OFF Controller so that the heating element is activated a few degrees above the
set point and is disabled some degrees below the set point. The hysteresis (difference between
ON/OFF temperatures) introduced by this dead band not only extends the life of components in
the system, but it also prevents system instability in the form of oscillations.
149
Figure 10-6 shows the output graph of an ON/OFF controller with a dead band of +/– 10 ºC
around the set point of 150 ºC. Therefore, when the temperature reaches 160 ºC, the heating is
turned off and conversely, at 140 ºC the heater is switched on..
Heater ON
Heater OFF
160 ºC
UTP
150 ºC
Setpoint
140ºC
LTP
20 ºC
Figure 10-6. Output graph of the ON/OFF Controller with dead band of 20 ºC.
We can say that the “dead band” is the space in which the error signal changes without
producing any effect on the controller's output.
In equation form, the dead band is:
Dead band = UTP – LTP
Where:
UTP: Upper Trigger Point.
LPT: Lower Trigger Point.
Replacing values for our example, we have:
Dead band = 160 ºC – 140 ºC = 20 ºC
150
Figure 10-7 shows an ON/OFF Controller with an additional op-amp circuit that provides the
dead band.
VEE
-15V
R3
4
Vprocess
R1
4
2
741
R2
Setpoint
6
2
741
3
Output
6
3
7 1 5
7 1 5
R4
VCC
15V
Dead band circuit
Figure 10-7. Basic ON/OFF Controller with dead band.
R5
R6
151
Problem Statement
Build an ON/OFF temperature control. This system should control the temperature of a reaction
chamber whose internal temperature must be between 250 °C and 450°C throughout the reaction.
The RTD to be used has the output response shown in Figure 10-8 that responds to temperatures
variation between – 200 ºC to 750 ºC.
Temperature ( ºC )
500
450
400
300
250
25
1
2
5
6
Process Variable
7
8
9
10
11
V
Figure 10-8. RTD Sensor temperature versus output response.
Note that the RTD’s output response shown is limited to the range from 250 °C to 500 ºC.
Solution
The circuit shown in Figure 10-9 is an example of implementing the problem statement
requirements.
152
VCC
15V
VEE
-15V
R9
22kOhm
73%
Key = A
1kOhm
R3
4
R1
Vf
R7
Temp Adj
53%
R6
220 Ohm
Key = B
10kOhm
22kOhm
R2
4
4
U1
2
741
6
741
3
22kOhm
7 1 5
3
7 1 5
XMM2
R8
15V
R5
741
6
R4
3
VCC
15V
XMM1
6
10kOhm
7 1 5
22kOhm
R10
22kOhm
VCC
XMM3
2
U3
2
U2
Key = C
2.2kOhm
D1
1N4001GP
37%
Deadband Adjust
VCC
R11
1.5kOhm
Figure 10-9. ON/OFF Temperature
Control.
LED1
15V
Q1
2N3904
Circuit Analysis
U1: Differential amplifier. The gain is determined by R3/R1 or R8/R2; hence R3 = R8 and
R1 = R2. Since resistors R1, R2, R3 and R8 are of the same value, the Gain is equal to 1. The
output of the U1 stage is given by the following equation:
Vo = VTemp Adj – Vf
Resistor R7 controls the set point or desired temperature. Vf is the Vprocess variable. Processvariable feedback is provided by R9 which simulates the RTD sensor assembly suspended inside
the reaction chamber.
The Vprocess variable or Vf is determined by the equation: Vf = [R6/(R6 + R9)] (VCC).
As the temperature increases, the resistance of R9 increases and therefore the Vprocess variable
or Vf decreases because the voltage drop across R6 is applied to the inverting input of U1.
Although the temperature control must be between 250 ºC to 450 ºC, the thresholds are
established between 300°C and 400°C. This threshold setting accommodates the oven’s thermal
inertia. This thermal inertia is caused by a heat propagation delay between the heating element
and temperature sensor response time.
153
Because the heater (simulated by an LED in this circuit) is off until the temperature decreases to
300 °C, the temperature will actually fall below this value to approximately 250 °C, due to
thermal inertia. Likewise, when the heater is shut off at 400 °C, the temperature will continue to
rise to approximately 450 °C. It is clear from this example that thermal inertia results in an on/off
overshoot/undershoot which must be corrected by the dead band settings.
From Figure 10-8 the Vprocess variable or Vf for 300 °C is 8 V and for 400 °C is 7 V.
Vtemp adj
Knowing these values, Vtemp adj (R7) is adjusted to 7.5 V to allow the error voltage to vary
– 0.5 V at 300 °C to + 0.5 V at 400 °C.
Window Comparator (U2)
To maintain the 300 °C to 400 °C temperature range, the comparator must switch when one
of these two thresholds (UTP = + 0.5 V and LTP = – 0.5 V) is reached.
Potentiometer R10 (along with R4) controls the values of the Upper Trigger Point (UTP) and the
Lower Trigger Point (LTP). The equations for calculating UTP and LTP are:
UTP =
R10
(+Vsat )
R 4 + R10
LTP =
R10
(−Vsat )
R 4 + R10
Buffer (U3)
U3 is a voltage follower that isolates the load from U2 to prevent asymmetrical saturation
voltages.
Diode D1 prevents –Vsat from reaching the base of transistor Q1.
System Operation
The circuit of Figure 10-9 is powered with +Vcc = +15V and –Vcc = –15 V. By considering the
2 V internal voltage drop for a 741 op-amp, we see the maximum available output voltages or
saturation voltages (Vsat) are:
+Vsat = +13V and –Vsat = –13 V.
The circuit function will be discussed in the beginning with the output and ending with the input,
in other words, from right to left. We will assume that the heating element, represented by the
LED, is initially off.
154
Therefore, initially, U3 Vo = –Vsat = –13V
Vout, comparator (U2) Vo = –13 V
–13 V at U2’s pin 6, means the voltage drop across R10 will be negative and equal to – 0.5 V.
This voltage is applied to U2’s pin 3; therefore: voltage on U2 pin 3 = LTP = – 0.5 V.
Process Variable = Vprocess var = + 11 V (See Figure 10-8, Temperature = 25°C)
Verror = Vo, U1 = Vtemp adj – Vprocess var = 7.5 – 11 = – 3.5 V
Since the voltage at pin 2 of comparator (U2) = – 3.5 V (Verror) and the voltage at pin 3 of
Vout, comparator (pin 6) = + Vsat = + 13 V. Voltage at the
comparator (U2) = – 0.5 V,
non-inverting input is more positive than at the inverting input.
Thus, the heater is turned ON and the voltage at pin 3 of comparator becomes UTP = + 0.5 V.
From Figure 10-8, as temperature increases the Vprocess var (or Vf) decreases and the Verror
increases. (Verror = 7.5 V – Vprocess var).
When the temperature is greater than 400 °C, the Vprocess variable becomes less than 7 V. The
Verror (Vo,U1) becomes greater than + 0.5 V and the Vout, comparator (Vo,U2) = –Vsat = –13V.
Now, the voltage at the inverting input is greater than the voltage at the non-inverting input.
Under these conditions, the heater turns OFF. However, the chamber temperature may continue
to rise slightly. At this point the voltage at pin 3 of comparator becomes LTP = – 0.5 V.
VCC
15V
VEE
-15V
R9
22kOhm
73%
Key = A
1kOhm
R3
4
R1
Vf
R7
Temp Adj
53%
R6
220 Ohm
Key = B
10kOhm
22kOhm
R2
4
4
U1
2
741
6
741
3
22kOhm
7 1 5
3
7 1 5
XMM2
R8
15V
R5
741
6
R4
3
22kOhm
VCC
15V
XMM1
6
10kOhm
7 1 5
R10
22kOhm
VCC
XMM3
2
U3
2
U2
Key = C
2.2kOhm
D1
1N4001GP
37%
Deadband Adjust
VCC
R11
1.5kOhm
Figure 10-9. ON/OFF Temperature
Control.
LED1
Q1
2N3904
15V
155
Procedure/Tasks Using Multisim
Build the circuit shown in Figure 10-9 using Multisim. Use virtual resistors and virtual
potentiometers.
1. Turn on the power switch.
2. Press the C or SHIFT-C keys to adjust the voltage at pin 3 of U2 to approximately – 500 mV
or + 500 mV.
3. Press the B or SHIFT-B keys to adjust the Vtemp adj (R7 wiper) voltage to approximately
7.5 V
4. Press the A or SHIFT-A keys to adjust the voltage Vf until it is higher than 8 V. When this
happens, the heater turns ON (in this case the LED is ON).
5. Now, press the A or SHIFT-A keys to adjust the voltage Vf until it is lower than 7 V. When
this happens, the heater turns OFF (in this case the LED is OFF). Notice that the LED
remains ON while Vf is adjusted from approximately 8 V to 7 V.
6. Finally, press the A or SHIFT-A keys to adjust the voltage Vf until it is higher than 8 V.
When this happens, the heater turns ON (in this case the LED is ON). Notice that the LED
remains OFF while Vf is adjusted from approximately 7 V to 8 V.
Steps 5 and 6 demonstrate that the output will not change within the 7 to 8 V window because it
is typical of ON/OFF controllers with dead band. See Figure 10-10.
Temperature ( ºC )
500
450
400
300
250
Dead band
25
1
2
5
6
7
8
Figure 10-10. Dead band graph.
9
10
11
V
156
Questions
1. Replace the three 741 ICs by a single quad op-amp such as the LM324AJ. Note that the
LM324AJ has four sections A, B, C and D. Each section will have its own power supply
terminals pin 4 (+V) and pin 11 (– V). You only need to connect the respective power
supplies to any section. Pin 4 should be connected to VCC and pin 11 should be connected to
ground. Does the circuit behave the same? Explain any discrepancies.
2. Perform the necessary adjustments if we need to control the temperature from 250 °C to
500 °C. Test your design. How can you verify that your design is correct?
3. If you want to replace the LED by a 500-W heater what modifications will you do? Test your
design using Multisim.
157
Procedure/Tasks – Hardwired Circuit
Now that you have tested the circuit to satisfy the problem statement using Multisim, it is time to
hardwire the circuit depicted in Figure 10-9 using real components. Repeat what you did in
Lab 1, that is, going through a checklist of components and the equipment that you need to
complete this task. This will reduce the careless errors and damaging to components.
List of components
Item #
1
Component Description
National ADC0804 (or equivalent)
Equipment List
Reference
Designators
Quantity
A1
1
158
It is good practice to have a standard procedure checklist to use in hardwiring circuits. Such a
checklist will enable you to minimize errors in the circuit assembly, prevent malfunction, and
consequently reduce damage to components. This checklist should always be used, but it is not
limited to the following:
•
Ensure all components are checked before powering up the circuit for the first time.
•
Check your circuit schematic against the data sheet for each component used in the
circuit design. Most common problems include the following:
-
Wrong component pinouts, especially between DIP & SOIC parts. For example, it
is not uncommon for IC manufacturers to use different pinouts between DIP8 and
SOIC8 packages for the same part. Sometimes a circuit designer will layout a
schematic using the pinout of a SOIC part and the person doing the wiring of the
circuit might use a DIP part. The consequence of this is an incorrectly wired
breadboard resulting in faulty circuit operation and possible IC damage.
-
VCC, VEE or ground being connected to the incorrect pin on the IC
-
Pins left floating that should be tied to high or low, depending on the part
requirements in the data sheet or application notes.
DIP part
SOIC part
•
Ensure that every IC has its own noise decoupling or bypass capacitor (e.g., 0.1 uF)
connected directly between the IC’s VCC and ground pin and VEE and ground pin. This is
especially important when there is high speed digital or high load current circuit
combined with sensitive analog circuit (such as a Wheatstone Bridge).
•
If the power supply leads to the breadboard are long (i.e., > 6 inches), then a tantalum
bypass capacitor of 10 - 33μF should be used between power and ground points where the
power supply leads connected to the breadboard. Make sure the polarity of the capacitor
is correct and that its working voltage (WV) is at least 1.5 times the maximum voltage
used in the circuit. e.g., the working voltage rating of a capacitor is 10V; the supply
voltage should be at least 15V.
•
Ensure all amplifier feedback loops are as short as possible. Ideally, feedback resistors
should be routed from the amplifier’s output pin directly to the input pin. This helps to
reduce the possible amplifier’s feedback loop pick up and amplifies the unwanted noise.
•
All component leads should be kept as short as possible. Additionally, signal paths from
one IC to another should be kept as short as possible to minimize noise pickup. If a signal
159
path must be long for whatever the reason, ensure it is routed away from other signal
paths to reduce the possible crosstalk.
•
Prevent ground loops and loops in power supply connections. On the breadboard, all
ground buses and power buses should be terminated at one point. That is, you should not
be able to trace a loop from the ground or power supply connection to the breadboard to
all component connections and then back to the power or ground source.
•
If it is possible, separate analog and digital power supplies and grounds from one another.
These should be routed back and terminated at the single power and ground termination
point as previously discussed.
•
Whenever possible, choose a CMOS part over a high current TTL part (e.g., LMC555
over a TTL 555), unless the design calls for the high current capacities of TTL.
Procedure/Tasks
1. Apply power to the circuit.
2. Adjust R10 potentiometer until the voltage at pin 3 of U2 to approximately – 500 mV or
+ 500 mV.
3. Adjust R7 potentiometer until the Vtemp adj (R7 wiper) voltage is approximately 7.5 V.
4. Adjust R9 potentiometer until the voltage Vf is higher than 8 V. When this happens, the
heater turns ON (in this case the LED is ON).
5. Now, adjust R9 potentiometer until the voltage Vf is lower than 7 V. When this happens, the
heater turns OFF (in this case the LED is OFF). Notice that the LED remains ON while Vf is
adjusted from approximately 8 V to 7 V.
6. Finally, adjust R9 potentiometer until the voltage Vf is higher than 8 V. When this happens,
the heater turns ON (in this case the LED is ON). Notice that the LED remains OFF while Vf
is adjusted from approximately 7 V to 8 V.
7. Replace the three 741 ICs by the LM324.
8. Repeat steps 1 to 6 and compare the results using a single LM324 instead of three 741 ICs.
160
Questions
1. Does the hardwired circuit respond the same as the one you tested using Multisim? Explain
any discrepancies.
2. Do you get the same results when replacing three 741 ICs by a single LM324 IC? Explain
any discrepancies.
Conclusions.
After completing the closed-loop system both in Multisim and hardwire, what are your
conclusions?
161
MATERIALS FOR TECH 167 KIT - LAB EXPERIMENTS
Quantity
Description
1
1
1
5
1
2
2
10
1
1
1
1
1
Breadboard (Jameco: Part No.: 20722CJ)
DAC 0800 IC LCN – DIP (14904)
ADC 0804 IC LCN – DIP (10153)
741 IC OPAMP (24539)
LM324AN IC OPAMP (212169)
2N3904 BJT NPN transistor – In stock
2N3906BJT PNP transistor – In stock
LEDs, red (Jameco: Part No.: 333171CJ)
1N4001GP DIODE (35975PS)
1N4002GP DIODE (76961PS)
2N5064 SCR (211431PS)
HT-32 DIAC (160098)
SC146B TRIAC (31819)
1
1
1
1
1
12V Incandescent Lamp (Jameco: Part No.: 209998CJ – T1 wire terminal)
120V – 15V AC TRANSFORMER (All Electronics, page 55)
250 V - 2 AMP FUSE (10381)
SPDT SWITCH (Jameco: Part No.: 21910CJ)
DIP SWITCH (Jameco: Part No.: 38842CJ)
8
8
7
1
4
1
1
1
1
1
5
2
220 Ω - ¼ W resistor
330 Ω - ¼ W resistor
1 kΩ - ¼ W resistor
1.5 kΩ - ¼ W resistor
2.2 kΩ - ¼ W resistor
3.3 kΩ - ¼ W resistor
3.6 kΩ - ¼ W resistor
4.7 kΩ - ¼ W resistor
5.6 kΩ - ¼ W resistor
10 kΩ - ¼ W resistor
22 kΩ - ¼ W resistor
100 kΩ - ¼ W resistor
½ W, 3/8” Square, Single Turn Trimming Potentiometers Top Adjustment
1
1
1
2
2
1
1
500 Ω potentiometer (Jameco: Part No.: 254318CJ)
1 kΩ potentiometer (Jameco: Part No.: 254326CJ)
2 kΩ potentiometer (Jameco: Part No.: 254334CJ)
5 kΩ potentiometer (Jameco: Part No.: 254342CJ)
10 kΩ potentiometer (Jameco: Part No.: 254351CJ)
100 kΩ potentiometer (Jameco: Part No.: 254393CJ)
1 MΩ potentiometer (Jameco: Part No.: 254431CJ)
162
1
2
1
1
1
0.01 uF capacitor – 25 V
0.1 uF capacitor – 25 V
10 uF capacitor – 25 V
100 pF capacitor – 25 V (15341CC)
47 pF capacitor – 25 V (15510CC)
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