Download 251_Manual_1998

640-251
Electronics and
Instrumentation
School of Physics
University of Melbourne
Jon M Pearce
1998
ii
Introduction
Electronics & Instrumentation
iii
Electronics & Instrumentation
Table of Contents
Introduction to Electronics and
Instrumentation Laboratory Work
v
1.
Signals
1-1
2.
Investigating a Transducer
2-1
3.
Analysing RC and RL Circuits
3-1
4.
Filtering Signals
4-1
5.
Resonance
5-1
6.
Introduction to Op Amps
6-1
7.
Designing with Operational Amplifiers
7-1
8.
The Loudspeaker as a Transducer
8-1
9.
Diodes and Their Applications
9-1
10-. The Field Effect Transistor
10-1
11. Projects
11-1
12. Developing a Data-logging System
12-1
Appendix
A-9
Resistor Colour Code
Author: Jon Pearce, 1998
Back Cover
Introduction
iv
Introduction
Electronics & Instrumentation
Electronics & Instrumentation
v
Introduction to Electronics and
Instrumentation Laboratory Work
1. Introduction
Welcome to the Second Year Physics Laboratory. This subject has been designed in a way which, we
hope, will greatly enhance your electronics knowledge. We have introduced a range of computer
controlled experiments which utilise a virtual instruments package known as LabView. This package was
not written as just an educational tool. It is a powerful programming language and an industry standard
among professional scientists. Its strength lies in its simplicity in addition to its ability to control complex
experiments. In several of the experiments you will also be using a Rubbery Ruler. This recent
technological innovation was designed here in the Physics Department and is being used to closely
monitor the bodily movements of Astronauts in space. This laboratory is the only undergraduate class in
the world lucky enough to have access to the Rubbery Ruler! We hope that you will find all the
experiments interesting and informative. This is still a reasonably new laboratory course which means
that your feedback is extremely important. Any suggestions you may have during the semester are most
welcome.
2. Preparation
The experiments in the laboratory are designed to be finished within the three hours allotted. This does
assume that adequate preparation has been done before class. You must read the notes, complete the prelab questions and familiarise yourself with the appropriate theory so that valuable time will not be
wasted. We also pre-empt some of the laboratories with tutorial classes. These tutorials are specifically
designed to aid you in the laboratory and will often introduce new areas of LabView and other equipment
you are not familiar with.
3. Laboratory Report
As there are a large number of students in each class, your laboratory report is required for us to assess
you properly. It is most important for your report to tell your demonstrator what you have learnt during
the lab session. Make sure you write your report as you go. It is, after all, a log of what you have done,
not what you planned to do. If something goes wrong during the experiment we want to know that too.
Make sure all information is put directly into you book. Do not use scap paper. Marks are not generally
allocated for presentation but are allocated for you ability to communicate through your report. If the
report is unreadable or has a confusing layout your demonstrator will be unable to ascertain your level of
understanding.
The report should begin with a statement of the experimental title, the date and the name of your partner
(please write in pen, not pencil!). This is followed by a statement containing your aim. The aim should tell
us what it is you hope to achieve. If for example you are trying to verify a physical relationship then
include this in your aim. It is also helpful to include a line or two on how you intend to achieve your aim.
Author: Jon Pearce, 1998
Introduction
vi
Electronics & Instrumentation
For example you may check the characteristics of a meter by measuring a variety of signals with varying
frequency and voltage. This part of your lab report can be written before you enter the lab.
If you feel it is necessary to include some theoretical background in order to communicate your ideas then
you are most welcome to do so, but it is generally not necessary. We discourage the reproduction of
theory from texts or lecture notes. If you do happen to quote from a text book or from any other source be
sure to reference this correctly.
Electrical circuit diagrams and schematics of apparatus should be included whenever it is informative to
do so. As a general rule you should always draw a diagram of the circuit you are about to wire up in
your report.
Make sure that any results that you present are related back to your aim. Any discrepancies should be
explained and measurements should only be repeated if necessary.
Your conclusion should contain information which relates back to your aim and should summarise what
you have learnt. You should briefly state your main findings and whether or not they were expected.
The report should be clear and concise, not lengthy and verbose. Marks are allocated for the quality of
your work, not the quantity.
4. Demonstrators
It is important to understand the role of the demonstrators in the laboratory so that you can get as much
from them as possible. Primarily they are your guides in the laboratory. They are not employed to tell you
what to do, but to help you carry out the goals set out in the laboratory manual. A three hour session will
fly by once you start working on the experiments. If a problem with equipment or theory presents itself
that you cannot quickly resolve then you should seek the advice of your demonstrator. You should also
seek advice if you are unsure as to the correct use of your equipment. Discussion with other students is
also encouraged if it helps your progress in the experiment.
Remember that your demonstrators have put a large amount of time into understanding the experiments
you are doing. Please make good use of these people as they are employed to help you and create a
friendly working environment.
5. Deadlines
Your laboratory report is due in at the end of the session. Make sure you begin to finalise your report
about ten minutes before the end of the session so that you may write an appropriate conclusion.
Your demonstrator will assess your work and return it to the pigeon holes in the laboratory within two
days of the laboratory session. (eg. the Tuesday books will be available by noon Thursday) If you have
any queries about the assessment please fell free to consult your demonstrator or the general laboratory
staff.
Introduction
Electronics & Instrumentation
vii
6. Illness
If you miss a class due to illness you are required to present a Medical Certificate to the lab staff and
organise a ‘make up’ date for the completion of the missed experiment. If situations require you to change
classes for a certain week arrangements can be made in advance with the laboratory staff.
----------------------------------------------------------------------Once again we welcome you to the Electronics and Instrumentation course.
If you have any problems or queries please feel free to contact us.
Jacinta Den Besten
Jon M Pearce
February, 1998
Author: Jon Pearce, 1998
Introduction
1-1
Electronics & Instrumentation
Laboratory Exercise 1
Signals
Good instruments => good measurements?
You pay good money for a high quality meter or cathode ray oscilloscope (CRO) and
you expect an instrument that will give you accurate and correct readings. Right?
Wrong!!
Accuracy will depend on the quality of the instrument and the nature of what it
intended to do. Most CROs, for example, are better used for viewing a waveform
changing with time rather than obtaining an accurate voltage reading.
Correctness comes down to a basic idea in physics that you can’t measure anything
without affecting the quantity you are measuring. In electronic measurements, it is
usually the small current that the instrument draws that can have a very significant
effect on your circuit. You’ll see!
This means that you need to know the limitations of your instruments. This week’s
laboratory acquaints you with several instruments and lets you confront their limits.
Lab Overview
Signals
1. Getting to
know your
instruments
2. Measuring
voltage
3. Frequency
response of voltage
measurements
4. Measuring
current
Author: Jon Pearce, 1998
Lab 1: Signals
1-2
Electronics & Instrumentation
Instruments with suggested initial settings
Cathode Ray Oscilloscope
Time-base
(set to 10 sec/cm)
Adjust horizontal
position of trace
Adjust vertical
position of trace
Select
channel 1
On/Off
switch
Set AC/DC
switch to AC
Set trigger
to channel 1
Adjust Y-gain
(set to 2 V/cm)
Channel 1 input
(connect signal in here)
Yokogawa multimeter
On/Off
Slider to allow use
of current ranges
Press “ select” button to
cycle through volts>Hertz->auto->dB
settings
Switch to AC
Turn dial to the
AC volts setting
Turn dial fully
anticlockwise to the
AC volts setting ( ~V )
Connect probes to COM
and V-  terminals
Lab 1: Signals
Escort Multimeter
Connect probes to COM
and V-  Hz terminals
1-3
Electronics & Instrumentation
Signals
1. Getting to know your instruments (1/2 hr)
It is essential that you quickly become proficient and confident in using the instruments in this lab—after
all, they are the only things that tell you what’s going on! So, just so you are not too confident in what you
measure, we have a little exercise to get you started. You will be measuring the AC voltage and
frequency of a signal using each of 3 devices: the CRO, a Yokogawa multimeter and an Escort
multimeter. You will find that you often appear to get very different values for the same quantity! This
should be a quick introductory exercise, so don’t hang about—get into it!
1 (a) A simple task!
Measure voltage and frequency of a sine wave
“A simple task”, you say! So simple, in fact, that we give you three different ways to do it . . .
(i)
Use a BNC-to-banana lead to attach your board with the mounted resistor in
parallel to a signal generator, and set the frequency to about 20 kHz (press the
10K range button—it’s a multiplying factor—and turn the dial to 2.0). Turn the
Amplitude dial of the signal generator to about half way. (See the page opposite
for a reminder on using instruments.)
Attach the output from the board to your CRO as shown in the diagram above
(use another BNC-banana) and adjust the setting on the CRO to give a steady
picture of several wavelengths and adjust the sig gen’s output to an amplitude of
1.5 volts (peak-to-peak). Obtain a reasonably careful measurement of the
amplitude and frequency of the sine wave. Copy the table shown on the next
page and start to fill it in.
BNC
Banana
Note that you read peak-to-peak voltages from the CRO, but we need them converted to
Root Mean Square (RMS) values in order to compare them with the meter readings later
on. You do this by dividing the p-p value by 2√2. This is explained in more detail later in
this lab.
Author: Jon Pearce, 1998
Lab 1: Signals
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Electronics & Instrumentation
Instruments connected one at a time
Freq‘y
Voltage (V rms)
(Hz)
CRO
(p-p) =
Instruments connected all together
Freq‘y
Voltage (V rms)
(Hz)
(rms)
(p-p) =
(rms)
Yokogawa
Escort
(ii)
Disconnect the CRO and repeat using your Yokogawa multimeter; enter these values into
the nect row of your table.
(iii)
Disconnect the Yokogawa multimeter and repeat using your Escort multimeter; enter values
into your table. (If this meter displays a “1”, it means you need to change the range!)
(iv)
Now, for real confusion, re-connect the CRO and Yokogawa and repeat the measurements
with all 3 instruments measuring simultaneously. Fill in the last column of the table.
Assuming that the instruments give reasonably accurate readings, there are two likely
explanations for the variety of values you obtained when measuring the same signal:
1. the instrument was loading the output of the signal source, hence changing its value;
2. the instrument was giving an incorrect reading (e.g. some parameter is outside its allowed
range).
At the end of this lab session you will be asked to explain each of your readings in these terms.
Meanwhile, continue with this lab exercise with a determination to find out as much about these
instruments, and their limitations, as you can.
2. Measuring voltage (1/2 hr)
Because voltage is measured by connecting a meter in
parallel across a load, the internal resistance of a
voltmeter must be very high so that the combined
resistance of the load and the internal resistance of the
voltmeter is not significantly lower than the load
resistance alone. The total resistance RT of two resistors
in parallel, R1 and R2 is
1
1
1


RT R1 R2
The table shows the internal resistances of the various
instruments you will be using in these labs.
Lab 1: Signals
Meter
Range
Internal
Resistance
Yokogawa
500 mV DC
1000 M
Yokogawa
>500 mV DC
11 M
Yokogawa
all AC
11 M
Escort
all
10 M
CRO
all
1 M
1-5
Electronics & Instrumentation
2 (a) DC voltage measurement
It is important to realise that even expensive, accurate meters do not give correct readings all the
time. For example, when simply measuring voltage . . .
Check the limitations of your meters
You have on your workbench a board comprising 6 pairs of resistors, arranged as potential
dividers, on which you will make some quick measurements.
(i)
Use the colour code (displayed on the wall and on the back cover of this manual) to
determine the value of each resistor, then measure the voltage across each resistor attached
to the zero volt side of the supply when about 5.0 volts DC is applied to the circuit.
Do this using the Yokogawa meter, Escort meter and CRO, and compare the measurements
with the expected value. Tabulate your results.
Comment
Note any discrepancies between your measured voltages and your expected voltages and summarise
the differences between the three instruments. Show that they are approximately consistent with
the given internal resistances of the meters.
2 (b) AC voltage measurement
Beware of free electricity!
Before quickly repeating the previous voltage measurements using an AC signal, you should be
aware of misleading meter readings that can occur when measuring voltages across very large
resistances.
Unconnected terminals from a CRO or multimeter effectively act as antennae and will pick up
50 Hz background electromagnetic radiation from the mains, as well as signals from other sources
such as radio and TV. The mains power, being the closest, will make the 50 Hz signal stronger
and more troublesome than the radio and TV signals. Terminals from a CRO or a multimeter will
Author: Jon Pearce, 1998
Lab 1: Signals
1-6
Electronics & Instrumentation
certainly pick up this signal if they are not connected to a circuit. But they also will if you try to
measure the voltage across very high resistances, such as 10 M.
Hence, the measured AC potential difference that you observe across a 10 M resistor can be
affected by the induced emfs from the mains power supply even if you have no power supply
connected to your circuit! Watch out for this.
(Turn on one of your meters now, with leads attached, switch to AC and see what it reads. Do this
also with a lead attached to the CRO and you will see “50 Hz pick-up”)
Root mean square, peak-to-peak, and all that
It is important to remember, when measuring AC voltage and
current on a multimeter, that the meters display the root
mean square (RMS) voltage, not the peak-to-peak (p-p)
voltage that you observe on a CRO. Root mean square gives a
measure of the energy the signal would dissipate in, say, a
resistor. The relationship between peak-to-peak voltage and
RMS voltage for a sinusoidal signal is
v
v0 -p
v rms
v p-p
time
Vpp  2 2 Vrms
If you get disagreements by a factor of 2√2 between sinusoidal signals measured on the CRO and
on your meters, check that you haven’t forgotten to convert somewhere.
Check your meters’ internal resistance for an AC voltage measurement
(i)
Attach your signal generator to your set of resistors and set it on about 1 kHz sine wave to
generate an AC signal of about 2 V RMS. Measure the voltage across the lower 1 k
resistor with each of the three instruments and check that they all agree.
(ii)
Try using the CRO to measure the top resistor (that is, the 10M one) of each pair on the
board, rather than the bottom one. Note any strange result! Explain.
3. Frequency response of voltage
measurements
(1/2 hr)
If you applied such an AC voltage to a DC voltmeter it would measure the average voltage, which, for an
AC sinusoidal signal, is zero volts.
However, an AC voltmeter is designed to measure the RMS voltage. It will do this over a range of
frequencies, but the meters you use in the lab each have a stated frequency limit beyond which the
voltage measurements are not accurate.
The aim of this section is to quickly establish the useful frequency limits of the Yokogawa meter, the
Escort meter and the CRO.
Quick voltage measurements
Lab 1: Signals
1-7
Electronics & Instrumentation
(i)
Connect the three instruments directly to the output of your signal generator. Set the signal
generator to 1 V (RMS) and monitor each instrument’s reading as you slowly increase the
frequency from 1 kHz to 1 MHz. Record what you feel is the limit of each instrument to
measure accurately voltages under these conditions. What assumption are you making
about the output of the signal generator? Can you check this?
(ii)
Repeat this with an input voltage of about 50 mV.
Comment
Summarise what you now know about the useful frequency ranges of these meters and the CRO.
4. Measuring current
In order to measure current, an ammeter must be connected in series with the circuit. This means that an
ammeter must have a very small internal resistance in order not to significantly affect the magnitude of
currents in the circuit. The Escort and Yokogawa multimeters have resistances of about 12  when on the
current scale. In this section you will see how this resistance affects a circuit and obtain an estimate for its
value.
Your circuit will be constructed on a breadboard. Have a careful look at the diagram at the end of this
exercise to see where the connections are within the breadboard. The diagram also shows a suggested
layout for your initial circuit—it is very important to layout your circuits, and instruments, in a neat
fashion to make debugging easier and reduce the chance of mistakes.
4 (a) Using light emitting diodes
The red light emitting diodes (LEDs) that you have require a voltage of about 1.7 volts and each
draw a current of about 20 mA. You will power two of these in parallel from a 5 volt supply as
shown in the diagram and then use your Yokogawa meter to measure the current in the circuit.
Power
Supply
+5 volts
R
1.7 volts
Construct your circuit
(i)
Calculate the value that the resistor in the circuit must have (its function is to drop the
voltage across the diodes from 5 volts down to 1.7 volts, while each diode draws its 20 mA)
and choose the nearest preferred value resistor.
Author: Jon Pearce, 1998
Lab 1: Signals
1-8
Electronics & Instrumentation
(ii)
Construct the circuit neatly and measure the voltage across the resistor using your
Yokogawa meter (the longer lead of the LED is the anode—attach it to the positive
side of circuit). Hence calculate the current drawn from the supply.
Measure current using a meter
(iii)
-
Insert your Yokogawa meter to measure the current from the supply. Explain the
+
discrepancy between your measured and calculated values for this current by
measuring the voltage drop across the Yokogawa meter, using the Escort meter,
while the Yokogawa is measuring the current. Calculate the internal resistance of the
Yokogawa meter for the current range. Compare this value with the manufacturer’s stated
value of 12 .
5. Concluding questions
1. Explain each column of the table you compiled in section 1 in terms of:
• the instruments giving wrong values,
• the instruments affecting the quantity being measured,
• the instruments varying in accuracy.
2. Carry out any calculations you can to help justify the measurements made in section 1.
Lab 1: Signals
1-9
Electronics & Instrumentation
Layout of Laboratory Breadboard with LED Circuit Constructed
Remember: it pays to layout neatly both your benchtop instruments as well as the actual
layout of your circuit. Try to make them follow the layout of the diagram you draw in
your lab book.
to power
supply
BNC connections
to use with CRO
or sig gen
Connected to
earth of BNC
Circuit for
section 4 (a)
Note the
break here
Voltage rails
Author: Jon Pearce, 1998
Lab 1: Signals
2-1
Electronics & Instrumentation
Laboratory Exercise 2
Investigating a Transducer
Useless!
Try to think of something absolutely useless, it’s hard to go past the idea of an electronic system without a
transducer on the input and on one the output. This laboratory session will introduce you to two
transducers. One is a powerful output transducer—the computer. The other is an unusual input
transducer which recently won a “R&D 100 Award” in the US. It was invented by staff here within the
School of Physics and has been used for applications as diverse as measuring the rate of growth of
oranges to monitoring astronauts‘ bodily functions on the Space Shuttle. It is known as the Rubbery Ruler.
The “electronics”, which usually completes a “system” by gluing these things together, we will come to
another day . . .
Lab Overview
Investigating
a Transducer
1 Introduction to
measurement with
LabView (1 hr)
1 (c) Displaying
waveforms
1 (a) Measuring
voltage
2 Rubbery
ruler
1 (b) Measuring
current
2 (a) Displaying
a currentvoltage graph
Author: Jon Pearce, 1998
2 (b)
Investigating
the rubbery
ruler
Lab 2: Investigating a Transducer
2-2
Electronics & Instrumentation
Why Virtual Instrumentation?
Much electronics today involves setting up a computer to measure signals and display the output. A VI
(that’s hi tech lingo for virtual instrument) is a computer program that makes the computer take on the role
of data-logger, controller, analyser and display. For us, such a device has mixed blessings: we don’t want
the computer to take over too much of the role of the electronics or you will not learn any electronics
yourself!
In this course we have tried to strike a balance so that you can learn modern methods of using the
computer effectively to help you in gathering, analysing and displaying data, whilst still interacting
closely with the real electronic circuits.
We have chosen LabView as the programming environment
and a National Instruments LabPC+ interface card for this lab
course. LabView was chosen because of its graphical, objectorientated programming interface, which will let you
concentrate on the fundamental design of what you want to
do, rather than the computer code. However, it is a full
programming environment, with extensive mathematical
analysis tools, that can be used for many tasks—especially
useful for simulations and graph plotting with sliders
controlling variables that affect the graph in real time. You can
The LabPC+ Card slotted into each lab PC
even buy your own student copy for $100 (full version $3,500!).
(LabView, Student Edition User’s Guide, Lisa Wells, Prentice
Hall.)
Your use of LabView will gradually increase in complexity so that, by the end of the course, you will be
able to construct simple VIs with ease.
Lab 2: Investigating a Transducer
2-3
Electronics & Instrumentation
Investigating a Transducer
This laboratory session is primarily to introduce you to using the software LabView, a powerful graphical
programming environment for monitoring and controlling equipment using Virtual Instruments (VIs).
This software will be used to measure voltages and currents via an interface card, inside the lab
computers, called LabPC+. A working knowledge of LabView is an important part of this course.
You will set up a LabView program to measure the characteristics of a device known as a rubbery ruler.
This is an extremely versatile device invented by staff within this Physics department.
1. Introduction to measurement with LabView
(1 hr)
To help you get familiar with LabView, you will use a variable voltage which comes out of the
LabPC+ Interface Box, as an input into one of the voltage channels.
You will make use of the following five VI’s produced especially for this course. Feel free to open
up their block diagrams and see how they were constructed (several are very simple inside!).
VOLT.VI
Inputs a channel number; outputs the DC
voltage on that channel of the interface.
V-WAVE.VI
Inputs a channel number, number of
sample to measure (n) and a sampling
rate; outputs an array of n voltage
values, the RMS value of the array, and
an accurate value of the sampling rate
used.
I-DC6.VI
Outputs the DC current on channel 6 (or 7) of the interface.
Channel 7 VIs have two versions: choose the appropriate one
according to your position of the Range switch on the
interface.
I-AC6.VI
Inputs the number of sample to measure (n)
and a sampling rate; outputs an array of n
current values in channel 6 (or 7), the RMS
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-4
Electronics & Instrumentation
value of the array, and an accurate value of the sampling rate used. Channel 7 VIs have two
versions: choose the appropriate one according to your position of the Range switch on the
interface.
LabPC+ Interface Box
Have a quick look at the diagram to see the features of the interface box.
Note in particular the analogue inputs. “Floating” voltage inputs means that you can insert two probes
from here to anywhere in your circuit—they genuinely measure the voltage between the two inputs. The
other voltage inputs measure with respect to earth, as your CRO does, so take care where you connect
these in your circuit! The current channels are both floating.
The digital input and output channels will not be used until lab 12.
Lab 2: Investigating a Transducer
2-5
Electronics & Instrumentation
1 (a) Measuring voltage
We will start by obtaining a simple DC voltage measurement from LabView. As a voltage source
you will use the variable test voltage that is generated within the box and is controlled by a
potentiometer on top of the box. In this exercise you will use a sub-VI called VOLT.VI which
simply reads an analogue channel (you specify which one: 0 to 5) and outputs its value in volts.
Connect the voltage to be measured
(i)
Study the layout of the LabPC+ Interface Box on the page opposite. Connect the ±5 volt
test output from the box into Channel 0 of the Analogue Inputs. Since this channel (and
Channel 1) are floating inputs (meaning that they have no electrical relation to
earth/ground) you must also connect the negative side of the input channel to the analogue
ground on the box. We will represent the connection to the interface box as follows:
± 5 volts from
interface box
V 0
LabView
Interface
Box
So that you can check what the computer tells you, connect a Yokogawa multimeter to this
voltage as well.
Construct your VI
(ii)
Now run the LabView program by double-clicking on the LabView icon. You should now see
an untitled front panel and, behind it, the block diagram. From the control menu choose a
digital indicator which will be used to display your voltage. Label it something like
“Measured Voltage (V)”:
(Alternatively, you can use right-mouse-click, to drop the menus where you are on the
screen—it’s quicker!)
Your digital indicator
(iii)
Bring the block diagram to the front and load the VOLT.VI VI using the Functions menu.
How? Functions and select VI ... then VOLT.VI. A faster way is to press rightmouse-click anywhere and then choose VI ...
Also place on the diagram a string constant into which you will enter the channel number
that you wish to use—this must be a string quantity, not numeric.
How?
Author: Jon Pearce, 1998
Menu Functions->Struct & Constants->String Constant (
)
Lab 2: Investigating a Transducer
2-6
Electronics & Instrumentation
Your channel number will be “0”—the left-most on the interface box. Type it into the string
constant now (if you don’t do this straight away, you will need to select the hand
the text icon
or
in order to enter a value).
Go to the block diagran and use the solder icon
to wire up your diagram as follows (get
into the habit of turning Help on—ctrl-h—as this shows you what each connector does on
the VI you are wiring: very useful for more complex ones later on!):
How? Right-mouse-clicking on each object (this is called “popping-up“ on the
object) will drop down a menu enabling you to choose show and then
label; hence you can label each object with a descriptive name.
Remember:
• all displays must be added on the front panel,
• VI connections to the front panel takes place in the block diagram,
• Always label your icons so that both your partner and your demonstrator can read them
clearly,
• ctrl-h gives you help, depending on where you point the cursor. Use it freely!

(iv)
Save the VI you are constructing with a unique name now!!
Go back to the front panel and run your VI in a continuous loop.
How? Click on the arrow:
To run in a continuous loop, first click the pencil:
which will change this menubar so that you can click the loop button:
which will then become a “pause” button.
Try varying the voltage over its complete range (i.e. turn the knob!). Verify the voltage
readings obtained by simultaneously measuring several points with the Yokogawa meter.
Hint:
If your run arrow is “broken”:
, it means that something is wrong with your circuit.
Try Edit -> Remove Bad Wires (or ctrl-B) first—this removes any unconnected wires left
lying around. If there is still no obvious problem, run the VI anyway and follow the
excellent help window to locate the problem.
Lab 2: Investigating a Transducer
2-7
Electronics & Instrumentation
1 (b) Measuring current
We will now add current measurement to our VI.
(i)
On the same block diagram as above, load I-DC7-Lo.VI using the Function menu and
construct the following circuit below the one above (this filename tells you that it measures
current, DC, channel 7 with the range switch on the interface set to Lo). You will need first
to place another numeric indicator on your front panel to display the current output. You
will be using channel 7 to measure the current.

(ii)
Save your VI to disk now!!
Modify your (physical) circuit to include the current measurement by sending the current
from the test output voltage through a 100 k resistor and then into the current input on
channel 7 (attach the resistor to the ends of 2 alligator clips). The voltage output is not
designed to output a very large current, hence the high value resistor.
Note that there are two pairs of current input terminals on the interface box. Each of these
measures current by measuring the voltage across a low valued resistor inside the box and
the LabView VI then calculates the current (at least it understands Ohm’s Law!). The righthand input has a switch next to it which selects one of two resistors. Hence, in total, we
have three different ranges of current measurement available, each with a different internal
resistance:
Channel 6: range is ± 50 mA; internal resistance = 1 
Channel 7: range is ± 2 mA; internal resistance = 25  with switch in “high I range”
range is ± 0.1 mA; internal resistance = 500  with switch in “low I range”
Make sure you don’t exceed these currents or the internal resistors will get hot!!
Use the 0.1 mA range for this exercise (channel 7); switch the range to “Lo I” (otherwise the
values displayed will be wrong!).
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-8
Electronics & Instrumentation
Diagrammatically, your connections should look like this:
LabView
Interface
Box
± 5 volts from
interface box
100 k
V out
V 0
LabView
Interface
Box
This time verify the current readings using the Yokogawa meter wired into the circuit as a
DC ammeter.
1 (c) Displaying waveforms
In the above exercise both the current and voltage were read, in a point-by-point fashion, as a
single value. For time varying signals this is inappropriate as we often want to see a waveform,
rather than individual data values. Putting the VOLT VI in a LabView loop is one way to do this,
but a loop will iterate far too slowly for the kind of frequencies we will be dealing with (several
kHz). A better solution is to use a LabView VI which takes a fixed number of data readings at a
fast predetermined rate, then send them to a Waveform Graph to plot them.
In this section, you will produce such a time-based display of your voltage signals.
We will use a sub-VI called V-WAVE which outputs a set number of data readings as an array,
and we will send this array to a Waveform Graph to display it. This VI is “homemade”. You can
double-click on it to see its simplicity—it simply calls a LabView VI that communicates with the
LabPC+ card inside the PC. We have done things this way simply to keep your circuit looking less
messy.)
Monitoring voltage waveforms: the easiest way first
First, we will send data to a Waveform Graph to display it graphically.
(i)
Open a new VI.
How? Select New from File menu
On the front panel, place two Digital Controls into which you will enter the number of data
points you want to read and the rate at which you want them read.
How? Front panel: select a Digital Control from Controls -> Numeric
Label these with appropriate names as you create them (or do it later, by popping-up—i.e.
right-mouse clicking—on the object and selecting show->label).
Also place a Waveform Graph on the panel in which the data will be displayed.
How? Front panel: select Waveform Graph from the Controls -> Array & Graph
menu.
Lab 2: Investigating a Transducer
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Electronics & Instrumentation
Your front panel should look something like this:
On the block diagram screen load the V-WAVE.VI VI.
How? Block diagram: select V-WAVE.VI from Functions -> VI ...
This VI reads the number of samples you specify (from the channel you specify, at the rate
you specify) and outputs a 1-d array containing the data. This array of voltage values we
will send straight into the Waveform Graph which will repeatedly display the complete
array of values.
Add a string constant to the diagram and enter “0” into it as your channel number.
Now wire up the following block diagram:



Save your VI to disk now!!
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-10
Electronics & Instrumentation
If you run this VI without first entering a
coupe of constants, it will crash the
computer! So, you must input the rate at
which you want it to sample the data
(which, for an AC signal, you would
generally set to at least 10 times higher
than the highest frequency component of
the signal). See the ‘help’ screen opposite.
You must also go to the front panel and enter 100 into the Number of Samples control so
that V-WAVE will measure a waveform 100 points long.
Set the sampling rate to a low value—10 per second. (For an AC signal, you would
generally set this rate to at least 10 times higher than the highest frequency component of
the signal. Here our signal is very slow so it doesn’t matter.) The actual rate at which the
waveform is collected is the ADC sampling rate which V-WAVE also returns as an output,
but we do not use it here.

Save your VI to disk now!!


(ii)
After saving your VI, run it from the front panel. (Warning: unless you have valid values in
the Number of Samples and Sampling Rate on your front panel, it will crash and lose your
work! Check them now.)
Vary the voltage and confirm the CRO-like
appearance on the screen. (You can stop the
graph from autoscaling by popping-up on the
graph and following the menus. Then just
type the maximum and minimum values you
want, directly onto the graph’s axes.)
This is a “quick and dirty” way to display a
waveform. If you set the program running in
a loop (
) and increase the Sampling Rate
to about 1000 Hz, you will notice that the
chart behaves like a CRO (screen refresh rate
will be 1000 Hz/100 samples = 10 updates per
second). There is no time scale—it simply
displays your 100 samples across the x-axis
each time.
(iii)
Digitising Data Dangers
Take care with your combination of
sample rate and number of points
displayed. For example, your 1 kHz
signal has a period of 1 msec. With a
40,000 Hz rate, and 100 samples, you are
sampling every 1/40 of a msec for a
duration of about two-and-a-half periods
of the wave. This gives a reasonable
display. But explore what happens as
you increase the frequency of your sine
signal: switch the signal generator up to
the 10 kHz range, then the 100 kHz range
and then slowly increase the fine control
until you appear to get a sine wave!
What’s happening here? Why has the
apparent period become large again? Try
to explain it. (It’s called aliasing.)
Change your (physical) circuit so that the
voltage you are monitoring is the output of
your signal generator set on about 1 kHz
(disconnect the current input). Increase the
sampling rate to 40,000 Hz. You should now be able to see the sine wave.
Save your VI for later use.
If you want to specify an x-scale on your graph, you can still use Waveform Graph, and enter the
extra parameters of starting value and interval. This requires you to get your data into an array
first, bundle it with the start value and interval, then send it to the Waveform Graph VI. That’s
for another day!
Lab 2: Investigating a Transducer
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Electronics & Instrumentation
In the next section we will use the other graphing display—XY Graph—so that we can produce a
true XY graph of current vs voltage.
2. Characteristics of a rubbery ruler (1 1/2 hr)
As an example of a capacitive transducer. i.e. a transducer whose capacitance changes with a physical
change, we are going to investigate the rubbery ruler. The rubbery ruler is a device, invented by staff at
this university, whose capacitance changes inversely with its length. The transducer itself is basically a
double helix shaped spring, open circuited at each end, covered by an elastomer material as shown in the
figure below. As the transducer is stretched, the two wires of the double helix separate in a uniform
manner controlled by its silicone covering. The capacitance of the helical structure can be modelled by
unwinding the wires, treating them as a parallel wires forming a capacitor.
Unstretched rubbery ruler
Elongated ruler showing increased wire separation
The purpose of this exercise is to use the rubbery ruler as a variable capacitor, and to explore the
current-voltage behaviour of such a capacitor, and how it is affected by frequency.
2 (a) Displaying a current-voltage graph
Our intention is to connect the rubbery ruler to the output of a signal generator and to produce a
plot showing how the current varies with the applied voltage at a particular frequency. You will
vary the amplitude of an AC signal applied to the ruler, and the I vs V graph will be drawn as
you increase the voltage.
To do this, we need to employ the LabView ideas of putting data into an array, running
continuously in a While Loop and using a Shift Register as a device to accumulate new data in
the array as the While Loop runs.
Wire up the circuit
(i)
Use your Escort multimeter as a capacitance meter to get an idea of the range of
capacitance of the rubbery ruler as you stretch it to about one-and-a-half times its natural
length.
(ii)
Attach the ruler (shown below as a variable capacitor) directly to the signal generator and
make connections so that you can monitor voltage and current using the LabPC+ interface.
(Use the most sensitive current range.)
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-12
Electronics & Instrumentation
monitor
current
I
Sig
Gen
0
V out
V 0
monitor
voltage
Construct a VI to plot I vs V
Constructing this VI involves four new ideas: While Loops, Arrays, Bundling and Shift
Registers. The steps you will follow are:
1. Take a number of samples of the voltage data using V-WAVE.VI and display them on a
graph. Also display the RMS value using the VI RMS. You will enclose this in a While
Loop so that it can be made to run continuously. These data will be put into an array.
2. You will do the same inside the loop for current measurement using I-AC7-Lo.VI, and
bundle these two arrays and send them to an XY-Graph display.
3. You will use a Shift Register to feed the array of data back into the While Loop so that the
next value can be appended to the array, and initialise the arrays.
Let‘s do it.
Step 1:
Set up a VI to display a Waveform Graph of channel 0 data as you did in the earlier section
(use the VI VWAVE). Set the channel number to the appropriate value; set the number of
samples to 100 and Samples/second to the maximum allowed of 75,000. Test this VI by
running it in a continuous loop with the signal generator set on about 1 kHz:
To plot an I vs V graph we need to obtain the RMS voltage of the signal—not just the
waveform. The VI V-WAVEI calculates the RMS value from the values in the array and
puts it out one of its outputs. Use this output (add a display to indicate the RMS value on
your front panel), run your VI and check the output with a meter.
(If you are curious, have a look at the wiring of the RMS VI (which is within V-WAVE), by
double-clicking on it and opening its block diagram. It’s not that complicated!)
The circuit below has been enclosed in a While Loop [Menu: Functions -> Structs &
Constants ->While Loop, then drag to enclose your entire circuit] and the bottom right-
Lab 2: Investigating a Transducer
2-13
Electronics & Instrumentation
hand corner shows the ways to keep the loop running for ever: it is a Boolean Constant
switch [Menu: Functions -> Structs & Constants -> Boolean Constant], which initially has
a false value until you click on it using the hand (
) to switch it to True. This switch is
wired into the
which keeps the loop running while there is a true condition going into
it. (Phew! Get all that? Read it again slowly!) Modify your circuit to be like this one and
check that it now runs continuously when you click the Run icon (
).
Next we send the data from the RMS output of V-WAVE into an array (
have labelled V data array.
) which we
How to make an array? Menu: Functions -> Array & Cluster -> Build Array.
Add the array to your VI,



save your VI to disk!!
and check that your VI stills works. You won’t see any difference in operation, but each
RMS value measured is now being stored into an array.
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-14
Electronics & Instrumentation
Step 2:
Now duplicate a similar set-up for logging current, using I-AC7-Lo.VI and bundle
(
) the 2 arrays into an XY-Graph.
How to bundle? Menu: Functions -> Array & Cluster -> Bundle.
(If you need to increase the size of your While Loop, grab it at the bottom right corner &
drag.)

Again, you can check for errors by first
saving your VI to disk, then running your it,
but you won’t see ant change in the output yet. 
Step 3:
To ensure that the old values in the array are passed around the loop each time, we must
wire the output of each array to a Shift
Register on the output edge of the loop
Why Use a Shift Register?
(right-hand side) and back in at the input
edge of the loop (left-hand side). Pop-up on Enclosing your program in a While Loop is like
the edge of the loop and select Add Shift
pressing the
button. However, any values
Register.
calculated are not stored, they are discarded
each time the loop repeats. The shift register is
To enable old values to be passed into your
a way of keeping the old values, and adding
array, drag the bottom corner of your array
the new ones onto them—in an accumulative
from
to
. Pop-up on the
fashion. The metaphor is one of shifting the
bottom input of
and select change to previous values along in a queue, and making
space for the next value, rather than simply
array, ready to accept the incoming array
overwriting it.
Lab 2: Investigating a Transducer
2-15
Electronics & Instrumentation
from the shift register. It should then look like:
. Wire it up as shown below.
Repeat this for your I-data array.
Finally, we need to initialise our arrays to zero else each time they run, as the previous
values will still be there from the last measurement. From Array & Cluster choose
Initialise Array and wire with a zero as shown outside the loop, on the left, in the diagram
below.
Author: Jon Pearce, 1998
Lab 2: Investigating a Transducer
2-16
Electronics & Instrumentation
That’s it! It looks complicated, but you will quickly become familiar with such VIs and be able to
construct them quickly. (Believe me, it’s true!)
 Save your VI to disk now!!
Run this one, fix any bug. To test it, turn the amplitude of your sig gen right down to 0 volts, (at
about 1 kHz), then run the VI and slowly increase the amplitude. You should get a straight line
plot of I vs R. Now you are ready to use it in the next section. Oh—and of course you didn’t forget
to save it, did you? 
2 (b) Investigating the rubbery ruler
The final goal of this section is to measure some of the characteristics of a rubbery ruler, which are
similar to any other variable capacitor.
Measuring capacitance at different extensions
(i)
Produce three IV graphs each at a frequency of 20 kHz. Vary the length of the ruler from its
natural length to extensions of 5, and 10 cm, respectively.
Produce these graphs by varying the voltage from 0 to 3 volts RMS slowly so that you get
good plots (remember that the interface card can handle a maximum voltage of 5 volts
peak, or only 3.5 volts RMS, and a maximum RMS current of 70 A at the most sensitive
input). It might be advisable to set LabView to plot points rather than lines so that, as you
decrease the voltage back to zero (ready for the next plot), it doesn’t draw a second line.
[Pop-up on the graph Legend and choose Interpolation -> none.]
(You might find it better to turn off the autoscaling on the axes and set the maximum values to 80
A and 3 volts, respectively. Right-click on the axes to turn off autoscaling.)
For each extension calculate the capacitance of the ruler. Compare this with values
measured using the meter. Reminder:
Z 
v
1


i C
Measuring impedance at different frequencies
(ii)
With the ruler fixed at approximately its natural length, produce three more IV graphs for
frequencies 5, 10 and 20 kHz on the one set of axes.
Print your graphs and use the slopes to help you calculate the impedance of your capacitor
at each frequency (use the appropriate capacitance value calculated above). Compare your
values with what you would expect from the relationship above
3. So what?
You should now have a good idea of some of the capabilities of LabView and developed some expertise in
using it. Borrow the manual and practice! There is so much that you can do with the program, but as with
anything, the more you practise, the more value you will get.
You are welcome to borrow a manual and develop some VIs before coming the the next lab that uses
LabView.
Lab 2: Investigating a Transducer
3-1
Electronics & Instrumentation
Laboratory Exercise 3
Analysing RC and RL Circuits
Roll over Kirchhoff!
You construct a simple series circuit of signal generator, resistor and capacitor. You check the voltages
around the circuit with your trusty meter and find that the sum of the resistor and capacitor voltages do
not add up to the voltage from the signal generator! You change the frequency and suddenly they do add
up! What’s going on here? And who was Kirchhoff anyway??
What’s it all about?
This lab gives you the chance to explore the behaviour of circuits comprising resistors, capacitors and
inductors. You will grapple with both amplitude and phase of a signal. With luck, you will even play with
a phasor diagram driven by the signals from your circuit (no extra charge for this one!).
Lab Overview
Author: Jon Pearce, 1998
Lab 3: Analysing RC & RL Circuits
3-2
Electronics & Instrumentation
Analysing
RC and RL
Circuits
1. Voltages in
series RC
circuits
2. Currents in
parallel RC
circuits
3. Exploring
phase in RL
circuits
What do capacitors look like?
Here are some common capacitors—note the large variation in size. Unlike resistors and resistance, the
size of capacitors tends to reflect their capacitance. At least, that is true until you vary what they are made
from.
For example, ceramic capacitors tend to be physically small, and have small capacitance. Electrolytic
ones boost their capacitance/size ratio by using an electrolyte inside, hence they have relatively large
values for a fairly small size (top two in picture). Tantalum capacitors again are small for a given
capacitance (bottom two).
One could write a book on what sort of capacitor is best suited for a particular task—let alone what value
to use!
The large capacitor is about 4 cm across.
Lab 3: Analysing RC & RL Circuits
3-3
Electronics & Instrumentation
Analysing RC and RL Circuits
Unlike purely resistive circuits, circuits that contain capacitors and inductors have a frequency
dependent, non-algebraic response. Kirchhoff’s Law still works (Hey! It has to, since it is merely the
conservation of energy applied to a unit of charge travelling around a loop!) but we can be mislead into
thinking it doesn’t. In this laboratory you will investigate the frequency dependence of the phase
relationship between the voltage across a capacitor and resistor, in both series and parallel RC circuits.
Series RL circuits will be looked at in a novel way!.
1. Voltages in series RC circuits (1 hr)
Strange things happen with AC circuit elements! Since the voltage across a capacitor is not in phase with
the current through it (yet for a resistor it is in phase) we have to be very careful when measuring signals
in circuits containing combinations of Rs, Cs and Ls. Remember that an RMS measurement can give no
information about phase; you need instantaneous values to compare phase (from the same instant too!).
This exercise explores some of these effects.
1 (a) Observing voltage phase differences
A quick look at phase differences
Let’s begin by finding out what doesn’t work.
(i)
Construct the circuit shown below and set the signal generator to 5 V RMS (use a meter).
2 k
Signal
Generator
vR
v RC
vC
0.1 F
(ii)
Use the multimeter to make a quick (in precise) measurement of the RMS voltage across
vRC, vR and vC at a frequency of about 4 kHz (“quick” means only spend 5 minutes here—2
sig. figs is fine). Verify that there is something strange about the sum of vR and vC compared
with vRC (i.e. check that they don’t add up!). (It might be wise to check the value of your
capacitor first by measuring it with a meter—remove it from the circuit to do this!)
(iii)
Observe vC and vRC using both channels of the CRO as you do a quick sweep through
frequencies from about 100 Hz to 10 kHz. Watch the changing phase differences between
the signals, as well as the changing amplitude (the aim here is simply to observe this
effect). Sketch the relative phases and amplitudes at low (100 Hz) and high (10 kHz)
frequencies. Set your sig gen to the frequency you calculated in the pre-lab for a 45o phase
Author: Jon Pearce, 1998
Lab 3: Analysing RC & RL Circuits
3-4
Electronics & Instrumentation
difference (see box below) and check that the CRO display illustrates this (make a sketch
showing the relative phases and amplitudes). What is the ratio of vC to vRC at this
frequency? What is the expected value?
Questions
1. Why can you not use the CRO to observe vR directly
(as well as vC)?
2. What would you observe if you tried to do this using
both channels of the CRO?
(Hint: think about earths in your circuit.)
Reminder About RC Circuits
1
ZC
j C
vC 
v RC 
VRC
1
ZR  ZC
j C  R

1
1  jRC
v RC
Hence the phase of vC compared to vRC is
determined by the complex term. Its
value is given by artan (-RC). You
can work out for what value of  this
gives a phase of 45o for your circuit!
Analysing algebraically
We will now take some careful measurements and use phasor diagrams to explore the phase
relationship between voltages in our RC circuit.
(iv)
Use the Yokogawa multimeter to make careful measurements of the RMS voltage across
vRC, vR and vC at a frequency of 1 kHz (make sure vRC remains constant at about 1 volt
RMS).
(v)
Confirm that vR + vC ≠ vRC and confirm that vR2 + vC 2 = vRC2 for your measurements.
(vi)
Calculate the phase angle that you expect between these two voltages at this frequency.
Comment
Explain qualitatively the changing phase differences and amplitudes in the above data.
Analysing using phasor diagrams
(vii)
Taking vRC as a constant, construct a large (half
page), scaled voltage phasor diagram: draw a
“unit circle” of radius vRC, and construct
phasors for vR and vC by scaling the voltage
values measured above to the appropriate
lengths, and drawing them in the appropriate
directions. See the example opposite. Label
your diagram clearly.
Measure your phase angle  (use a protractor)
and compare this value with the angle
calculated in (vi) above.
Lab 3: Analysing RC & RL Circuits
Im

Re
3-5
Electronics & Instrumentation
2. Currents in parallel RC circuits (1 hr)
In the previous section the circuit being studied was a series circuit and therefore a voltage divider. The
circuit to be studied in this section is a parallel circuit and therefore a current divider. This means that the
phasor diagrams will have current vectors instead of voltage vectors.
2 (a) Observing current phase differences
(i)
Set up the following circuit with the signal generator set to 1.0 V (0-to-peak) at 1000 Hz
(monitor using the CRO). Use a meter to monitor AC current.
i
mA
Signal
Generator
(ii)
v
iC
0.1 F
iR
R
Keeping the input voltage constant, measure and record the current from the signal
generator for R = 1 k and 10 k. Calculate the current in the resistor,
iR (= v/R), in each case.
Analysis using phasor diagrams
(iii)
Use your values measured above to help you to draw accurate current phasor diagrams
and measure from the diagrams the value of iC and the phase angle  between i and ir in
each case.
(iv)
Calculate the theoretical values of iC and  and compare them with the above
measurements.
Questions
1. The phase angle  between iR and i is also equal to the phase angle between the current i
through the whole circuit and the voltage v across the whole circuit. Why is this the case?
Author: Jon Pearce, 1998
Lab 3: Analysing RC & RL Circuits
3-6
Electronics & Instrumentation
3. Exploring phase in RL circuits (1/2 hr)
One could do similar experiments using an inductor instead of a capacitor and find out that there are
similar phase relations, except that there is an important sign change for the inductor.
However, we will be more adventurous and try to look at the phase for an inductor using a LabView VI
which plots phasor diagrams directly for us, in real time!
3 (a) RL series circuit
We will begin by exploring the voltage phasor diagram for a series RL circuit.
Set up the circuit
(i)
Measure the DC resistance of your inductor using a meter. Wire the inductor in series with a
2 k resistor and signal generator.
(ii)
Use channels 0, 1 and 2 of your LabPC+ interface box to monitor vR, vL and vRL,
respectively. It is important that the resistor is connected to channel 0 as this will be our
reference for phase (i.e.  = 0). It is also important that any non-earthed component be
connected to the other floating input—i.e. channel 1.
Your demonstrator will give you more details about component values, frequency ranges,
etc.
Do your own exploring
(iii)
(iv)
Load and run the PHASOR.VI VI and explore this set-up thoroughly. Be tolerant of
inaccuracies on the computer’s part (phase measurement is not easy) but, at the same time,
look out for the influence on the diagram
of the DC resistance of the inductor. See if
How far can I go?
you can do any calculations to explain
To see what the limits of frequency are when
this. Printing an appropriate phasor
using the LabPC+ card, do some sums:
diagram might enable you to make
Max sample rate = 76,000 Hz
measuremtns to verify the value of the DC
If using 2 channels => 38,000 Hz
resistance.
If want at least 20 points per cycle, => 1,900 Hz
Try some other circuits—your
And that is not a very high frequency. Doesn’t
demonstrator will have ideas (!).
even cover the audio range (50 - 20,000 Hz)!
Comment
Comment on, and explain, what you have done!
Lab 3: Analysing RC & RL Circuits
4-1
Electronics & Instrumentation
Laboratory Exercise 4
Filtering Signals
What’s it all about?
Wearing sunglasses, making coffee, coloured lightglobes, tuning a radio,
adjusting the tone control on a hi fi, hearing yet not being distracted by the
noise of your blood rushing past your eardrums. They are all examples of
filtering signals, and the parameter being filtered is frequency (well, except for
the filtered coffee—unless you subscribe to the wave theory of coffee grounds
. . . !).
This lab investigates filtering electronic signals, in the same way that you do
when you adjust your tone control, or a treble/bass control on a sound system.
A useful way to look at the response of a filter circuit is the Bode Plot. You might already have
(unknowingly) seen such plots on a range of audio goods: audio cassette tape packets, amplifier
specifications, headphone packaging, etc. This way of looking at the system leads into the ideas of Fourier
Analysis.
Lab Overview
Filtering
Signals
1. Simple RC
low-pass filter
1 (a) Exploring
the filter
Author: Jon Pearce, 1998
1 (b)
Applications
of filters
2. Another view
of filters - Fourier
analysis
Lab 4: Filtering Signals
4-2
Electronics & Instrumentation
Filtering Signals
When dealing with DC signals, a pair of resistors in series forms a voltage divider which gives an output
voltage dependent on the relative values of the two resistors:
Vout 
R1
R1 R2
Vin . This, of course, has the proviso that no current is drawn
across the load (what if it is?). If instead of a DC voltage an AC signal is
applied across the inputs, the above relationship still holds. However, if
reactive components are used instead of resistors, the impedance of the
components (effective AC resistance) must be used in place of resistance,
and these values will vary with the applied frequency. (Recall that the
impedance of a capacitor is Z  j1C and that of an inductor is
Z  jL ). The fact that the impedance changes with frequency can be
used to make a voltage divider where the output voltage depends on the
input frequency—that is, a filter!
1. Simple RC low-pass filter (1 1/2 hr)
1 (a) Exploring the filter
Obtaining a Bode plot
(i)
Construct the following RC circuit:
10k
v in
0.01F v
out
(ii)
Use the CRO to view simultaneously the input and output signals with the input voltage
set to 1.0 Vp-p at 1kHz. Sketch the two signals.
(iii)
Take measurements to enable you to (quickly! 2 sig. figs is fine) construct a Bode plot (that’s
20log(vout/vin) vs log(f)) of the frequency response of this filter in the range of 20 Hz to 20
kHz. You will need to record in a table both the voltage across the capacitor (on the CRO)
and the voltage across the resistor (using a DMM), and make a plot of both values on the
same graph. (1 point per decade will suffice, except in the range 1-10 kHz where more
points should be taken).
Lab 4: Filtering Signals
Electronics & Instrumentation
(iv)
4-3
Also estimate the relative phase of the input and output signals and sketch a separate
graph of phase vs log(f).
Author: Jon Pearce, 1998
Lab 4: Filtering Signals
4-4
Electronics & Instrumentation
Comment
From your graph, read the frequency values and attenuation at the crossover point, and
determine the slope (in dB/decade) of the falling sections of the curves. What is the expected
attenuation at the crossover point? (Crossover occurs where the voltage across the resistor equals
the voltage across the capacitor.) Does your value agree?
1 (b) Applications of filters
Variable cut-off filter
(i)
To create a variable cut-off filter, replace the 10k resistor with a 10k trim pot
(which enables the resistance to be varied continuously between 0 and 10k.
Set the trim pot to about mid range and check on the CRO that the circuit works
Trim pot
(watch input and output simultaneously).
Computerised Bode Plotter
(ii)
Put together a VI to produce a log-log plot of voltage vs frequency. Base your VI on the
one you used in Lab 2 to give multiple plots of I vs V. Clearly you need to make a few
changes:
• x-axis plots voltage; y-axis plots
frequency
• graph scales need to be log—simply
pop-up on the graph in the front panel
to choose this.
To obtain frequency values, use the
frequency output of the FFREQ VI (clever
name, eh!). Note that it requires some of the same data that the V-WAVE VI needs, so your
circuit will look, in part, like this (compare it with the diagram from Lab 2 and see how you
can modify one to get the other):
Lab 4: Filtering Signals
4-5
Electronics & Instrumentation
Note that the V-WAVE VI has an output called Real Sampling Frequency. This is a more
accurate value for the actual sample rate than the one that you input from the front panel.
Get your VI working (save it!) and obtain a Bode Plot.
(iii)
Do a few more Bode plots, altering the resistance each time so as to observe any effects of
changing resistance values on the cut-off frequency and overall structure of the graph (for
example the fall-off rate, shoulder structure, etc.). Make sketches to summarise what you
see (perhaps a series of graphs for different resistances to illustrate the point?).
(iv)
Your Bode Plot is not really correct unless your vertical axis shows gain (or attenuation, in
this case) rather than voltage. If you think you have time, modify your VI to calculate and
display gain (in dB) on your graph. (Hint: you will need to add another V-WAVE VI to
monitor the input voltage.)
Audio tone control
Variable filters such as those investigated above can be used as a simple tone control system for
filtering audio signals. To illustrate this:
(i)
you are provided with a source of random noise in the frequency range 5 kHz upwards.
Mix the output of this noise source with a sine signal from your signal generator, using the
summing amplifier provided.
Sig
Gen
Gain: 1
Noise
Source
Filter
Circuit
Gain: 1 to 10
Summing
Amplifier
Gain 1 to 100
Set the gain of the noise source channel of the amplifier to 1 (knob fully anti clockwise), and
adjust the output of the signal generator until the sine wave shows considerable noise (say,
a 2 volt p-p sine at 2 kHz). Look at the output before and after the filter (at each extreme of
R) to see that the filter actually does filter out the noise.
(ii)
Connect the output of the pocket radio provided to the amp input in place of the signal
generator and listen to the output of this very noisy signal through the earphones. Describe
the effect of altering the filter cut-off frequency on what you hear—what do you notice
about the level of hiss as opposed to the sound quality of the output?
This circuit you have constructed is a simple tone control used in many audio amplifiers.
Keep this set-up for the next section.
Author: Jon Pearce, 1998
Lab 4: Filtering Signals
4-6
Electronics & Instrumentation
2. Another view of filters - Fourier analysis
When you observe filter output signals on the CRO, and watch the voltage-time graph change as you vary
the frequency, you are looking at the filter’s behaviour in the time domain. Another extremely powerful
way to examine behaviour of circuits is to look at them in the frequency domain. This is what you are
doing when you look at a Bode plot, for example.
The mathematical technique called Fourier Analysis is a technique for converting signals from the time
domain to the frequency domain. It can be done by computer using a process called the Fast Fourier
Transform (FFT) which is one of the built-in programming modules provided by LabView. We will use
that facility here to explore further the behaviour of the simple RC filter. Before looking at the filter,
however, you will look at some simple signals in the frequency domain in order to become acquainted
with the idea.
The VI we will be using is called Spectrum (where do we get such clever names, you ask?). Load it up
now—it is straight forward and obvious to use.
2 (a) Power spectrum analysis
The Fourier power spectrum gives us the power delivered into each frequency component of the
total signal. Hence, a pure sine wave should produce a single peak in the power spectrum. Let’s
check that.
First . . . a perfect sine wave
(i)
Connect the signal generator to the channel 0 of your interface box and, using Spectrum.VI,
observe the power spectrum of a 2Vp-p, 1 kHz sine wave. If you do not get a single peak
check your circuit and, if you still do not get the right output, consult your demonstrator
now.
(ii)
Once you see what you expect, adjust the frequency and amplitude of the sine wave and
observe what happens to the power spectrum. If you want to get adventurous, mix two
sine waves from two signal generators (use the summing amplifier in your amplifier
module) and see what you get.
Next . . . square and triangular waves
(iii)
Reconnect just one signal generator to the interface box (as you did for the sine wave
above) but set the waveform to a square wave. Observe the power spectrum at different
frequencies and try to explain what you see in terms of the shape of the wave and the
components required to make it up. Repeat for the triangular wave.
And finally . . . just noise!
(iv)
Having seen what the power spectrum represents, take your noise source (from amplifier
module—use the >5 kHz output, and remember to turn on the switch!) put its output into
the interface box. Observe the audio power spectrum and comment on its structure.
(v)
Now filter the noise signal using the filter you constructed above, and put the filtered
signal into the interface box. Observe the effect of changing the cut-off frequency on the
noise power spectrum.
Lab 4: Filtering Signals
5-1
Electronics & Instrumentation
Laboratory Exercise 5
Resonance
Shattering wine glasses; tuning radios
What do they have in common? It is said that some sopranos can explode wine glasses by singing a
sustained high note. Basses can’t! The reason is that the soprano can cause the glass to resonate, meaning
that more and more of the singer’s energy goes into the vibrations until . . .
A radio is tuned using the same principle, except that it doesn’t explode. It is an electrical resonance
which favours one radio station’s frequency over all others. We observe the voltage getting bigger and
bigger in electrical resonances and, yes, they can get dangerously big (usually dangerous for the
component, rather than you!).
This lab explores resonance and lets you make a radio. When you have finished it, you might like to
tackle that wine glass . . .
Lab Overview
Resonance
1. First, a
reminder of
some theory . . .
2. Investigating
a series RLC
resonant circuit
3. Using an RLC
circuit to tune-in
radio signals
Author: Jon Pearce, 1998
Lab 5: Resonance
5-2
Lab 5: Resonance
Electronics & Instrumentation
5-3
Electronics & Instrumentation
Resonance
1. First, a reminder of some theory . . .
1 (a) Complex impedance
The impedance of a series RLC circuit is a complex quantity can be expressed
1
in the form: Z  R  jL  jC
It can also be expressed in polar form:
where
Z  Z e
j
Z is the magnitude given by: Z  R 2  L  1C 
2
(ohms)
The angle  is the phase angle between the voltage applied and the current
drawn by the circuit. It is given by:
1 

L 
C   arccos R 
  arctan 
Z 
 R



Imaginary
1 ) are plotted
jC
on the complex plane they form a phasor diagram.
The diagram opposite is a phasor diagram of the
voltages in such a circuit. Note how the phase of the
total voltage, v(t), can be determined by adding
vectorially the other three phasors.
If the three components (R, jL and
vC
v(t)
v
L

v
vx
Real
R
1 (b) When ZL and ZC cancel . . .
1
jC vary in exactly opposite ways as frequency is changed, there will be a
frequency at which they “cancel” and the resultant impedance is simply R—a minimum. This
frequency is called the resonant frequency and must be given by:
Since jL and
jL +
Author: Jon Pearce, 1998
1
jC = 0 or
0 
1
LC
Lab 5: Resonance
5-4
Electronics & Instrumentation
At this frequency, clearly the phase angle will be zero (think of the phasor diagram when the 2
imaginary components cancel out).
A typical plot of the way current varies with frequency for various resonant circuits is shown.
These plots are “normalised” to a maximum current of 1.0. Your plots not be normalised and
hence will look different. Can you predict how?
A plot of the changing phase angle is also shown.
i/i
max

2
1.00
Qo = 100
Q = 1
o
Qo = 10
Qo = 5
0.707
Q = 5
o
Qo = 1
0
0.9
1.0
1.1

o
Q = 10
o
0.00
0.8
0.9
1.0
1.1
Q = 100
o
 o
1.2
-

2
 o
f or Qo = 5
1 (c) A measure of quality
The quality factor, Q, is a measure of how “sharp” this resonance is. That is, how quickly the
current rises to its peak and falls again as you scan through frequency values. Its value, can be
1
obtained from the above graph by measuring the width of the resonance peak at 2 of its
maximum (“half power”). It is defined as:
Q
o

Its value can also be obtained from component values and can be shown to be:
Q
X L  XC   o L 1 L

or
 
R 
R 
R
R C
As you can see, the higher the Q, the sharper the peak; the higher the R the broader the peak.
1 (d) Don’t forget the coil resistance
An important consideration when calculating the quality factor of a resonance is the intrinsic
resistance of the inductor. As was seen in the lab 3, real inductors always have a DC resistance,
which is the resistance of their windings, which is in series with the inductor. This resistance, R L,
this must be added to any other resistance in series with the inductor when calculating the
expected value for Q.
Lab 5: Resonance
5-5
Electronics & Instrumentation
2. Investigating a series RLC resonant circuit
(1 1/2 hr)
In this section you will explore the resonance of your circuit and then measure the quality factor, Q.
2 (a) Find and measure the resonance
Preliminary data
(i)
Calculate the resonant frequency for the circuit shown, so that you know where about to
look for it when you construct the circuit. Measure the DC resistance of the inductor for use
later. Now you will take a quick look at the resonant current and voltage.
L
Sig
Gen
0.01 F
1 k
Check the resonant current
An easy way to view the current is to monitor the voltage across the resistor using the CRO (are
there any phase problems doing this? Explain.).
(ii)
Set up the RLC circuit, with the signal generator set to a low output voltage, and watch the
voltage (i.e. current) across the resistor as you sweep through a range of frequencies
around the resonant value. (Make sure your resistor is on the earth side of your circuit.
Why?) Record a value for the resonant frequency, o. No need to plot a curve.
Check voltage at resonance
(iii)
Rearrange the circuit so that you can monitor the voltage across the LC combination as you
sweep through the resonance region. How does this differ from the current? Check your
resonant frequency is consistent with the one above.
2 (b) Measuring the quality factor, Q
To measure the Q of your circuit, you need to obtain a plot of current vs frequency. To compare
the effect of different values of R on the value of Q, it is convenient to “normalise” all current
measurements so that the maximum current is always the same—say, 1 mA. So, for each circuit
below, begin by going to the resonant frequency, and setting the signal generator to give a current
in the circuit of 1 mA.
Author: Jon Pearce, 1998
Lab 5: Resonance
5-6
Electronics & Instrumentation
You will set up LabView VI to plot graphs of
I vs  for 3 different values of R. You will
vary the frequency of the signal generator
by hand (slowly) as LabView draws the
graphs. You could set up LabView to control
the signal generator frequency changes too,
and fully automate the process, but it is
more instructive stay in full control at
present! To measure the RMS current of a
signal, you will need to use the VI named IAC7-Hi.VI, which you use with the Hi
setting of channel 7 current input (2 mA). Of course, you will also need to use the frequency VI
FFREQ.VI
Obtain current-frequency data
(i)
Construct your VI so that you can accumulate plots of current vs frequency on the one set
of axes. Set your maximum current to 1 mA and then obtain plots for about one decade
either side of the resonant frequency, using values or R of 500 , 1 k and 2.2 k. Keep an
eye on the voltage from the signal generator to ensure that it doesn’t drop in value as the
current gets larger.
Obtain a printout of your graph. (You can add gridlines to your graph by popping-up on
the front panel graph and following the menus. The might help with your analysis.)
Calculate Q
(ii)
For each plot, use the value of at 0.707 mA to calculate Q (0.707 because this is imax/√2).
Don’t forget to include all resistances in the circuit (coil, current meter resistance, etc.).
Compare these values with the expected values.
Questions
1. Is the resonance symmetric ? If not why not ? (Look at the equation for impedance; can you see
what must happen at very low frequencies compared with what must happen at very high
frequencies?)
2. From your resonant current value, determine the maximum voltage across the capacitor and
inductor, respectively, at resonance (use Ohm’s law: v = iZ). Express the result in terms of Q
(that is, by what factor, compared with Q, is the voltage magnified each time?). What are
consequences of this relationship for the maximum voltages tolerated by capacitors in series
resonant circuits?
Lab 5: Resonance
5-7
Electronics & Instrumentation
3. Using an RLC circuit to tune-in radio
signals (1 hr)
3 (a) About AM radio
An AM (amplitude modulation) radio signal is a superposition of a high frequency wave (100’s
to 1000’s of kHz) called a carrier wave (this is the “RF” signal) and a signal in the audio
frequency range (only about 100 Hz to 7.5 kHz for the AM band in Australia). The carrier
frequency range in the standard commercial AM radio band is between about 550 kHz and
1600 kHz.
In order to “tune” to a station we need to filter out all unwanted carrier frequencies either side of
the desired station. This is easily done with a parallel resonant circuit—the resonant peak being
narow enough to tune only one station, yet wide enough to encompass the range of signal
frequencies (carrier ± signal).
For high fidelity sound it is necessary to have a bandwidth of 20 kHz. However, to pack more
radio stations into the limited AM radio frequency range, the maximum modulating frequency is
limited to 7.5 kHz. Incidentally, FM radio, being transmitted at around 100 MHz can have a
higher modulating frequency range, up to 20 kHz, which is why FM radio is higher fidelity than
AM.
A very simple AM radio receiver circuit is shown in the diagram. It contains a
parallel LC circuit with a variable capacitance to tune the resonant frequency to
that of the desired carrier wave frequency (most radios use variable
capacitance tuning but the inductor could be used for tuning instead). To a first
order approximation, the resonant frequency and quality factor of a parallel
RLC circuit are given by
0 
1
and Q 
Antenna
oL
, where the R is the resistance in series with the
R
LC
inductor. These formulae are the same formulae as used for series RLC circuits.
In order to extract the modulating signal from
the carrier signal, the signal is first passed
through a germanium diode, which passes
only the positive half-wave. This is called
rectification and will be investigated in Lab
9. The signal is then passed through a lowpass filter to smooth out the ripple from the
carrier signal. That is, just the amplitude of the
signal that you wish to listen to is remaining.
This demodulating of the signal cuts out the
carrier wave leaving only the audio signal to
be amplified.
Tuning
Why a germanium diode?
As will be seen in Lab 9, diodes pass current
only in the positive direction, provide the
voltage is greater than the turn on voltage.
The RF signal will be very weak so a
germanium diode (Vturn on = 0.2 V) will be
used rather than a silicon diode (Vturn on = 0.6
V). To improve the quality of the radio an RF
amplifier is usually used between the filter
and the diode.
A strong signal is needed in order to overcome the germanium diode‘s turn-on voltage. For this
reason an antenna of a few metres length is used.
Author: Jon Pearce, 1998
Lab 5: Resonance
5-8
Electronics & Instrumentation
3 (b) Constructing a tuner
In this section you will construct an unusual radio tuner—one that is tuned using a rubbery ruler!
(If you possess an old great-grandfather, ask him how he used to make a radio using only a
crystal, a cat’s whisker and a headset!). Note that some lab locations give a poor reception—you
might need to move around to get a strong signal!
Calculating components
Choose an AM station that you want to design your radio to tune.
Local Radio Frequencies
(i)
Use a meter to measure the range of capacitance of your
rubbery ruler. Choose a middle value of capacitance and
calculate the value of inductance that you require to tune to
your station. Stray capacitances in your circuit might amount to
about 100pF.
(ii)
Your demonstrator will give you an inductor close to that value
(check its value using the RLC meter—there are two of these
meters in the lab). Measure its DC resistance and calculate the
bandwidth of your LC circuit.
(Bandwidth:   
o
Q

o
oL R

R
)
L
Will this give the desired tuning range of carrier ± signal?
3RN
Magic
3LO
3CR
3UZ
News Radio
3BM
3SBS
3AW
3MP
3XY
3AK
3RG
621 kHz
693 kHz
774 kHz
855 kHz
927 kHz
1026 kHz
1116 kHz
1224 kHz
1278 kHz
1377 kHz
1422 kHz
1503 kHz
1593 kHz
Constructing the radio
(iii)
Construct a tuned circuit using the inductor (calculated above), your
rubbery ruler as a tuning capacitor and an antenna several metres long
(draped below the ceiling of the lab). Use the most sensitive setting on
the CRO and observe the feint RF signal as you “tune” your receiver—
you are looking for small modulations as you tune near to the radio
station’s frequency. A time-base of about 1 sec per cm might be a good
scale to start with.
(iv)
With your circuit “tuned” to a station, add a diode and resistor to rectify
Tuning
the signal (why do you need the resistor as well as the diode?) and a
capacitor to filter out the RF frequency. The signal will be weaker due to
the current now being drawn through the resistor. You can expect only 1 or 2 mV with
features about 0.2 msec apart.
Antenna
Ge diode
use co-axial
cable here to
connect the ruler
to the circuit
47 M 
Tuning
Lab 5: Resonance
Rectification
Filtering
10 pF
Antenna
5-9
Electronics & Instrumentation
(v)
Finally, connect your demodulated signal to an earphone and listen to the beautiful music!
You can’t do this directly as your weak signal cannot provide the power, so you will need
to use your amplifier module. Connect it first to the unity gain amplifier (gain = 1; very high
input impedance; low output impedance so that it won’t load down your signal) and then
to the gain 1 -> 100 amplifier (to increase the voltage) and finally to the audio amplifier (to
boost the current to power the speaker).
Radio
Receiver
co-axial
x1
x 50
+
Unity Gain Amplifier
Audio Amplifier
Which station is that?
A neat way to measure the frequency of your station is to generate beats using your signal
generator as a second RF source. When the frequency of the signal generator is adjusted to stop
the beating, you have found the RF frequency.
(vi)
Attach another wire to the antenna connection of your radio and lie it against your signal
generator (it will pick up the signal generator signal this way). Set the signal generator to a
few volts sine output.
(vii)
With your radio station tuned, slowly sweep the signal generator frequency across the AM
frequency range (600 kHz to 1600 kHz) and listen for a sharp whistle in the headset—then
you have found the station’s frequency!
(viii) Now measure directly the capacitance that your rubbery ruler is stretched to and do a
calculation to compare your calculated frequency with the one you are actually tuned to.
Assume any discrepancy is due to additional capacitance, calculate the magnitude of this
capacitance and think hard as to its physical origin.
Author: Jon Pearce, 1998
Lab 5: Resonance
6-1
Electronics & Instrumentation
Laboratory Exercise 6
Introduction to Op Amps
What’s this about?
We have come a long way from the first point contact transistor (right) invented
by Shockley, Brattain & Bardeen in 1947, to modern IC chips with literally
millions of transistors on them. The point contact
transistor was quickly replaced by the junction
transistor (left) in 1950 and then developed into
integrated circuits in 1958.
The operational amplifier (1964) was first used as a
building block for analogue computers (try and find
one of those now!). Now it is part of a large family of
amplifiers and has replaced the transistor as the basic
building block for many circuits.
Point Contact Transistor
(3 cm across)
In this week’s lab you will use the most popular of the op amp family—the 741. In
next week’s lab you will meet some other varieties.
Lab Overview
Author: Jon Pearce, 1998
Lab 6: Introduction to Op Amps
6-2
Electronics & Instrumentation
Introduction
to Op Amps
1. Introduction
to the device
2. The Inverting
Amplifier
3. Multiple inputs:
the summing
amplifier
4. Some practical
considerations .
Working with integrated circuit (IC) packages
As you can see, there is very little on the IC package telling you what each of the pins do or how to use
the device. This essential information can be found in the manufacturer’s data book, provided one knows
where to look. The icon/sprite/graphic at the top left provides the manufacturer details—in this case the
two wavy lines indicate that the product is made by the National Semiconductor corporation. The
remaining characters on that line contain such details as the manufacture date and/or batch number and
are not relevant for our purposes (they are used to identify faulty batches, etc.). The remaining line of text
identifies the product type— in this case ‘LM741N’ identifies that the device is an LM741 amplifier with
the ‘N’ identifying (once again) that it is made by National Semiconductor. Once you have
this information you can look up the data book to find out the product information.
A copy of the data book entry for the National Semiconductor LM741 amplifier is in the
Appendix. Have a good look at it to see what information it contains.
Connecting to the real world
The integrated circuit package on its own does nothing without being connected to the rest of the world
in an appropriate way. The legs (pins) of the IC are referred to by number. Each IC has a small
indentation at one end of the package. View your IC with this end at the top, and the top left hand pin in
then refereed to as pin one; the rest are numbered in an anticlockwise direction. On your IC, identify the
pins for the supply voltage, the 2 inputs, the output pins and the pin that has No Connection, NC, which is
simple there to stop the little chip developing a limp!
Note that although the amplifier is presented in a dual in-line package (“DIL”) with pins down either
side, it is customary to represent amplifiers by the block diagrams as shown on the data sheets, with the
pin numbers shown on the block diagram. This is equivalent to the diagram below:
Lab 6: Introduction to Op Amps
6-3
Electronics & Instrumentation
There is no magic method for working out how to
use integrated circuits. Unless you have used the
package before (or have a demonstrator or
electronics whiz handy) it is necessary to look at
the ‘typical applications’ section of the data book
entry to find out how the device should be
integrated in with other components to make a
complete amplifier. Although these circuits often
do not contain exactly the application you are
after, they are a useful starting point.
+15 V supply
offset null
inverting input (-)
output
non-inverting input (+)
offset
-15 V supply
What’s inside an Op Amp chip?
Thought you’d never ask! Here is a picture through a
microscope. The square pads at the sides are where the wires
connect to the legs of the chip. In all, there are only about 12
transistor on this chip (that’s not many—current
microprocessors have several million!).
Author: Jon Pearce, 1998
QuickTime™ and a
Video decompressor
are needed to see this picture.
Lab 6: Introduction to Op Amps
6-4
Electronics & Instrumentation
Introduction to Op Amps
1. Introduction to the device
Operational amplifiers are difference amplifiers with high input impedance, wide frequency bandwidth
and an open loop gain
(the gain without feedback) of at least a few hundred thousand. Thus op
amps produce large output voltages for very small input voltages. They come in many of different
specifications, some of general use, others tailored with specific properties such as high speed. We will
use the general purpose 741
op amps and its FET input counter-part the 13741
. The layout of
the mini-DIP packaged 741 op amps is
shown in the diagram.
NC (this means
8
1
Offset Null
The output is the amplified difference of
“no connection”!!)
the two inputs, marked + ( NonInverting Input
+V cc
2
7
Inverting
) and - ( Inverting
). The
(-)
+
Non-inverting Input
op amp is a very useful circuit when
Output
3
6
(+)
negative feedback is applied. The
-V cc
Offset
analysis of an op amp circuit with
5
4
negative feedback can be greatly
simplified by the assumptions that:
741 Op Amp
(a) the current into (or out of) each input
terminal is approximately zero,
Mini DIP package
(Top View)
(b) the voltage difference between the input terminals is approximately zero.
Output voltages can swing up to about 80% of the supply voltages. The 741
op amp require both
positive and negative power supplies in the range 12-15 Volts. In drawing op amp circuits the power
supply lines are often ignored. This does not mean that they are not required.. All amplifier circuits are
active devices, they get power from the external power supplies.
It is often necessary to by-pass the power supply to ground
with a capacitor added between the power
supply and ground. This provides a low impedance path to ground for any AC ripple on the DC supply
voltage. Hence, if you have problems with your circuits (e.g. oscillations), try adding 0.1 F capacitors
across each supply line.
Lab 6: Introduction to Op Amps
6-5
Electronics & Instrumentation
2. The inverting amplifier (3/4 hr)
2 (a) Testing the gain
Build and test the circuit
(i)
Construct the inverting amplifier circuit, as illustrated, to give a voltage gain of 10 using Rin
=1 k, (Rf determined in PreLabs—check with demonstrator if you are still unsure about
what value to use). Don’t forget to wire up the circuit’s power supply of ±15 volts to pins 4 and 7,
even though they are not shown in the diagram!
Rf
V in
(ii)
R in
2
-
3
+
6
V out
Measure and record the DC voltage gain (Vout/Vin) using another DC power outlet to give a
DC input voltages (Vin) of 0.1, 0.5 and 1.0 V (don’t vary the supply voltage to the op amp—
this stays fixed at ±15 volts no matter what you do to the circuit). If you do not get what
you expect check your circuit now.
Having constructed a working circuit, we can test its AC behaviour:
Applying an AC input
(iii)
Apply a 1 kHz, 1V (p-p) signal to the input using the signal generator, and use the CRO to
observe the input and output simultaneously, recording the gain, relative phase and any
distortion in the output signal.
(iv)
Now observe the signal at the inverting (-) and non-inverting (+) inputs to the operational
amplifier and comment on what you see (you will have to increase the CRO sensitivity to
maximum to see anything). Is it what you expect?
Author: Jon Pearce, 1998
Lab 6: Introduction to Op Amps
6-6
Electronics & Instrumentation
3. Multiple inputs: the summing amplifier (1
hr)
Having seen how a single input can be amplified using an operational amplifier, a natural question to ask
is what happens if there are multiple inputs? Consider, for example, the following circuit where an
additional resistor has been added to the input:
Rf
v1
R1
v2
R2
-
v out
+
Since the inverting input (-) is at earth potential (virtual earth), the voltage v1 across R1 must cause a
current of value i1 = v1/R1 to flow through Rf. Similarly, v2 injects a current of i2 = v2/R2 into Rf. The result
is a summing of these two currents in Rf and a corresponding output voltage drop across rf of
 v
v 
v out  (i1  i2 )Rf   1  2 R f
 R1 R2 
or
 R f 
R f 
v out   v1   v 2
 R1 
 R2 
Hence the output voltage is a weighted sum of the two input voltages.
3 (a) The basic summing amplifier
Modify your inverting amplifier
Expand your inverting amplifier into a summing amplifier as shown in the above diagram.
(i)
Using Rf = 10 k construct an amplifier which has a gain of -10 on each input channel.
(ii)
Apply a signal of 1V (p-p) at about 1 kHz to one input channel and another signal of 1V (pp) at about 10 kHz to the other input. Observe both of the inputs and the output on the
CRO, and comment on the gain. You may also like to try altering the input frequencies, but
remember to record anything interesting you observe.
Adding variable gains
Now to make the gain of each input channel independently variable.
Lab 6: Introduction to Op Amps
6-7
Electronics & Instrumentation
(ii)
Replace the fixed value input resistors with the 10 k potentiometers supplied, to allow for
easy adjustment of the input gain. Applying the same inputs as above, investigate the effect
of adjusting the potentiometers (to vary the gain) and record what you observe. Once
again, you may like to investigate the effect of varying the frequencies.
(Remember, in using a
potentiometer as a variable
often drawn as
resistor, you only wire two
inputs. If it is important that
the value of resistance never gets to zero, then put a small resistor in series with the pot; a 1
k resistor might be a good idea in this case.)
3 (b) Application: audio mixing
Now for something different. Our aim is to mix two audio signals.
(i)
On you bench you will find a transistor radio, a microphone and a speaker (or earphones).
Connect the headphone output of the radio to one input of your operational amplifier
mixer, the microphone to the other input (you will probably need an op amp circuit with a
gain of gain 5 or 10 to buffer the microphone’s output before connecting it into this circuit),
and the speaker to the output as shown below.
10k 
1k 
10k 
Radio input
-
M icrophone input
(after op amp buffer)
+
1k 
v out
10k 
Now select you favourite radio station, talk into the microphone and listen using the speaker.
Remember that you can adjust the gain of both channels using the potentiometers. Note anything
interesting you hear (such as noise, distortion etc.).
If you noticed that the sound quality was poor, how could you improve it? How could this circuit
be modified so that it has a microphone level and a master volume control (as is found on
Karaoke machines)?
4. Some practical considerations . . . (1 hr)
Although the op amp is delightfully simple to use, it does have its limitations. Here we will look at some
of the more important ones that you should keep in mind when designing with op amps.
4 (a) Input offset voltage
This voltage is a slight difference in potential between the two inputs of the op amp. It is most
noticeable when you have large gains and are amplifying DC signals.
Author: Jon Pearce, 1998
Lab 6: Introduction to Op Amps
6-8
Electronics & Instrumentation
(i)
Return your amplifier to a simple inverting amplifier; give it a gain of 100. Now connect
the amplifier input to earth and observe the output. (Use the CRO in DC mode, and don’t
forget to set your zero point!).
The presence of an offset is normal (what was the value of your offset voltage at the input?)—the
trim pins on the DIP package are there so that you can remove this signal. To do so, connect the
trim pot as illustrated in the following diagram, and adjust the trim pot so that the output is null
for a null input.
4 (b) Slew rate
If you put a square wave into an op amp and look carefully at the rising edge of the output signal,
you will observe that it does not rise vertically, but has a definite finite slope. This slope is called
the slew rate and is due to the finite time that it takes to charge capacitances internal to the op
amp. It is a measure of the maximum rate at which the output can change and hence is quoted in
volts per sec. For the 741 op amp this value is typically 0.5 V/s.
Slew rate limits the frequency response for an amplifier but it primarily important in switching
applications where you want the rising edge of a square pulse to be fast.
Measuring slew rate
(i)
Using your existing circuit of a gain 100 amplifier, put in a square wave of about 0.5 volts
and observe the output signal at medium (5 kHz) and high (100 kHz) frequencies. Sketch
these and measure the slew rate for your chip. Compare this with the nominal value.
4 (c) Bandwidth
You might not have time to complete this part. I this is the case, an arrangement will be set up to allow you
to plug in your IC and plot out its bandwidth curves. Do it yourself if you can!
If you look at the op amp’s data sheet, you will see a Bode Plot showing the amplifier to have an
open loop bandwidth of only 10 Hz! All it not lost, however, as this bandwidth is traded for
closed loop gain such that the product gain x bandwidth is approximately constant.
Measuring bandwidth
Lab 6: Introduction to Op Amps
Electronics & Instrumentation
6-9
Replace the 1 k resistor in your existing circuit with a 10 k trim pot, and make the feedback
resistor 10 k, so that you can vary the gain from 1 to a large value.
(i)
Make a Bode plot of the amplifier voltage gain (ie: gain in dB vs frequency) for several gains
from 1 upwards. A LabView VI is available (called BODEPLOT.VI) to make this quick for
you. Print out the graphs (on one set of axes) and indicate the -3dB point on each graph and
determine the gain-bandwidth product for each one. Comment.
Author: Jon Pearce, 1998
Lab 6: Introduction to Op Amps
7-1
Electronics & Instrumentation
Laboratory Exercise 7
Designing with Operational Amplifiers
Think about it . . .
What do the following have in common:
the exposure control in a camera
the door-operated delayed interior light in a motor car
variable-delay windscreen wipers
a charge amplifier in a nuclear detector?
The answer is that, conceptually at least, they all could use the principle of a device that integrates (or
accumulates) charge over a period of time. In the exposure control, the charge is related to the intensity
and duration of light falling on a meter, and the voltage resulting from the integration is used to
determine when to close the shutter. The interior light in some cars remains alight for a few seconds after
closing the door until a set time period has elapsed. Here a current is integrated until the accumulated
charge is great enough to cause a relay to change state.
Similarly, the windscreen wipers and charge amplifier apply the useful the idea of accumulating charge
causing some action to occur.
In this lab exercise you will build up the idea of the camera shutter control. We leave it as a thought
exercise for you to design circuits to carry out the other functions!
Lab Overview
Author: Jon Pearce, 1998
Lab 7: Designing with Op Amps
7-2
Electronics & Instrumentation
Designing with
Operational
Amplifiers
1. Resistance
to voltage
conversion
2. Simple
exposure
meter and
shutter control
Designing with Operational Amplifiers
In this section, several applications of operational amplifiers will be investigatedÑthe aim is to explore
the multitude of applications of this gadget without detailed investigation of the properties of each of the
devices used.
Please note that although you are asked surprisingly few direct questions in the text, this does not mean
that you are free to hand in a skimpy report. The mark you get for this laboratory will depend to a large
extent on how clearly and thoroughly (the two are not mutually incompatible!) you document your work.
This does not require you to go overboard and produce a mini thesis—just to make careful and concise
comments about what you are doing and what you observe.
Note: apart from the first one, the circuits you construct here all build up to the final circuit. So don’t dismantle
them as you go!
1. Resistance to voltage conversion (1 hr)
1 (a) Investigating CdS cell resistance
The CdS cell on your bench is a light dependent resistor (LDR)—its
resistance varies continuously according to the amount of light incident
on it from about 1 k in daylight to over 20 M in the dark. The
approximate relationship of incident intensity to resistance is given by
R
where
 
R0
I0
1
Ik
  is a constant, I is the intensity of light and k is a constant
R0
I0
between 1 and zero. This relationship appears as a straight line when plotted on a log-log graph.
Measure the cell resistance
Lab 7: Designing with Op Amps
7-3
Electronics & Instrumentation
(i)
To see this effect, measure the cell resistance using a multimeter under a number of
different lighting conditions (in particular, move near a window and use bright daylight to
get the illuminated resistance, and cover the resistor with a black cloth to get the dark
resistance).
This effect is characteristic of a range of transducers including wire strain gauges and
thermistors where variation in a physical parameter is manifested as a change in the resistance of
a transducer.
Such variations in resistance can be measured using a voltage divider with one of the resistors
being the transducer of interest. However, such a system is sensitive to variations in the input
impedance of the voltage measuring device, which in effect becomes a part of the voltage divider
set-up rather than just measuring the voltage.
The high input impedances of op amps can be used in two ways to assist in this task, as you will
explore in the next two sections.
1 (b) Using a high impedance buffer
Consider measuring resistance changes by including the variable
resistor (in this case the CdS cell) in a voltage divider and using a
voltmeter to measure the resulting voltage changes:
Vout 
Rvar iable
R1  Rvar iable
Vin
Although voltmeter internal resistances are quite high (1 M for
the CRO, and 10 M for the Yokogawa meters), if the resistance of
the variable resistor approaches this resistance, the voltmeter will
start to affect the voltage it is trying to measure. For example, the
CdS cell you will be using here has a resistance of up to 20 M
when covered by a black cloth—since the internal resistance of the
multimeter is less than this, you are in fact measuring
a voltage due more to the resistance of the voltmeter
than that of the CdS cell!
To avoid this problem, one can take advantage of the
high input impedance of operational amplifiers to
buffer the circuit using a voltage follower (also called
a unity gain buffer).
Consider, for example, the circuit below which acts as
a voltage buffer.
Op amp input impedances
The 17741 bipolar op amp has a typical
input impedance of the order of 2 M; the
LF-13741 J-FET op amp has a typical input
impedance of the order of 5x105 M, and
higher impedances are available—see the
data sheets in your lab book.
The input impedance of this circuit is effectively just
the op amp input impedance (several M), however
because of the feedback, the output signal is the same
value as the input signal. As such, this circuit is useful
In
when one has to measure the voltage produced by a
device which has a relatively low output impedance or
one in which the current drain must be kept to a minimum.
-
Out
+
Constructing and testing a high impedance buffer
Author: Jon Pearce, 1998
Lab 7: Designing with Op Amps
7-4
Electronics & Instrumentation
(i)
To illustrate how useful buffering can be, wire up the voltage divider circuit illustrated
above using R1 = 10 M and, using either the multimeter or CRO, measure the voltage
across the CdS cell when it is placed in darkness, under a black cloth. Now place a voltage
follower in between the voltage divider and the multimeter using a J-FET op amp (the
LF13741 has the same pin-outs as 741 op amp) and observe any differences. Which is the
more accurate reading?
1 (c) Variable gain amplifier
One of the disadvantages in using a voltage divider is that the transducer resistance is translated
into voltage according to the relatively complicated relationship Vout  R1  Rvar iable Vin . Although it is
possible to compensate for this using an appropriate scale calibration, there are times when a
more direct relationship between resistance and output voltage is desirable (for example, when
using analogue electronics for measuring the accumulated intensity to initiate some action). For
such applications, it is much more convenient to have a voltage which varies either linearly or
inversely with transducer resistance than one which varies according to some complex formula.
Rvar iable
By including the transducer as one of the feedback resistors in an inverting op amp circuit it is
possible to obtain circuits in which the output voltage varies either linearly or inversely with the
transducer resistance (we will only construct the inverse version in this lab). To see how this
works, consider the inverting amplifier studied last week
and recall that the output voltage is given by
Vout 
Rf
Rin Vin . Thus, if you keep Vin at a constant voltage
you can obtain a either linear variation with resistance (by
including the transducer as the feedback resistor), or an
inverse relationship (by using the transducer as the input
resistor). Furthermore, it is possible to select the output
gain by selecting appropriate values for the other (nontransducer) resistor.
Constructing an inverse linear resistance-to-voltage amplifier
To construct a resistance to voltage converter which has an inverse relationship between
resistance and output voltage:
(i)
connect the CdS cell as the input resistor as shown below. Use Vin = +5 V from the blue
power supply, and choose a feedback resistance so that you can get a sensible output for
CdS cell resistances of between 1 k and 20 M.
Lab 7: Designing with Op Amps
Electronics & Instrumentation
(ii)
7-5
Observe the voltage output on the CRO, and note the effect of altering the incident light on
the output using the CRO (where does the 100 Hz ripple come from?). Note especially how
the voltage increases with increasing illumination and that there is a direct relationship
between incident light and output voltage.
Keep this circuit to use in Part 2(b)
Author: Jon Pearce, 1998
Lab 7: Designing with Op Amps
7-6
Electronics & Instrumentation
2. Simple exposure meter and shutter control
(1 1/2 hr)
In a camera, the exposure of the negative depends on the amount of light shining onto the film. For a
fixed aperture lens, you need to open the shutter for a shorter period of time on a bright summer day at
the beach than on a dismal winter evening. Many modern cameras use an automatic exposure control in
which a photosensor detects the amount of light which has entered the lens and closes the shutter after
enough has entered to make a well exposed negative. The same principle is also used in auto exposure
flashes which stop the flash pulse once enough light has been sensed reflected from the subject.
In this section, you are going to make a simple shutter control using the photosensor you have already
investigated. This will require detecting the total amount of light which has hit the photoresistor over a
period of time, and then using this signal to trigger a shutter release once the appropriate exposure has
been made.
2 (a) First - the integrating circuit
A combination of an input resistor and feedback capacitor will integrate the input signal from the
photodetector. Consider, for example, the following circuit:
C
As the inverting input acts as a virtual
earth, the current flowing through Rin
is simply
Iin 
+
Vin
Rin
-
R in
V in
and, since the high input impedance of
the op amp means that there is
negligible current drain through the
op amp itself, all of this current flows
into the feedback capacitor. The
charge on the (ideal leak-free)
capacitor is therefore given by the accumulation of this current:
-
V out
+
t
Qc   I in dt
0
t
  Rinin dt
V
0
and, as the inverting input is a virtual earth, the output voltage is given by:
Vout  
Qc
C
t

1
Rin C
V
in
dt
0
(the negative sign comes from a positive voltage at the input causing positive charge to build up
on the input side of the capacitor, which makes the output side of the capacitor negative relative to
Lab 7: Designing with Op Amps
Electronics & Instrumentation
7-7
the virtual ground at the non-inverting input. If you think about it for long enough it will make
sense!)
There are, however, a few problems with implementing this circuit. Firstly, any input offset
voltages will also be integrated, so it is necessary to use a low offset op amp such as the 13741 JFET op amp (see the spec sheets to verify this for yourself). Sometimes it may also be necessary to
trim out offsets using the offset bias adjustment terminals on the op amp.
Secondly, it is necessary to include some method by which the integrator can be reset or stopped
(unless, of course, you want to integrate the input voltage over all time, forever into the future!).
Simply including a discharge switch in parallel with the capacitor as a reset solves this problem.
In applications this is usually done electronically using a FET switch, but as a last resort, we can
always discharge the capacitor by bridging a resistor across it for a little while with the input
disconnected.
Construct and test an integrator
(i)
Design and construct an integrating circuit suitable for integrating the output of your light
detector. Test the circuit using a DC input voltage to see that it is integrating the input as
expected.
(ii)
Once you are satisfied with the performance of the integrator, connect it up to your light
intensity sensing circuit so that it integrates its output, and verify its operation before
proceeding to the next section.
2 (b) Next - the comparator and triggering
Since the open loop gain of an operational amplifier is very high, if feedback is removed from the
op amp circuit any small voltage difference between the input terminals is greatly amplified. For
example, if the op amp has an open loop gain of just 10 6 (typical data sheets show an open loop
gain of about 90 to 120dB) a voltage difference of just 15V will be amplified into a saturated
output of +15V! This high sensitivity to the difference between input voltages can be effectively
used to sense when a voltage has risen above some predetermined reference voltage (which can
be generated by something as simple as a voltage divider circuit).
In the present application, we wish to switch off a shutter when the total intensity of light which
has fallen on the sensing cell has risen above some predetermined value. We have already created
a device which integrates the intensity in the previous section, with the output voltage increasing
as more light falls on the sensing cell, so all we have to do is to sense when the integrated
intensity has risen above a desired value. To do this we can use the circuit described below as a
simple comparator.
Construct and test a comparator
(i)
Wire up the circuit below using a 10 k potentiometer as the variable voltage supply,
connected to earth at one end and +15 V at the other (remember that the integrated signal
goes negative for a positive input, but that the detector output is itself negative), and a
17741 op amp. Verify its operation using a suitable test signal.
Author: Jon Pearce, 1998
Lab 7: Designing with Op Amps
7-8
Electronics & Instrumentation
+15 V
V in
-
10 k
V out
+
(Why use a 17741 op amp? Although a 13741 could always be used, low input impedance
and low offsets are not essential in this particular implementation and the 17741 is
cheaper!)
(ii)
Now set the reference voltage to a mid-range reference voltage (say +7 to +10V), connect
the input of the comparator to the integrator, and observe the output. Also observe the
effect of changing the triggering level when the cell is under identical illumination
conditions.
(iii)
To see the triggering effect more clearly, connect the comparator output to a LED as shown
below—the LED will be on whilst the ‘shutter’ is open. Don’t forget to use a 200  series
resistor to limit the current flowing through the LED so that it doesn’t get cooked!
The strong point about this circuit—high sensitivity to input signal differences—is also one of its
disadvantages. Consider, for example, what happens when a slowly rising but noisy signal
approaches the reference voltage. As the signal level varies about the reference voltage, the
output of the comparator swings wildly from high to low (as it is meant to do). This causes
problems for some switching operations (for example a motor) for which rapid switching on and
off around the threshold voltage is undesirable.
For example, connect your intensity meter (from Part 1(c)) to the input and adjust the incident
light whilst viewing Vout and Vin on the CRO. What happens at Vref?
To rectify this oscillation problem the comparator circuit can be modified by including a feedback
resistor which effectively drops the reference voltage once it is exceeded, and raises it again when
the signal drops below the new reference level. If one selects the feedback level so that the size of
the reference voltage jump is greater than the noise level, the problem of oscillation at the
Lab 7: Designing with Op Amps
7-9
Electronics & Instrumentation
threshold voltage will be effectively cured. Such a modified circuit, called a Schmitt trigger, is
found in many electronic sensing and control applications. It is draw below.
Construct and test a Schmitt Trigger
(i)
Construct a Schmitt trigger using a 4.7 k resistor for feedback purposes, and observe both
the input signal and reference voltage on the CRO. If you like you can change the value of
the feedback resistor—the magnitude of the change in reference voltage is directly linked to
the size of resistor used, and by varying the feedback resistance you can tune the trigger so
that noise effects are cut out whilst keeping the trigger as sensitive as possible to further
changes in signal level.
Your shutter control is now complete. Test and evaluate its performance.
Author: Jon Pearce, 1998
Lab 7: Designing with Op Amps
Electronics & Instrumentation
8-1
Laboratory Exercise 8
The Loudspeaker: An Electromechanical
Transducer
Author: Jon Pearce, 1998
Lab 8: The Loudspeaker as a Transducer
8-2
Electronics & Instrumentation
The Loudspeaker: An Electromechanical
Transducer
1. Introduction and Aims
The loudspeaker is an example of a device which is both electrical and mechanical, and the electric and
magnetic systems are strongly coupled. Other examples are piezoelectric, electrostatic and
magnetostrictive transducers. The general ideas of this laboratory study also apply to them.
Because the electric and magnetic systems of the loudspeaker are so strongly coupled, the electrical
behaviour of the loudspeaker depends strongly on the mechanical (acoustical) environment of the
loudspeaker, and the mechanical behaviour depends strongly on the electrical loading of the speaker.
The aim of this investigation is to study this interconnection, which is characterised by the elements of a
2x2 matrix. In abstract, the device may be regarded as a 2-port in which one port is electrical and the
other mechanical . (See the diagram below.)
2. Theory (Short Version)
The extended theory of the loudspeaker is given in Appendix 2. Appendix 1 gives the AC conventions
used below.
The voltage across the speaker is given by
V = ZeI + GU
(1a)
As usual Ze = R + IXe is the electrical impedance of
S
the speaker, R is the electrical resistance, and Xe is
N
the reactance which is essentially inductive ( 2fLe).
U
Ze is the electrical impedance you measure when
the velocity of the speaker U = 0.
The term proportional to U arises from the fact that
when the speaker assembly moves, the magnetic
field in the gap induces an EMF in the speaker coil,
proportional to the velocity, U. The proportionality
factor, G, is the electromechanical coupling constant.
Lab 8: The Loudspeaker as a Transducer
F
S
I
I
V
0
V = voltage applied to speaker
I = current in the speaker coil
F = force applied to the speaker cone assembly
U = velocity of the speaker cone assembly
(assumed rigid at low frequencies)
8-3
Electronics & Instrumentation
S
The external mechanical force, F, is given by
F = Zm U - G I
(1b)
I
S
The term GI is the (internally supplied) force due to the current I
flowing in the magnetic field B. (A model shows that this is the
same G as before, a fact required by energy conservation.)
These two equations in the matrix form of a two-port read:
V   Z e G I 
   
 
F  G Zm U 
B
N
S
S
Radial magnetic field
in the gap
(2)
where the two-port is represented by the diagram below:
I
V
F
0
U
2 - Port
The overall electrical impedance of the system, Z, when it is loaded with an extra mechanical impedance
Zm is given by equation B7 as
3a
Z  V / I  Z e  G 2 /(Z m  zm )
 (R  jL) 
 R  j2 fL 
2
G
jMo  D  K / j
G2
2fr Mo j( f / fr  fr / f )  1/ Q
3b
3c
where the resonant frequency r = √(K/Mo) = 2fr
4a
and 1/Q = D/Mor.
(Q is mechanical oscillator quality factor.)
4b
The resonance width is (fr/Q) in frequency
4c
Author: Jon Pearce, 1998
Lab 8: The Loudspeaker as a Transducer
8-4
Electronics & Instrumentation
3. Qualitative Investigations
The speaker as a microphone
First convince yourself that the speaker will behave as a microphone by attaching it to the CRO
and speaking into it (the speaker, not the CRO, that is!).
Finding resonances
There are three ways to mount the speaker:
(a)
dangling in the open air,
(b)
mounted in the box, with speaker front uncovered, and
(c)
mounted in the box, with speaker front covered with a rigid plate.
For each of these configurations the stiffness constant is very different.
(a)
Open air: K = Ko
(b)
Mounted, open front: K = Ko + Ka
The calculated value of Ka for your speaker and box is given on the data sheet.
(c)
Mounted, closed front: K >> Ko
The air between the speaker and plate is so hard to compress that the speaker can
hardly move at all at low frequency. Thus U ≈ 0, and equation (1a) yields V = Z eI.
Equations 3 show that a mechanical resonance will appear as an electrical resonance in Z.
By scanning slowly through the frequency range, say 0 - 1.7 kHz, find and record the
approximate resonant frequencies for cases a, b and c above.
4. Quantitative investigations
Investigation of the mass of the speaker
We can determine the mass of the speaker by measuring the various resonance frequencies.
Resonance frequency of open speaker, fo
Resonance frequency of speaker in box (open front), fb
The rough relationship is:
(2fo)2M = Ko
(2fb)2M = Ko + Ka
where Ka is the extra stiffness due to the air entrapped in the box (see data sheet).
Lab 8: The Loudspeaker as a Transducer
8-5
Electronics & Instrumentation
Hence you can find M and Ko from your measured frequencies.
This is only rough due to the air loading on the speaker. Compare M with the given value in the
data sheet.
Data Sheet
Diameter of speaker:
d = 5.50 cm
Area of speaker:
A = (d/2)2 = 23.8 cm2
Volume of box (inside):
V = 10.85 x 8.2 x 5.3 = 471.5 cm3
Adiabatic bulk modulus of air:
(P is the air pressure)
P = 1.421 x 105 Pa
Stiffness constant of air in sealed box:
Ka = P A2/V = 1.71 x 103 Nm-1
Mass of the moving assembly:
M = 1.030 gm
Length of wire:
S = 2.56 m
Diameter of coil:
14.0 mm
References
Fraden J, AIP Handbook of Modern Sensors: Physics, Designs, Applications, American Institute of
Physics, 1993.
Lion K. S Elements of Electrical and Electronic Instrumentation. 1st edit, McGraw-Hill, 1975.
Horowitz P and Hill, The Art of Electronics, 2nd edit, Cambridge UP, 1989.
Neubert H. K. P Instrument Transducers, Oxford UP, 1963.
Diefenderfer A. J. and Holton B. E, Principles of Electronic Instrumentation, 3rd edit, Saunders, 1994.
Storey N., Electronics: A Systems Approach, 1st edit, Addison-Wesley, 1992.
Author: Jon Pearce, 1998
Lab 8: The Loudspeaker as a Transducer
9-1
Electronics & Instrumentation
Laboratory Exercise 9
Diodes and Their Applications
Curse that recharger!
You buy a new Walkman/Game Boy/mobile phone/remote controlled dune buggy (take your pick). It
requires yet another battery recharger, yet your house is festooned with these devices—each boasting its
own combination of voltage, current and power. Must you buy another? Can a 9 volt, 400 mA model
recharge the Walkman that wants 9 volt, 50 mA? What will it deliver: 9 volts or 400 mA or both? Why
can’t it make up its mind?
Some batteries have printed on them “Fast charge, 150 mA; slow charge 30 mA”. What determines the
current? Does the battery “know” when it is “full” and stop charging, or does curernt keep flowing
through making the battery hotter and hotter?
The basis of these battery rechargers (and other low voltage power supplies) is the diode. We will study it
here in a variety of ways. We won’t address all the above questions, but you should think about them as
you work and challenge your demonstrator to answer them!
Lab Overview
Author: Jon Pearce, 1998
Lab 9: Diodes and Their Applications
9-2
Electronics & Instrumentation
Diodes and
Their
Applications
1. CurrentVoltage
Characteristic
Curves
2. Constructing a
DC power supply
3. A Zener
regulated power
supply
Lab 9: Diodes and Their Applications
9-3
Electronics & Instrumentation
Diodes and Their Applications
The current-voltage characteristic curve for an ideal diode is drawn below. It shows zero current flowing
in the reverse bias direction and zero voltage across the diode when forward biased.
Real diodes however depart from this ideal response. The reverse
current is not zero (although it is so small that we can usually
approximate it to zero: a few nanoamps, maybe) and the forward
biased voltage is of the order of hundreds of mV up to a few volts.
I
V
Diodes depart from the ideal response at high reverse bias voltages. All
diodes will breakdown and pass significant current in the reverse
direction if the reverse bias is too high. This critical reverse bias is of the
order of a few hundred volts for most of the standard diodes. The
IN4004 silicon diode used later in this laboratory has a breakdown
voltage of 400 V. Another diode type that will be used at the end of this prac is the Zener diode. Zener
diodes are deliberately made with specified breakdown voltages between about 2 V and 70 V and are
used only in the reverse biased direction.
1. Current-Voltage Characteristic Curves (1 hr)
In this section you will measure the current-voltage curves for various types of diodes. The first one you
will do by hand, the rest by setting up a computer to measure and plot the curves for you.
1 (a) Various types of diode
Set up a circuit to measure VI characteristics
(i)
Set up the circuit below to allow you to measure a range of voltages across the diode as
well as the currents through it. (The 1 k resistor is there to limit the current to about 10
mA. That way, if you accidentally twist the supply knob to a maximum the diode might
not go zap!)
You will find in your pile of diodes a germanium, Schottky and Zener diode as well as
three different coloured LEDs (which are actually GaAs diodes).
Author: Jon Pearce, 1998
Lab 9: Diodes and Their Applications
9-4
Electronics & Instrumentation
Measure I-V characteristics
(ii)
Set up a LabView program to produce current-voltage plots for these diodes. Your VI will
be very similar to your previous ones to measure plots of I vs V, or V vs except that the
signals are DC, not AC. This means that you will use the VIs VOLT.VI and I-DC6.VI.
Make sure that you measure the voltage directly across the diode (not across the power
supply).You might need to check that any offset (reading when there is zero input) is
adjusted to zero by subtraction within your VI.
Let the voltage range from about -5 volts to +5 volts, but note usually a diode will never
have a forward voltage across it that is much larger than its “turn-on” voltage (why?).
(ii)
Create (and print out) three different graphs, one for the three coloured LEDs; one for the
silicon, germanium and Schottky diodes; and one for the Zener diode. Note the features of
each of the characteristic curves, ie. the turn-on voltage, differences in forward and reverse
resistance and any other important features.
Questions
1. What is the difference between the behaviour of germanium and silicon diodes? What about
the three different coloured LED’s ? What are the turn-on voltages of the Germanium and
Silicon diodes and the LED’s ?
2. What is the breakdown voltage of the Zener diode ? Once the Zener diode is at the breakdown
voltage, what would happen to the voltage measured across the diode if the current were
increased?
3. What is the difference in behaviour between the Schottky diode and the silicon and
germanium diodes?
Lab 9: Diodes and Their Applications
9-5
Electronics & Instrumentation
2. Constructing a DC power supply (1 hr)
Rectification is the process by which an AC signal is converted into a DC signal. The mains power supply
is 50 Hz AC but there are many devices, such as computer chips, that require stable DC voltages to
operate. The first stage of converting AC into DC is to rectify the signal, this is done using a full-wave
rectifying circuit. The full-wave rectifier directs current to flow only one way through the load of the
circuit by using a bridge arrangement of diodes.
2 (a) Using diodes to rectify AC signals
The rectifier you build here will be an unusual one in that you will use light emitting diodes
(LEDs) in place of regular diodes so that you can see when each diode is conducting. This also
means using a much lower frequency than the 50 Hz of the mains so that you can watch each
individual diode turn on.
Build a visible rectifier
(i)
Calculate a safe voltage to light two LEDs in series with a single 100  resistor, as shown in
the diagram below. Base your calculations on a LED requiring about 1.8 volts, 20 mA to
light brightly.
(ii)
Set up the half-wave rectifier circuit shown. The 100  resistor will act as a load (think
about what would happen if there were no load). Lay out the LEDs physically as shown in
the diagram—two more LEDs will be added later to complete the circuit. The positive end
of a LED is the end with the longer terminal.
Sig
Gen
100 
Study the operation with the signal generator set to about 1 Hz (slow enough to observe
the LEDs operating) and slowly increase the voltage to that calculated above (increase the
voltage further if the LEDs are not bright enough to see). Sketch what you would expect the
waveform across the load to look like (why can’t you view it directly with the CRO?? Think
of Mother Earth!).
(ii)
Add two more LEDs to complete the full-wave rectifier. Will the same signal generator
voltage be safe? Think! Again study the operation and sketch the expected waveform across
the load.
Author: Jon Pearce, 1998
Lab 9: Diodes and Their Applications
9-6
Electronics & Instrumentation
Sig
Gen
100 
View the output waveform
One way of avoiding the earthing problems above is to use the output of a transformer to power
your circuit. Since the transformer’s output windings are not physically connected to earth (they
are “floating”) your rectifier circuit is also floating—i.e. it has no earth, and you can connect the
CRO’s earth anywhere you like. The transformer you are supplied with runs from the mains and
reduces the mains voltage from 240 V (rms) to 12 V (rms).
(i)
Swap your signal generator for the 50 Hz, 12 AC transformer. Add a decade box (R ~ 1000
) in series with your load resistor so that you can vary the total load. (The 100  resistor
should remain as a safeguard in case the decade box is turned down to zero; there is a 0.75
A fuse on the AC supply).
Did the earth move for you? Well, note that it has in the diagram below!
Observe on the CRO the signal across the load resistor, and sketch it in your log book.
Question
4. Explain the signal you observe. What is the frequency and why ?
2 (b) Smoothing the rectified signal
The rectified signal in the last section still needs to be smoothed out in order to make it into a
steady DC signal. To do this a low pass filter, or smoothing circuit, will be added. The 3 dB cutoff frequency of a low pass filter is given by
fc 
Lab 9: Diodes and Their Applications
1
.
2RC
9-7
Electronics & Instrumentation
Calculate component values
(i)
Calculate the values for an appropriate capacitor and resistor such that the cut-off
frequency of the low pass filter is less than 50 Hz. The capacitance should be >100 F and
the resistance should be <100 . Once you have chosen these components, obtain the
resistor and capacitor that most closely matche your requirements.
Add the low pass filter to your circuit, still keeping the 100  resistor in series with the
decade box.
Observe the signal across your load (resistor plus decade box) for RL ~ 200  and 10 k.
Record the ripple voltage and DC voltage of your signal for 5 or more values of RL
between 100  and 1000  and plot ripple voltage versus load current IL (IL = VDC/RL).
Keep your circuit for the next section.
Questions
5. How are the ripple voltage and DC voltage related to the load current?
6. Why is the use of a large R and small C to obtain small ripple voltages not recommended?
Author: Jon Pearce, 1998
Lab 9: Diodes and Their Applications
9-8
Electronics & Instrumentation
3. A Zener regulated power supply (1/2 hr)
Your power supply now delivers a reasonably constant output voltage, but it has deficiencies: the
absolute value of the voltage is unknown, it may vary as you change the load, and it contains ripple. A
regulated supply addresses each of these problems. The regulation device in this case will be a Zener
diode.
Look again at the characteristic curve obtained from the Zener
diode in the first section of this laboratory. Your diagram
should look something like the one shown.
As you saw earlier, the Zener diode has a reverse bias
breakdown voltage that is quite low. For this reason, Zener
diodes can be used to regulate DC power supplies. The Zener
diode is always used in the reverse bias orientation. Once the
reverse bias voltage reaches the breakdown voltage, it will
remain the same over a wide range of current. You will have
noticed in the previous section that your rectified and filtered
circuits still contain some ripples. So long as those ripples don’t
correspond to a change in current great enough to depart from
this regulating region, the regulated signal across the load should not have a noticeable ripple.
In this section you will design and test a 5.6 V regulated DC power supply using a 5.6 V Zener diode.
Your circuit will look like the one below.
3 (a) Designing the supply
The extra resistor in this circuit is there to drop the difference in voltage between the unregulated
power supply output (about 12 volts) and the Zener voltage (5.6 volts). We need to calculate its
value:
If the maximum power dissipation that the Zener can handle is Pmax, then the maximum current
through the Zener must be
I Zmax 
Lab 9: Diodes and Their Applications
Pmax
VZ
9-9
Electronics & Instrumentation
This maximum occurs when the resistance in the circuit is a minimum. Assuming the worst case of
RL = ∞, we can calculate what R needs to be:
Rmin 
V
A
 VZ 
I Zmax
.
Calculate the component values
(i)
Calculate the value of R for your circuit assuming a 500 mW, 5.6 volt Zener (not the same
Zener as you used earlier). Design so that the current will never exceed Iz(max)/2. Check
this value with your demonstrator.
(ii)
Calculate the minimum value that the load resistance can have, RL(min), to maintain IZ  > 1
mA (this is the minimum current required through the Zener for regulation).
Construct and test circuit
(iii)
Add the Zener diode (reverse biased) to your circuit in the previous section. Put it in series
with the resistor chosen in the previous step. Connect your load resistor (decade box)
across the Zener diode and observe the signal across the load on the CRO as the load
resistance is varied. Note the load resistance in which the voltage is no longer regulated.
Questions
7. What is the advantage of keeping R small, but still > Rmin of course ?
8. If the output is shorted, will this destroy the Zener diode ?
9. How did the Zener regulated ripple voltage compare with the ripple voltage of the
unregulated signal?
Author: Jon Pearce, 1998
Lab 9: Diodes and Their Applications
10-1
Electronics & Instrumentation
Laboratory Exercise 10
The Field Effect Transistor
Think about it . . .
You connect four light globes in series across a laboratory power supply. They light up. You short three of
them out. What happens to the intensity of the fourth? You might predict that it would become very
bright—or even burn out? What if you connected them across another power supply and, on shorting
three, the fourth maintained its original brightness? What sort of power supply would do that?
This laboratory investigates the field effect transistor (FET) and some of its applications, including a
circuit that produces the counter-intuitive behaviour mentioned above.
The FET is a “discrete” device (rather than an integrated circuit) yet is still valuable on its own, as well as
a building block for integrated circuits (e.g. the FET-input op amp). FETs have properties that make them
good for use in amplifiers, high input impedance voltage followers, voltage controlled resistors, sampleand-hold circuits, analogue switches and constant current sources. We have only time to investigate a few
such circuits here.
Lab Overview
The Field
Effect
Transistor
1. Characteristic
curves of a FET
2. Constant
current source
3. Switching
circuits
Author: Jon Pearce, 1998
Lab 10: The Field Effect Transistor
10-2
Electronics & Instrumentation
The Field Effect Transistor
Discrete semiconductor transistors are the fundamental building blocks on which most modern
electronics are based. A sound understanding of transistors, their characteristics and various
modes of operation, is therefore essential to an understanding of how “solid state” electronic
devices work. For example, both the op amps and audio amplifier you have used already
contain a number of discrete transistors, and it is the characteristics of these transistors which
determine how the device functions as a whole.
In this laboratory, you will investigate the characteristics of a field effect transistor —a
discrete semiconductor device which in effect acts as a voltage controlled resistor. You will
then go on to use these characteristics in designing circuits which exploit the properties of
discrete FETs.
1. Characteristic curves of a FET (1 hr)
An N-channel field effect transistor (or FET) comprises a channel of n-type ohmic semiconductor (drain
to source) sandwiched between two regions of p-type semiconductor (gate). The current that passes
through this channel is controlled by a voltage on the gate
. The width of the reverse-biased junction
from gate to channel determines the width of the channel and thus the current flowing from source to
drain. At some negative voltage, known as the pinch-off voltage
(V P ), the channel will completely
close and no current will flow.
Drain
ID
In effect, the FET acts as a variable resistor which is controlled by the
electric field applied to the PN junction (hence “field effect”). Very little
power is expended in the control signal due to the low reverse current
of the junction. The p-channel
FET is similar with the p and n-type
materials reversed.
+
Gate
-
p
V DS
p
V GS
+
n
Source
-
1 (a) Measuring the FET characteristic
curves
You should have had experience in measuring FET characteristic curves during the electronics
component of the first year physics laboratories (whenever you happened to do them). Those of
you with long memories may even remember that this is an extremely tedious task. To speed it
up we have created a LabView virtual instrument which automatically collects the data and plots
the I vs V graphs for you.
Your circuit will have two power supplies, one which you vary by hand, the other by using a
slider on the computer, as the computer measures and plots the current vs voltage curves.
Lab 10: The Field Effect Transistor
Electronics & Instrumentation
10-3
Wire the circuit
(i)
Construct the circuit below using the 2N5459 JFET provided, making the 3 connections to
the interface box as shown. Both power supplies should be independently variable, as
explained below. Connect to the LabPC+ interface to monitor the voltage V DD and the
current ID. (Note that the voltage VDD is too large to be monitored directly by the interface,
so we divide it down by a factor of 3 using three resistors.)
The 560  resistor (Rd) in series with the drain power supply is there to limit the current
flow to below about 30 mA for VDS=15 V. The 1 M resistor across the gate stabilises the
gate voltage (Rg).
The gate junction of a FET must always be reverse biased (or else current will flow from the
channel material into the gate and no depletion region will form). It is therefore necessary
to reverse bias the gate . We do this be applying a negative voltage to the gate, relative to the
source. Hence we need a second computer-controllable voltage source for VGS,
programmed in such a way that VGS is always negative . To do this, use the Analogue
Output DAC1 on your interface box, and check later that your VI is set to make this output
voltage negative.
Drive the computer
(i)
Use the VI FETCURVE.VI to log VDS, IDS and VGS, and plot your characteristic curves form
this data with VGS = 0, -0.5, -1.0, -1.5, -2.0 and -2.5V. You should be able to produce a plot
with each of these curves on the one set of axes..
Author: Jon Pearce, 1998
Lab 10: The Field Effect Transistor
10-4
Electronics & Instrumentation
Analysis
Explain, in terms of the construction of the FET and semiconductor physics, why the first part of
the graph is approximately ohmic in nature whilst for higher values of VDS the current is
dependent on VGS.
2. Constant current source (1/2 hr)
As you can see from the characteristic curves, when VDS is above about 2V the output current
is determined by VGS rather than by VDS, and is in fact almost independent of drain voltage.
For example, if the source and gate in the above circuit are shorted together as shown in the
diagram VGS = 0 and the current drawn by the JFET will remain constant provided the
voltage across the FET is above the “knee voltage” on the graph. This is in contrast to the
power supplies you have used so far which have provided a constant voltage with the current
varying according to the load.
V in
Using a constant current source can have some interesting (possibly also counter-intuitive)
results, especially if one is used to working with constant voltage sources. The following
exercise serves as an illustration of this.
2 (a) First, a constant voltage source with variable load
Measure the LED voltage (quickly!)
(i)
Using the multimeter, check the turn-on voltage of the clear, low current LEDs (these draw a
current of less that 10 mA) by connecting them to the power supply with a 1 k resistor in
series (for protection!). Increase the power supply voltage slowly as you measure the LED
voltage.
Observe the behaviour
(ii)
Connect up the following circuit using clear, low current
LEDs. Expect to see only very dim LEDs to begin with.
Record in a table the supply voltage (use a meter) and the
LED brightness (use your eyes) and current passing through
the system (another meter) as you progressively short out the
LEDs. (Remember that these LEDs emit light in a small cone
out of the ends, so you will have to look directly into the
curved top to see any light).
Comment
Explain the behviour of the LEDs as you progressively shorted
them out.
Lab 10: The Field Effect Transistor
mA
+
10-5
Electronics & Instrumentation
2 (b) Next, a constant current source with variable loads
Add a FET
(i)
Using the same set-up from the section above, insert a FET
constant current source using the 2N5459 JFET you used in
part 1 above.
Note that you will have to increase the power supply voltage
to 15V to ensure that there is enough voltage both to turn on
the LEDs brightly and keep the FET above the VGS=0 knee
voltage of 4V.
mA
+
Observe the voltage across the FET using the DMM and once
again record the LED brightness and current passing
through the system as you progressively short out the LEDs.
Comment
Explain this LED behaviour too by referring to its characteristic
curves.
Regulate the current
By altering the value of VGS it is possible to regulate the amount of current
provided by the current source by simply moving the FET characteristics from
one of your plotted curves to another. As the current IDS is approximately
constant (after all, this is a constant current source!) this adjustment can be made
by simply inserting a variable resistor after the source and before the feedback
loop as shown opposite
10 k
As the current IDS is constant, so is the voltage across the resistor, and by varying
the resistance it is possible to adjust VGS, and hence the current provided by the
current source.
(ii)
Construct a variable current source using a 10 k trim pot inserted into the circuit as
shown above.
Adjust the resistor so that the total amount of current flowing through the circuit is 2.0 mA
and once again record the LED brightness and current passing through the system whilst
observing the voltage across the FET as you progressively short out the diodes.
Explain, with reference to your characteristic curves, why this current source provides a
more constant output than your previous current source.
Author: Jon Pearce, 1998
Lab 10: The Field Effect Transistor
10-6
Electronics & Instrumentation
3. Switching circuits (1 hr)
Another common application of the FET is as a voltage controlled switch. As you can see from your
characteristic curves, as the gate bias voltage increases the number of available charge carriers in the gate
region decreases. If one increases the bias on the gate further, the depletion zone between the gate
electrodes join up and no current can flow, because there are no longer any charge carriers available in
the conduction channel. (Similarly, if you squeeze the sides of a garden hose, the water flow will drop off,
and if you squeeze hard enough no water will flow at all.) The voltage at which this occurs is called the
Pinch-off voltage—as the name suggests, this is the voltage at which the conduction channel is “pinched
off” and the FET can no longer conduct.
Once can take advantage of this property for switching purposes—if the gate voltage is zero the FET will
conduct, but if it is below the pinch-off voltage it will not. This form of switching is quite common in
modern electronic devices because it eliminates the need for mechanical switches (such as relays), and
being a solid-state device it is compact and immune to dust and vibration. Although the FET is of limited
use for high-power switching (due to the current throughput of only a few mA), its cousin, the thyristor,
is commonly used for power switching applications and power rectification.
3 (a) A simple switching circuit
The circuit below shows a simple switching circuit to switch a LED on and off.
Construct and test the circuit
(i)
Wire the above circuit. Use the signal generator on square wave output to provide the
switching pulse. Remember that the gate voltage should vary between 0V and -5V (to
ensure pinch-off) and must be negative with respect to the source and that the signal
generator output is referenced to earth. To get this gate voltage right, observe the output
Lab 10: The Field Effect Transistor
10-7
Electronics & Instrumentation
using the CRO while adjusting the signal generator output using the gain and offset
controls such that the output is correct. Once you have done this, adjust the frequency to
about 1 Hz so that you will be able to see the LED flash on and off.
Make sure that the supply voltage is more than sufficient to turn on the diode and use the
560  resistor once again to limit the current flow as you did when measuring the
characteristic curves. Simply use your 2N5459 JFET as the switching transistor (since you
already know its characteristics).
Hopefully you are now observing the circuit switching the LEDS.
3 (b) Sample and hold
The sample and hold circuit is used to “freeze” the value of a quickly varying input signal. It is
used, for example, to store an input voltage for long enough to digitise the voltage in an analogue
to digital converter.
Consider the following circuit:
v in
560 pF
trigger
When the FET switch is ON, the circuit is said to be sampling the input voltage because the second
follower output is equal to the voltage of the capacitor, which is being charged by the output of
the first voltage follower. When the HOLD state is established by switching the FET OFF, the last
sampled voltage is held on the capacitor. The high input impedance of the second follower holds
this output voltage until the next sample state is entered.
The second follower needs to have a low input bias current so as to reduce the leakage of current
from the capacitor during the hold state, as any current flow discharges the capacitor and causes
the output voltage to drop. For the same reason, the capacitor must be of a low leakage type. The
first follower must have a low output impedance because it is supplying charge to the capacitor.
Constructing a sample-and-hold amplifier
(i)
Construct the above circuit using two JFET op amps (LF353N), a 560 pF low leakage
polystyrene capacitor and your 2N5459 FET. So as to reduce the amount of wiring
required, we have provided you with an LF353N dual JFET op amp chip which has two op
amps in the one IC package, each of which is equivalent to the 13741 FET op amp you have
already used. The connections for this device are as follows:
Author: Jon Pearce, 1998
Lab 10: The Field Effect Transistor
10-8
Electronics & Instrumentation
Output A
1
8
V+
Inverting
Input A
2
7
Output B
Non-inverting
Input A
3
6
Inverting
Input B
V-
4
5
Non-inverting
input B
-
+
+
-
TOP VIEW
LF353N
(ii)
Using the second signal generator, set the output to be a 0.5 V sine wave at about 250 Hz
and connect it to the input of the first voltage follower. Check that both voltage followers
are working by observing the output.
(iii)
Check thaqt your trigger is working by attaching a loose wire to -5 V and touch the other
end to the gate of the FET.
If all is ok, apply a square wave trigger pulse of 0 to -5 V at 250 Hz to the trigger (ie: to the
gate of the FET) and observe the output. Remember that this is an n-channel FET, so the
trigger signal must be negative with respect to the source.
The output will probably be very confused because both of the signal generators are not
operating at exactly the same frequency. Slightly adjust the relative input frequencies until
you see a single, stable output when triggering on the input signal—at this point the two
signal generators should be operating at about the same frequency and any frequency
difference between the signal generators will be manifested as a slow movement of the
output signal.
Observe and sketch the input signal, the voltage across the capacitor and the output signal
using the CRO, paying particular attention to any drop in held voltage.
(iv)
For the same input frequency sketch the output signal when the trigger is set to twice and
ten times the input frequency. Explain what you see, and comment on its significance. You
may also like to investigate sampling at other frequencies where you can get the output to
remain steady on the CRO.
For real sampling applications you want the sampling time to be as short as possible so that more
time is spent in the held state for sampling. You will have noticed that for a square wave trigger
the sampled signal follows the input voltage half of the time and holds for the other half. Ideally,
the following time should be short and the hold time long. In order to achieve this, you will need
a trigger pulse which is briefly at 0 V but which lingers at -5 V.
Vary the duty
(v)
To create such a pulse, adjust the “duty” knob on the signal generator whilst watching the
trigger pulse on the CRO—you will notice that the spacing between the peaks increases but
that the signal spends most of the time at 0 V rather than at -5 V. To fix this, invert the
waveform by pressing the “inv” button. Setting the duty knob to maximum (to obtain the
greatest hold time), adjust the frequency so that the distance between sample pulses is once
again at about 250 Hz (hint: the time spent at -5 V has been increased by about a factor of
10, so just press 10 kHz range button instead of the 1 kHz button).
(vi)
Set the sampled signal to about 100 Hz and observe the output of the sample-and-hold,
with the CRO triggering off the sample-and-hold output signal. Adjust the frequency of the
signal generator to achieve a clear, stable output and comment on the sampled signal.
Lab 10: The Field Effect Transistor
Electronics & Instrumentation
(vii)
10-9
Set the trigger frequency to 80 kHz (remember that with the duty knob set to maximum the
actual frequency is a factor of 10 less than what is shown on the dial, so you actually have
to set the dial to 800 kHz) and look at the effect of sampling various frequency signals,
including frequencies greater than the sampling rate—for clarity of display, pick
frequencies where there are an integral number of samples per cycle (use the DMM to give
a clear frequency reading).
(viii) Record what you see (but do not record as much detail as in the previous investigation). At
what frequency do you cease to be able to see a sine wave in the sampled output? 80 kHz is
the maximum sampling frequency of the interface card which LabView uses—what do your
results tell you about the limitations of the analog to digital conversion used in
computerised data collection?
This arrangement will be set up in the lab as a demonstration so that you can play with it even if
you run out of time getting yours set up.
Author: Jon Pearce, 1998
Lab 10: The Field Effect Transistor
11-1
Electronics & Instrumentation
Laboratory Exercise 11
Projects
This week’s laboratory will involve you in doing a project, with your partner, which will expand on
some on the work done in earlier labs, or be of your own design. Full details follow, but the general
guidelines are:
you are expected to prepare (yes, prepare!) your project at least three weeks ahead and submit
a preliminary report,
the practical work will be completed in this one week; your final report to be submitted one
week later,
the nature of the project can be of your own choosing, but by necessity must be simple (not
over-ambitious, as is the temptation!),
the assessment of the project will be one-fifth of your lab mark (i.e. 10% out of the 50% you
get for these labs).
Read on . . .
Author: Jon Pearce, 1998
Lab 11: Projects
11-2
Electronics & Instrumentation
Electronics & Instrumentation: the Project!
Introduction
This lab session will be devoted to you and your partner working on a project (albeit a very simple
project) of your choice. However, this project requires you to do some preliminary work three weeks
ahead of the lab class in order to plan carefully what you will do during the very short three-hour lab
session. The assessment of this project will be based on your preliminary work, your achievements
during the lab session and a report you will submit one week later. Together these three components
will comprise 10% of your assessment for the subject (i.e. 10% out of the 50% allocated to the lab
component of the course).
The general aim of this project is to let you explore an area that you want to and to allow you to
demonstrate your initiative, skills and competence in electronics. Communicating the outcomes of
your project via a formal report is also an important aim.
Summary of schedule:
Design Document:
To be submitted to Jon Pearce (room 205) the day before your lab during Week 9 (starting
April 27). This will be returned to you with any comments during a later lab class.
Practical Work:
To be done during Week 11 (starting May 11). The preceding tute sessions (either Thursday
May 7th or Monday May 11th) will give you some extra time to do preliminary work.
Report:
To be submitted by 5 pm seven days after your practical work session. Harsh penalties may
be applied to late submissions!
Choice of project
Due to limited time and equipment, this cannot be a “free for all” project! We have to restrict you to
projects that are not too ambitious, do not require much in the way of equipment or components
beyond what you have already used in the lab, and ones which we anticipate you can make
reasonable progress through in the short time given. That’s a tall order!
An ideal project will give you plenty of opportunity beforehand to do preparatory work: designing a
circuit, programming a VI, planning your lab time. Your project might be exploratory in nature, rather
than trying to design and test a particular circuit, and hence it might not have a set “end point”. You
might wish to spend your time testing the performance of a particular device. You might choose to
extend something you started during one of the lab sessions. Nevertheless, it is important that you are
able to plan several stages so that both you and your demonstrator can see what you are achieving
during the lab session.
Lab 11: Projects
11-3
Electronics & Instrumentation
You will work with one partner for this project.
The three components of the project
Design (Assess: 15%)
You should prepare a brief document of about one page in length which clearly describes
your intended project under the following headings:
 General aim: outline what you intend to investigate and what you hope to achieve.
 Background: give any rough circuits or ideas that might be starting points in your lab
investigation. Describe any VIs that you might plan to program.
 Equipment: list all equipment and components that you think you might need. Highlight
anything which is not the regular lab equipment (or components) that you have been using
during the semester. (We don’t expect there to be anything much in this category—and
you should discuss such things with Jon Pearce or your demonstrator beforehand to check
that it can be arranged).
 Starting point: describe briefly the first (practical) thing that you intend to do during the lab
session.
Make sure that this document has your name and your partner’s name on it, together with the
lab group that you belong to. Please submit it to Jon (room 205) the day before your lab
session of Week 9 (starting April 27).
Practical session (Assess: 35%)
You are already aware of how time consuming little bugs (electronic or computer) can be
during any practical work. So come prepared! Spend some time planning what you hope to
do, what problems you might have, and what changes to your plans you might make if things
go off track. Good planning and good laboratory techniques could save you here. If
appropriate, start out with a small, simple circuit to test a transducer’s operation, then build it
up to a more complex circuit if necessary. Above all, make sure you document well your lab
session as you proceed so that you can retrace steps, write a good report, etc. You need
something to show if all collapses in a heap!
In assessing this part of the project, your demonstrators will be looking for good techniques:
appropriate and competent use of equipment; careful circuit layout and wiring; good
decisions. They will also, of course, be there to try to help you with any problems you may
have.
Report (Assess: 50%)
This should be a formally typed report (set out as for a scientific paper) with headings such as
introduction, aim, design/theory, laboratory investigation, results/outcomes/difficulties,
conclusions and references.
At the end of your report, please write a short comment about what you learnt:
 about electronics;
 about working on projects, and
Author: Jon Pearce, 1998
Lab 11: Projects
11-4
Electronics & Instrumentation
 about working with a partner.
Your report should describe in a logical and coherent manner: what you aimed to do, how
you went about doing it and what the outcomes were. Explain how your circuits work and
link your explanations to an appropriate diagram.
Details of how you went about your lab session work are not required, just any significant
events, problems and relevant results, together with any data you collected in an appendix.
The length of this report will vary. Although a description of any relevant theory is required,
this should not be used to “pad out” the report! I anticipate that the introduction and aim
might be 200 words, the design/theory 400-600 words, report on your lab work, together with
results etc., about 500-700 words, conclusions and references about 200 words. That totals to
about 1500-1700 words—that’s only about 3 or 4 pages (with additional liberal use of circuit
diagrams, of course!). This is only an estimate by me—if you find it is unrealistic then please
let me know.
Project ideas
Some projects are suggested below which cover a wide range of styles from fairly well specified
exercises, extensions to lab exercises, to vague ideas for you to pursue. You might have some better
ideas. Use these as a starting guide. Choose a style that you feel most comfortable with. But
remember, you only have 3 hours of lab time—that is not long—don’t be too ambitious!
0.
Extend an idea from a lab session.
Probably a pretty safe project! But be clear about what you aim to achieve beyond the set lab.
1.
Hall effect device for measuring magnetic fields
We have some simple four-legged Hall effect transducers that give a linear output
proportional to a magnetic field. A copy of the data sheet is appended. Many ideas spring to
mind: plotting the field around a bar magnet; sensing the earth’s magnetic field; calibrating a
system to measure the distance between the device and a magnet; calibrating a system to
measure and monitor non-invasively the current in a wire, etc.
Design Note: the magnetic field from a typical “lab sized” current (100’s of mA) is very weak!
2.
IR remote control (* Some rough thoughts appended at end)
Remote controller for TVs send out a sequence of infra-red pulses. You can easily detect these
using an IR detector and then display them (using LabView).
3.
Optical communications (* Some rough thoughts appended at end)
Using an audio signal (from a radio, for example) to control the brightness of a LED enables
you to transmit a light signal which can be picked up by another LED (acting as a detector)
and converted back to an audio signal. This is the basis of an optical communications system.
Warning: This is a very ambitious project!
4.
DAC from LabView & op amp
Lab 11: Projects
11-5
Electronics & Instrumentation
LabView can be used to output a digital signal of one byte width (8 binary values on 8 wires).
You could use this as an input to explore the construction of digital-to-analogue converters
using op amps—try some different designs.
5.
Automatic Bode plotter
Your use of LabView during the labs has usually involved you controlling a voltage amplitude
or frequency by hand and watch the graphs being plotted. This was done deliberately so that
you kept full control over what was going on. But LabView can output a changing analogue
signal (via the LabPC+ interface) and the signal generators you used can have their frequency
controlled by such a signal (over a range of 3 decades, or so. This means that you could set up
a system to automatically produce the Bode plot, for example, of a circuit.
If you choose to do this, you need to be careful to remember some of the limits of the
equipment. LabView can generate a variety of waveforms to output via its digital-to-analogue
converter (DAC), but its frequency range is limited (hence controlling a sig gen is a good way
to go instead). The current that the LabPC+ card output is small—but this could be amplified
by a suitable buffer circuit if need be.
6.
Transistor curve tracer
You might like to set up a LabView control circuit to automate fully the tracing of the
characteristic curves of a transistor (sse lab 10). Again the LabPC+ digital-to-analogue (DAC)
outputs can be used (with buffering) to vary the voltages you require.
7.
Response of car brake lights
A significant factor on how much warning a car behind you gets when you slam on the brakes
is the time taken for the brakelight globes to light up. Using bright LEDs instead of
incandescent globes might be a considerable advantage. Set up a circuit to compare the light
up times of LEDs and incandescent globes. Do the calculations as to how any differences
translate in to stopping distances.
Design note: LabView might be a good tool to use here.
For further information on any of the these projects, please talk to Jon Pearce or your demonstrator.
Rough thoughts on some of the project
ideas!
2.
IR remote control
What you might do
Firstly, you have to capture the infra-red signals from the remote control using a photodiode
as a transducer. You might choose to design a LabView instrument to display these signals.
The Photodiode
Author: Jon Pearce, 1998
Lab 11: Projects
11-6
Electronics & Instrumentation
A suitable photodiode is a Philips BPW50 infra-red photodiode. It generates sufficient output
voltage when used in photovoltaic mode to drive both the CRO and LabView, so the interface
circuitry is quite simple. The maximum reverse bias voltage is 32V, and the peak spectral
response is at 930nm. See the spec sheets for more detailed information about its performance
and characteristics.
3.
Optical communications
Introduction
Much of modern telecommunications is now conducted using optical signals transmitted via
optical fibre rather than using electrical signals and cables.
Whilst it is common knowledge that LEDs emit light, it is not so well known that they can also
be used as photodiodes. This project involves constructing a basic optical transmission
system using two LEDs - one as the transmitter and one as the receiver.
What you might do
You might aim is to design and construct a system to transmit optically a radio signal. First
you will have to construct a transmission system using a high-efficiency LED, then you will
have to construct a circuit to detect optical signals using the same LED. This would form the
basis of your optical transmission system.
Suggestions
 Look up the section on Photodiodes in the Melles Griot catalogue and select an
appropriate sensing circuit, describing the process of selection. These pages are copied
straight form a commercial distribution catalogue, and contain information you will
commonly be presented with when selecting devices.
 Build the detection circuit and verify that it works.
 Use a trans-impedance amplifier with Rf = 10M— the resistive loads don’t work well
enough.
 Construct a transmitter—as a suggestion, try varying the intensity of the light as a means
of carrying the information. You will have to work out how to do this using the LED.
 Try to transmit a simple signal from the signal generator first, before attempting the more
complex audio signal from the radio.
Lab 11: Projects
Electronics & Instrumentation
Author: Jon Pearce, 1998
11-7
Lab 11: Projects
12-1
Electronics & Instrumentation
Laboratory Exercise 12
Developing a Data-logging System
Arthur C. Clarke once wrote:
“Any sufficiently advanced technology is indistinguishable from magic”.
So far, the use of the LabPC+ card, controlled by the software LabView has been “magic“ is the sense that
we have not looked at how a computer, a basically digital device, can “measure” an analogue voltage.
In this lab we look at some of the electronics that a computer needs in order to do such a task. Although
we will use the LabPC+ card to help us, we are really focussing on what makes it tick. This course does
not cover digital logic systems, hence we can’t go very far in this direction. However, it is important that
you get some understanding of how the interface that you have used all semester actually does its work.
In another life, or your next degree, you might explore deeper into microprocessor sub-systems that
provide the same functions that we will construct today using a desktop PC, interface card and circuit.
The astounding fact is that it can all now be fitted into one IC chip and embedded into a device the size of
a piece of PK-chewing gum!
Lab Overview
Developing a
Data-logging
System
1. The
temperature
transducer
2. Analogueto-digital
converter
3. Handling
multiple
channels of data
Author: Jon Pearce, 1998
Lab 12: Developing a Data-logging System
12-2
Electronics & Instrumentation
Developing a Data-logging System
Overview of the System
The general idea
During this lab session you will put together components that will enable a computer to read and monitor
the output from a temperature transducer. What’s the big deal, you ask? Can’t you connect the
transducer’s output directly into the LabView interface box and simply read the voltage it generates? Well,
yes, you could. But we will use some devices to help you understand what goes on in the LabPC+ card that
LabView drives. Although we will still use LabView to control our circuit, it would be a small step to
replace the whole computer, LabPC+ interface and LabView with a small microprocessor chip running a
low level program.
So, the aim is to work with some of the basic ideas behind interfacing, data-logging and control.
The transducer
There are dozens of ways to obtain a voltage from a temperature: thermistors,
thermocouples, even a simple diode can be used as a sensitive temperature
monitor. We will use a three-legged temperature sensor (looks like a transistor,
but it’s not) called an LM35. Its advantage over other methods is that its output
is calibrated to be 10 mV per degree centigrade. There are no offsets, no nasty
non-linearities to deal with.
The analogue-to-digital converter
This is an integrated circuit chip (ADC0802) that takes in an analogue signal (0 to +5 volts) and converts it
into an 8-bit digital signal that can be read into a computer. Two important parameters for such devices
are their resolution and their conversion time.
The ADC0802 maps the voltages 0 to +5 volts onto 8-bits—i.e. the numbers 0 to 255. This gives it a
resolution of 5/256 = 19.5 mV. This is not too good for our purposes since that resolution represents a
temperature change of 2 degrees, which hence becomes the final resolution of our system. There are two
ways we could improve this: use a differential amplifier (differential so that any undesired offset could be
zeroed out) or we could make use of a feature of the IC which allows the range of voltages measured to be
varied. This latter method we will utilise.
Initially we will make the ADC free run, without the aid of the computer, and display its output on 8
LEDs. Then we will add the computer to control the data capture and to display the output. Finally we
will use the digital-to-analogue converter of the LabPC+ card to send out an analogue signal to set up an
appropriate range of temperatures and effectively vary the resolution of our system.
In each of these cases the ADC you have previously used (built into the LabPC+ card) is being replaced
by your ADC integrated circuit on your breadboard.
Lab 12: Developing a Data-logging System
12-3
Electronics & Instrumentation
1. The temperature transducer (15 mins)
We will start with a quick look at the temperature transducer, LM35.
1 (a) Testing the transducer
Wire your LM35 to the breadboard so that you can monitor its output when
powered from +5 volts from your supply. Check that the value it gives for room
temperature is about right (there is a thermometer in the lab) and that when warmed
by holding in your hand it responds as expected.
LM35
Gnd Vout +Vs
Top View
V s : 4 V to 20 V
+5 V
LM35
V out :
10 mV/ o C
Power
Supply
LM35
V out :
10 mV/ o C
2. Analogue-to-digital converter (1 Hr)
We will begin by wiring this ADC to “free run”, that it, not require any external computer to control it.
The input voltage will come from a power supply; the output will be displayed on LEDs. Later we will
use the temperature transducer as an input and connect a computer to control the device and display the
output.
2 (a) Free running ADC
The ADC0802 takes one analogue input and converts it into a single 8-bit number. All such digital
devices need a clock pulse to drive them—simply a high frequency square wave—the ADC0802
one has one built into the chip, the frequency of which is determined by an external RC circuit.
We will begin by wiring up the complete circuit, then we will look at the operation of various
parts. The diagram below show a functional block diagram, i.e. it shows the functions of the IC
grouped together in a logical way rather than the order on the chip itself. In your lab book draw a
pin-out diagram, i.e. one showing the IC outputs ordered from 1 around to 20 as they are on the
chip—a useful diagram to wire from.
More details on this device can be found in extracts from the manufacturer’s data sheet in the
Appendix.
Author: Jon Pearce, 1998
Lab 12: Developing a Data-logging System
12-4
Electronics & Instrumentation
Wiring the circuit
+5V
1
Vcc
CS
2
5
10 k
CLK R 19
RD
3
20
CLK IN 4
WR
150 pF
INTR
11 DB7
12 DB6
ADC0802
13 DB5
6
14 DB4
V IN (+)
15 DB3
V IN (-) 7
16 DB2
17
A GND
DB1
18
V REF/2
DB0
D GND
diff
inputs
Analogue
voltage in
8
9
span
adjust
10
Functional Block Diagram
(i)
Wire up the circuit shown. You are provided with a strip of LEDs to make this part of your
circuit neater. (These must be low current LEDs since the output of the chip can only source
5 mA of current.)
(ii)
Measure the frequency of your clock output (pin 19) and compare it with that described in
the data sheet (p. 3-33) of fCLK ≈ 1/1.1RC.
(iii)
The analogue input to the ADC is between pins 6 and 7 (it is a differential input). For now
we will leave pin 7 at earth and use pin 6 as the input. Wire a test analogue input for your
circuit by connecting the output of a 10 k potentiometer to pin 6, as shown below. (The
conversion won’t have begun yet—read on!)
+5 V
10 k
to analogue
input
Running the ADC
Before making the chip operate, there are things we need to understand about the three control
inputs, CS , RD and WR , as well as the output INTR .
These inputs are Chip Select, ReaD, WRite and INTeRrupt respectively. The “bar” on top of the
labels means that they do whatever they do when a logic low signal is applied rather than a logic
high signal. Logic LOW => 0 volts; Logic HIGH => +5 volts. This negative logic use is also indicated
on the diagrams above by a “bubble” (
) on the output of the relevant pins of the chip.
Lab 12: Developing a Data-logging System
12-5
Electronics & Instrumentation
But what do they do? These signals are used when the ADC is connected to a computer, or
microprocessor chip, and they control the flow of information to and from the chip:
Three inputs to the chip:
RD (Read)
- when this input is LOW the 8-bit data are loaded onto the output pins
ready to be read by a computer or microprocessor chip. When it is HIGH
these pins are in what is called a tri-state mode—this is a high impedance
mode allowing the outputs from many chips to be connected together, as
long as only one is being read (or written to) at any one time.
WR (Write)
- the conversion process is started by this signal going LOW, and then HIGH
again.
CS (Chip Select)
- the RD and WR signals will only control this chip when this input is LOW
and the chip is said to be selected. This allows one to join the outputs from
several chips together, yet only select one at any one time as the one you
want to read to or write from.
And one output:
INTR (Interrupt) - when the conversion is complete (it takes about 100 msec) a low is sent
out on this interrupt line.
To make this chip free run, the diagrams above show the CS and RD pins connected to LOW so
that the chip is always ready to operate. The WR and INTR pins are wired together so that the
end of conversion signal is used to automatically start a new conversion (clever, eh?). However, to
get it started the first time, there must be a HIGH to LOW transition on these pins.
(You might like to try to interpret the timing diagram on p. 3-20 of the data sheet.)
(iv)
Connect the WR and INTR pins permanently together; the chip should now start to run
continuously. (If it stops, just break and touch this connection momentarily to LOW .) Check
the operation by varying the input pot and recording several voltages and their binary
outputs in a table (remember your binary numbers?). Calculate what you expect each of
these outputs numbers to be, given the analogue voltage values.
Add the temperature sensor
(v)
If all is well, connect your temperature sensor in place of the pot and test its operation.
Improving sensitivity
(vi)
The default range of voltage mapped onto the 256 possible binary numbers is 0 to 5 volts.
This can be reduced, to give better sensitivity or resolution, by connecting a voltage to the
VREF/2 input (pin 9). The range (referred to as “span” in the data sheet) then becomes
double this value. Use your pot to convert your system into one that measures over the
range 0o to 40 o (rather than 0o to 500 o). Test your circuit.
Author: Jon Pearce, 1998
Lab 12: Developing a Data-logging System
12-6
Electronics & Instrumentation
2 (b) Controlling by computer
In this section we will leave the ADC free running, but read its output to the computer scene, and
control its sensitivity by an on-screen slider.
Display your output
When using the LabView interface box, remember that it has separate analogue and digital
grounds. They can be connected together for this exercise, and connected to the ground in your
circuit.
(i)
Use a “ribbon cable” connector to connect the
output of your ADC to one of the three
digital input ports (eg. Port A) of your
interface box. You can read this port and
display its contents on the screen by using
the LabView built-in VI Read From Digital
Port.VI under Data Acquisition in the
Functions menu. The device input should be
set to 1 (numerical input) and the port
number set to 0 for Port A, 1 for Port B or 2
for Port C (but this input is a string—that’s
why it is pink!).
Read From Digital Port
Hence the simplest VI to read data from Port A will look like this:
Set up a VI to read your display and run it in a loop to test it displays correctly.
Control the sensitivity
(i)
Use one of the digital-to-analogue outputs
(DAC0) from your interface box to output a
DC signal to vary the sensitivity (pin 9) of
your system. A slider control would be
appropriate here. You will need to use the
LabView built-in VI AO Update
Channel.VI. This simply sends a number to
the digital-to-analogue converter (DAC) to
be converted to an analogue voltage.
AO Update Channel.VI
Lab 12: Developing a Data-logging System
12-7
Electronics & Instrumentation
The simplest VI to do this is:
(ii)
You can make your system very sensitive (even enough to respond to you just blowing over
the sensor!) by adding an offset to the VIN(-) input (pin 7) equal to the lowest you want to
measure. VREF/2 should still be set at half the desired range. See what you can do with a
second slide control here and the other DAC output.
3. Handling multiple channels of data
(extension!)
Extension work for the speedy!
You can make your system choose from one of many channels by ading a multiplexer to its input. This is
a device that lets you choose one of 4 (or 8) channels by outputting a binary value to it. You could use an
8 channel multiplexer here (CD4051) or 4 channel differential input one (CD 4052). If you have time, play
around with one and see if you can make your system log one of several inputs on demand.
4. Comment
Comment on the performance of your data-logging system.
Author: Jon Pearce, 1998
Lab 12: Developing a Data-logging System
A-1
Electronics & Instrumentation
Appendix
Data sheets
LM1875 20 Watt Power Audio Amplifier
A-2
LM741 Operational Amplifier
A-5
LF13741 JFET Input Operational Amplifier
A-7
ADC0802 Analogue-to-Digital Converter
A-9
Other devices
LabPC+ Interface Card
A-15
Rubery Ruler
A-18
LM35 Temperature Sensor
A-20
JFET Data Sheet
A-22
Resistor Colour Code
Back Cover
Author: Jon Pearce, 1998
Appendix
A-2
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-3
Appendix
A-4
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-5
Appendix
A-6
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-7
Appendix
A-8
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-9
Appendix
A-10
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-11
Appendix
A-12
Appendix
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Electronics & Instrumentation
Author: Jon Pearce, 1998
A-13
Appendix
A-14
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-15
Appendix
A-16
Appendix
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Electronics & Instrumentation
Author: Jon Pearce, 1998
A-17
Appendix
A-18
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-19
Appendix
A-20
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-21
Appendix
A-22
Appendix
Electronics & Instrumentation
Electronics & Instrumentation
Author: Jon Pearce, 1998
A-23
Appendix
A-1
Electronics & Instrumentation
Resistor Colour Code
The standard resistor colour code is:
Colour
Value
Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Grey
8
White
9
There are two types of coded resistors in use in this laboratory, the traditional fourband resistor and the newer high tolerance five-band resistor.
1st figure
2nd figure
3rd figure
Multiplier
Tolerance
The last band, the tolerance band, represents the expected variation from the nominal
value:
Colour
Author: Jon Pearce, 1998
Tolerance
Gold
5%
Red
2%
Brown
1%
Appendix
A-2
Electronics & Instrumentation
The background colour, ignored here, represents the power rating of the resistor.
Appendix