lab manual dr s. worrall autumn semester...

2ND Year Laboratories – Autumn

Lab Manual

Dr S. Worrall

Autumn Semester 2009/10

Department of Electronic Engineering

Second Year Laboratories Autumn Semester: 2009/10

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Contents

1. GENERAL INSTRUCTIONS .................................................................................................................... 3

2. SAFETY IN 2ND

YEAR LABS ................................................................................................................... 6

3. ASSESSMENT ............................................................................................................................................. 8

4. SECOND YEAR LABORATORY PROJECT ....................................................................................... 10

5. LOCATION OF LABORATORIES ........................................................................................................ 13

6. EXPERIMENT A: PERL AND CGI PROGRAMMING ...................................................................... 14

7. EXPERIMENT B: ELECTRONIC MEASUREMENT OF AND E ................................................. 15

8. EXPERIMENT I1: LINEAR SYSTEMS AND FEEDBACK ................................................................ 20

9. EXPERIMENT I2: LINEAR SYSTEMS AND FEEDBACK ................................................................ 24

10. LABVIEW EXPERIMENT ...................................................................................................................... 32

11. EXPERIMENT M: POWER ELECTRONICS SIMULATIONS USING SPICE............................... 39

12. RUNNING EXCEED ON 2ND

YEAR LAB PC’S.................................................................................... 53


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Department of Electronic Engineering

Second Year Laboratory classes

1. General Instructions

Students are required to provide a minimum of stationery and equipment in order to carry out

experiments satisfactorily. The minimum requirements are provision of a laboratory logbook

with alternate pages of graph and lined paper (available from the university bookshop), a

calculator, and a mini tool kit consisting of at least wire cutters and strippers and a small

screwdriver. Any electrical items must be submitted to the laboratory technicians for testing

prior to use in the laboratory. All items should be obtained in advance of the first

experimental session.

Marking will normally be carried out by the demonstrators towards the end of the

experimental session, although occasionally it may be necessary to collect Lab books in order

to mark them. Work carried out as preparation for experiments will be marked upon arrival in

the laboratory. It is very important that you do the preparation work before the day of the each

experiment in order to be fully prepared for the day ahead.

Lab Groups

In the lab lectures, held on Monday in week 1, you will be given:

A list saying which lab group each student is in.

A lab timetable, which can be used in conjunction with your lab groups to find out

the experiment that you are doing in each week.

Experiments such as e and pi, and Linear Systems must be carried out by dividing yourselves

into teams of 2-3. You are free to select who you work with on each experiment, but you must

work with someone in your own lab group.

Under no circumstances may students change lab groups without express permission of the

laboratory organiser Dr Stewart Worrall. Doing so may result in a reduction of the awarded

mark for a given experiment or even a score of zero to be recorded. Wanting to work with a

friend is not a valid reason to change lab groups. Working with others is a valuable part of

your education as an engineer.

Furthermore, under no circumstances should students rearrange the dates of particular

experiments without the express permission of the laboratory organiser, Dr Worrall. Doing so

may again result in a reduction of the awarded mark for a given experiment or even a score of

zero being recorded.

The project work

More than half of the scheduled laboratory periods in the first semester are used for work on

your second year project. There is a choice of one of three different projects. You are

expected to form a project group of three to five people. Every member of each project group


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must attend all the project sessions scheduled for project work. A mark is given for attending

the labs, so make sure that your demonstrator has noted your presence. Otherwise you may

lose marks.

If you need to leave the labs for any reason (e.g. research in the library), you should ask the

academic in charge of that particular lab.

More Information

Please see the webpage:

http://info.ee.surrey.ac.uk/Teaching/Courses/ee2.laba/


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The Experiments

Second year lab experiments have been divided into subject streams. In the autumn semester

all students take the project and a further four weeks' worth of experiments. Students on the

“software/computing” (ECE) degree title streams take a two day LabVIEW experiment, a

one-day experiment on Perl and CGI, plus an experiment on calculating e and pi. Students on

“EE” degree titles take a lab on linear systems instead of the Perl and CGI experiment. The

matrix shows each experiment and the various pathways/streams.

AUTUMN SEMESTER

pathway

Instru

ctions

EE

EC

E

Med

ia E

ng

A PERL & CGI web X C X

B e and web C C X

LabVIEW X C X

I1 Linear Systems C X C

I2 Linear Systems C X X

Project (6 weeks) C C C

SPICE C C X

Digital Audio Synth. (2 weeks) X X C

Microphone Response X X C

C = compulsory

X = not available

Lab Lectures (Semester One):- Introduction, safety STW

Documentation & assessment STW

Errors and uncertainties NGE


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2. Safety in 2nd

Year Labs

READ THESE NOTES CAREFULLY

You should be aware that you are required to follow all university safety procedures, and

therefore it is your responsibility to know what they are. Prior to taking part in any laboratory

class, you are required to sign the “acknowledgement of hazards” form, associated with

second-year experiments. Any student failing to sign the form will not be permitted to begin

any laboratory class, and will score 0 for that experiment. The hazard form will be distributed

during the first week Lab lectures, and must be returned to Dr Worrall. It can be handed in to

the general office in BB Level 4, or without fail brought to the first lab session and handed in

right at the beginning of the class. A risk assessment has been made of each experiment and

the paperwork is held by the technicians in the second year laboratory. This is available for

students to read at any time, but must not be removed from the laboratory.

Types of hazard

There are certain known hazards associated with the experiments you will undertake. It is

important that you're aware of these hazards in order to minimise the risk of injury. The types

of hazards are categorised as follows:

Class A: use of terminals and stand-alone computers

Class B: low-voltage open wire experiments

Class C: open mains and high-voltage

Class D: three-phase electrical and rotating machines

Class E: hazardous materials and chemicals

Class F: chemical hazards and tools

Class G: radiation hazards such as microwaves, X-rays, or optical beams

All work must be supervised by an academic member of staff, but work involving hazards in

classes C, D, E and G are higher risk and must be closely supervised. In particular, all wiring

and instrumentation must be checked by an academic member of staff before power is turned

on.

Warning of specific hazards associated with particular experiments will be given in laboratory

lectures, and may also be included in laboratory manuals. Consequently, the laboratory

lectures are compulsory. Any student who has not attended the appropriate laboratory

lectures may be prevented from performing the experiment. In these circumstances the student

will score 0. There'll be no alternative opportunities to perform an experiment you have

missed.


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There are some general safety rules that must be followed at all times:

No student may work in the laboratory without the supervision of an academic

member of staff. At the end of the timetabled classes all students must leave

promptly and may not stay behind.

If in doubt about any equipment or procedure, ask for help.

Any incident involving any person or piece of equipment, however trivial, must be

reported immediately to a supervisor or technician.

Never run in laboratories under any circumstances

Turn soldering irons off when not in use, and keep cables, books, papers, clothes

well away from them

Be aware of the location of safety information and equipment such as fire

extinguishers, emergency meeting places, eye baths, emergency notices, etc.

Never block aisles or doorways with bags or equipment. Also, do not leave bags

and clothing on work benches where the equipment and tools and soldering irons

may cause an unnecessary hazard.

Do not eat or drink during laboratory classes. If you need food because, for

example, you are breaking a fast or you are diabetic, please simply ask a

demonstrator for permission to leave the laboratory briefly.

Laboratory class attendance

In order to pass each laboratory module, students must complete and achieve a pass grade in

each module (possibly via compensation). Note that missing an experiment cannot be excused

and it is extremely unlikely that we will be able to rearrange one except in exceptional

circumstances such as serious illness documented by a doctor's certificate. If an experiment

has been missed and not been rearranged for a valid reason, a score of zero will be recorded

for that experiment. Rearrangement of your lab timetable can only be done with the express

permission of Dr Worrall.

Working Hours are from 10.00 to 12.50 and 2.00 to 4.50.

Prompt arrival is required in case any announcements are made or hand-outs are distributed.

You are encouraged to leave promptly after 12.50 so that demonstrators can

have a lunch break; you cannot remain in the lab without supervision.


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3. Assessment

Laboratory assessment will normally be performed during each laboratory session. You will

be given a letter grade for each component of the assessment. The three components are

Preparation

Lab performance

Your preparation will be marked at the start of the session. You are required to write in your

lab book BEFORE THE LAB a summary of relevant theory, sample calculations, expected

results and any design work asked for in the experiment. Note that marks are not awarded for

simply copying theory from text books. You need to demonstrate understanding of the

experiment, and may be asked questions to check that you have understood what you have

written.

Your lab performance will be marked on your ability and your understanding, the effort you

make and the progress made on the experiment. Some experiments are quite lengthy and it is

not necessary to complete all parts in order to pass. However, the award of A or S level grades

is reserved for work demonstrating full understanding of the experiment and some use of

initiative. The lab performance mark will also be based upon the quality of your log book.

Your log book will be marked in terms of tidiness, quality of results, conclusions drawn1, and

proper documentation of the experimental set-up. You may be asked questions to check your

understanding of what you have done.

Additional hints and tips on preparing for some experiments will be posted online.

For each component the gradings are:-

S* Outstanding

S Excellent

A Very Good

B Good

C Satisfactory

D Pass

E Very Poor

F Equivalent to a 20% mark

The preferred mode of communication for important enquiries (e.g. notification of absence

due to illness, certified by a Doctor) is by e-mail :-

[email protected]

1 Conclusions are considered to be very important, and you will be awarded a low grade if you do not write any

conclusions or analysis of the results.


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Laboratory Log Books

An accurate and detailed record of what happened so that the experiment

could be exactly repeated by another person at a later date.

Part 1: Preparation

Date*

Summary of relevant theory*

Summary of experiment methodology*

Prediction of results based on theory*

Calculations using expected values

Description of what would be seen during experiment

Sketches of expected graphs

Sketches of expected oscilloscope waveforms

Diagrams of any circuits required for the experiment

Part 2: Experimental Work

Date*

List of equipment*

Serial numbers of equipment*

Any other relevant environmental parameters

Labelled diagram of set-up, showing connections (very valuable)

Note of what was done (method)*

Note of what went wrong and was changed*

Comments on method*

Comments on measured and calculated values

Comments on possible errors and uncertainties on measured values

Graphs: titled with labelled axes

Tables: titled with SI units

Conclusions on results, method, value of experiment* (what engineers actually get paid for)

Items marked “*” will probably be essential in all experiments. If these are missing it would

be difficult to call log book satisfactory

Note: you should use outline numbering throughout your log book.

R. Seebold

21st March 2002

Updated: S. Worrall

July 2008


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4. Second year laboratory project

4.1. Project Overview Each team must choose one of the following three projects, and you are expected to have

made a reasonable start in terms of project planning by the end of the first project day:-

1. Build a audio amplifier for a Walkman CD or cassette player to drive a pair of

small loudspeakers at an audible level from the headphone socket. The amplifier

should run on 3 AA batteries and use components available in the lab.

2. Build a battery-powered electronic doorbell which will play a tune at an audible

level. Use components available in the lab. Most often, a “PIC” Development

Board is programmed for this project.

A list of available components will be provided in the lab. You are not permitted to order

specialist components such as single chip FM radios and audio power amplifier modules. You

are only allowed to use two boxes, as supplied from the lab office. However, exceptions may

be made if you propose an interesting design. Contact Dr Worrall with details of your design

to discuss whether an exception is possible.

Each team will produce a design, the documentation package and the finished prototype. It is

expected that each group will organise itself so that the workload is partitioned fairly. Each

member of the group will be required to keep a project logbook in the form of a lab notebook

containing all work related to the project. These will be checked at regular intervals during the

project. The specific items of coursework which will be assessed are:-

1. Project specification

2. Project plan

3. Preliminary design

a. schematic diagrams

b. circuit descriptions

c. mechanical sketches

d. Spice simulations2

4. Documentation package

a. final schematic diagrams

b. printed circuit layout ( if applicable)

c. mechanical drawings

d. assembly drawings

e. parts list

f. test at specification

g. operating manual

5. Finished prototype

6. Presentation (EDPS Semester 2)

Items 1-4 should be kept as four separate reports, and should be made available for inspection

at the time of marking. Item 5, the finished prototype, will be inspected at the same time. Item

6, the presentation, will be marked in a separate session on the same day.

2 This applies mainly to the audio amplifier project, and not the doorbell project.


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There are six weeks of lab work dedicated to the project to, totalling 36 hours of lab time. A

7th week will be used for demonstrators to assess your project work and documentation.

4.2. Project Planning Remember that a team does not consist of one person doing the work and 4 watching, nor

does it consist of 5 people doing the same thing. Early in the project you should break the task

down into “workpackages” (e.g. electrical design; mechanical design; PCB layout;

specifications; testing; report writing) and ensure that each member of the team is busy

working at all times. A Gantt chart should be used to achieve this. An example is shown

below, in Figure 1. The example below was produced using Microsoft Visio which is freely

available to students via MSDNAA3.

ID

Task Name

(Person

Responsible)

Start Finish Duration

Sep 2008 Oct 2008 Nov 2008

7/9 14/9 21/9 28/9 5/10 12/10 19/10 26/10 2/11 9/11 16/11 23/11

1 2w19/09/200808/09/2008Plan Project (all)

2 4.8w16/10/200815/09/2008Task X (Bob)

3 2.4w06/10/200819/09/2008Task Y (Jack,

Anna)

4 4w20/10/200823/09/2008Task Z

(Muhammad)

5 3w04/11/200815/10/2008Task 5

6 2w24/10/200813/10/2008Task 6

7 1.8w31/10/200821/10/2008Task 7

8 2w13/11/200831/10/2008Task 8

9 3w25/11/200805/11/2008Testing

10 2w02/12/200819/11/2008Report Writing

Figure 1: Example Gantt chart for project planning.

The above is a SIMPLE example of the minimum level of planning you need. Real projects

need much more detailed plans, with milestones, critical reviews, deliverables, links between

work packages, etc.

4.3. Guidelines for Audio Amplifier Many different circuits can be found on the web and in books for audio amplifiers. However,

it is strongly recommended that you follow the guidelines set out here. They are intended to

help you design a circuit that you can understand and get working inside the six lab sessions

allocated to the project.

The first recommendation is that you consider the design, and construction of the circuit to be

made up of a number of stages. Examples of such stages are shown in Figure 2. Clearly, more

advanced circuits will give you better marks, but only if they work. By treating the amplifier

as a series of modules, it is possible to gradually upgrade the amplifier.

3 For details: http://info.eps.surrey.ac.uk/SCS/guides/msdnaa/


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The second recommendation is that you pick circuits that you understand. You may need to

adapt the example circuits that you find, so it is important to be able to understand how they

will work with slightly different components. Electronic Devices, by Floyd (621.381)

contains some useful example circuits. There are also some web links on ULearn. The

following are hints and tips for designing and building your circuit:

o Read about impedance matching.

o Read about different amplifier types, e.g. class A, class B.

o Consider a circuit involving op-amps for the pre-amp stage.

o Look for circuits involving transistors for the output stage.

o Take care when designing the tone controls. Simple designs are recommended that use

low pass and high pass filters.

o It should be possible to get the circuit working with 4.5V (e.g. 3 AA batteries), but

will probably work better with 5-6V. Extra credit will be given for getting it working

with lower voltages (e.g. fewer batteries).

Finally, make sure that you really know how the circuit works, as you may be asked questions

during the marking session. The idea of the project is that you learn more about electronic

circuits, rather than how to copy circuits from the Internet.

Bridge Amplifier

Pre-AmpOutput

Stage

Tone

Control

Output

Stage

(Inverted)

Pre-AmpOutput

Stage

Tone

ControlPre-Amp

Output

Stage

Figure 2: Example block diagrams for audio amplifier.

Updated November 2009.

S. Worrall.

(a) Simple audio amplifier.

(b) Simple audio amplifier with tone control.

(c) Simple audio amplifier with tone control and bridge amplifier.


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5. Location of Laboratories

All labs will be held in or near the main 2nd

year laboratory. If you cannot find your

experiment, then simply ask the academic in charge, or one of the lab technicians.

Figure 3: Location of main second year laboratories.

Main 2nd Year Lab

Tels lab

RF lab, power lab

Te

cn.

Stores

1st Year Lab

DJF

EW

S

SHOP

etc

BB building

Bridge to fourth floor (Elec Eng Reception)


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6. EXPERIMENT A: Perl and CGI programming

Lab Location: Main UG Labs

6.1. Quick Introduction to Perl: Perl and CGI form a powerfully combination, which is widely used in many current web

applications. However, Perl is not just a web based technology. It can be used for a wide

variety of applications, and is particularly strong at manipulating text. It has powerful features

that allow certain tasks to be performed simply, which are very difficult to perform using

other languages, such as C. Applications of Perl include interfacing with databases, scientific

calculations, and network programming.

In recent years Perl has lost ground to PHP4, for web-based development, in terms of

popularity. This is largely due to PHP‟s simplicity. However, the simplicity of PHP brings

with it limitations that make it unsuitable for more complex applications. Thus, the power of

Perl and the wide variety of modules available on the web, make it an important language.

6.2. Aim: This experiment sets out to teach the fundamentals of the computer language PERL and to get

the student to write a simple application using PERL to manipulate data returned from an

HTML form on a web server. The very basics of CGI (Common Gateway Interface)

programming will, therefore, be covered.

6.3. Preparation: Material to assist your preparation is provided on the web on the 2

nd year labs webpage:

http://info.ee.surrey.ac.uk/Teaching/Courses/ee2.laba/

You should make notes on the PERL language and make sure you know how to edit, compile

and execute a PERL program. There is a simple program to demonstrate this. You should

make the modifications to this program as instructed to gain some experience in the use of the

system.

6.4. Experimental Work: The experimental work is described on the webpage for 2

nd year laboratories.

Updated by S. Worrall, July 2008.

4 Perl and PHP have many similarities, so you will find it easy to learn PHP in future if you know Perl.


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7. Experiment B: Electronic measurement of and e Lab Location: Main UG Labs

Introduction This experiment aims to familiarise students with measurement techniques and the use of least

squares fitting for the treatment of experimental data. The values of and e are measured

experimentally using very simple circuits. Two methods for each are described. Items that

should be covered in the preparation are preceded by →.

Additional background material is provided on the Labs webpage.

7.1. Measurement of : first method

→ Show that the mean value, , of a half-wave rectified sine wave of amplitude Vo Volts

is

A straightforward method for measuring therefore, is to measure the peak and mean values

of a half-wave rectified sine wave and calculate the ratio , which should be close to .

Figure 4: (a) Calibration, (b) measurement of .

Experiment

You must use an analogue AVO meter for this part - why? (You need to explain this

rather carefully.)

Perform a simple calibration at d.c. as in Figure 4(a). Use a d.c. power supply to

generate 1V, say, as measured by the AVO (correctly zeroed and horizontal). Check

that the oscilloscope also reads 1V - if not, use the variable gain to adjust this.

Explain how this method of calibration will give the right value for , even if the

AVO reads wrongly by a constant factor.

What frequency are you going to set the signal generator to, and why?

Use the circuit of Figure 4(b) for several different values of (measured by the

oscilloscope) and (from the AVO).


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Find the ratio and average the values obtained to estimate .

7.2. Measurement of : second method Consider the one stage filter shown in Figure 5.

Figure 5: One stage filter.

→ Show, stating any assumptions that you make, that

(1)

Where f is the (linear) frequency of the input. How is τ defined?

According to equation (1), a plot of against will be a straight line of

gradient . The y-intercept of this line should be 1.

→ For a set of N data points show that the gradient m that minimises S, where

(2)

subject to the constraint that the y-intercept c = 1, is given by:

(3)

assuming the errors in x are much smaller than those in y. All the sums in (3) go from 1

to N.

It is also possible to calculate the standard error on m. It is given by:

(4)

Experiment

If your signal generator offers a choice of output impedance, which impedance will

you use and why?


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Choose values for R and C, measure them accurately and calculate τ; make sure you

include RS.

Using a DVM, measure vi and vo at 10-15 frequencies. Use a frequency counter to

measure f .

Plot against .

Use equations (2) and (3) to calculate S, the least squares gradient, and hence your

Use equation 4 to find the standard error on m.

Compare with the true value of and explain the sources of error.

7.3. Measurement of e: first method

Using the same circuit as before, but with square wave input, it is possible to plot an

exponential decay curve on the oscilloscope screen.

→ Show that if v(t) is a decaying exponential with time constant τ, then:

(5)

for all t.

Experiment

Set up the apparatus so that an exponential curve is displayed on the oscilloscope

screen. Choose the timebase, signal generator frequency and vertical positioning of

the trace appropriately.

The measurements are made much easier if τ is a whole number of divisions; decide

how you will achieve this. Can you rely on the output impedance of the signal

generator? If not, what can you do about it?

Measure and for at least 10 different values of t.

Calculate a value of e from equation (5) for each of these values of t. Find the mean,

the standard deviation σ, and the standard error on the mean, ( , where N is

the number of measurements), which is an estimate of the error on your

measurement of e. Tabulate your results.

Compare your results with the true value of e, 2.7182818.

7.4. Measurement of e: second method The exponential curve displayed on the oscilloscope in the previous experiment was of the

form:

(6)

where v(0) is the voltage at t = 0. From experimental measurements of v(t) at various times t,

it is possible to find the values of in the truncated series:


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(7)

using the method of least squares. In this case, there are 5 unknowns and the

arithmetic would be very tedious to carry out by hand. Hence, an Xmaple programme is

provided for carrying out the calculation for you (see last section).

→ Show that if v(t) is given approximately by equation (7), then

(8)

Experiment

Again, set up the apparatus so that an exponential curve is displayed on the

oscilloscope screen.

Measure v(t) for 10-15 different times t.

Tabulate v(t) and . Plot a graph of against t. Estimate error bars for

each point.

Using the provided Xmaple programme, calculate .

Using equation (8) estimate and hence e.

7.5. Help with Xmaple Xmaple is a large programme designed to perform algebraic calculations by computer. That

is, it can do symbolic operations, e.g. rather than just numerical

calculations. We use it in this experiment to solve the 5 linear equations that arise when

performing the least squares fit to the experimental exponential decay curve.

In order to use xmaple, log in to a Unix/Linux system (Linux PCs are available in the lab, or

see section 12 for help on how to log on to a Linux machine from a Windows PC). When you

have logged on, type: xmaple

After a short while an xmaple window will come up with a > prompt in it. You now have

three things to do:

1. Open a new document in “Worksheet” mode.

2. Load the xmaple programme I have written to do the calculations for you.

3. Type in your experimental data in the right form.

To load the program, type: read “/vol/examples/teaching/engmaths2/leastsqrs”;

in the xmaple window, followed by return. Xmaple will give you two warnings, which you

can ignore.

Your experimental data needs to be in the form of two lists called x and y. List x is the values

of t/τ at which you measured v. List y is the corresponding values of v(t)/v(0). Suppose you

had made the following measurements:


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t/τ 0 0.205 0.409 0.512 0.645

v(t)/v(0) 1 0.813 0.663 0.594 0.400

In order to define list x, type:

x := [0, 0.205, 0.409, 0.512, 0.645];

(return) and similarly for list y:

y := [1, 0.813, 0.663, 0.594, 0.400];

To perform the least squares fit for equation (7) to your data, type

lsf();

Xmaple will do the calculations and reply with the coefficients in the power series:

a0 = 1.000000

a1 = -0.527579

a2 = -4.027930

a3 = 12.928134

a4 = -11.86223

7.6. Extra work

Devise a method to measure 2 electronically. There are several ways you could do this.

Credit will be given for ingenuity. Could you extend your method to find, say, 5 ?

7.7. References Second year Engineering Maths notes, chapter 9: The method of Least Squares.

J.H.B.DEANE, MAY 2001.

Updated S. Worrall, N. Wright, July 2006.

Updated S. Worrall, November 2009


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8. EXPERIMENT I1: LINEAR SYSTEMS AND FEEDBACK

I1: FREQUENCY DOMAIN AND TIME DOMAIN


8.1. Aim

The aim of the first day of this two-day experiment is to study the frequency and time-domain

responses of first and second-order linear systems. This experiment supports material taught

in the Linear Systems Analysis and Analogue Electronics courses.

8.2. Preparation

Before coming to the laboratory you should carry out the following preparatory work.

Learn about asymptotic straight-line approximations for sketching frequency response:

magnitude and phase (Bode plots - see the Appendix).

Learn about first and second-order systems.

Learn about Laplace transform methods, in particular how the frequency response and

step response of a circuit are related.

For each of blocks B, C and D, showing important numerical values:

o Find the transfer function (as a function of s);

o Sketch a pole-zero diagram of the transfer function

o Sketch an asymptotic Bode plot (magnitude and phase) - Sketch the step

response (time domain)

See Figure 6 for details of the circuits used.

[Hint: For block B, it is quickest to use nodal analysis, making use of the fact that the circuit

contains a unity-gain amplifier.]

8.3. Equipment and materials

Pre-assembled PCB for Experiment I “Linear Systems”

Dc power supply, ±15V (dual/split rail)

Oscilloscope

Sine/square wave signal generator

Scaled log-linear graph paper

Calculator, 2mm patch leads, etc.


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8.4. Experimental Work

The experiment is concerned with circuit operation within the frequency range 10Hz to

10kHz.

Before commencing the experimental work, ensure the switches on the PCB are set up as

follows, with the board orientated so the text Experiment I “Linear Systems” is in the upper

left hand corner:

S 1 A to S 1 D all toggles to left hand position

S2A to S2D all toggles to left hand position

S2E toggle to right hand position

A-B, B-C both toggles to left hand position

C-I-D toggle to centre position.

Pot R2 - turn fully anti-clockwise

Block C (a first-order system)

Transfer your theoretical straight-line approximate bode plot (magnitude and phase)

to a sheet of the graph paper provided.

Measure the frequency response (magnitude and phase) and plot it on the same sheet

of graph paper as used above. (i.e. so the theoretical and measured results are

overlaid, remember to keep the scales for each axis the same, use a different colour

for each curve so they may be easily identified)

[Hint: It is quicker to take all of the gain measurements together, then all of the phase

measurements together. Measure at say three frequencies per decade in a 1-2-5 sequence, then

return to any interesting regions for a more detailed look]

Compare the theoretical and experimental plots. [Hint: high-frequency discrepancies

can be explained theoretically: think about the op amp's imperfections!]

From your experimental Bode plot, find the bandwidth of the circuit, i.e. the

frequency fB at which the gain is 3dB less than its low-frequency value. Calculate

the time constant from the relationship

Bf2

1

Compare this value of with the theoretical value from your preparatory analysis.

Observe the step response of the circuit by applying a square wave at a suitable

frequency. Measure the circuit‟s time constant and compare your value with the

theoretical prediction.

Measure the 10-to-90% rise time of the step response. For low-pass filters of any

order, a useful „rule of thumb‟ (with some theoretical basis) is:

Bandwidth × Rise Time = 0.35

How well do your results accord with this?


22

Block D (another first-order system)

Transfer your theoretical straight-line approximate Bode plot (magnitude and phase)

to a new sheet of the graph paper provided.

Measure the frequency response (magnitude and phase) and plot it on the same

sheet. Compare the theoretical and experimental plots. In a single sentence, state the

action of this circuit.

Find the frequency at which the output lags the input by 90˚, and compare this with

the theoretical value from your preparatory analysis.

Observe the step response and hence find its time constant. Compare this with the

theoretical value from your preparatory analysis.

Block B (a second-order system)

Transfer your theoretical straight-line approximate Bode plot (magnitude and phase)

to a new sheet of the graph paper provided.

Measure the frequency response (magnitude and phase) and plot it on the same

sheet. Compare the theoretical and experimental plots.

Find experimentally the natural frequency nf [Hint: consider the phase angle.]

The gain at nf is theoretically ½ξ, where ξ; (zeta) is the damping factor. (You should

be able to verify this formula.) Hence find experimentally a value for the damping

factor ξ.

Measure the frequency mf at which the circuit has maximum gain. This frequency is

given theoretically by:

221nm ff

Hence find a second value for ξ.

Measure the 3dB bandwidth of the circuit.

Observe the step response by applying a square wave at a suitable frequency.

Measure the fractional overshoot h. (E.g. if the response peaks at 3V and settles to

2V, then h = (3 - 2)/2 =1/2) The damping factor is given theoretically by:

Using this formula, find a third value for ξ.

Compare your three measured values of ξ with the theoretical value derived from

your preparatory analysis.

Measure the 10% to 90% rise time of the step response. How well do your

measurements accord with the bandwidth-rise time rule?


23

As best you can, find the frequency of the damped ringing. Compare it with the

theoretical value:

21nd ff

(Note that maxf and df differ from each other and from nf however, as ξ→ 0, both

maxf and df approach nf ).

Which method for finding ξ do you consider the best?


24

9. EXPERIMENT I2: LINEAR SYSTEMS AND FEEDBACK

I2: CLOSING THE LOOP


9.1. Aim

The aim of the second part of this experiment is to support the material on feedback, control

and stability taught in the Linear Systems Analysis and Analogue Electronics courses.

9.2. Preparation

Before coming to the laboratory you should carry out the following preparatory work.

Analyse block A to find its operation. Plan an experiment to test your results.

Review your Part-I results for Blocks B, C and D.

Learn about feedback control systems; in particular, find out about the criteria for

stability of a feedback system, including the idea of gain and phase margins.

See Figure 6 for details of the circuit used.

9.3. Equipment and materials

Pre-assembled PCB for Experiment I “Linear Systems”

Dc power supply, ±15V (dual/split rail)

Oscilloscope

Sine/square wave signal generator

Scaled log-linear graph paper

Calculator, 2mm patch leads, etc.

9.4. Experimental Work

The experiment is concerned with circuit operation within the frequency range 10Hz to

10kHz.

Before commencing the experimental work, ensure the switches on the PCB are set up as

follows, with the board orientated so the text Experiment I “Linear Systems” is in the upper

left hand corner:

S 1 A to S 1 D all toggles to left hand position

S2A to S2D all toggles to left hand position

S2E toggle to right hand position

A-B, B-C both toggles to left hand position

C-I-D toggle to centre position.

Pot R2 - turn fully anti-clockwise


25

Block A (a differential amplifier)

Operate switches S1A and S2A (so toggles are to the right) and ensure Pot R2 is turned fully

anti-clockwise. (So that Z1 = Z2 = 10kΩ)

(Note: The resistance of the potentiometer R2 can be checked by measuring the resistance

between the test point „TP1‟ and terminal „Output A‟. When measuring, for best results

ensure switches „S2A‟ and „A-B‟ are in the left hand position, further please ensure that the

power supply is disconnected from the board when making this measurement.)

With 1Z = 2Z = 10KΩ, check that Block A performs as you would expect from

theory, at a frequency of 1kHz. (Note: unused inputs should be properly terminated.)

Blocks B + C (a third-order system)

Ensure that switch „B-C‟ is closed (Toggle to the right) to connect block B to Block

C. From your Part-I experimental Bode plots, deduce the frequency at which the

total phase angle should be 180°.

Measure this frequency experimentally and compare it with your prediction. Also

measure the magnitude of the gain at this frequency.

System 1

Connect Blocks A, B and C as a negative feedback system (System 1), as shown in

Figure 6. To do this set the switches as follows:

S1A on (Toggle Right), SIB to SID off (Toggle Left), S2A on (Toggle Right), S2B

to S2D off (Toggle Left), S2E on (Toggle Right), Switches A-B and B-C both on

(Toggle Right), Switch C-I-D to position C (Toggle Left). Turn Pot R2 fully

clockwise initially for minimum resistance.

With these settings, 1Z = 10KΩ, and 2Z = R2=0Ω. (Value to be determined)

The loop gain depends on R2. Calculate the maximum value of R2 that will allow

stable operation. Predict the frequency of oscillation if R2 is increased slightly

beyond this value.

Adjust Resistor R2, accordingly, taking experimental measurements to confirm your

predictions. Explain why it is impossible in practice to obtain a steady, undistorted

sine wave with this simple oscillator circuit.

Note, the resistance of R2 can be measured using the following procedure:

Firstly, note the current positions of switches S2A and A-B. Next ensure switches

„S2A‟ and „A-B‟ are placed in the left hand position (Toggle Left). Now turn off,

and disconnect the power supply from the board. Once this has been done, you can

measure the resistance between the test point „TP1‟ and terminal „Output A‟ using a

suitable meter. Adjust R2 to obtain the desired resistance reading. When complete,

remove the meter connections, reconnect the board as before and return the switches

to their previous settings.

Reduce R2 to avoid oscillation, and measure the step response of the system.

Observe the effect of varying R2. Set R2 to a value that gives, in your judgement, a

satisfactory step response. In a unity-feedback control system such as this, the output


26

is supposed to follow the input closely; compare the two waveforms to see how well

this is achieved.

Measure the value of R2 using the procedure given above and make a note of this

value.

Using your chosen value of R2, calculate the DC loop gain. Break the loop at an

appropriate point, and measure the DC (low frequency) loop gain and compare it to

the calculated value. Does the feedback system have sufficient loop gain for good

results?

In system 1, Block A is described as a proportional controller, because its output is

proportional to its differential input. In control terminology, blocks B & C form a

third-order plant. The only advantage of proportional control is its simplicity; a

major disadvantage is that the loop gain is usually low, to ensure stability. The result

is a large steady-state error and little improvement in dynamic performance.

Proportional control is therefore seldom used on its own.

System 2

Re-configure Block A by setting up the switches as follows:

SIC on (Toggle Right), S1A,S1B & SID off (Toggle Left), S2B, & S2C on (Toggle

Right), S2A & S2D off (Toggle Left), S2E on (Toggle Right), Switches A-B and B-

C both on (Toggle Right), Switch C-I-D to position C (Toggle Left).

With these settings, MZ 11 and uFMZ 1||12

Break the loop at an appropriate point, (see the hint below) and by measuring the

loop gain find the gain and phase margins of the system. How do they compare with

the commonly accepted values of 15dB and 50˚ for satisfactory stability?

[Hint: the loop can be broken at 3 different points by using either switch A-B, B-C

(Toggle Left to switch off so disconnecting blocks) or C-I-D (by putting into

position I). It's up to you to choose the correct one to use, consider the circuit as a

whole before deciding which to use. Note, Switch C-I-D determines which block's

output is applied to the feedback input on block A, this can be from either block C or

block D. the centre position (I) isolates the feedback input leaving it disconnected]

Reconnect the loop and measure the closed-loop system's step response, recording

the rise time and overshoot. How well does the output follow the input with this

controller? How well does the system obey the bandwidth-rise time rule of Part I?

What is the effect of changing nFMZ 470||12 ? Why?

Note: To change Z2 to 1MΩ||470nF, turn S2C off (Toggle Left) and turn on S2D

(Toggle Right)

This controller achieves system stability by brute force: it introduces a low-

frequency dominant pole that makes the system behave as if it were a very slow-

acting first-order system. With a dominant pole, the gain-bandwidth product of a

feedback system is almost constant. The advantage of a dominant-pole controller (a

practical approximation to an integral controller) is that it allows a higher DC gain

than a proportional controller, and hence smaller steady-state errors; its disadvantage

is that the system has a small bandwidth and hence responds slowly.


27

System 3

Re-configure Block A by setting up the switches as follows:

S1B & SID on (Toggle Right), S1A,S1C off (Toggle Left), S2B & S2D on (Toggle

Right), S2A, S2C, & S2E off (Toggle Left), Switches A-B and B-C both on (Toggle

Right), Switch GI-D to position C (Toggle Left).

With these settings, and

5.6 Ω

(Makes for a very good controller, values optimized for this circuit)

Again, confirm by open-loop measurements that the system will be stable when the

loop is closed, recording the gain and phase margins, the DC gain, and the unity-

gain bandwidth.

Close the loop and check for stability. Measure the system‟s step response,

recording the rise time and overshoot. How well does the output follow the input

with this controller? How well does the system obey the bandwidth-rise time rule of

Part I?

Further work

An empirical relationship for the step response of a closed-loop system is:

Fractional overshoot (%) = 75 - Phase Margin (°)

Use your measured results for Systems 2 and 3, plus others obtained by your own

circuit modifications, to investigate how well the rule applies in this experimental

system.

Block D may be included in the loop by selecting position D for switch GI-D, as

shown by Figure 6. Assuming the values of Z1 and Z2 given for system 2, you

should be able to predict whether this new system will be stable or unstable. Check

your answer experimentally.

D.C. Hamill 30/7/93

Updated S. Worrall and N. Wright, July 2006

Text revised for new “Experiment I Linear Systems” breadboard developed by:

C.W. Murray, 2007

Appendix

Asymptotic Bode Plots

To ease sketching of gain and phase plots, asymptotic approximations are often used. The

following apply to poles, but can be adapted for zeros by reflecting the plots in the frequency

axis.


28

Laplace Transform Techniques

The transfer function of a linear system is an s-domain description of the relation between its

input and output. For electrical circuits the most commonly used transfer function is the

voltage gain Vo/Vi. It can be found by letting the impedance of a resistor be R, a capacitor

1/sC and an inductor sL, and applying the rules of circuit analysis, e.g. Kirchhoff‟s laws.

Normally the transfer function is obtained in the form H(s) = N(s)/D(s), where N(s) and D(s)

(numerator and denominator) are polynomials in s, the Laplace-transform variable, or

„complex frequency‟.

An nth-degree polynomial has n roots, which may be real or complex; if complex, they come

in conjugate pairs. The roots may be found numerically or by factorisation. The roots of N(s)

are called the zeros of the transfer function, because substituting these values of s makes H(s)

= 0. The roots of D(s) are called poles; substituting these values makes H(s) = .

A pole-zero diagram can then be drawn by plotting the positions of poles and zeros in the

complex s-plane (writing js ), a pole being represented by x and a zero by O. With

the exception of the dc gain (i.e. the limit of H(s) as s→ 0), a pole-zero diagram presents all

the information of H(s), in a compact graphical form.


29

The transfer function is a useful description of a linear system. It can give information about

both the frequency-domain and time-domain properties of the circuit. It is easy to extract the

frequency-domain information: just substitute js to get the frequency response .

This is in a complex form; for practical purposes the magnitude and the phase

can be found in the usual way.

It is rather more difficult to find time-domain characteristics such as the response to a unit

step. To get this, H(s) is multiplied by 1/s (the Laplace transform of a unit step) to get F(s)

and the inverse Laplace transform of F(s) is taken. To avoid tedious mathematics, standard

tables of Laplace transform pairs are usually consulted. The result is a function of time f(t),

which often contains exponentials and sinusoids. In analysing the systems in this experiment,

the following Laplace-transform pairs are of use:


30

Figure 6: Linear Systems Experiment Circuit Blocks.


31

Figure 7: Pre-assembled PCB Layout.


32

10. LabVIEW Experiment Lab Location: Main Labs

LabVIEW by National Instruments is a graphical programming language. LabVIEW is most

widely used in automatic test equipment and measurement systems. It is extremely widely

used in industry. Almost every piece of test equipment has a GPIB interface. Drivers for

almost every such piece of test equipment are available in LabVIEW. As a result it is

extremely easy to build up surprisingly complicated programmes for controlling whole racks

of test equipment and even large systems.

The purpose of this experiment is to familiarise students with LabVIEW. You will only touch

the surface of its capabilities, since in one day it would not be practical to learn everything

about it. The vi you create will demonstrate the basic principles of the Fourier transform.

Your programme will generate a sine wave and its harmonics, and the user will be able to

tweak the amplitude of each harmonic and see the resulting waveform in real time.

10.1. PREPARATION 2 hours recommended

1. Read about LabVIEW and look at some example files - either on the web-site

(www.ni.com) or by running LabVIEW itself. You can download an evaluation copy

from the web site. Note that even if you can run LabVIEW “at home”, it is

COMPULSORY to attend the lab sessions to do the work. This ensures that all

students are assessed on their own work, not that of others. You can run LabVIEW

Version 8.0 from a university Linux terminal by typing: /vol/ee/teach/NIlabview/bin/labview80

2. Read about the basics of Fourier series; how is a square wave represented as the sum

of a fundamental and its harmonics? How do you calculate their relative amplitudes?

3. Read all the following instructions.

10.2. Experiment Step 1 Get basic familiarity with the LabVIEW environment:-

Programs are referred to as “vi”s, standing for virtual instruments. The vi‟s can, of course, be

nested so that one vi is used inside another: the sub-vi appears as a single icon with connector

terminals for the input and output of data.

There are two main windows in a vi. One is called the diagram. This is a graphical

representation of the program function. The second window is called the panel. This is the

user interface, and includes displays of results and input controls. Because LabVIEW is a

graphical language, it is not necessary to memorise detailed rules for syntax, etc. On the other

hand, a fairly simple equation may be quite tedious to enter into LabVIEW. However,

LabVIEW can be linked with Matlab scripts and Excel.

It is important to realise that there are a number of cursor modes. The hand-shaped cursor is

for entering data. The “+” or arrow cursor is for selecting, moving, deleting, etc. The cursor


33

which looks like a spool of wire is for connecting up blocks on the diagram. The tools palette

can be used to toggle the cursor type. The tools palette can always be called up from the view

menu at the top of the screen.

The functions palette for the diagram window can be accessed by right-clicking in the

window, or from the window menu.

The controls palette for the panel window can be accessed by right-clicking in the window,

or from the window menu.

CREATE a vi which multiplies two user-input numbers together and

displays the result in a box:-

The user-input numbers are CONTROLS

The result can be shown using an INDICATOR

There are many ways to create this simple example. Here is the slow-but-clear method:-

1. In the PANEL window, right-click to call up the Controls palette, and select Modern -

Numeric – Numeric Control. This gives the user a box in which he can input one of

the numbers

2. Repeat (1) for the second user-input

3. In the PANEL window, select Modern - Numeric – Numeric Indicator from the

Controls palette. This gives a box to display the answer in.

3. Switch to the DIAGRAM window. The 3 items should be there; with the data cursor,

type in sensible names.

4. Right-click to call up the Functions palette, and select Programming - Numeric -

Multiply.

5. With the “connect wire” cursor, connect up the blocks

7. TEST the vi; select “run continuously” at the top of either window.


34

Figure 8: Diagram Window, showing A x B note tools and functions palettes shown.

Figure 9: Panel Window, showing A x B with simple digital controls and indicator.


35

10.3. Experiment Step 2 Create a simple sine wave on a graph:-

Open a new vi and move to the diagram window.

Firstly, create a for loop using Programming - Structures - For Loop.

You need to draw a box using the cursor, after selecting the command.

Insert the various numeric elements which build up the simple equation A cos t.

This can be done by using the I symbol of the loop to represent t, with some scaling: The FOR

loop is no different to any other language, that is for n = 1 to N, whatever is inside the box is

repeated. N is set by adding a Programming - Numeric - Numeric Constant item and

wiring it to the symbol for N. The “I” symbol inside the loop has an output terminal which

gives the value of n for each iteration.

Suppose then you set N=2000; the loop will create 2000 samples of the sine wave, BUT

LabVIEW works in radians, so they will be far too far apart in time. So, “n” should be

divided by say 100 to give a maximum of 20 radians (just over 3 cycles, for a nominal

frequency of one).

The frequency and amplitude can be set as user controls with the “connect wire” cursor by

right clicking in the diagram window near the desired terminal of the relevant numeric item

and choosing create-control. The controls then also appear on the panel window. Switch to

the panel window and observe these controls. Now insert a waveform graph in the panel

window by right-clicking to bring up the controls palette.

Go back to the diagram window. The sine wave samples from the loop have to be grouped to

form the graph. There are many ways of dealing with arrays and clusters of data. A simple

method here is to insert Programming – Cluster & Variant - Build Cluster Array. This,

and the graph, must be outside the loop structure, since it is building up all the individual

outputs from the loop. The cluster output can now be connected to the graph icon in the

diagram window. LabVIEW recognises any differences in data type and won't connect nodes

properly unless the data is consistent.

Complete the vi and run it using the “run continuously” command at the top left our

each window. Play with the frequency and amplitude controls and check that your vi

works.

In the panel window, try changing the controls to fancy knobs and sliders and change the

scales and ranges of everything. [Hint: try right clicking on everything to call up special

menus]. You have to stop the programme in order to alter the programme itself, but you can

change the scales of things like graphs whilst the programme is running.


36

Figure 10: Example Panel for successful completion of Step 2.

10.4. Experiment Step 3 Make a sub-vi out of your sine-wave generator:-

Save your vi, then save it with a new name such as oscsub.vi.

Delete the build cluster array item and the waveform graph (you can only delete the graph in

the Panel window).

At the signal output, use the connect wire cursor and right-click on the output node to Create

- Indicator. LabVIEW then knows this is an output and adds the value as an item in the panel

window.

Now, you need to set the controls (ie the amplitude and frequency) and output signal to be

terminals using the connector pane. The connector pane is the small box at the top right

hand corner of the panel window. Right-click on it to set show connector. The icon will

change to a white box with sub boxes. Each sub box is an individual connector. When you

click on a sub box the cursor changes to wire mode, and you wire the connector to the control

or indicator that you want. Actually no wire appears, unlike in the diagram window, but the

terminals have label names. As each one is connected, the boxes are coloured-in to confirm

success.

Once you have the amplitude and frequency inputs and the signal output set as terminals, save

this sub-vi.

Now, open a new vi. Call up the sub-vi in the diagram window using functions-select a VI.

This is at the bottom left of the palette. Your previous vi now appears as a fixed block, with a

single icon and 3 terminals. Reconnect the amplitude and frequency controls, and put back the

cluster array builder and the waveform graph at the output. Check that this new hierarchical vi

works exactly as before. Save it.


37

Figure 11: Diagram window for the hierarchical version of the sine generator.

10.5. Experiment Step 4 Use your sub-vi to create the Fourier series demonstrator:-

Now that you have the sine wave generator as a sub-vi, you can easily set up a number of

identical generators to generate a fundamental signal and its second, third, 4th and 5th , etc.

harmonics. Sum up the signals to display the overall waveform.

Create a nice user-interface on the PANEL, with knobs or sliders to tune each frequency

component.

See if you can create a square wave or triangle wave by varying the amplitudes. (TIPS: (1)

some amplitudes may have to be negative, (2) the number of samples might need more

thought, since you are going up in frequency, (3) if you only have cosine terms, you can only

get an EVEN function)


38

Figure 12: Example square wave.

Once you have completed a VI which demonstrates the basic principles of the Fourier

series, with a reasonable user interface and display, you have completed the main part of

this lab with a SATISFACTORY grade (assuming full attendance and that it is your

own work).

To achieve a higher grade, you are invited to take the initiative and create something quite

impressive. Here are some examples of things which you could add to your program:-

1. Add a spectrum display to show the harmonics in the frequency domain

2. Add controls to allow sine or cosine terms for the harmonics for more flexibility

3. Implement a number of pre-defined waveforms such as a triangle wave, for which the

harmonic components are well-known

4. Re-do the vi completely using LabVIEW's own signal and/or function generators

5. Improve your user interface so that it provides a mini tutorial for the user

6. Convert your vi into a format which can be run stand-alone using either the LabVIEW

player or a Web browser.

IDR, version 1, Aug. 2003.

Updated S. Worrall, August 2007.


39

11. EXPERIMENT M: POWER ELECTRONICS

SIMULATIONS USING SPICE Lab Location: Main Labs

11.1. Introduction

SPICE (Simulation Program with Integrated Circuit Emphasis) is software that can be used to

simulate electronic circuits on a PC. Any voltage or current waveform in your circuit can be

viewed and plotted. SPICE performs simulations to calculate the voltages and currents against

time (Transient Analysis) or against frequency (AC Analysis). Many SPICE implementations

also permit other types of analysis, such as DC, Sensitivity, Noise and Distortion.

SPICE was originally developed by researchers at the University of California, Berkeley

during the mid-70s. It was the arrival of the integrated circuit that created a need for a method

to test and tweak circuit designs before the expensive fabrication process.

SPICE is currently available from many vendors, who have added a variety of different

enhancements on to the original simulator, such as schematic drawing tools for the front end

and graphics post processors to plot the results. Over time, SPICE simulators and applications

have expanded to permit analysis of analogue and digital circuits, microwave devices, and

electromechanical systems.

SPICE is particularly useful in analogue and power electronics because it can numerically

solve the non-linear differential equations that govern this type of circuit. From the design

point of view, this means that analogue and power electronic circuits can be tested on a

computer before they are constructed. Thus minimising prototyping costs and providing a

useful insight into circuit operation. One of the most useful aspects of SPICE is the ability to

add imperfections to the circuit in order to provide an accurate representation of the practical

circuit being tested. Potential problems can then be identified and eliminated before the circuit

is built.

SPICE has proved to be very useful to 3rd

year project students, as it is more time and cost

efficient than prototyping. You may also find it helpful to simulate your lab project circuits to

identify any potential problems.

11.2. Aim

The aim of this experiment is to provide a basic understanding of SPICE. You will learn how

to interpret and create netlists to be used in SPICE simulations. You should also learn how to

analyse circuits. The experiment also reinforces knowledge about switched mode converters.

11.3. Preparation

It is important to carry out preparation in two areas: power electronics and SPICE. Note that

some of the answers to the preparation questions are contained in the experiment instructions.


40

Power Electronics Preparation

Switch-Mode Power Supplies (SMPS) deliver power while wasting very little. The switch

state is toggled, from ON to OFF, to deliver pulses of current to the output. Very little power

is dissipated in the switch. This is an important feature, as conserving power is essential in

battery/portable device design.

Make notes on switched mode converters, mainly on the Buck converter. (A good source for

this is Power Electronics converters, applications and design by Mohan, Underland and

Robbins)

Answer the following questions in brief:-

1. What is the main difference between continuous and discontinuous mode operation?

2. What are the main advantages of switched mode converters?

3. What are the main disadvantages of switched mode converters?

4. With a Buck converter what is the basic difference between the input and output

voltages?

5. Express Duty factor in terms of the switch on time TON and the period TS.

6. What is Equivalent Series Resistance (ESR)?

SPICE Preparation

See ULearn for links to SPICE resources. It is strongly recommended that you use the version

of SPICE (DuSpice) specified on ULearn, as the experiment has been tested on this version.

There may be some minor compatibility issues with other SPICE software.

11.4. Buck Converter Background Material

The Buck Converter provides an output voltage that is smaller than the input voltage. It

consists of just a handful of components (see Figure 13). The current pulses are transformed

via the switch, SW1, into a constant voltage at the load. This experiment will examine some

voltage/current waveforms, and changes component values, so that you get a feel for each

component‟s role, and how to optimize the performance of the Buck Converter.


41

VIN

VCTRL

RLC1

L1

D1

SW1

0

10

1 2 3 Vo

Figure 13: Circuit diagram for a Buck converter.

Buck Converter Basics

The Buck Converter operation can be understood by examining the two main states of

operation: SW1 ON and SW1 OFF.

SW1 ON: L1 delivers current to the load

With a voltage (VIN - Vo) across L1, the current rises linearly. The rise (in amps per second)

is given by:

VIN RLC1

L1SW1

0

1 2 3 Vo

I

+ VL -

Figure 14: Buck Converter when SW1 in ON.

L1‟s current changes are smoothed out by C1, to produce a stable voltage at Vo. C1 should be

big enough to ensure that Vo does not change significantly during one switching cycle. D1 is

reversed biased, meaning that it can be removed from the diagram for now.

SW1 OFF: L1 maintains current to the load


42

Current falls linearly in L1, as its magnetic field collapses. The fall in current (amps per

second) is again determined by the voltage across L1 and its inductance:

RLC1

L1

D1

0

2 3 Vo

I

- VL +

-

VD

+

Figure 15: Effective Buck Converter circuit diagram when SW1 is OFF.

Although L1‟s current direction is the same, its voltage is reversed. When the applied voltage

is removed, following the change in state of the switch, L1 maintains its current flow by

reversing its voltage. When the voltage of L1 becomes negative, diode D1 switches on, which

provides a path for L1‟s current to flow.

Switching Frequency Vs Output Voltage

Voltage in a Buck Converter is typically controlled by using a Pulse-Width-Modulation

(PWM) signal to drive SW1. This implies that a pulse train is needed, which has the

following features:

o A switching period of TS

o An adjustable Pulse Width of TON, which is the time that SW1 is ON

o A Duty Cycle, S

ONT

TD

The desired output voltage can be obtained by adjusting the duty cycle. The pulse train is

typically in the range of 10‟s to 100‟s of kHz. The reasons why such high frequencies are

used are:

1. As frequency increases, the parts usually get smaller, lighter and cheaper, which is a

huge advantage for portable, battery powered devices. Large amounts of power can be

obtained from a small volume of components. This means that there is a high power

density (W/cm3).

2. The switching time causes a delay from input to output. Clearly, if the switching time,

Ts, is smaller, then the delay should be shorter. The delay becomes a problem when a

Buck Converter is used in a control loop. It can lead to effects such as overshoot,

ringing, or oscillation.


43

The Simulation Challenge

Simulation and analysis of switch-mode supplies is challenging due to the different time

frames that need to be considered:

1. The short period of the pulse train turning SW1 ON and OFF (in μsec). This

simulation requires only a few switching cycles.

2. The longer response of LC components as they respond to input or load changes (in

msec). Thousands of cycles are needed to look at the overall response.

11.5. Experiment Part 1: Buck Converter Simulations

A netlist, buck_basic.cir, is provided, which represents the Buck Converter shown in

Figure 13. At this point, it is a good idea to cut out the netlist from page 52, and make

comments, briefly describing what each line does. This will help you learn some basic netlist

aspects.

Here are some of the less obvious points that may be useful when making your comments:

VCTRL generates a pulse train of period TS = 20μs and pulse-width TON = 5μs.

When VCTRL is 5V, SW1 drops to 0.01 Ω connecting 20V (VIN) to L1.

When VCTRL is 0V, SW1 changes to 1 MΩ, effectively disconnecting VIN from L1.

RL represents the load (analog/digital circuitry, motors, lights, etc.) powered by the

Buck Converter.

First Spice Run: Longer Overall Response

Run the simulation and take a look at Vo by plotting V(3). Use the graph to answer the

following questions:

1. How much overshoot occurs due to the LC components?

2. What voltage does the output settle to?

Vo could be expected to be related to VIN and D:

Add VCTRL to the plot by including trace V(10). Change its duty cycle by increasing or

decreasing TON from 5 μs to values like 2.5, 10 or 15 μs. To do this, change the 5US

parameter in the PULSE definition of VCTRL. Does the above equation predict Vo

accurately?

Finally, examine the current through L1. Can you explain what is happening in the plot?

Print the plots, and put them in your log book.


44

Cycle By Cycle

Now it is time to look at the shorter term response. We need to look at only a few cycles of

the Buck Converter‟s operation, but we want to see the simulation results after a few hundred

cycles, when the supply has settled to a steady state. The Transient Analysis command caters

for this kind of requirement, as it lets you discard simulation results up to a specific delay

time. For example, this statement:

.TRAN 0.1US 840US 800US 0.1US

simulates the circuit up until 840μs, but discards the data before 800μs. The 40μs saved

represents two switching cycles. This statement is already included in the given netlist, but is

commented out. Uncomment the command and comment out the other .TRAN statement.

Set TON to 5μs and run a simulation of BUCK_BASIC.CIR. Plot Vo at V(3), VCTRL at V(10)

and in a separate plot window, view the inductor current, I(L1). You should see I(L1) rising

and falling as SW1 turns ON (VCTRL = 5 V) and SW1 turns OFF (VCTRL = 0 V).

Inductor Current

The next check on the circuit we can carry out is to examine the two different paths the

inductor current takes as it rises and falls. Open a new plot window and add SW1‟s current.

SW1‟s current should be the same as L1‟s current, but only when SW1 is ON. Then it drops

to 0 A. D1‟s current should initially be 0, then should equal L1‟s current when D1 turns ON.

Find D1‟s current, and plot it. Note that it may not be possible to plot it directly using Spice.

Finally take a look at the SW1‟s voltage at V(2). VSW1 should be VIN = 20V, and then it drops

to -0.3V as D1 (Schottky diode) turns ON, providing a pathway for L1‟s falling current.

Does L1‟s current rise and fall as expected? Check by first calculating the expected rise rate,

TI . Then calculate the total rise, ∆I, while SW1 is ON for 5μs.

Now, compare the expected rise against your plots. You might see a small difference between

the expected and actual values. Why is this?

What do you notice about the rise and fall of L1‟s current? This current change is called the

inductor ripple current, ΔI.

Find the average inductor current, Iave. This can be found either from the graph, or from the

Excel plot (go to the “tabelle” tab to find the raw data). Iave is important because this is the

current that gets delivered to the load RL. It can be calculated using:

L

oo

R

VI

Does Iave match Io? Now, suppose the demand for Io increases. What happens to the ripple and

average inductor current? Double Io by changing RL. Rerun the simulation and examine ΔI


45

and Iave? What do you notice? Can you explain what is going on? Next, we‟ll discover how

the inductor ripple current plays a factor in the output ripple voltage.

Output Voltage Ripple

One of the most important aspects of the power supply, is the amount of voltage ripple, ΔVo,

that appears at the output. This voltage ripple is applied to anything driven by Vo, such as

transistors, speakers, motors, and IC‟s. Large values of ΔVo could cause unexpected

behaviour or poor performance from the components driven by the supply.

Set TON = 5μs and RL = 5Ω. Run a simulation from 800 to 840μs. Plot the output V(3) and

inductor current I(L1) in separate windows. How big is ΔVo? There should be about 160

mVp-p ripple at the output.

What if the design goal is less that 50 mVp-p of ripple? First, return the components to their

original values: L1 = 50 μH, C1 = 25 μF and RL = 5. Now change the component values to

achieve a ripple less than 50 mV p-p. You can use the following hints to help you adjust the

values. Find the best combination of values for optimum performance, and justify your

choices by explaining the trade-offs.

CAPACITOR - C1 For a given an inductor ripple current, C1 has the sole responsibility for absorbing ΔI to

minimize ΔVo. Try increasing C1 from 25 μF to a value like 50 or 100 μF. Has ΔVo reduced?

Note that you might have to extend the simulation delay from 800 to 1000 μs. Why do you

need to do this?

INDUCTOR - L1 ΔVo can also be reduced by decreasing ΔI. The equation:

tells us how ΔI can be made smaller. Try changing the inductor value to reduce the ripple.

Rerun the simulation. Did ΔVo shrink as expected?

What are the advantages and disadvantages of using very large inductors in the circuit?

SWITCHING TIME – TS The equation above shows us another ripple reducing parameter: ΔT. How can ΔT be reduced

without changing the output voltage, Vo? Rerun the simulation with the changed parameters.

Has ΔI shrunk as expected?

Why might faster switching times be a disadvantage?

Continuous Vs. Discontinuous Mode


46

We‟ve previously seen current flowing continuously through L1. But there is also a mode

were the current goes to zero during the last portion of the switching cycle, called

discontinuous mode.

Table 1: Comparison of current through L1 for continuous and discontinuous mode of the Buck

Converter.

Continuous Mode – L1 has

2 states

Discontinuous Mode – L1

has 3 states

SW1 ON L1 current rises L1 current rises

SW1 OFF L1 current falls L1 current falls

L1 current falls to 0 Amps

We can change the netlist to see when L1‟s current goes to zero. First, set TON = 5μs, TS =

20μs and RL = 5Ω. Now run a SPICE simulation and plot the output V(3) and inductor

current I(L1). You should see ΔI, with Iave = 1A. Now reduce the load by raising RL to 10Ω.

Rerun the circuit. Comment on what happens to the following:

o The current in L1. What is the reason?

o Vo. Is SON TTVINVo still true? Raise RL to 20Ω and vary TON to find out.

Now, plot SW1‟s voltage, V(2), and inductor current, I(L), for the following two

configurations:

1. TON = 5μs, TS = 20μs, RL = 5Ω

2. TON = 5μs, TS = 20μs, RL = 10Ω

Comment on the differences that you see. Why do you think they occur? HINT: look at the

“non-ideal” parameters specified in the diode model.

Design Notes

It is usually recommended that supplies are run in continuous mode. There are two main

reasons for this:

1. The gain is stable. In continuous, Vo, can be approximately set using only VIN and the

duty cycle. However, in discontinuous mode, Vo depends on VIN, the duty cycle, L1,

RL, and TS.

2. For continuous and discontinuous modes, the frequency responses are different. This

means that a circuit optimized for use in continuous mode might respond significantly

differently in discontinuous mode.

For a given load, how should you ensure your supply is in continuous mode?

Capacitor ESR

We have previously used C1 to reduce ΔVo, which has worked successfully because an ideal

capacitor has been assumed. However, real capacitors behave as if there is a small resistor in

series with its capacitance, which is known as the Equivalent Series Resistance (ESR).

Change the C1 statement to the following two statements:

C1 3 4 25UF

RC1 4 0 0.5


47

RC1 = 0.5Ω models the ESR of C1. Remember that with L1 = 50μH, C1 = 25μF and RL =

5Ω, we saw that ΔVo ≈ 160 mVp-p.

Run a simulation and plot the V(3) and I(L1). How big is ΔVo? The inductor ripple ΔI, is

normally absorbed by C1, but now flows through the ESR, adding to the voltage ripple. The

ripple can be predicted using the following equation:

Does this equation match what you see in the simulations?

What happens when you increase C1 to 50 or 100μF? Is the ripple reduced?

How can the voltage ripple be reduced? Carry out some simulations to demonstrate how you

can reduce the voltage ripple.

11.6. Experiment Part 2: Buck Converter Power Loss

VIN

VCTRL

RL

C1

L1

D1

SW1

0

10

1 2 3Vo

RL1

RC1

4

5

Figure 16: Buck Converter circuit with equivalent series resistors for L1 and C1 included.

One of the most important areas in Switch Mode Power Supply (SMPS) design is

minimization of the power lost. Ideally, all power should power should be delivered to the

load. However, non-ideal components introduce losses into the system. In this part of the

experiment, we will examine:

1. Where power is lost in the circuit.

2. How power loss can be minimized.


48

3. How to evaluate the supply‟s power efficiency by comparing the average power

output versus average power input.


49

Where Power is Lost

Most of the power in an SMPS goes to the load. However, the resistive and semiconductor

elements convert power into heat. Also, real world components have parasitic elements

modelled as resistance in series with their reactance. The table below summarises where these

losses occur, and how they can be plotted using SPICE.

Table 2: Summary of areas where power might be lost in a Buck Converter.

Power

Dissipating

Element

Comment Plotting Instantaneous

Power in SPICE

SW1 Power is lost while SW1 is ON

and current is flowing through L1.

Power is also lost while

transitioning between OFF and ON

states.

V(1,2)*I(SW1)5

RL1 Power is lost in the equivalent

series resistance of inductor L1.

V(3,4)*I(RL1)

RC1 Power is lost in the equivalent

series resistance (ESR) of

capacitor C1.

V(5)*I(RC1)

D1 Power is lost while SW1 is OFF

and D1 provides a path for L1‟s

current.

V(0,2)*I(D1)

Instantaneous power is variable, and it is therefore the average power that we are interested in.

Basic Buck Converter Set-up

1. Modify the Buck Converter netlist, so that it includes the ESR‟s for the capacitor and

the inductor.

2. Change the parameters, so that the switching supply runs at 50kHz (Ts = 20μs), Ton =

8.33μs for SW1, and the input VIN = 12V.

3. Change the simulation time parameters, so that you can look at just one cycle (20μs)

of operation after a 1000μs delay, allowing the supply to settle.

4. Run a SPICE simulation of your netlist, and plot the output at V(4). You should see

Vo ≈ 5 V, with a ripple ΔVo ≈ 300mVp-p.

SW1 Power Loss

To see how much power gets lost in SW1, plot SW1‟s instantaneous power:

V(1,2)*I(SW1). The plot shows units of Volts, but it is of course Watts. (Note that SW1 is

typically a MOSFET, but for simplicity, it is modelled here using a voltage controlled

switch.)

Note the power spikes in the instantaneous power plot. What causes these spikes?

5 Note that this is just an indication of how the power is calculated, rather than something that can be entered into

SPICE. For example, to plot V(1,2) in SPICE, type plot V(2)-V(1).


50

What switch parameters could be changed to reduce the average power loss? Run SPICE

again after these parameters have been adjusted to show the reduction in power loss.

The parameters that you should have adjusted simulate selecting a MOSFET with different

specifications. So during the design of a SMPS, you might find the maximum requirements of

these parameters, and select the MOSFET based on those requirements.

Inductor And Capacitor Power Loss

Why would power be lost in the inductors and capacitors? Plot the instantaneous power

through the series resistances.

What are typical values for ESR in inductors and capacitors? Simulate ESR‟s at the extreme

ends of the typical values that you identified (i.e. smallest vs. largest) to show the difference

in power loss that might typically be seen without careful selection of components.

It should be noted that there is some power lost in the inductors core in real components that

is not modelled here.

D1 Power Loss

Although the Schottky diode used in this example has a lower ON voltage, 0.3V, compared

with the silicon diode, 0.7V, the power loss in the Schottky is still significant. Plot

V(0,2)*I(D1).

Compare the power lost in the diode to that lost in the switch, the inductor, and the capacitor.

Which is the most significant source of power loss?

A better diode is not available, which means that it is necessary to find an alternative to the

diode to reduce power loss further.

SYNCHRONOUS CONVERTER

In the Buck Converter, D1 acts as an automatic switch, which provides a current path for L1

when SW1 switches OFF. But, as shown in Figure 17, D1 can be replaced by an actual

switch. Because switches are low on resistance, they can reduce power loss during this part of

the switching cycle.

Remove D1 by commenting it out. Add SW2 to the netlist, and a corresponding model.

Remember SW2 should be ON when SW1 is OFF, and vice versa. You should now have a

netlist for the synchronous converter.

Run a new simulation, and plot a trace for SW2‟s power V(2)*I(SW2). Note that it may be

necessary to look at SW2‟s power in two plots: one where SW2 is OFF, and another where it

is ON. Is the power lost, lower than with D1?

Adding a switch changes the supply from a Buck Converter to a synchronous converter.

Although it is more complex, some battery powered applications may require this type of

converter to minimize the amount of power lost.


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VIN RL

C1

L1

SW1

0

1 2 3Vo

RL1

RC1

4

5SW2

Figure 17: Synchornous converter circuit diagram.

11.7. Final Conclusions

You should now have a feel for how a basic switch-mode power supply works, and how

SPICE can be used to experiment with different component values before building the actual

circuit. Make sure you write some conclusions, summarising what you have learnt in this

experiment. For example, what are the major issues that should be considered when designing

a SMPS.

July 2007.

S. Worrall.

N. Wright.


52

11.8. Netlists

Buck_basic.cir

BUCK_BASIC.CIR - BASIC BUCK CONVERTER

*

* SWITCH DRIVER

VCTRL 10 0 PULSE(0V 5V 1NS 0.01US 0.01US 5US 20US)

R10 10 0 1MEG

*

* INPUT VOLTAGE

VIN 1 0 DC 20

*

* CONVERTER

SW1 1 2 10 0 SWI

D1 0 2 DSCH

L1 2 3 50UH

C1 3 0 25UF

*

* LOAD

RL 3 0 5

*

*

.MODEL SWI SW(VT=4.5V VH=0V RON=0.01 ROFF=1MEG)

.MODEL DSCH D( IS=0.0002 RS=0.05 CJO=5e-10 )

*

* ANALYSIS

.TRAN 1US 800US

*.TRAN 0.1US 840US 800US 0.1US

*

* VIEW RESULTS

.PLOT TRAN V(2) V(3)

.PROBE

.END


53

12. Running Exceed on 2nd

Year Lab PC’s

12.1. Introduction This section describes how to bring up a unix/linux terminal window on the Windows PC‟s in

the main second year lab. This may be needed to complete the XMaple work included in the e

and π experiment.

12.2. Instructions 1. Run the XStart software, whose shortcut is featured on the desktop.

2. Select “Wizard…” on the Help menu.

3. Ensure that you use the settings shown in the following screenshots.


54

4. Leave these next settings as they are.

5. Enter your username and password on the next screen


55

6. Accept these settings

7. Click finish


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8. Click “Run!” on the menu bar.

9. If you get an error message box, such as the one below, click the “Send” button.

You should now see some terminal windows in which you should be able to run linux

software, such as xmaple.

S. Worrall, July 2006.

lab manual dr s. worrall autumn semester...

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