53-230 modulation and coding principles manual v2p3 cd

Electricity & Electronics

Control & Instrumentation

Process Control

Mechatronics

Telecommunications

Electrical Power & Machines

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Modulation and Coding Principles 53-230

Feedback Instruments Ltd, Park Road, Crowborough, E. Sussex, TN6 2QR, UK. Telephone: +44 (0) 1892 653322, Fax: +44 (0) 1892 663719.

email: [email protected] website: http://www.fbk.com Manual produced from software version: v2.3

Date: 11/02/2010 Feedback Part No. 116053230

Modulation and Coding Principles Preface

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THE HEALTH AND SAFETY AT WORK ACT 1974

We are required under the Health and Safety at Work Act 1974, to make available to users of this equipment certain information regarding its safe use.+

The equipment, when used in normal or prescribed applications within the parameters set for its mechanical and electrical performance, should not cause any danger or hazard to health or safety if normal engineering practices are observed and they are used in accordance with the instructions supplied.

If, in specific cases, circumstances exist in which a potential hazard may be brought about by careless or improper use, these will be pointed out and the necessary precautions emphasised.

While we provide the fullest possible user information relating to the proper use of this equipment, if there is any doubt whatsoever about any aspect, the user should contact the Product Safety Officer at Feedback Instruments Limited, Crowborough.

This equipment should not be used by inexperienced users unless they are under supervision.

We are required by European Directives to indicate on our equipment panels certain areas and warnings that require attention by the user. These have been indicated in the specified way by yellow labels with black printing, the meaning of any labels that may be fixed to the instrument are shown below:

CAUTION - RISK OF DANGER

CAUTION - RISK OF

ELECTRIC SHOCK

CAUTION - ELECTROSTATIC

SENSITIVE DEVICE

Refer to accompanying documents

PRODUCT IMPROVEMENTS We maintain a policy of continuous product improvement by incorporating the latest developments and components into our equipment, even up to the time of dispatch.

All major changes are incorporated into up-dated editions of our manuals and this manual was believed to be correct at the time of printing. However, some product changes which do not affect the instructional capability of the equipment, may not be included until it is necessary to incorporate other significant changes.

COMPONENT REPLACEMENT

Where components are of a Safety Critical nature, i.e. all components involved with the supply or carrying of voltages at supply potential or higher, these must be replaced with components of equal international safety approval in order to maintain full equipment safety.

In order to maintain compliance with international directives, all replacement components should be identical to those originally supplied.

Any component may be ordered direct from Feedback or its agents by quoting the following information:

1. Equipment type 3. Component reference

2. Component value 4. Equipment serial number

Components can often be replaced by alternatives available locally, however we cannot therefore guarantee continued performance either to published specification or compliance with international standards.

Modulation and Coding Principles Preface

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OPERATING CONDITIONS

This equipment is designed to operate under the following conditions:

Operating Temperature 10C to 40C (50F to 104F) Humidity 10% to 90% (non-condensing)

DECLARATION CONCERNING ELECTROMAGNETIC COMPATIBILITY Should this equipment be used outside the classroom, laboratory study area or similar such place for which it is designed and sold then Feedback Instruments Ltd hereby states that conformity with the protection requirements of the European Community Electromagnetic Compatibility Directive (89/336/EEC) may be invalidated and could lead to prosecution.

This equipment, when operated in accordance with the supplied documentation, does not cause electromagnetic disturbance outside its immediate electromagnetic environment.

COPYRIGHT NOTICE

Feedback Instruments Limited All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Feedback Instruments Limited.

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WARNING:

This equipment must not be used in conditions of condensing humidity.

Chapter 1 Modulation and Coding Principles Familiarisation

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Familiarisation

Objectives To become familiar with the circuit blocks available on the workboard

To become familiar with the interconnection of the workboard, terminal and PC

To determine that the set-up is functioning as required

To learn how to navigate the software


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The Workboard an Introduction

The Modulation & Coding Principles 53-230 workboard contains a number of circuit blocks that may be interconnected in many ways to demonstrate the principles and operation of typical analogue and digital modulation and coding circuits used in modern telecommunications equipment.

The workboard is designed to operate with the Real-time Access Terminal (RAT) 92-200, into which it plugs to obtain power and to provide, in conjunction with a personal computer (PC), the instrumentation required by the assignments.

Both the workboard and the RAT require USB connection to the PC.

Interconnection between the various circuit blocks on the workboard is by 2 mm, stackable patch leads. It is recommended that no more than two leads be stacked, as more than this is mechanically vulnerable and can lead to damage of the lead or the workboard.


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Practical 1: The Circuits Available

Objectives and Background This Practical is an exercise to get you conversant with the circuit blocks that are available on the Modulation & Coding Principles workboard. There is no patching or measurement associated with this Practical.

At this stage, do not worry if you dont understand the description or function of the circuit blocks. As you progress through the assignments their functions and operation should become clearer.


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Practical 1: The Circuits Available

Perform Practical

This Practical requires no workboard patching connections and there are no measurements to be taken.

This Practical is an exercise to get you conversant with the circuit blocks that are available on the Modulation & Coding Principles workboard. Read through the descriptions below and identify each of the circuit blocks described.

At this stage, do not worry if you do not understand the description or function of the circuit blocks. As you progress through the assignments their functions and operation should become clearer.

The Micro Controller

Towards the top left-hand corner of the workboard you will see the Micro Controller and A/D - D/A circuit block.

This block contains the circuitry and firmware that provides the modulation source for many of the assignments. It also provides waveforms and timing signals for a number of the assignments.


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It has associated with it a number of controls to set up waveform amplitudes, offsets and delays. The functions and use of these controls will be explained in the relevant assignments.

The Carrier Source

Just below the Micro Controller block you will find the Carrier Source, together with its associated phase shift circuitry.

This circuit block provides signals at various phases for use in many of the assignments. Fixed phases of 0, +45 and 180are provided, together with a 45 output that has an associated variable control.

The source also has a f input that allows the frequency of the signal to be changed by the application of a control voltage.

There is also a second, very similar circuit on the workboard that is also used as a signal source in some of the assignments. This is to be found towards the lower right-hand part of the board and is called the Local Oscillator circuit block.


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Filters

There are a number of filter circuits provided on the workboard. Some of these are low-pass filters, others are band-pass. Their use and function is dependent on the assignment in which they are used.


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IQ Modulator and IQ Demodulator

These circuits are used in many assignments to produce and detect different forms of modulated signals, such as amplitude and frequency modulated signals (AM and FM).


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In addition to the IQ Modulator and Demodulator blocks, there are also two, rather simpler, Multiplier blocks that can perform somewhat similar circuit functions. These are located to the right-hand edge of the workboard. Their operation will be covered in the relevant assignments.

Transmission Channel

This circuit block, to be found to the upper centre of the workboard, is used to simulate a communications channel, in that noise and phase changes can be introduced to investigate system performance and tolerance in the presence of such unwanted additions.


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Function Generator

This circuit block, to be found half-way up the left-hand edge of the workboard, produces either a sinusoidal, square-wave or triangle wave output, dependent on the rotary switch position. The output waveform frequency may be set using a potentiometer control and a range switch (Slow or Fast).


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Angle Generator

The Angle Generator circuit block, to the lower left-centre of the workboard, produces output waveforms that are proportional to the sine and cosine of an input waveform. These waveforms are most often used to provide the in-phase and quadrature carrier inputs to the IQ Modulator circuit block.


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dc Source

Two variable dc voltage sources are provided. These are located in the bottom left-hand corner of the workboard. They are used in assignments where such things as voltage controlled oscillators or dc offset voltages are required.


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Bi-phase Coder and Decoder

These two circuit blocks produce and decode bi-phase signals and are used to investigate a form of encoding commonly used in digital communications systems.

Frequency Multiplier

This circuit block, to be found in the right-hand top corner of the workboard, accepts a signal input and produces outputs that have a x2, x4 or x8 frequency component. A buffer amplifier circuit that can also be used to square up the waveform, where a square pulse output is required, is also provided in this block.


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Locked Sine and Clock Sources

Square wave frequency sources of 10kHz, 20kHz and 62.5kHz are provided, most usually for timing purposes required of the Micro Controller. These sources are to be found in the bottom left-hand corner of the workboard.


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Instrumentation Inputs

Signals present at any of the sockets available on the workboard may be measured and displayed on a PC using a Real-Time Access Terminal (RAT) and the Discovery software that accompanies the product.

The points to be monitored must be patched to the Instrumentation Input sockets that are to be found at the top centre of the workboard. The figures associated with these sockets correspond to the numbers on the monitoring points as seen on the diagrams associated with each Practical activity.

Other Circuits

There are a number of other circuits on the workboard. These, and their functions, will be described as required in the assignments.


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Practical 2: Connections to the PC

Objectives and Background This Practical will familiarise you with the connections required to operate the Modulation & Coding Principles 53-230 workboard with a PC.


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Practical 2: Connections to the PC

Perform Practical


Identify the multiway connector on the top edge of the workboard.

This connector plugs into its female counterpart on the front edge of the Real-Time Access Terminal (RAT) 92-200. The diagram below shows a workboard plugged into a RAT, together with a laptop PC.


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Both the RAT and the workboard require USB connection to the PC. They may be USB1 or USB2 ports. If you do not have two available USB sockets on your PC, an external hub will have to be used. It may be either powered or un-powered.

For correct operation the PC must have the relevant Discovery software and the RAT and product drivers installed. If it does not, you will need to consult your tutor.

If the Discovery software has been installed the workboard and the RAT should automatically be recognised on switch-on and the system will be ready for use.


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Practical 3: Operational Check

Objectives and Background In this Practical you will perform a very simple operational check to confirm that the PC, the RAT and the workboard are communicating with each other and that the set-up is ready to perform further Practicals.


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Practical 3: Operational Check

Perform Practical


Ensure that you have connected the equipment as described in Practical 2 of this Assignment.

Ensure that the PC and the RAT are switched on.

Launch the Discovery software associated with the product.

After a Discovery Courseware splash screen has been briefly displayed, you should see a window showing all the assignments that are available for the product, of the form shown above. There may be a smaller or greater number of assignments available to you than shown. The precise appearance of this window, such as the choice of colours and how the buttons are arranged, is determined by your tutor. Note that you cannot close this window whilst any assignment is open, and you can have only one assignment open at any time.

To select an assignment to perform, left-click on the appropriate button.

After an Assignment loading dialog has been briefly displayed, the assignment window should appear. The assignment window is full-screen, consisting of a title bar across the top, a side bar at the right-hand edge, and the main working area. Initially the overall objectives for the chosen assignment are shown in the main working area. A typical


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screen shot is shown below. The precise appearance of the assignment window is determined by your tutor.

If the hardware has not been connected properly, the following Discovery Warning message is immediately displayed on the screen:

If this warning message is shown, you must acknowledge it by clicking the OK button before you can continue. In this event, it is recommended that you resolve the problem before attempting to perform the assignment. You will need to close the assignment, correct the hardware problem and then restart the assignment.

On the screen shot of the assignment window, notice the three red indicators within the side bar. These are marked F, H and A. These are warning indicators. If any one of them is visible on your screen then you have a fault condition, as follows:

indicates that there is a firmware communications error;


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indicates that the hardware is incorrectly connected, probably your workboard is incorrectly connected to your PC, or that the workboard driver is not installed correctly;

indicates that there is a data acquisition error, probably your RAT is incorrectly connected to the PC, or that the RAT driver is incorrectly installed.

If you do not see any of these warning indicators on your screen then your set-up is correct and you may perform any of the Practicals in the assignment. You can still open a Practical when a fault condition exists, but you will not be able to use any test equipment that may be required to perform that Practical. The hardware must be correctly connected before starting an assignment in order to use the test equipment in any of the Practicals within that assignment.

The next Practical takes you through the navigation of the software.


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Practical 4: Navigating the Discovery Software

Objectives and Background Although the Discovery Laboratory environment is very easy to operate, these notes will help you use all its facilities more quickly.

If there is a demonstration assignment, slider controls in the software perform functions that would normally be performed on the hardware. In normal assignments, if the any of hardware systems fail to initialise the system reverts to demonstration mode. This means that none of the test equipment is available.


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Practical 4: Navigating the Discovery Software

Perform Practical


The assignment window opens when an assignment is launched as described in the previous Practical. The assignment window consists of a title bar across the top, an assignment side bar at the right-hand edge, and the main working area. By default, the overall assignment objectives are initially shown in the main working area whenever an assignment is opened. The assignment window occupies the entire screen space and it cannot be resized (but it can be moved by dragging the title bar, and it can be minimised to the task bar). The title bar includes the name of the selected assignment. The side bar contains the Practicals and any additional resources that are relevant for the selected assignment. The side bar cannot be repositioned from the right-hand edge of the assignment window. An example of an assignment window is shown below.

The precise appearance of the assignment window will depend on the skin that has been selected by your tutor. However, the behaviour of each of the buttons and icons will remain the same, irrespective of this.

The clock (if you have one active) at the top of the side bar retrieves its time from the computer system clock. By double clicking on the clock turns it into a stop watch. To start the stop watch single click on the clock, click again to stop the stop watch. Double clicking again will return it to the clock function.


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There are a number of resource buttons available in the assignment side bar. These are relevant to the selected assignment. In general, the resources available will vary with the assignment. For example, some assignments have video clips and some do not. However, the Technical Terms, Help and Auto Position buttons have identical functionality in every assignment. You can click on any resource in any order, close them again, or minimise them to suit the way you work.

Practicals are listed in numerical order in the side bar. When you hover the mouse over a Practical button, its proper title will briefly be shown in a pop-up tool-tip. There can be up to four Practicals in any assignment. You can have only one Practical window open at any time.

To perform a Practical, left-click on its button in the assignment side bar. The assignment objectives, if shown in the main working area, will close, and the selected Practical will appear in its own window initially on the right-hand side of the main working area, as shown below. You can move and resize the Practical window as desired (even beyond the assignment window) but its default size and position allows the test equipment to be displayed down the left-hand side of the main working area without overlapping the instructions for the Practical.

Again, the precise appearance of the Practical window can be determined by your tutor but the behaviour of each of the buttons and icons will remain the same, irrespective of this. Whatever it looks like, the Practical window should have icons for the test equipment, together with buttons for Objectives & Background, Make Connections, Circuit Simulator and Test Equipment Manuals. These resources are found in side bar, located on the right-hand edge of the Practical window. The resources will depend on which Practical you have selected. Therefore not all the resources are available in every Practical. If a


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resource is unavailable, it will be shown greyed out. To open any resource, left-click on its icon or button. Note that when you close a Practical window, any resources that you have opened will close. You may open any resource at any time, provided it available during the Practical. The Circuit Simulator will only be available if you have one loaded.

Note that if the hardware is switched off, unavailable, or its software driver is not installed, all the test equipment is disabled. However, you can open any other window. If you switch on the hardware it will be necessary to close the assignment window and open it again to enable the test equipment.

Resource Windows

These are windows may be moved, resized and scrolled. You may minimise or maximise them. The system defaults to Auto Position, which means that as you open each resource window it places it in a convenient position. Most resource windows initially place themselves inside the practical window, selectable using tabs. Each one lays over the previous one. You can select which one is on top by clicking the tab at the top of the practical window. You can see how many windows you have open from the number of tabs. If you want to see several windows at once then drag them out of the practical window to where you wish on the screen. If you close a window it disappears from the resources tab bar.

If you want to return all the windows to their default size and position simply click the Auto Position button in the assignment side bar.

Make Connections Window

This movable and resizable window shows the wire connections (2mm patch leads) you need to make on the hardware to make a practical work. Note that some of the wires connect the monitoring points into the data acquisition switch matrix. If this is not done correctly the monitoring points on the practical diagram will not correspond with those on the hardware. The window opens with no connections shown. You can show the connections one by one by clicking the Show Next button or simply pressing the space bar on the keyboard. If you want to remove the connections and start again click the Start Again button. The Show Function button toggles the appearance of the block circuit diagram associated with the Practical.

Test Equipment

The test equipment will auto-place itself on the left of the screen at a default size. You may move it or resize it at any time. Note that below a useable size only the screen of the instrument will be shown, without the adjustment buttons. Each piece of test equipment will launch with default settings. You may change these settings at any time. There is an auto anti-alias feature that prevents you setting time-base or frequency settings that may give misleading displays. If auto anti-alias has operated the button turns red. You can turn


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off the anti-aliasing feature, but you should be aware that it may result in misleading displays.

You may return to the default settings by pressing the Default button on each piece of test equipment. If you wish to return all the equipment to their original positions on the left of the screen click Auto Position on the side bar of the assignment window.

Note that if you close a piece of test equipment and open it again it returns to its default position and settings.

If you want more information on how a piece of test equipment works and how to interpret the displays, see the Test Equipment Manuals resource in the Practical side bar.

On slower computers it may be noticeable that the refresh rate of each instrument is reduced if all the instruments are open at once. If this is an issue then only have open the instrument(s) you actually need to use.

Test Equipment Cursors

If you left click on the display of a piece of test equipment that has a screen, a green cursor marker will appear where you have clicked. Click to move the cursor to the part of the trace that you wish to measure. If you then move the mouse into the cursor a tool-tip will appear displaying the values representing that position. Note if you resize or change settings any current cursor will be removed.

Perform Practical Window

This window contains the instructions for performing the practical, as well as a block, or circuit, diagram showing the circuit parts of the hardware board involved in the Practical. On the diagram are the monitoring points that you use to explore how the system works and to make measurements. The horizontal divider bar between the instructions and the diagram can be moved up and down if you want the relative size of the practical instruction window to diagram to be different. Note that the aspect ratio of the diagram is fixed.

Information Buttons on Practical Diagrams

On many of the symbols on the diagram you will find a button that gives access to new windows that provide more information on the circuit that the symbol represents. Note that these windows are modal, which means that you can have only one open at a time and you must close it before continuing with anything else. A Further Information point looks like this


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Probes

The practical diagram has probes on it, which start in default positions. These determine where on the hardware the signals are being monitored.

Selecting and Moving the Probes

Probes are indicated by the coloured icons like this .

If this probe is the selected probe it then looks like this (notice the black top to the probe). You select a probe by left clicking on it.

Monitor points look like this

If you place the mouse over a monitor point a tool-tip will show a description of what signal it is.

You can move the selected probe by simply clicking on the required monitor point. If you want to move the probe again you do not have to re-select it. To change which probe is selected click on the probe you want to select.

You can also move a probe by the normal drag-and-drop method, common to Windows programs.

Probes and Test Equipment Traces

The association between probes and traces displayed on the test equipment is by colour. Data from the blue probe is displayed as a blue trace. Yellow, orange and green probes and traces operate in a similar way. Which piece of test equipment is allocated to which probe is defined by the practical.

Note that the phasescope shows the relative phase and magnitude of the signal on its input probe using another probe as the reference. The reference probe colour is indicated by the coloured square to the top left corner of the phasescope display.

Practical Buttons

On some Practicals there are buttons at the bottom of the diagram that select some parameter in the practical. These can be single buttons or in groups. Only one of each button in a group may be selected at one time.


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Slider Controls

Where slider controls are used you may find you can get finer control by clicking on it and then using the up and down arrow keys on your keyboard.

Chapter 2 Modulation and Coding Principles Signals in the Time and Frequency Domain

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Signals in the Time and Frequency Domain

Objectives To understand the concepts of time and frequency domains as applied to a waveform

To appreciate the concept of the spectrum of a waveform and the bandwidth it occupies

To examine three fundamental waveforms: the sine wave, the triangle wave and the square wave with respect to their spectrum requirements

To examine the effects of filtering on waveshape and bandwidth restriction

To appreciate the waveform and spectrum of a noise signal and the effect of filtering on the noise

Concepts of Modulation

These assignments will introduce you to the concepts of modulation, carriers, baseband signals and demodulation of both analogue and digital signals.

A carrier is simply a single frequency of constant amplitude, phase and frequency. More properly, this is called an un-modulated or plain carrier. You may say of course that it is simply an oscillation and the fact that it does not carry any information does not mean it will do. This is true, but when referred to as an un-modulated carrier the implication is that some information will be carried on it at some time. The carrier transports the information to be carried, hence the name. As it is an oscillation it is sometimes also referred to as a wave.

How is information to be carried? This information can be of many forms and can, by the time it reaches the carrier, be either analogue or digital. Even if the information is digital the process of transmission is analogue because the real world is analogue. So, in general, there is no difference between the processes involved in carrying analogue or digital information. Information to be carried is often referred to as baseband. The reason for this name will be come clearer later on.

In order to be decoded at the far end some characteristic of the carrier has to vary to represent changes in the baseband signal. There are only three carrier characteristics that can be varied: its amplitude, frequency, or phase. Some schemes vary more than one and also, as you will see, in some cases varying one may unintentionally vary another so it is important not to think of each in isolation.

The term modulation arises from the implication that some part of the carrier characteristic is changing. When carrying information, the carrier is said to be modulated, and the sub system responsible for doing this is called a modulator. The baseband information is sometimes referred to as the modulation.


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The opposite process to modulation is demodulation in which the baseband signal recovered. The trick is to try and recover the baseband signal so that it is as near as possible to the original even when it has been severely weakened and distorted during transmission. Another consideration is to use as little transmission bandwidth as possible so that as many signals as possible can be sent down a cable or via a radio link as possible. Transmission power is also important; usually the minimum that can be used to achieve a usable output is desirable.

The concept of signal-to-noise ratio will also be introduced and how it is a measure of the quality of both the modulated and baseband signals.

These assignments will introduce all the modulation and demodulation concepts vital to an understanding of information transmission.


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Time Domain and Frequency Domain There are two main ways of looking at, or describing, a signal. The first is how it varies with time and the second is what is the frequency of the signal, or the frequencies of the components of the signal.

Consider the simple case of a sine wave signal. It is called a sine wave because that is the mathematical shape that it plots out when looked at with respect to time, and how it can be mathematically described.

The classic way to show this is using a rotating vector and projecting its point out, as shown in the diagram below.

Because this is a plot of how the instantaneous value of the waveform varies with time, it is often referred to as the plot of the waveform in the time domain.

A pure sine wave comprises only a single frequency component. The frequency of the waveform is given by how many cycles (rotations of the vector) are performed in one second (one Hertz is one cycle per second). A picture of the sine wave in the frequency domain will, therefore, only comprise one component and will be a single vertical line. The height of the line represents the amplitude of the signal. This is shown in the next diagram.


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A more complex waveform (for instance, a triangle waveform) has more than one frequency component. What is more, these components have different amplitudes. The picture of such a waveform in the frequency domain may look more like the diagram below.

Its corresponding picture in the time domain is also shown. It can be seen why this waveform is commonly known as a triangle wave.


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Practical 1: Waveshape and Spectrum of Sine, Triangle and Square Wave Signals

Objectives and Background In this practical you will investigate how the waveshape in the time domain affects the spectrum in the frequency domain. This is an important relationship to understand in order to be able to adjust how much frequency spectrum is occupied by a signal. You will examine the spectrum of three fundamental waveforms.

These are:

the sine wave, which in the absence of any distortion contains only one frequency

the triangle wave, which does contain frequencies other than the fundamental but does not contain sharp edges

the square wave, which contains very sharp edges


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Block Diagram

Make Connections Diagram


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Practical 1: Waveshape and Spectrum of Sine, Triangle and Square Wave Signals

Perform Practical

Use the Make Connections diagram to show the required connections on the hardware.

In the Function Generator block, set the frequency range switch to fast and the Frequency control to full scale.

Set the Signal Level Control to half scale.

From the test equipment available, open the frequency counter and reduce the Frequency control in the Function Generator block until a frequency of approximately 50kHz is shown.

From the test equipment available, open the oscilloscope. Select a sine wave using the waveform selector in the Function Generator block.

From the test equipment available, open the spectrum analyser. Notice that one frequency component is of significantly greater amplitude than any other. The scale of the analyser is logarithmic (in dB), so that the trace shown on the display increases to a lesser extent as the signal level increases.

Using the oscilloscope cursor, measure the time for one cycle and, from this, calculate the frequency of the waveform. Remember that the frequency is the reciprocal of the time. Compare this calculated frequency with a direct measurement made using the frequency counter.

In the Function Generator block, change the waveform to triangle. Notice that the spectrum on the analyser now contains a number of other frequencies at much greater amplitude than before. Use the cursor to confirm that they are all multiples of the fundamental (called harmonics). Now change to a square waveform. Notice that the amplitude of the harmonics is significant up to at least ten times the fundamental (called the 10th harmonic). The spectrum analyser may change frequency range automatically so that all the significant frequencies are seen.

Adjust the Signal Level Control and note that on the frequency spectrum all the signals change amplitude by the same amount.


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Practical 2: Effect of Filtering on Waveshape and Spectrum

Objectives and Background In this Practical you will look again at the spectrum of the three waveshapes, but this time you will examine the effect of adding a low-pass filter.

It is important to understand the effect of adding the filter, and hence restricting the bandwidth, on both the waveshape in the time domain and the spectrum in the frequency domain.


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Block Diagram



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Practical 2: Effect of Filtering on Waveshape and Spectrum

Perform Practical


Select the sine waveform and set the frequency range switch to Fast on the Function Generator block on the workboard.

Set the Signal Level Control to half full scale.

Open the Oscilloscope and adjust the Frequency control on the Function Generator block so that two complete cycles of the signal are shown on the oscilloscope Channel 1 when the time-base is set to its default setting.

Change the signal to square-wave. Use the two channels of the oscilloscope to compare the input and output of the Pre-modulation Filter (a low-pass filter) and also use the spectrum analyser to examine the spectra. Notice that the filter has reduced the sharp transitions on the square wave to a more gentle slope and that this has the effect of reducing significantly the amplitude of the higher harmonics in the frequency spectrum.

Repeat the observations using the triangle wave and then the sine-wave.


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Practical 3: Noise Signals in the Time and Frequency Domain

Objectives and Background In this Practical you will look at the time domain waveform and the frequency spectrum of noise. You will then see the effect of adding a low-pass filter.

The noise source is contained on the board in a block called Transmission Channel. This block has an input and an output and is used for other assignments. If no signal is applied to the input the output contains only noise.


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Block Diagram



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Practical 3: Noise Signals in the Time and Frequency Domain

Perform Practical


Set the Noise Generator Amplitude control to half full scale.

Open the oscilloscope and notice that the signal on Channel 1 is a random waveform. Such a signal is referred to as noise.

Open the spectrum analyser and examine the spectrum. It contains random noise at approximately the same amplitude at all frequencies up to a certain frequency. This upper frequency limit is determined internally by the noise generator.

Adjust the noise Amplitude control and notice how much easier it is to measure noise amplitude differences on the analyser.

Check the Ch2 Show box on the spectrum analyser and examine the spectrum of the output of the filter. Note that the upper frequency limit of the noise has reduced significantly. The oscilloscope shows that faster transitions have been removed but, again, it is easier to see what has happened on the analyser.

Chapter 3 Modulation and Coding Principles Sampling and Time Division Multiplex

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Sampling and Time Division Multiplex

Objectives To understand the concept of sampling a continuous analogue waveform

To investigate sampling a waveform using an analogue to digital converter

To investigate the effects of sampling rate and to understand the concept of aliasing

To appreciate the Nyquist limit applied to sampling rate

To investigate time division multiplexing of signals


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Sampling Signals in the real the world are analogue. In a digital communications system the first process is to turn these analogue signals into digital format.

The signals could be anything: speech, television or representing the pH of a liquid, for example. However, the common factor linking analogue signals is that they are time continuous. This means that they are varying in time in a smooth manner. The diagram shows a typical time continuous varying signal.

A digital signal is a series of discrete numbers that describes the signal, where each number represents the signal at a particular point in time. This means that analogue signal has to be sampled at various points in time and each value converted to a digital number. This concept of sampling is very important to understand.

In order for the digital signal to be useful, three further factors have to be considered:

the sampling has to be regular; the time interval between samples has to be short enough to follow the fastest changes in the analogue signal; in a digital signal not only is the time domain in discrete steps but so is the signal itself.

For example a signal may be represented by zero to fifteen amplitude states, which might mean that some of the finer detail may be lost. The number of steps to which the signal is digitised is an important consideration.

The terms used to describe these digitising parameters are:

Time

Signal


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the rate at which the signal is sampled regularly is called the sampling rate; the number of levels in the digital signal is called the resolution; the resolution is often a power of two as this represents steps in the number of bits in a binary system.

For example 16 levels requires 4 bits and 256 levels requires 8 bits.

The following diagram shows the same signal but sampled and digitised to 8 levels

Note that the output steps between the available levels and is timed at the sampling points. Note also that some of the detail of the signal has been lost due to both the lack of resolution and the low sampling rate. In a digital system the choice of resolution and sampling rate must be made very carefully.

If the sampling rate is far too low, then the wrong waveshape can be produced from time repetitive signals. This effect is called aliasing and is described in another Theory section.

There are several methods of implementing both the analogue to digital process and the digital to analogue process and these are described in another Theory section.

Time

1 Si

Sampling points

Available

levels

Digitised

output


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Aliasing

Digital communications systems must usually meet specifications and constraints in both the time domain (e.g. settling time) and the frequency domain (e.g. signal-to-noise ratio). As an added complication, designers of systems must contend with aliasing and imaging problems. Sampled-data constraints can have a significant impact on system performance.

In most digital communications systems, the continuous-time-to-discrete- time interface occurs in the digital-to-analogue (DAC) and analogue-to-digital (ADC) conversion process, which is the interface between the digital and analogue domains. The nature of this interface requires clear understanding, since the level-sensitive properties associated with conversion between digital and analogue domains (e.g., quantization) are often confused with the time-sensitive problems of conversion between discrete time and continuous time (e.g., aliasing). The two phenomena are different, and the subtle distinctions can be important in designing and debugging systems.

The Nyquist theorem expresses the fundamental limitation in trying to represent a continuous-time signal with discrete samples. Basically, data with a sample rate of Fs samples per second can effectively represent a signal of bandwidth up to Fs/2Hz. Sampling signals with greater bandwidth produces aliasing: signal content at frequencies greater than Fs/2 is folded, or aliased, back into the Fs/2 band.

This can create serious problems: once the data has been sampled, there is no way to determine which signal components are from the desired band and which are aliased.

Most digital communications systems deal with band-limited signals, either because of fundamental channel bandwidths (as in an ADSL twisted-pair modem) or regulatory constraints (as with radio broadcasting and cellular telephony). In many cases, the signal bandwidth is very carefully defined as part of the standard for the application; for example, the GSM standard for cellular telephony defines a signal bandwidth of about 200kHz, IS-95 cellular telephony uses a bandwidth of 1.25MHz, and a DMT-ADSL twisted-pair modem utilizes a bandwidth of 1.1MHz. In each case, the Nyquist criterion can be used to establish the minimum acceptable data rate to unambiguously represent these signals: 400kHz, 2.5MHz, and 2.2MHz, respectively. Filtering must be used carefully to eliminate signal content outside of this desired bandwidth.

The analogue filter preceding an ADC is usually referred to as an anti-alias filter, since its function is to attenuate signals beyond the Nyquist bandwidth prior to the sampling action of the A/D converter. An equivalent filtering function follows a D/A converter, often referred to as a smoothing filter, or reconstruction filter. This continuous-time analogue filter attenuates the unwanted frequency images that occur at the output of the D/A converter.

At first glance, the requirements of an anti-alias filter are fairly straightforward: the passband must of course accurately pass the desired input signals. The stopband must attenuate any interferer outside the passband sufficiently that its residue (remnant after the filter) will not hurt the system performance when aliased into the passband after


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sampling by the A/D converter. Actual design of anti-alias filters can be very challenging if passband distortion (both amplitude and phase) and stopband attenuation requirements are to be met.

Aliasing has a frequency translation aspect, which can be exploited to advantage through the technique of undersampling. To understand undersampling, one must consider the definition of the Nyquist constraint carefully. Note that sampling a signal of bandwidth, Fs/2, requires a minimum sample rate greater then Fs. This Fs/2 bandwidth can theoretically be located anywhere in the frequency spectrum [e.g., NFs to (N+1/2)Fs], not simply from dc toFs/2. The aliasing action, like a mixer, can be used to translate an RF or IF frequency down to the baseband. Essentially, signals in the bands NFs


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filters are impossible, most systems employ some degree of oversampling, or rely on system specifications to provide frequency guard-bands, which rule out interferers at immediately adjacent frequencies). On the other hand, sampling at 1.6MHz moves the first critical alias frequency out to 1.4MHz, allowing up to 1.2MHz of transition band for the anti-alias filter.


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A/D and D/A Converters

A/D Conversion

Continuous electrical signals are converted to the digital language of computers using analogue-to-digital (A/D) converters. In addition to the converter itself, sample-and-hold circuits, an amplifier, a multiplexer, timing and synchronization circuits, and signal conditioning elements also may be on board (Figure 1). The logic circuits necessary to control the transfer of data to computer memory or to an internal register also are needed.

Figure 1: Analogue Input Flow Diagram

When determining what type of A/D converter should be used in a given application, performance should be closely matched to the requirements of the analogue input transducer(s) in question. Accuracy, signal frequency content, maximum signal level, and dynamic range all should be considered.

Central to the performance of an A/D converter is its resolution, often expressed in bits. An A/D converter essentially divides the analogue input range into 2N bins, where N is the number of bits. In other words, resolution is a measure of the number of levels used to represent the analogue input range and determines the converter's sensitivity to a change in analogue input.

This is not to be confused with its absolute accuracy! Amplification of the signal, or input gain, can be used to increase the apparent sensitivity if the signal's expected maximum range is less than the input range of the A/D converter. Because higher resolution A/D converters cost more, it is especially important to not buy more resolution than you need-if you have 1% accurate (1 in 100) temperature transducers, a 16-bit (1 in 65,536) A/D converter is probably more resolution than you need.

Absolute accuracy of the A/D conversion is a function of the reference voltage stability (the known voltage to which the unknown voltage is compared) as well as the comparator performance. Overall, it is of limited use to know the accuracy of the A/D converter itself.


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Accuracy of the system, together with associated multiplexer, amplifier, and other circuitry is typically more meaningful.

The other primary A/D converter performance parameter that must be considered is speed-throughput for a multi-channel device. Overall, system speed depends on the conversion time, acquisition time, transfer time, and the number of channels being served by the system:

Acquisition is the time needed by the front-end analogue circuitry to acquire a signal. Also called aperture time, it is the time for which the converter must see the analogue voltage in order to complete a conversion.

Conversion is the time needed to produce a digital value corresponding to the analogue value.

Transfer is the time needed to send the digital value to the host computer's memory. Throughput, then, equals the number of channels being served divided by the time required to do all three functions. A/D Converter Options

While all analogue-to-digital converters are classified by their resolution or number of bits, how the A/D circuitry achieves this resolution varies from device to device.

There are four primary types of A/D converters used for industrial and laboratory applications:

successive approximation,

flash/parallel,

integrating, and

ramp/counting.

Some are optimized for speed, others for economy, and others for a compromise among competing priorities (Figure 2). Industrial and lab data acquisition tasks typically require 12 to 16 bits; 12 is the most common. As a rule, increasing resolution results in higher costs and slower conversion speed.

Figure 2: Alternative A/D Converter Designs

DESIGN SPEED RESOLUTION NOISE IMMUNITY COST

Successive approximation Medium 1016 bits Poor Low

Integrating Slow 1218 bits Good Low Ramp/counting Slow 1424 bits Good Medium


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Flash/parallel Fast 48 bits None High Successive approximation

The most common A/D converter design used for general industrial and laboratory applications is successive approximation (Figure 3). This design offers an effective compromise among resolution, speed, and cost. In this type of design, an internal digital-to-analogue (D/A) converter and a single comparator-essentially a circuit that determines which of two voltages is higher-are used to narrow in on the unknown voltage by turning bits in the D/A converter on until the voltages match to within the least significant bit. Raw sampling speed for successive approximation converters is in the 50kHz to 1MHz range.

To achieve higher sampling speeds, a redundancy technique allows a fast initial approximate conversion, followed by a correction step that adjust the least significant bit after allowing sufficient settling time. The conversion is therefore completed faster at the expense of additional hardware. Redundancy is useful when both high speed and high resolution are desirable.

Figure 3: A/D Conversion by Successive Approximation

Flash/parallel

When higher speed operation is required, parallel, or flash-type A/D conversion is called for. This design uses multiple comparators in parallel to process samples at more than 100MHz with 8 to 12-bit resolution. Conversion is accomplished by a string of comparators with appropriate references operating in parallel (Figure 4). The downside of this design is the large number of relatively expensive comparators that are required. For example, a 12-bit converter requires 4,095 comparators.


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Figure 4: A/D Conversion by Flash/Parallel Technique Integrating

This type of A/D converter integrates an unknown input voltage for a specific period of time, then integrates it back down to zero. This time is compared to the amount of time taken to perform a similar integration on a known reference voltage. The relative times required, and the known reference voltage, then yield the unknown input voltage. Integrating converters with 12 to 18-bit resolution are available, at raw sampling rates of 10500 kHz.

Because this type of design effectively averages the input voltage over time, it also smoothes out signal noise. And, if an integration period is chosen that is a multiple of the ac line frequency, excellent common mode noise rejection is achieved. More accurate and more linear than successive approximation converters, integrating converters are a good choice for low-level voltage signals. Ramp/counter

Similar to successive approximation designs, counting or ramp-type A/D converters use one comparator circuit and a D/A converter (Figure 5). This design progressively increments a digital counter and with each new count generates the corresponding analogue voltage and compares it to the unknown input voltage. When agreement is indicated, the counter contains the digital equivalent of the unknown signal.

A variation on the counter method is the ramp method, which substitutes an operational amplifier or other analogue ramping circuit for the D/A converter. This technique is somewhat faster.


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Figure 5: A/D Conversion by Counting/Ramp Technique

Multiplexing & Signal Conditioning

As shown in Figure 1, A/D converters seldom function on their own but must be considered in a systems context with associated circuitry for signal conditioning, multiplexing, amplification, and other functions. Every application will dictate a unique mix of add-ons that may be implemented in a variety of physical configurations-on a PC I/O board, inside a remote transmitter, or at a local termination panel.

Multiplexing: In many industrial and laboratory applications, multiple analogue signals must be converted to digital form. And if speed is not the limiting factor, a single A/D converter often is shared among multiple input channels via a switching mechanism called a multiplexer. This is commonly done because of the relatively high cost of converters. Multiplexers also allow amplification and other signal conditioning circuitry to be time-shared among multiple channels. Software or auxiliary hardware controls the switch selection.

Sample-and-hold: It is important to acknowledge that a multiplexer does reduce the frequency with which data points are acquired, and that the Nyquist sample-rate criterion still must be observed. During a typical data acquisition process, individual channels are read in turn sequentially. This is called standard, or distributed, sampling. A reading of all channels is called a scan. Because each channel is acquired and converted at a slightly different time, however, a skew in sample time is created between data points (Figure 6).


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Figure 6: Alternative Methods for Eliminating Time Skew Among Multiplexed Channels

If time synchronization among inputs is important, some data acquisition cards offer burst mode operation or simultaneous sample-and-hold circuitry. Burst mode, or pseudo-simultaneous sampling, acquires each channel at the maximum rate of the board, then waits a user-specified amount of time before sampling again.

True simultaneous sample-and-hold systems can sample all channels within a few nanoseconds of each other, eliminating phase and time discontinuities for all but the fastest processes. Essentially, a switched capacitor on each channel tracks the corresponding input signal. Before starting the A/D conversion process, all switches are opened simultaneously, leaving the last instantaneous values on the capacitors.

Signal scaling: Because A/D converters work best on signals in the 110 V range, low voltage signals may need to be amplified before conversion-either individually or after multiplexing on a shared circuit. Conversely, high voltage signals may need to be attenuated.

Amplifiers also can boost an A/D converter's resolution of low-level signals. For example, a 12-bit A/D converter with a gain of 4 can digitize a signal with the same resolution as a 14-bit converter with a gain of 1. It's important to note, however, that fixed-gain amplifiers, which essentially multiply all signals proportionately, increase sensitivity to low voltage signals but do not extend the converter's dynamic range.

Programmable gain amplifiers (PGAs), on the other hand, can be configured to automatically increase the gain as the signal level drops, effectively increasing the system's dynamic range. A PGA with three gain levels set three orders of magnitude apart can make a 12-bit converter behave more like an 18-bit converter. This function does, however, slow down the sample rate.

From a systems perspective, amplifier performance should be on par with that of the A/D converter itself-gain accuracy should be specified as a low percentage of the total gain. Amplifier noise and offset error also should be low.

Other conditioning functions: Other A/D signal conditioning functions required will vary widely from application to application. Among the options:


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Figure 7: Conversion of 420 mA to 1-5 V

Current-to-voltage conversion: A 420mA current signal can be readily converted to a voltage signal using a simple resistor (Figure 7). A resistor value of 250ohms will yield a 15 V output.

Filtering: A variety of physical devices and circuits are available to help separate desired signals from specific frequencies of undesirable electrical noise such as ac line pick-up and other electromagnetic/radio frequency interference (EMI/RFI). If the signal of interest is lower in frequency than the noise, a low-pass filter can be used. High-pass and notch-band filters are designed to target low frequency interference and specific frequency bands, respectively.

Excitation: Voltage supplied by the data acquisition card or discrete signal conditioner to certain types of transducers such as strain gages.

Isolation: Used to protect personnel and equipment from high voltages. Isolators block circuit overloads while simultaneously passing the signal of interest.

Figure 8: Single-ended & Differential Analogue Input configurations

Single-Ended & Differential Inputs

Another important consideration when specifying analogue data acquisition hardware is whether to use single-ended or differential inputs (Figure 8). In short, single-ended inputs are less expensive but can be problematic if differences in ground potential exist.


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In a single-ended configuration, the signal sources and the input to the amplifier are referenced to ground. This is adequate for high level signals when the difference in ground potential is relatively small. A difference in ground potentials, however, will create an error-causing current flow through the ground conductor otherwise known as a ground loop.

Differential inputs, in contrast, connect both the positive and negative inputs of the amplifier to both ends of the actual signal source. Any ground-loop induced voltage appears in both ends and is rejected as a common-mode noise. The downside of differential connections is that they are essentially twice as expensive as single-ended inputs; an eight-channel analogue input board can handle only four differential inputs. D/A Conversion

Analogue outputs commonly are used to operate valves and motors in industrial environments and to generate inputs for electronic devices under test. Digital-to-analogue (D/A) conversion is in many ways the converse of A/D conversion, but tends to be generally more straightforward. Similar to analogue input configurations, a common D/A converter often is shared among multiplexed output signals. Standard analogue output ranges are essentially the same as analogue inputs: 5V dc, 10V dc, 010V dc, and 420mA dc.

Essentially, the logic circuitry for an analogue voltage output uses a digital word, or series of bits, to drop in (or drop out, depending on whether the bit is 1 or 0) a series of resistors from a circuit driven by a reference voltage. This ladder of resistors can be made of either weighted value resistors or an R-2R network using only two resistor values, one if placed in series (Figure 9). While operation of the weighted-value network is more intuitively obvious, the R-2R scheme is more practical. Because only one resistor value need be used, it is easier to match the temperature coefficients of an R-2R ladder than a weighted network, resulting in more accurate outputs. Plus, for high resolution outputs, very high resistor values are needed in the weighted-resistor approach.

Figure 9: Weighted Value & Single Value Resistor Networks for D/A Conversion

Key specifications of an analogue output include:


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Settling time: Period required for a D/A converter to respond to a full-scale setpoint change.

Linearity: This refers to the device's ability to accurately divide the reference voltage into evenly sized increments.

Range: The reference voltage sets the limit on the output voltage achievable.

Because most unconditioned analogue outputs are limited to 5mA of current, amplifiers and signal conditioners often are needed to drive a final control element. A low-pass filter may also be used to smooth out the discrete steps in output.


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Multiplexing Multiplexing is a generic term used to describe a system that passes more than one signal through a single block in a system. In terms of communication is means transmitting more than one signal through a transmission system such as a cable or a radio link. Multiplexing is a method for increasing the signal carrying capacity of a system without proportionally increasing the hardware and/or bandwidth required.

There are three main types of multiplexing:

Frequency Division Multiplex (FDM) Time Division Multiplex(TDM) Code Division Multiple (CDM)

FDM and TDM have been used since the earliest days of electrical communication whereas CDM is a more recent development. It is important that you understand FDM and TDM because they are in very common use. CDM is more complex and is applied to specific systems. As such it is outside the scope of these assignments.

FDM

Frequency division multiplex is simply a matter of transmitting different information on different carrier frequencies. The most common example is ordinary radio where the different stations are on different frequencies. All the signals pass through the common parts of the system like the antenna and the amplifiers at the front end of the receiver but are separated out later in the tuning system. The same process used to used to send many telephone calls down the same cable by using different single sideband transmission carrier frequencies.

Another more subtle example is stereo radio using the pilot tone system. The (left+right) signal is sent at baseband and the (left-right) is sent as a dsb suppressed carrier signal centred on 38kHz.

The diagram shows an FDM system

Amplitude

Signal 1 Signal 2 Signal 3


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TDM

Time division multiplex is when the available time on a link is divided between more than one information signal.

These time-slots are timed regularly at a known rate such that both signals can be separated and re-created with minimum distortion. Such a system means both signals have to be sampled and the same considerations apply as for sampling one signal in terms of sampling rate.

Early TDM systems were entirely analogue but the whole concept is more suited to digital transmission. Most forms of modern digital communication system involve some form of multiplexing.

The diagram shows a simple TDM system

Sample Period

Multiplex

Signal 3

Signal 2

Signal 1

Amplitude

Time


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Although the TDM process could be done with analogue signals prior to being digitised the easiest method is interleaving the digital samples. Sophisticated systems do not use the same number of samples for all signals; they may send more than one sample at a time in what are called packets and attach identification tags to each packet to tell the system how to deal with it.


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Practical 1: Sampling Analogue Signals

Objectives and Background Sampling In this practical you will investigate the effects of sampling a continuous analogue signal using an analogue to digital converter.

Read the Resources section on Sampling if you do not understand the process of sampling an analogue signal, or parameters such as resolution and sampling rate.

The set-up for the practical is a sinusoidal analogue signal digitised by an analogue to digital converter (A/D) at a constant rate of 20 kHz and then passed back out to a digital to analogue converter (D/A).

The frequency of the sinusoidal signal can be varied, so the effect of the ratio between signal and sampling rate can be observed. The resolution of the A/D and D/A is 8 bits (i.e. 256 levels). In the practical you will change the resolution to 4 bits (16 levels) and 2 bits (4 levels) to see the effect. You will also see from the resulting waveshape that, at first glance, it is difficult to tell whether a signal is being sampled at insufficient resolution or insufficient sample rate.

The A/D and D/A are part of the on-board microprocessor system on the hardware. The data is passed through the microprocessor, where the resolution is changed as required. The functions of the on-board microprocessor are controlled by commands automatically sent by you when you start the practical or press a button on the practical diagram.


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Block Diagram



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Practical 1: Sampling Analogue Signals

Perform Practical


Identify the Micro Controller and A/D D/A circuit block, located towards the top, left-hand corner of the board.

Associated with this circuit block, set the A/D 1 Offset, the A/D 1 Amplitude and the D/A 1 Offset to mid position.

Set the Function Generator to Slow.

Set the Signal Level Control for maximum output.

Open the frequency counter and set the Frequency (in the Function Generator block) to approximately 400Hz. Close the frequency counter and open the oscilloscope. In the Function Generator block, use the waveform selector to select a sine wave output.

On the oscilloscope, note that the output signal is very similar to the input signal and that the system is set to 8 bit resolution

Increase the size of the oscilloscope so you can see the waveforms more easily. Change the resolution to 4 bit and notice that the output has more steps in it. Now try 2 bit resolution and note that the output contains only a few discrete levels.

Try the different resolutions and also adjust the amplitude of the signal using the Signal Level Control. Note that at 2 bit resolution most of the signal waveshape is lost.

With 2 bit resolution, change from sine to triangle waveform and note that it hard tell the difference.

Return to a sine wave and select 8 bit resolution and maximum amplitude. Now increase the frequency of the function generator gradually. You will need to increase the timebase speed on the oscilloscope so you can see only a cycle or two to see what is happening. Note that the waveshape has steps in it now. This is because the signal frequency is such that there is only time to take a few samples in each cycle. Note that the effect on the output is similar to reducing the resolution.

If you increase the frequency too far, some strange effects occur as a result of aliasing. This is examined further in Practical 2.


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Practical 2: Aliasing

Objectives and Background The Effects of Aliasing

In this practical you will investigate the effect of sampling an analogue signal at sample rates near to and below its frequency.

Aliasing can be a significant problem in any sampling system and can result in completely misleading results.

The lowest rate that can be used to sample a signal is twice the frequency of the signal you are trying to sample. Even then the results may not be satisfactory.

For example, if you sampled a sinusoidal signal at twice its frequency and looked at the result all you would see is that the signal is one level during one sample and another level during the next sample. This may be all you need to know, as it does convey the frequency of the signal - but all the other detail of the signal has been lost. A sampling rate at twice the signal frequency is called the Nyquist limit.

You may wonder what happens beyond this limit (sampling at less than twice the signal frequency) and you might be thinking that you get nothing out. This would be rather satisfactory but, in reality, you get waveforms out that imply the frequency is below the Nyquist limit. This is rather like a multiplying or mixing process using the sampling rate at the multiplying signal.

This effect is called aliasing, because the waveform you get is not real and is an alias of the frequency being sampled.

There is more detailed information on this quite complex problem in the section on aliasing. The important thing is to recognise that aliasing can happen; to recognise when it does and not to be misled by its effects. In the Practical you will be able to see aliasing at work.

Interestingly, there are situations when the effect can be used to digitise a high frequency signal. This is called sub-sampling, but is outside the scope of this practical.

In the practical, only a single frequency signal is used; but in reality the signal being sampled may contain many frequencies. The Nyquist limit says that you must sample at twice the highest frequency present in the signal. In some cases some of the higher frequencies may not be of interest but, to prevent them appearing as aliases, a low pass filter with a cut-off at half the sampling frequency is used. This is sometimes referred to as an anti-aliasing filter.


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Block Diagram



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Practical 2: Aliasing

Perform Practical


The hardware setup used is similar to that used in Practical 1. In this Practical you will only be using 8 bit resolution.

Set the A/D 1 Amplitude, the A/D 1 Offset and the D/A 1 Offset to mid position.

Set the Function Generator to Fast.


Open the frequency counter and set the Frequency to approximately 2kHz.

Open the oscilloscope. In the Function Generator block, select a sine wave.

Note that the output signal has some steps due to the sampling rate (20kHz) being only 10 times the signal frequency, which means that there are only 10 samples per signal frequency cycle.

Increase the signal frequency and note that the sampled signal becomes more and more ragged. Near to the Nyquist limit (10kHz) notice that rather strange things start to happen. It is possible to sample at the Nyquist limit but here the results are difficult to interpret. This is because the sampling rate and signal are not synchronised. Note that, very near to 10kHz, the amplitude of the waveform appears to vary at a lower frequency. As you will see from a later Assignment, this waveform resembles a double sideband suppressed carrier signal. This confirms that sampling is a multiplying process.

Set the frequency to about 9.5kHz. Move the frequency counter probe to the output of the D/A Converter (monitor point 2). Now, slowly raise the frequency. As the frequency is raised above 10kHz note that frequencies appear below 10kHz. These are aliases.

Set the signal frequency to 15kHz (you will need to move the frequency counter back to monitor point 1, temporarily). Note the result on the oscilloscope. Move the counter back to the sampled output signal and measure the frequency. How do you think it is related to the input frequency?

Notice, also, that further effects occur above the sampling frequency (20kHz).


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Practical 3: Time Division Multiplex

Objectives and Background In this practical you will investigate time division multiplex using two A/D converters and a single D/A converter.

Two analogue signals: one a sinusoid and the other a variable dc voltage are fed into the two a/d converters. The microprocessor samples the two alternatively at 20kHz. The multiplexed signal is passed to a D/A and you can see it on the oscilloscope.

Note that, if the overall sample-rate is 20kHz, then for two signals the sampling rate is 10kHz, with the associated problems of this lower sampling rate.


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Block Diagram



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Practical 3: Time Division Multiplex

Perform Practical

Use the Make Connections diagram to make the required connections on the hardware.

Set the A/D 1 Amplitude and A/D 2 Amplitude to maximum.

Set the A/D 1 Offset, the A/D 2 Offset and the D/A 1 Offset to mid position.

Set the Function Generator to Slow.


Open the frequency Counter and set the Function Generator Frequency to 1kHz.

Open the voltmeter and use it to set the variable dc Source to approximately zero.

Open the oscilloscope. On the Function Generator block, select a sine wave output.

Note the signal on the upper trace, containing samples of the sine wave alternating above and below the dc voltage. Adjust the dc Source voltage and note that the upper trace changes position relative to the zero volt line, but its waveshape remains constant.

Adjust the Function Generator frequency of the sine wave and confirm that the Nyquist limit is about 5kHz.

Chapter 4 Modulation and Coding Principles Amplitude Modulation

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Amplitude Modulation

Objectives To understand the concept of multiplying two sinusoidal waveforms

To recognise that the result of such a multiplication is amplitude modulation

To determine the modulation index of an amplitude modulated signal

To investigate the spectrum of an amplitude modulated signal

To investigate demodulation of an amplitude modulated signal using an envelope detector and subsequent filtering

To investigate demodulation of an amplitude modulated signal using a product detector and subsequent filtering


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Concepts of Modulation

A carrier is simply a single frequency of constant amplitude, phase and frequency. More properly, this is called an un-modulated or plain carrier. In itself, it does not carry any information. However, when referred to as an un-modulated carrier the implication is that some information will be carried on it at some time. The carrier transports the information to be carried, hence the name. As it is an oscillation it is sometimes also referred to as a wave.

How is information to be carried? This information can be of many forms and can, by the time it reaches the carrier, be either analogue or digital in form. Even if the information is digital the process of transmission is analogue, because the real world is analogue. So, in general, there is no difference between the processes involved in carrying analogue or digital information. Information to be carried is often referred to as baseband. The reason for this name will be come clearer later on. In order to be decoded at the receiving end of a communications channel, some characteristic of the carrier has to varied to represent differences in the baseband signal. There are only three carrier characteristics that can be varied: its amplitude, its frequency or its phase. Some schemes vary more than one of these characteristics and also, as you will see, in some cases varying one will inadvertently vary another. So it is important not to think of each in isolation. The term modulation arises from the implication that some part of the carrier characteristic is changing. When carrying information, the carrier is said to be modulated, and the sub system responsible for doing this is called a modulator. The baseband information is sometimes referred to as the modulation. The opposite process to modulation is demodulation, in which the baseband signal is recovered. The trick is to try and recover the baseband signal so that it is as near as possible to the original, even when it has been severely weakened and distorted during transmission. Another consideration is to use as little transmission bandwidth as possible, so that as many signals as possible can be sent down a cable or via a radio link as possible. Transmission power is also important; usually the minimum that can be used to achieve a usable output is desirable. The concept of signal-to-noise ratio will also be introduced and how it is a measure of the quality of both the modulated and baseband signals. The assignments will introduce all the modulation and demodulation concepts vital to an understanding of information transmission.


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Equations of Amplitude Modulation The equation of a sinusoidal voltage waveform is given by : v = Vmax.sin(t + )

where:

v is the instantaneous voltage Vmax is the maximum voltage amplitude is the angular frequency is the phase

A steady voltage corresponding to the above equation conveys little information. To convey information the waveform must be made to vary so that the variations represent the information. This process is called modulation. From the above equation, the basic parameters of such a waveform are:

its amplitude, Vmax

its frequency, (or f) its phase,

Any of these may be varied to convey information.

Amplitude Modulation Amplitude modulation uses variations in amplitude (Vmax) to convey information. The wave whose amplitude is being varied is called the carrier wave. The signal doing the variation is called the modulation.

For simplicity, suppose both carrier wave and modulation signal are sinusoidal.

i.e.: vc = Vc sin c t (c denotes carrier) and vm = Vm sin m t (m denotes modulation) We want the modulating signal to vary the carrier amplitude, Vc, so that: vc = (Vc + Vm sin mt).sin c t where (Vc + Vm sin m t) is the new, varying carrier amplitude. Expanding this equation gives: vc = Vc sin c t + Vm sin c t. sin m t which may be rewritten as vc = Vc [sin c t + m sin c t. sin m t]


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where m = Vm/Vc and is called the Modulation Index.

Now sin c t.sin m t = (1/2) [cos(c m) t cos(c + m) t] so, from the previous equation: vc = Vc [sin c t + m sin c t. sin m t] we can express vc as: vc = Vc sin c t + (mVc/2) [cos(c - m) t] (mVc/2) [cos(c + m) t] This expression for vc has three terms:-

The original carrier waveform, at frequency c, containing no variations and thus carrying no information

.A component at frequency (c - m), whose amplitude is proportional to the modulation index. This is called the LOWER SIDE FREQUENCY.

A component at frequency (c + m), whose amplitude is proportional to the modulation index. This is called the UPPER SIDE FREQUENCY.

It is the upper and lower side frequencies that carry the information. This is shown by the fact that only their terms include the modulation index m. Because of this, the amplitudes of the side frequencies vary in proportion to that of the modulation signal; the amplitude of the carrier does not. Sidebands If the modulating signal is a more complex waveform, for instance an audio voltage from a speech amplifier, there will be many side frequencies present in the total waveform.

This gives rise to components 2 and 3 in the last equation being bands of frequencies, known as sidebands.

Hence we have the upper sideband and the lower sideband, together with the carrier.


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Theory on Frequency Translation and Negative Frequencies Translating from zero frequency

The modulation process can be thought of as that of frequency translation. The baseband modulation is moved up in frequency by an amount equal to the carrier frequency. Therefore zero Hz (i.e. dc) becomes the carrier frequency and the baseband becomes the upper sideband.

From our observations that a dc offset in the mod

53-230 modulation and coding principles manual v2p3 cd

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