ESSENTIAL ELECTRONICS FOR AS –LEVEL BY CHRIS BARNES PhD Eng., MCIEA

Preface

Many students these days embark on an A-level Electronics Course without any prior knowledge whatsoever.  As a crucially helpful asset, the author has more than twenty five years experience in Electronics at Industrial and Teaching Levels and Examining Levels

This book aims to provide the essential elements of knowledge for AS-level.

It is particularly suited to the AQA Electronics Syllabus but will also have value as   a general reference text. It will also have value for GCSE Electronics courses and GCSE Design Technology Electronics Products courses.  

 

Nothing is more daunting than opening a book on Electronics and seeing its earliest pages and pages crammed full of calculation strewn diagrams before you have mastered the basics.  The early chapters of this book will therefore, assuming no prior knowledge, and address the very simplest aspects of Electricity and Electronics.

 

Firm foundations, however, will be quickly built upon leading to theoretical and practical examples covering the entire AS syllabus. It goes without saying then the parts of this book could also be used as a reference manual for other vocational and non-vocational courses in Electricity, Radio and Electronics, such as aspects of B-TECH Level 2 and 3 Engineering.     

If you intend to study Electronics at A2 level, the sister text Essential Electronics for A2 level will be an additional invaluable asset.  

 

 

 

 

 

 

 

 

 

CHAPTER ONE:  SOURCES OF ELECTRICITY

Electronic gismos are ubiquitous in our world, they all around us.  All these devices contain electronic systems and sub-systems, some with simple circuitry, some with very complex circuitry but all with one thing in common, they need a source of electricity to make them work. This electricity is converted into signals in the equipment which either process (change in some way) information and/or direct its flow from one point to another.       

When we think of sources of electricity we would probably think firstly of the power outlet  in our front room where the TV or Hi-fi is plugged in and secondly we would think of a battery, maybe in car or digital camera or T.V  remote or whatever and we would in one sense be right.  In another sense we could think that everything around us contains some electricity!  Atoms that we might vaguely remember from our Chemistry lessons make up everything and these in turn are made from ‘electrical’ particles. That is particles which carry an electric charge. The tiniest of these and the ones which move inside wires and electric circuits are called Electrons.    

There are subtle differences however between electricity from the mains and a battery of whatever type, wet and containing acid as in car, or dry and containing a special jelly-like material as in say our digital camera.

Electricity from batteries

Electricity from batteries is called D.C. or direct current and here the electrons can only flow in one direction through the circuit from out from one pole of the battery, called the negative and back in to another pole of the battery called the positive.    

 

 

 

 

                               +-

Fig 1.1

Practical battery                               Circuit symbol of battery

 

 

 

Fig 1.2 Practical diagram showing flow of electrons

 

Way back in history people were making batteries before they really knew about Electrons.  They were very misguided but in their infinite wisdom decreed that D.C Electricity flowed in exactly the opposite way which we now know to be true. In other words they defined what is still known to this day as Conventional Current Flow.

Conventional current flow was deemed to go from the positive pole of a battery, given the symbol (+ or +vet) to the negative pole, given the symbol (– or –vet). Of course, electrical current only ever flows when there is some kind of electrical connection or circuit joining these two poles of the battery.  Circuits can be drawn as real pictures of the components used or alternatively and more conveniently diagrammatically as circuit or schematic diagrams.  A range of symbols is used in circuit diagrams.  A suitable circuit might contain a component known as a resistor, given the symbol R which has a property known as resistance which restricts or cuts down current flow and gets warm or hot in the process.  In Electronics a flow of current is normally denoted by the symbol I and has units of Amperes (often abbreviated to Amps).

 

Fig 1.3 Battery- resistor circuits

 

 

Note the difference between wire in the practical set up diagram which may be curved or straight or take whatever route and the diagrammatic representation of wires in the circuit or schematic diagram which are by convention always shown as straight lines.

If wires from a battery are short circuited or joined together without a series resistor or bulb as a load then excessive current may flow and they may get very hot or even start a fire if the battery is big enough. This is a potentially dangerous situation. Wires alone have practically zero resistance to the flow of an electric current.

On the other hand if there is break in a circuit has a break in it no current flows. A break in a circuit can be thought of as like an infinitely high resistance.    A break is sometimes called an open circuit.

 

Fig 1.4 The open circuit

 

When the battery is connected in a circuit it is doing work. Its terminal voltage (V) measured in units of volts is pushing electrons through the circuit.  With an open circuit or no flow of electrons, the entire potential (voltage) of the battery is available across the break, waiting for the opportunity of a connection to bridge across that break and permit electron flow again. In an open circuit the break in the continuity of the circuit prevents current throughout. All it takes is a single break in continuity to “open” a circuit. Once any breaks have been connected once again and the continuity of the circuit re-established, it is known as a closed circuit.

We now have the basis for switching lamps on and off by remote switches. Because any break in a circuit’s continuity results in current stopping throughout the entire circuit, we can use a device designed to intentionally break that continuity (called a switch), mounted at any convenient location that we can run wires to, to control the flow of electrons in the circuit:

Figure 1.5 Wiring routes

This is how a switch mounted on the wall of a house can control a lamp that is mounted down a long hallway, or even in another room, far away from the switch. The switch itself is constructed of a pair of conductive contacts (usually made of some kind of metal) forced together by a mechanical lever actuator or pushbutton. When the contacts touch each other, electrons are able to flow from one to the other and the circuit’s continuity is established; when the contacts are separated, electron flow from one to the other is prevented by the insulation of the air between, and the circuit’s continuity is broken.

Perhaps the best kind of switch to show for illustration of the basic principle is the “knife” switch:

A knife switch is nothing more than a conductive lever, free to pivot on a hinge, coming into physical contact with one or more stationary contact points which are also conductive. The switch shown in the above illustration is constructed on a porcelain base (an excellent insulating material), using copper (an excellent conductor) for the “blade” and contact points. The handle is plastic to insulate the operator’s hand from the conductive blade of the switch when opening or closing it.

Here is another type of knife switch, with two stationary contacts instead of one:

Figure 1.6 Changeover Knife Switch

The particular knife switch shown here has one “blade” but two stationary contacts, meaning that it can make or break more than one circuit. For now this is not terribly important to be aware of, just the basic concept of what a switch is and how it works.

Knife switches are great for illustrating the basic principle of how a switch works, but they present distinct safety problems when used in high-power electric circuits. The exposed conductors in a knife switch make accidental contact with the circuit a distinct possibility and any sparking that may occur between the moving blade and the stationary contact is free to ignite any nearby flammable materials. Most modern switch designs have their moving conductors and contact points sealed inside an insulating case in order to mitigate these hazards. A photograph of a few modern switch types show how the switching mechanisms are much more concealed than with the knife design:

Figure 1.7 Selected switches

In keeping with the “open” and “closed” terminology of circuits, a switch that is making contact from one connection terminal to the other (example: a knife switch with the blade fully touching the stationary contact point) provides continuity for electrons to flow through, and is called a closed switch. Conversely, a switch that is breaking continuity (example: a knife switch with the blade not touching the stationary contact point) won’t allow electrons to pass through and is called an open switch. This terminology is often confusing to the new student of electronics, because the words “open” and “closed” are commonly understood in the context of a door, where “open” is equated with free passage and “closed” with blockage. With electrical switches, these terms have opposite meaning: “open” means no flow while “closed” means free passage of electrons.

Alternating Current (A.C)

We have seen how batteries generate D.C. electricity.  Imagine connecting a battery to a reversing switch and then to a lamp or torch bulb. Each time the reversing switch was operated, the flow of electricity through the circuit would be reversed. The lamp would momentarily go on and off.  However if you could operate the reversing switch fast enough the lamp would appear to be on all the time because you eye would not be able to respond to the flickering changes in brightness.

 

Figure 1.8 A.C. From reversing circuit

The red arrows show electric current going through the bulb from left to right (solid

lines on  reversing switch) and the blue arrows show the current having reversed direction through the bulb from right to left as through the dashed lines on reversing switch) .

A.C. Electricity fro a Mains Outlet behaves in exactly this manner.  A.C. electricity is generated from mechanical machines called generators or alternators which employ coils of wire and magnets. D.C. can also be generated from a mechanical machine of similar construction known as a dynamo.  With our reversing switch the change in direction of the current flow would be very sharp and abrupt but with most AC Electricity the change in direction of the current flow is smooth and continuous and is called a sinusoid or sine wave after the mathematical function that you will see on any scientific calculator.   A typical sine wave is shown below , note the smooth variation of the voltage with time, the current in the circuit reverses each time the line of the wave crosses zero. 

 

Figure 1.9 A.C. Sine wave

 

 

 

How fast does electricity flow?

It may surprise you to know that electricity in wires flows almost as fast as the speed of light! This is because wires, as with all electrical conductors, are always full of electrons. The current from the battery merely introduces extra electrons sequentially at one end of the wire and there is a ‘knock-on effect’ through the wire. If we were to follow the speed of any one single injected electron it alone would be much slower.  

 

 

 

 

 

 

There is a good analogy with marbles in a tube.

 

Figure 1.10 Marble-electron analogy

 

Pushing the marble in at the left of the tube makes the marble on the right drop out almost instantaneously but there is a considerable delay before the marble on the left drops out at the right. In fact, simplistically, as there are seventeen marbles in the tube we could say this delay is the transit time for all seventeen marbles plus the loading time for the tube to be refilled.

REVIEW

·         Batteries chemically generate D.C. electricity

·         Electrons are found in the atoms of all materials

·         An electric current is a flow of electrons

·         An electric potential or voltage does work in pushing electrons through a circuit

·         Conventional current flows from positive to negative 

·         Resistance is the measure of opposition to electric current

·         Resistors generate heat

·         A short circuit is an electric circuit offering little or no resistance to the flow of electrons. Short circuits are dangerous with high voltage power sources because the high currents encountered can cause large amounts of heat energy to be released.

·         An open circuit is one where the continuity has been broken by an interruption in the path for electrons to flow.

·         A closed circuit is one that is complete, with good continuity throughout.

·         A device designed to open or close a circuit under controlled conditions is called a switch.

·         The terms “open” and “closed” refer to switches as well as entire circuits. An open switch is one without continuity: electrons cannot flow through it. A closed switch is one that provides a direct (low resistance) path for electrons to flow through.

·         A.C Electricity may be simulated using a battery and very fast reversing switch.

·         A.C. Electricity is usually generated using Electromagnetic machines called generators or alternators. Electricity generated in this way has a smooth variation of voltage with time known as a sine wave.

·         An electric current in closed circuit is virtually instantaneous from the moment of switch- on, close to the speed of light, but single electrons drift more slowly.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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CHAPTER 2: BASIC ELECTRICAL CALCULATIONS

Take our battery and resistor series circuit from the last chapter. The greater the battery voltage or terminal potential difference the more ability it has to drive current round the circuit.  Thus the hotter the resistor gets. The voltage can be measured by an instrument known as a voltmeter which may be of moving coil or electronic (digital) construction. Likewise the current may be measured by an ammeter of either of the foregoing constructions.   The heat generated or the power dissipated in the resistor is a function of the work done driving electrons through it.

The fundamental equation linking Power (P) measured in Watts (named after James Watt inventor of the steam engine, they got hot too!) is

P= I x V

Or in words using units Watts= Amps times Volts.

Some students find the memory mnemonic, involving a fictitious Welsh girls’ name useful;     W= Ivy Watts.  This helps them remember the equation for Power contains the product of I and V. A product is two numbers multiplied together.

Worked example.

A circuit has a battery with open circuit terminal voltage of 12 volts.

When connected to a bulb the battery voltage does not significantly change and the current flowing through the bulb is 2 Amps.  Calculate the power dissipated (used up) by the bulb.

P=IxV       P = 2x12 =24 Watts

Answer 24 Watts

 

 

 

Decimal Prefixes

Mathematics used in technology and engineering often uses very large numbers. Instead of writing or saying these numbers, we can use several types of shorthand.

Prefixes - A prefix is added to the front of a unit (e.g. length or mass ) as a multiplier. ‘Kilo’ always tell you to multiply by a thousand. 1 kilogram is 1000 grams.

 

Symbols - Long numbers also have symbols, ‘k’ stands for ‘kilo’ or 1000. Instead of writing 0.000001 meter we can write ‘ m ‘ which is one micron ( 1 millionth of a meter ). For example, an average human hair is 100 micron thick.

 

To abbreviate long numbers engineers often use exponents. This is a small number that tells you how many zeros the actual number contains. Many calculators now have an engineering function key that allows you to key in numbers with exponents and to manipulate them to solve problems. This avoids keying in - and possibly becoming confused by very long numbers.

 

These general situations of decimal prefixes and exponents often apply  in Electronics we come across problems with smaller fractions of the fundamental or S.I. (International System) units which are decimal sub-divisions.

 

Sometimes we come across decimal multiples of S.I. units. These subdivisions and multiples are given special names and it is instructive to know and hopefully learn them at this stage.

 

 

Figure 2.1 Decimal prefixes

Note that the exponent 100 has no prefix or symbol because it is merely 1 S.I. Unit.

Examples

One thousandth of a volt    =   1/1000 volts = 10 -3 volt = 1 millivolt

1000 volts = 1 kilo-volt

One thousandth of an Amp = 1/1000 Amps = 10 -3 Amps = 1 milliamp One millionth of an Amp     = 1/1000, 000 Amps = 10 -6   Amps = 1 microamp Etc; etc.

It is very important to take decimal prefixes properly into account when calculated Power for example.

There are toe possible approaches to problems. Either convert everything (both the volts and amps) back to S.I. units with no prefix first OR if either is in ‘MILLI’ form the answer will automatically be in ‘MILLI’ form OR if both are in ‘MILLI’ form, the answer will automatically be in MICRO form since    10 -3  x  10 -3   =  10 -6   

WORKED EXAMPLES

1.      A twelve volt battery drives a current of 2 mA through a circuit.  Calculate the   power dissipated by the circuit.

 

Either P= I xV      P = 2x10-3  x 12 = 24 x  10-3 W = 24 milliwatts

 

OR          P= 2 Milliamps x 12 Volts = 24 Milliwatts (automatically!)

 

 

2.      A resistor in a complex circuit has 12 millivolts across it and a current               of 12mAflowing through it both as measured by a very high resistance digital multi-meter.  Calculate the power dissipated in the resistor.

 

          Either P= I x V     P = 12 x 10-3  x  12 x 10-3  = 144 x 10-6  W = 144 microwatts

 

          OR      P = 12 Milliamps  x 12 Millivolts = 144 Microwatts (automatically!)

 

 

Note how either method admirably obtains the correct answer.

 

Ohm’s Law

“One microampere flowing in one ohm causes a one microvolt potential drop.”

Georg Simon Ohm

How voltage, current, and resistance are  related

An electric circuit is formed when a conductive path is created to allow free electrons to continuously move. As we have seen this continuous movement of free electrons through the conductors of a circuit is called a current, and it is often referred to in terms of “flow,” just like the flow of a liquid through a hollow pipe.

The force motivating electrons to “flow” in a circuit is called voltage. Voltage is a specific measure of potential energy that is always relative between two points. When we speak of a certain amount of voltage being present in a circuit, we are referring to the measurement of how much potential energy exists to move electrons from one particular point in that circuit to another particular point. Without reference to two particular points, the term “voltage” has no meaning.  As we have seen in one of the pervious worked examples such a pair of points could be the terminal ends of a resistor.

Free electrons tend to move through conductors with some degree of friction, or opposition to motion. As we saw in Chapter One, this opposition to motion is more properly called resistance. The amount of current in a circuit depends on the amount of voltage available to motivate the electrons, and also the amount of resistance in the circuit to oppose electron flow. Just like voltage, resistance is a quantity relative between two points. For this reason, the quantities of voltage and resistance are often stated as being “between” or “across” two points in a circuit.

: To be able to make meaningful statements about these quantities in circuits, we need to be able to describe their quantities in the same way that we might quantify mass, temperature, volume, length, or any other kind of physical quantity. For mass we might use the units of “pound” or “gram.” For temperature we might use degrees Fahrenheit or degrees Celsius. Here are the standard units of measurement for electrical current, voltage, and resistance

Figure 2.2 Electrical quantities

The “symbol” given for each quantity is the standard alphabetical letter used to represent that quantity in an algebraic equation. Standardized letters like these are common in the disciplines of physics and engineering, and are internationally recognized. The “unit abbreviation” for each quantity represents the alphabetical symbol used as a shorthand notation for its particular unit of measurement. The strange-looking “horseshoe” symbol is the capital Greek letter Ω, (omega).

In fact as we progress in Electronics, we will come to realize that each and every unit of measurement is named after a famous experimenter in electricity or magnetism: for instance in the table above, the amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Volta, and the ohm after the German Georg Simon Ohm.

The mathematical symbol for each quantity is meaningful as well. The “R” for resistance and the “V” for voltage are both self-explanatory, whereas “I” for current seems a bit weird. The “I” is thought to have been meant to represent “Intensity” (of electron flow), and the other symbol for voltage, “E,” stands for “Electromotive force.” From what research I’ve been able to do, there seems to be some dispute over the meaning of “I.” The symbols “E” and “V” are interchangeable for the most part, although some texts reserve “E” to represent voltage across a source (such as a battery or generator) and “V” to represent voltage across anything else.

Strictly speaking capital letters are used where the voltage, current and resistance are stable over long periods of time and small letters for instantaneous values.  In you’re a-level course you will probably only meet the former.

One foundational unit of electrical measurement, often taught in the beginnings of electronics courses but used infrequently afterwards, is the unit of the coulomb, which is a measure of electric charge proportional to the number of electrons in an imbalanced state. One coulomb of charge is equal to 6,250,000,000,000,000,000 electrons, or the charge on 6.25 x 1018 electrons!.    The symbol for electric charge quantity is the capital letter “Q,” with the unit of coulombs abbreviated by the capital letter “C.” It so happens that the unit for electron flow, the amp, is equal to 1 coulomb of electrons passing by a given point in a circuit in 1 second of time. Cast in these terms, current is the rate of electric charge motion through a conductor.

As stated before, voltage is the measure of potential energy per unit charge available to motivate electrons from one point to another.  A 1 volt battery expends 1 Joule of energy pushing 1 Coulomb of electron charge round a circuit.   Since a volt is defined as 1 Joule per Coulomb, then a 9 volt battery would expend 9 Joules moving a Coulomb of electrons. 

Do not worry too much if you haven’t got the hang of Joules and Coulombs. The first, and perhaps most important, relationship between current, voltage, and resistance is called Ohm’s Law, discovered by Georg Simon Ohm and published in his 1827 scientific paper, The Galvanic Circuit Investigated Mathematically. Ohm’s principal discovery was that the amount of electric current through a metal conductor in a circuit is directly proportional to the voltage impressed across it, for any given temperature. Ohm expressed his discovery in the form of a simple equation, describing how voltage, current, and resistance are related:

V = I x R

In this algebraic expression, voltage (V) is equal to current (I) multiplied by resistance ®. Using algebra techniques, we can manipulate this equation into two variations, solving for I and for R, respectively:

I = V/R   AND   R =V/I

Many students prefer to use a memory triangle rather than trying to remember all three equations or even one and manipulating the algebra fro first principles

Figure 2.3 Ohm’s Law triangle

 

Let’s see how these equations might work to help us analyze simple circuits:

Figure 2.4 Electron flow

In the above circuit, there is only one source of voltage (the battery, on the left) and only one source of resistance to current (the lamp, on the right). This makes it very easy to apply Ohm’s Law. If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm’s Law to determine the third.

In this first example, we will calculate the amount of current (I) in a circuit, given values of voltage (V) and resistance ®:

Figure 2.5 Ohms law problem 1

What is the amount of current (I) in this circuit?

 

Note the arrows showing the flow of electrons. Another very important point is established here. In a series circuit, that is a circuit where all the components are connected end to end, the current has the same numeric value wherever the circuit is broken to measure it. In other words, in the above example I = 4A, in the top and bottom connecting wires and even inside the battery and bulb if we could physically invade their space with a measuring instrument or ammeter!

In this second example, we will calculate the amount of resistance ® in a circuit, given values of voltage (V) and current (I):

Figure  2.6 Ohms Law Problem 2

What is the amount of resistance R offered by the lamp?

In the last example, we will calculate the amount of voltage supplied by a battery, given values of current (I) and resistance ®:

Figure 2.7 Ohms Law Problem 3

What is the amount of voltage provided by the battery?

Ohm’s Law is a very simple and useful tool for analyzing electric circuits. It is used so often in the study of electricity and electronics that it needs to be committed to memory by the serious student. For those who are not yet comfortable with algebra, then use the memory triangle! 

REVIEW:

·         Voltage measured in volts, symbolized by the letters ‘V’

·         Current measured in amps, symbolized by the letter “I”.

·         Resistance measured in ohms, symbolized by the letter “R”.

·         Ohm’s Law: V = IR ; I = V/R ; R = V/I

 

An analogy for Ohm’s Law

Ohm’s Law also makes intuitive sense if you apply if to the water-and-pipe analogy. If we have a water pump that exerts pressure (voltage) to push water around a “circuit” (current) through a restriction (resistance), we can model how the three variables interrelate. If the resistance to water flow stays the same and the pump pressure increases, the flow rate must also increase.

If the pressure stays the same and the resistance increases (making it more difficult for the water to flow), then the flow rate must decrease:

If the flow rate were to stay the same while the resistance to flow decreased, the required pressure from the pump would necessarily decrease:

As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons. If you pursue further studies in physics, you will discover this for yourself. Thankfully for the electronics student, the mathematics of Ohm’s Law is very straightforward and simple.

Graphical Representation of Ohms Law

 

 

Figure 2.8 Graphical Ohm’s Law 

The straight-line plot of current over voltage indicates that resistance is a stable, unchanging value for a wide range of circuit voltages and currents. In an “ideal” situation, this is the case. Resistors, which are manufactured to provide a definite, stable value of resistance, behave very much like the plot of values seen above. A mathematician would call their behavior “linear.” 

This linear behavior shows us the graphical behavior of a resistor obeying Ohms Law.

Strictly speaking bulbs and lamps, although we have used them to illustrate some simple problems on Ohms Law are not very linear in resistance because their resistance changes as they got hot. 

Figure 2.9 Diode symbol

 

 

DIODES

 

A diode, literally meaning two electrodes,   is a one way device with a non-linear current –voltage characteristic.  Unlike a resistor, the amount of current through a diode will depend upon ‘which way round’ we apply the voltage.

Figure 2.10

In figure 2.10 ,Vd  is known as the diode turn on voltage it is usually about  0.6 -0.7 volts for a silicon diode. It is  0.2 volts for a germanium diode and even lower for metal-semiconductor or schottky barrier diodes.  So didode turn on voltage depends on the semi-conductor marterial from which the diode is made.

REVIEW:

·         With resistance steady, current follows voltage (an increase in voltage means an increase in current, and visa-versa).

·         With voltage steady, changes in current and resistance are opposite (an increase in current means a decrease in resistance, and visa-verse).

·         With current steady, voltage follows resistance (an increase in resistance means an increase in

·         In resistors current voltage characteristic is linear.

·         In hot bulbs it deviates from linear

·                    In diodes it is so highly non-linear they act as one way devices.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 3: PRACTICAL RESISTORS

Because the relationship between voltage, current, and resistance in any circuit is so regular, we can reliably control any variable in a circuit simply by controlling the other two. Perhaps the easiest variable in any circuit to control is its resistance. This can be done by changing the material, size, and shape of its conductive components for instance; a thin metal filament of a lamp creates more electrical resistance than a thick wire.

Special components called resistors are made for the express purpose of creating a precise quantity of resistance for insertion into a circuit. They are typically constructed of metal wire or carbon, and engineered to maintain a stable resistance value over a wide range of environmental conditions. Unlike lamps, they do not produce light, but they do produce heat as electric power is dissipated by them in a working circuit. Typically, though, the purpose of a resistor is not to produce usable heat, but simply to provide a precise quantity of electrical resistance.

Resistors come in all sorts of values form fractions of an ohm up to 1000 Mega Ohms and with power ratings from typically 1/8th watt to tens or even hundreds of watts.  Resistors come in three basic constructions been made either in wire wound found form using resistance wire usually on a ceramic or similar former the wire might be covered with a protective   layer or alternatively they may be of carbon film or metal/metal oxide film construction. On wire wound types the value in ohms is often physically written on the body of the resistor. With other types a printed color code is used. 

 

 

 

Colour codes

How can the value of a resistor be worked out from the colours of the bands? Each color represents a number according to the following scheme:

Figure 3.1 Resistor Color Codes

Number

Color

0

black

1

brown

2

red

3

orange

4

yellow

5

green

6

blue

7

violet

8

grey

9

white

 

 

 

 

 

 

 

 

 

 

 

Figure 3.2 Colour code worked example

For the resistor shown in figure 3.2, the first band is yellow, so the first digit is 4:The second band gives the SECOND DIGIT. This is a violet band, making the second digit 7. The third band is called the MULTIPLIER and is not interpreted in quite the same way. The multiplier tells you how many noughts you should write after the digits you already have. A red band tells you to add 2 noughts. The value of this resistor is therefore 4 7 0 0 ohms, that is, 4 700 , or 4.7 . Work through this example again to confirm that you understand how to apply the colour code given by the first three bands.

 

 

 

 

 

 

 

The remaining band is called the TOLERANCE band, see figure 3.3. This indicates the percentage accuracy of the resistor value. Most carbon film resistors have a gold-coloured tolerance band, indicating that the actual resistance value is with + or - 5% of the nominal value. Other tolerance colours are:

Tolerance

Colour

±1%

brown

±2%

red

±5%

gold

±10%

silver

Figure 3.3 Resistor Tolerances

When you want to read off a resistor value, look for the tolerance band, usually gold, and hold the resistor with the tolerance band at its right hand end. Reading resistor values quickly and accurately isn’t difficult, but it does take practice!

The actual tolerances of resistors readily available to purchase of the shelf depend on specific tolerance series known as E12 and E24.

E12 and E24 values

If you have any experience of building circuits, you will have noticed that resistors commonly have values such as 2.2 , 3.3 , or 4.7 and are not available in equally spaced values 2 , 3 , 4 , 5 and so on. Manufacturers don’t produce values like these - why not? The answer is partly to do with the fact that resistors are manufactured to percentage accuracy. Look at the table below which shows the values of the E12 and E24 series:

 

 

E12 series
10% tolerance

E24 series
5% tolerance

10

10

11

12

12

13

15

15

16

18

18

20

22

22

24

27

27

30

33

33

36

39

39

43

47

47

51

56

56

62

68

68

75

82

82

91

Figure 3.4 E12 AND E24 Series

Resistors are made in multiples of these values, for example, 1.2 , 12 , 120 , 1.2 , 12 , 120 and so on.

Consider 100 and 120 , adjacent values in the E12 range. 10% of 100 is 10 , while 10% of 120 is 12 . A resistor marked as 100 could have any value from 90 to 110 , while a resistor marked as 120 might have an actual resistance from 108 to 132 . The ranges of possible values overlap, but only slightly.

Further up the E12 range, a resistor marked as 680 might have and actual resistance of up to 680+68=748 , while a resistor marked as 820 might have a resistance as low as 820-82=738 . Again, the ranges of possible values just overlap.

The E12 and E24 ranges are designed to cover the entire resistance range with the minimum overlap between values. This means that, when you replace one resistor with another marked as a higher value, its actual resistance is almost certain to be larger.

From a practical point of view, all that matters is for you to know that carbon film resistors are available in multiples of the E12 and E24 values. Very often, having calculated the resistance value you want for a particular application, you will need to choose the nearest value from the E12 or E24 range.

Some exam boards such as, for example AQA give all the colour codes and tolerances in their data sheets so you don’t always have to worry about learning this stuff and you only need to know about the E12 series.

 

 

 

 

Power rating

We have seen that as a consequence of their action resistors dissipate heat according to P=IV.

A resistor’s ability to lose heat depends to a large extent upon its surface area. A small resistor with a limited surface area cannot dissipate (=lose) heat quickly and is likely to overheat if large currents are passed. Larger resistors dissipate heat more effectively.

Look at the diagram below which shows resistors of different sizes:

which resistor can take the biggest current without overheating?

FIGURE 3.5  Resistor power rating actual physical sizes

In keeping with their physical appearance the most common schematic symbol for a resistor is a small rectangular box, as seen previously. Sometimes, however, the zig zag symbol for a resistor is used

Resistor values in ohms are usually shown as an adjacent number, and if several resistors are present in a circuit, they will be labeled with a unique identifier number such as R1, R2, R3, etc. As you can see, resistor symbols can be shown either horizontally or vertically:

Real resistors look nothing like the zig-zag symbol. Instead, they look like small tubes or cylinders with two wires protruding for connection to a circuit. Here is a sample of some more different kinds and sizes of resistors:

Figure 3.6 Selected wire wound and film resistors

 

Printed codes

Wire wound ceramic coated resistors so made for heat dissipation often have printed codes stamped on them.

High power resistors get hot when used at the limit of their ratings and would quickly

discolour any paint bands, so their values are printed on to them in number form. You

will not find any decimal points on these markings, as they would easily be missed,

4.7kΩ is written as 4K7, where the K stands for thousand Ohms, the unit not being

included since all resistors are measured in Ohms.

The K is also placed where the decimal point would have been. R is used instead of Ω

so 4R7 is 4.7Ω. M is used for millions of Ohms in the same way so 4M7 is

4,700,000Ω.

Tolerance is also given by a letter code, J = 5%, and K = 10% are the two most

common.

 

 

Sometimes it is useful to create a variable resistor. These can have applications as resistive input transducers turning angular position into an output voltage or current.

                  

Variable resistor /potentiometer

Variable resistors must have some physical means of adjustment, either a rotating shaft or lever that can be moved to vary the amount of electrical resistance. Here is a photograph showing some devices called potentiometers, which can be used as variable resistors:

Figure 3.7 Selected variable resistors

Because resistors dissipate heat energy as the electric currents through them overcome the “friction” of their resistance, resistors are also rated in terms of how much heat energy they can dissipate without overheating and sustaining damage. Naturally, this power rating is specified in the physical unit of “watts.” Most resistors found in small electronic devices such as portable radios are rated at Ľ (0.25) watt or less. The power rating of any resistor is roughly proportional to its physical size. Note in the first resistor photograph how the power ratings relate with size: the bigger the resistor, the higher its power dissipation rating. Also note how resistances (in ohms) have nothing to do with size!

Although it may seem pointless now to have a device doing nothing but resisting electric current, resistors are extremely useful devices in circuits. Because they are simple and so commonly used throughout the world of electricity and electronics, we’ll spend some time analyzing circuits composed of nothing but resistors and batteries.    A potentiometer as its name suggests is useful in dividing electric potential or voltage.  If one connects the potentiometer across a battery then the voltage at the slider is determined simply by the ratio of the resistances in the two halves of the potentiometer.

For a practical illustration of resistors’ usefulness, examine the photograph below. It is a picture of a printed circuit board, or PCB: an assembly made of sandwiched layers of insulating phenolic fiber-board and conductive copper strips, into which components may be inserted and secured by a low-temperature welding process called “soldering.” The various components on this circuit board are identified by printed labels. Resistors are denoted by any label beginning with the letter “R”.

Figure 3.8 Modem PCB showing surface mount chip resistors and other components

This particular circuit board is a computer accessory called a “modem,” which allows digital information transfer over telephone lines. There are at least a dozen resistors (all rated at Ľ watt power dissipation) that can be seen on this modem’s board. Every one of the black rectangles (called “integrated circuits” or “chips”) contain their own array of resistors for their internal functions, as well.

Another circuit board example shows resistors packaged in even smaller units, called “surface mount devices.” This particular circuit board is the underside of a personal computer hard disk drive, and once again the resistors soldered onto it are designated with labels beginning with the letter “R”:

Figure 3.9 Computer floppy drive underside showing chip resistors

There are over one hundred surface-mount resistors on this circuit board, which is actually on the underside of a computer floppy disc drive and this count of course does not include the number of resistors internal to the black “chips.” These two photographs should convince anyone that resistors—devices that “merely” oppose the flow of electrons—are very important components in the realm of electronics!

In schematic diagrams, resistor symbols are sometimes used to illustrate any general type of device in a circuit doing something useful with electrical energy. Any non-specific electrical device is generally called a load, so if you see a circuit diagram showing a resistor symbol labeled “load,” especially in a tutorial circuit diagram explaining some concept unrelated to the actual use of electrical power, that symbol may just be a kind of shorthand representation of something else more practical than a resistor.

REVIEW:

·         Devices called resistors are built to provide precise amounts of resistance in electric circuits. Resistors are rated both in terms of their resistance (ohms) and their ability to dissipate heat energy (watts).

 

·         Resistor resistance ratings cannot be determined from the physical size of the resistor(s) in question, although approximate power ratings can.

 

 

 

 

 

 

 

 

 

CHAPTER FOUR: 

MORE CIRCUITS AND RESISTOR CALCULATIONS

Circuit wiring

So far, we’ve been analyzing single-battery, single-resistor circuits with no regard for the connecting wires between the components, so long as a complete circuit is formed. Does the wire length or circuit “shape” matter to our calculations?

When we draw wires connecting points in a circuit, we usually assume those wires have negligible resistance. As such, they contribute no appreciable effect to the overall resistance of the circuit, and so the only resistance we have to contend with is the resistance in the components. Exceptions to this rule exist in power system wiring, where even very small amounts of conductor resistance can create significant voltage drops given normal (high) levels of current.

Knowing that electrically common points have zero voltage drops between them is a valuable troubleshooting principle. If I measure for voltage between points in a circuit that are supposed to be common to each other, I should read zero. If, however, I read substantial voltage between those two points, then I know with certainty that they cannot be directly connected together. If those points are supposed to be electrically common but they register otherwise, then I know that there is an “open failure” between those points.  This will prove invaluable in diagnosing faults in any project circuits you might construct.

 

ESSENTIAL POINTS ON CIRCUIT WIRING:

·         Connecting wires in a circuit are assumed to have zero resistance unless otherwise stated.

·         Wires in a circuit can usually be shortened or lengthened without impacting the circuit’s function—all that matters is that the components are attached to one another in the same sequence.  The exception to this is with circuits which conduct very high frequency alternating currents.

·         Points directly connected together in a circuit by zero resistance (wire) are considered to be electrically common.

·         Electrically common points, with zero resistance between them, will have zero voltage dropped between them, regardless of the magnitude of current (ideally).

·         The voltage or resistance readings referenced between sets of electrically common points will be the same.

·         These rules apply to ideal conditions, where connecting wires are assumed to possess absolutely zero resistance. In real life this will probably not be the case, but wire resistances should be low enough so that the general principles stated here still hold.

.
Resistors in series and potential dividers

As we have already seen for a series circuit, the current flowing is the same at all points. The circuit diagram below shows two resistors connected in series with a 6 V battery:

current the same at all points Figure 4.1.Resistors in series

It doesn’t matter where in the circuit the current is measured; the result will be the same. The total resistance is given by:

In this circuit, Rtotal= 1+1= 2 . What will be the current flowing? The formula is:

Substituting:

Notice that the current value is in mA when the resistor value is substituted in.

The same current, 3 mA, flows through each of the two resistors. What is the voltage across R1? The formula is:

Substituting:

What will be the voltage across R2? This will also be 3 V. It is important to point out that the sum of the voltages across the two resistors is equal to the power supply voltage.  In other word the two series resistors are acting a potential divider. 

The essential circuit of a voltage divider, also called a potential divider, is:

it's a . . . voltage divider!

Figure 4.2 The potential divider

As you can see, two resistors are connected in series. With Vin , which is often the power supply voltage, connected above Rtop . It may help you to remember that Rbottom appears on the top line of the formula because Vout is measured across Rbottom .

Some text books use labels R1 AND R2 for Rbottom  and  Rtop  but unhelpfully some examination questions use R2 AND R1 OR even RA AND RB, hence the more unforgettable and less confusing method which has been adopted here.

Another way of thinking about a potential divider is to reference the negative pole of the battery to 0 volts and draw it at the bottom of the page. Then full maximum (positive) potential will be at the top of the diagram and you can think of climbing up the potential ladder of the resistors rather as counting up rungs of a number ladder. 

Potential divider circuits have important applications in sensor input sub-systems for example when used with LDR’S (Light dependent Resistors) to form light sensors or when used with Thermistors  (see later) to form temperature sensors.  

Resistors in parallel

The next circuit shows two resistors connected in parallel to a 6 V battery:

alternative pathways for current flow    Figure  4.3 Resistors in parallel

Parallel circuits always provide alternative pathways for current flow. Note the resistors are drawn side to side in the diagram not end to end as was the case in the series circuit. The total resistance for the parallel circuit is calculated from:

product over sum formula

This is called the product over sum formula and works for any two resistors in parallel. An alternative more general formula is:

reciprocal formula

This formula can be extended to work for more than two resistors in parallel, but lends itself less easily to mental arithmetic. Both formulae are correct.

What is the total resistance in this circuit?

The current can be calculated from:

How does this current compare with the current for the series circuit? It’s more. This is sensible. Connecting resistors in parallel provides alternative pathways and makes it easier for current to flow. How much current flows through each resistor? Because they have equal values, the current divides, with 6 mA flowing through R1, and 6 mA through R2.

To complete the picture, the voltage across R1 can be calculated as:

This is the same as the power supply voltage. The top end of R1 is connected to the positive terminal of the battery, while the bottom end of R1 is connected to the negative terminal of the battery. With no other components in the way, it follows that the voltage across R1 must be 6 V. What is the voltage across R2? By the same reasoning, this is also 6 V.

ESSENTIAL POINT:

When components are connected in parallel, the voltage across them is the same.

Here is a slightly more complex circuit, with both series and parallel parts:

series parallel combination

Figure 4.4 Circuit with series and parallel resistors

To find the overall resistance, the first step is to calculate the resistance of the parallel elements. You already know that the combined resistance of two 1 resistors in parallel is 0.5 , so the total resistance in the circuit is 1+0.5 = 1.5 . The power supply current is:

This is the current which flows through R1. How much current will flow through R2? Since there are two equally easy pathways, 2 mA will flow through R2, and 2 mA through R3.

The voltage across R1 is given by:

This leaves 2 V across R2 and R3, as confirmed by the calculation for R2:

Again, the sum of the voltages around the circuit is equal to the power supply voltage.

Check through this section carefully. A clear understanding of the concepts involved will help tremendously.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 5: SYSTEMS AND SUB-SYSTEMS 

Although from what you have read  so far you will now have some understanding of how very basic electronic components work, it is often easier to make sense of whole electronic circuits as systems in terms of their over all purpose and structure or major chunks thereof (sub-systems). Indeed this approach has radically changed the study and practice of electronics has changed in recent years.

Previously, electronic circuits were designed by looking at the behaviour of all their individual components such as resistors, capacitors and transistors.

Electronics designers have found that there are fairly standard ways of assembling components which allowed them to produce ‘building blocks’ or ‘system blocks’. In fact as such Engineers have a way of showing the functionality of Electronic gismos without necessarily showing all the complexity. This can be done by the use of what is referred to as    a System Diagram sometimes the word Block is inserted in place of the word System.

Using these building blocks it is possible to choose particular combinations which allow you to build almost any circuit you could wish to.

This is known as a systems approach to electronics. The building blocks are known as subsystems. Those of you who do Computer Studies may have come across a similar concept in Flow Diagrams, which also incidentally comprises part of the A2 content of this book.   

All known subsystems can be divided into one of four categories:

1.      Input subsystems.

2.      Output subsystems.

3.      Processing subsystems.

4.      Driver subsystems

A systems diagram in its simplest form consists of just these three basic elements. You must remember that a power supply will always be present even though it is rarely shown in a systems diagram and a Driver is often required between the Process and Output stages.

 Below Figure 5.1 Systems and sub-systems

 

 

 

 

The arrows connecting the subsystems together show the direction of the energy or information flow. This energy which carries the information is in the form of an electrical signal. The different kinds of signal are looked at later.

Input subsystems usually convert information from the outside world into electrical energy. A few, however, generate a signal independently.

Input subsystems: take information about the outside world from sensors and convert it into an electronic signal which is passed to the next subsystem (usually a process subsystem such as a Comparator or an Amplifier or a Logic stage). This is not true of all input subsystems however because some of them generate their own signal. Two of these are shown below:

 

Pulse Unit: Generates on/off pulses. Adjust the dial to vary the pulse rate

Voltage reference:  generates a very steady d.c. voltage which might be different from that of the power supply.

Signal generator /oscillator : generates sine waves and other time varying signals.

Neither must we forget that each and every sub-system needs powering up by a battery or a power supply in order to its job, but these are rarely if ever shown in system diagrams.

The desk top P.C and its typical input devices can be classically represented by a system diagram:

 

   

Figure 5.2 The desk top P.C. as a system diagram

 

 

The precise circuitry content of each subsystem depends on the job in hand which the system needs to perform.  Take a simple darkness sensor for instance. The input subsystem might contain an LDR (Light dependent resistor) in a potential divider network with a resistor.  The processing subsystem might a circuit to determine what light level (voltage output from divider) to turn on a lamp. Finally the output subsystem might contain a lamp or a circuit to drive the lamp and a lamp.

We now have a good idea about what an electronic system know as a darkness sensor does, without precise knowledge of the circuit detail within.    Thus system diagrams a very good for conveying a basic idea of how something works, or for that matter, the elements or building blocks required to make something work, or perform a particular function, without worrying too much about the detail. 

 

When all is said and done there is really no such thing as a new or novel electronic circuit. The fundamental building blocks of electronics have remained unchanged for some time now. However,   there may be novel ways of stitching these building blocks tighter to solve fundamental, everyday, problems electronically. This forms a fundamental part of much  GCSE and A-level coursework.  

Using a systems approach

 

Simple changes to one sub-system can bring about a huge change in the operation of the system as whole.  Take our darkness sensor, for example. If we change one component in the input sub-system say from an LDR to a Thermistor then our whole System would become a low –temperature indicator!   If we used a microphone in our input sub-system with an appropriate amplifier, our whole system would become a Sound to light converter!  Sensors are input subsystems that monitor changes in the environment. Inverting a Sensor subsystem reverses its operation. For example, a light sensor would become a dark sensor!

REVIEW

·         System Diagrams are a way of showing the functionality of Electronic gismos without necessarily showing all the complexity.

·         The simplest System Diagram has just three sub-systems; input, process and output.  

·         Simply changing a part of one sub-system can fundamentally change the purpose of the system as a whole.

 

 

 

CHAPTER 6: RESITIVE INPUT DEVICES, SENSORS AND SUB-SYSTEMS.

 

Some typical input sub-systems which may find themselves integrated into a resistive potential divider circuit during use are listed in the table below :

Light Sensor:  ( LDR) Measures the amount of light.

Moisture Sensor: Measures the moisture level.

Push Switch: Provides an intermittent ‘on’ switch.

Reed Switch: Provides a switch that operates when a magnet is brought near. 

Rotation Sensor: Measures rotation.

Sound Sensor: Measures the sound level.

Temperature Sensor: (often Thermistor) Measures the temperature.

Tilt Switch: Provides a switch that operates when tilted.

 

The input transducers described in this section and the associated calculations are key exam topics.

 

 

LDRS

Let us examine in more detail the Components and circuit detail required for a light (or darkness) sensor input subsystem. The main component is a specialist resistor known as an LDR or Light Dependent Resistor.  The device contains the semiconductor material Cadmium Sulfide and in some countries and texts may referred to as a CDS or CDS Sensor. 

                                                                     Figure 6.1 Light Dependent Resistors

 

An LDR is an input transducer (sensor) which converts brightness (light) to resistance. It has a resistance which decreases as the brightness of light falling on the LDR increases.

A multimeter can be used to find the resistance in darkness and bright light, these are the typical results for a standard LDR:

·         Darkness: maximum resistance, about 1Mohm.

·         Very bright light: minimum resistance, about 100ohm.

For many years the standard LDR has been the ORP12, now the NORPS12, which is about 13mm diameter. Miniature LDRs are also available and their diameter is about 5mm.

 

 

An LDR may be connected either way round and no special precautions are required when soldering.  A practical investigation of an LDR may be made as follows using a breadboard , a fixed resistor , a 9volt battery and a multimeter.

Figure 6.2 Measurement of LDR characteristic

If you set this up, you will be able to verify the behavior of the LDR in response to various light levels. 

Figure 6.3 LDR circuit arrangement                 Figure 6.4 LDR characteristic

Your experiment will convince you that in a practical input sub-system, one of the resistors in a voltage divider is replaced by an LDR. You may obtain a graph rather like  the one above. It is called a LOG- LOG plot. 

In the circuit below, Rtop is a 10 resistor, and an LDR is used as Rbottom :

it's a . . . voltage divider!

Figure 6.5 Dark sensor

Suppose the LDR has a resistance of 500 , 0.5 , in bright light, and 200 in the shade (these values are reasonable).

When the LDR is in the light, Vout will be:

In the shade, Vout will be:

In other words, this circuit gives a LOW voltage when the LDR is in the light and a HIGH voltage when the LDR is in the shade. The voltage divider circuit gives an output voltage which changes with illumination.

A sensor subsystem which functions like this could be thought of as a ‘dark sensor’ and could be used to control lighting circuits which are switched on automatically in the evening.  The HIGH voltage out is useful for driving LOGIC systems which we will meet later,     

.

Here is the voltage divider built with the LDR in place of Rtop :

it's a . . . voltage divider!

Figure 6. 6 Light sensor

What effect does this have on Vout ?

The action of the circuit is reversed. that is, Vout becomes HIGH when the LDR is in the light, and LOW when the LDR is in the shade. Substitute the appropriate values in the voltage divider formula to convince yourself that this is true.

You will realize that an LDR positioned hence in a potential divider can be used as a LIGHT SENSOR rather than a darkness sensor.

.
Temperature sensors

Replacing the LDR or light sensor with a temperature sensor would make an input sub-system with a very different function. Strangely, fundamentally the same resistive potential divider arrangement is used when using the common temperature sensor based on a temperature-sensitive resistor and  called a thermistor. There are several different types:

Figure 6.7 Various thermistors 

The resistance of most common types of thermistor decreases as the temperature rises. They are called negative temperature coefficient, or ntc, thermistors. Note the -t° next to the circuit symbol. A typical ntc thermistor is made using semiconductor metal oxide materials. (Semiconductors have resistance properties midway between those of conductors and insulators.) As the temperature rises, more charge carriers become available and the resistance falls.

Although less often used, it is possible to manufacture positive temperature coefficient, or ptc, thermistors. These are made of different materials and show an increase in resistance with temperature.

How could you make a sensor circuit for use in a fire alarm? You want a circuit which will deliver a HIGH voltage when hot conditions are detected. You need a voltage divider with the ntc thermistor in the Rtop position:

it's a . . . voltage divider!Figure 6.8 ‘Hot’ sensor

How could you make a sensor circuit to detect temperatures less than 4°C to warn motorists that there may be ice on the road? You want a circuit which will give a HIGH voltage in cold conditions. You need a voltage divider with the thermistor in place of Rbottom :

it's a . . . voltage divider!Figure 6.9 ‘Cold’ sensor

This last application raises an important question: How do you know what value of Vout you are going to get at 4°C?

To answer this question, you need to estimate the resistance of the thermistor at 4°C.

Lots of different types of thermistor are manufactured and each has its own characteristic pattern of resistance change with temperature. The diagram below shows the thermistor characteristic curve for one particular thermistor:

Figure 6.10 Thermistor  characteristic

On the y-axis, resistance is plotted on a logarithmic scale. This is a way of compressing the graph so that it is easier to see how the resistance changes. Between 100 and 1000 , each horizontal division corresponds to 100 . On the other hand, between 1000 and 10000 , each division corresponds to 1000 . Above 10000 , each division respresents 10000 .

As you can see, this thermistor has a resistance which varies from around 70  at 0°C to about 1 at 100°C. Suppliers catalogues usually give the resistance at 25°C, which was 20 in this case. Usually, catalogues also specify a ‘Beta’ or ‘B-value’. When these two numbers are specified, it is possible to calculate an approximate value for the resistance of the thermistor at any particular temperature from the equation:

Where:

RT is the resistance at temperature T in Kelvin (= °C +273)
R
T0 is the resistance at a reference temperature T0 in Kelvin. When the reference temperature is 25°C, T0 = 25+273. e is the natural logarithm base, raised to the power in this equation.B is the B-value specified for this thermistor.

You don’t need to think about applying this equation at the moment, but it is useful to know that the information provided in catalogues is sufficient to allow you to predict thermistor performance. With RT0 = 20 and B =4200, resistance changes from 0 to 10°C are as follows:

Figure 6.11 Thermistor  characteristic 0-10C 
From the graph, the resistance at 4°C can be estimated as just a little less than 60 . By calculation using the equation, the exact value is 58.2 . In the A-level examination you will most likely only have to estimate thermistor values from a given graph. Precise calculation will not be required.

KEY POINT:

The biggest change in Vout from a voltage divider is obtained when Rtop and Rbottom are EQUAL in value.

What this means is that selecting a value for Rtop close to 58.2 will make the voltage divider for the ice alert most sensitive at 4°C. The nearest E12/E24 value is 56 . This matters because large changes in Vout make it easier to design the other subsystems in the ice alert, so that temperatures below 4°C will be reliably detected.

Sensor devices vary considerably in resistance and you can apply this rule to make sure that the voltage dividers you build will always be as sensitive as possible at the critical point.

Thermistors turn up in more places than you might imagine. They are extensively used in cars, for example in:

·         electronic fuel injection, in which air-inlet, air/fuel mixture and cooling water temperatures are monitored to help determine the fuel concentration for optimum injection.

·         air conditioning and seat temperature controls.

·         warning indicators such as oil and fluid temperatures, oil level and turbo-charger switch off.

·         fan motor control, based on cooling water temperature

·         frost sensors, for outside temperature measurement

·         acoustic systems

·         to measure air flow, for instance in monitoring breathing in premature babies.

 

 

 

 

 

 

Rotary Potentiometer as an Angle Sensor 

In industrial electronics potentiometers are often used as angle and position sensors.

A typical input subsystem for this purpose is shown below:  

 

Figure 6.12 Angle Sensor

This block uses a potentiometer or variable resistor as an angle sensor.  If you wanted, you could attach a large knob or disc to the potentiometer marked in degrees.  Or you could use it to measure the position of something else using a gear wheel or pulley.  The 1k resistor is just for protection in case the output gets shorted but is not really necessary.

 

 

The output voltage at the slider will be directly proportional to the angle the slider is turned or rotated through if the potentiometer has good linearity.

 

 

Sound sensors

Another name for a sound sensor is a microphone. The diagram shows  a cermet microphone:

cermet microphone

Figure 6.13 Cermet (Electret ) microphone

Cermet’ stands for ‘ceramic’ and ‘metal’. A mixture of these materials is used in making the sound-sensitive part of the microphone. To make them work properly, cermet microphones need a polarizing voltage, usually around 1.5 V across them. A suitable circuit for use with a 9 V supply is:

 

microphone circuit     

Figure 6.14 Microphone  input circuit

The 4.7  and 1  resistors make a voltage divider which provides 1.6 V across the microphone. Sound waves generate small A.C. or time varying changes in voltage, usually in the range 10-20 mV. To isolate these small signals from the steady 1.6 V, a capacitor is used. Capacitors are described later but basically can either be used as D.C. blocking components or in timing circuits.

Signals from switches

When a switch is used to provide an input to a circuit, pressing the switch usually generates a voltage signal. It is the voltage signal which triggers the circuit into action. What do you need to get the switch to generate a voltage signal? . . . You need a voltage divider. The circuit can be built in either of two ways:

more voltage dividers

Figure 6.15 Logic signals from switches

The pull down resistor in the first circuit forces Vout to become LOW except when the push button switch is operated. This circuit delivers a HIGH voltage when the switch is pressed. A resistor value of 10 is often used.

In the second circuit, the pull up resistor forces Vout to become HIGH except when the switch is operated. Pressing the switch connects Vout directly to 0 V. In other words, this circuit delivers a LOW voltage when the switch is pressed.

In circuits which process logic signals, a LOW voltage is called ‘logic 0’ or just ‘0’, while a HIGH voltage is called ‘logic1’ or ‘1’. These voltage divider circuits are perfect for providing input signals for logic systems.

 

 

 

 

 

 

 

 

CHAPTER SEVEN:

INTRODUCTION TO LOGIC DEVICES AND CIRCUITS; A SPECIAL CLASS OF PROCESS SUB-SYSTEMS.  

 

Imagine we have a sensor whose output goes to zero or a very low voltage when it is activated. We   could imagine this might be a tripwire for a burglar.  Zero volts cannot directly activate an alarm so we might want to find some way of converting this zero or LOW (conveniently called Logic O in a Logic system) into a high voltage, say nearer the positive terminal voltage of the battery.  The Logic component or sub-system to do this is called an Inventor Gate or more commonly a NOT gate.  Our logic gate would be changing then the signal from an input sub-system so as such could be regarded as a special class of process sub-system. 

  

In the electronics we have met so far we have considered a full range of voltage levels from 0 to the battery terminal voltage.  This range is continuous and called analogue.

Rather like switches, the operation of Logic gates only uses  two discrete voltage levels, fully off or O and fully ON, or full supply voltage which in Logic terms we call LOGIC 1 . Logic gates therefore with only two possible states are said to work according to the Binary System of Arithmetic.  In fact for Electronics training purposes Logic gates are often represented by combinations of switches or relays (special electromagnetic switches which we shall meet later). However in practice logic gates contain solid state components (that is with no moving parts) and are implemented using various types of transistors and diodes or metal oxide semiconductor devices. 

 

The behavior of Logic Gates can be described to some extent by their symbols but more accurately by their Truth Tables or Boolean expressions. Boolean expressions are a feature of Boolean algebra a special type of Arithmetic relevant to Logic gates and Logic Systems. 

NOT GATE TRUTH TABLE   Image PreviewFigure 7.1 NOT gate symbol

INPUT

OUTPUT Q

A

NOT A

  0

1

1

0

Figure 7.2 NOT gate truth table

 

Not Gate Boolean Algebra:         

 

                                                                         _

Q = A

 

(The bar over the top means the opposite of the logic level of A.)

 

 

                              It reads ‘Q = A bar’.

 

 

AND GATES

Let us consider another problem. Imagine we want to make a very simple burglar alarm. We have an ‘arming’ switch for the alarm and a door sensor both giving high voltage outputs (LOGIC 1’S).  We do not want the alarm to go off during the day when we are opening and closing the day if we are in, so the arming switch is in the off (LOGIC 0) position.  At night when the alarm is armed, the condition of someone forcing the door needs to set off the alarm. In other words ‘armingAND ‘door forcing’ both need to give LOGIC 1 signals at an output together to set to set off the alarm.  The logic gate or sub-system to bring about this effect is called an AND gate.

Type

Distinctive shape

Rectangular shape

AND

AND symbol

AND symbol

 

Like a letter D in AND

 

Figure 7.3 AND GATE Symbol

Figure 7.4 AND GATE Truth Table

INPUT

OUTPUT Q

A

B

A AND B

0

0

0

1

0

0

0

1

0

1

1

1

Switch circuit diagram for AND gateFigure 7.5 AND gate switch

 

In figure 7.5, the switch circuit diagram for AND gate, comprising two normally open ‘push’ swithces in series.  The left hand connection goes to a battery or power supply positive terminal.

 

 

Boolean Algebra:      This is a way of writing an equation to represent an AND gate.

 

Q = A . B       

 

We borrow the dot from conventional algebra due to the similarity between multiplication and the AND process.  The table above could be a multiplication table for A × B, but it is important to remember that Q = A AND B is what is being represented here.

 

 

 

Switch circuit diagrams may help some students understand logic gates.

To do this you need think of the input action as being applied to the switches. A firm press is made to the switch corresponding to an INPUT at that letter, whereas no press is like LOGIC 0. Just remember with real logic gates the press at the input is given by a voltage usually +5 or sometimes +15 not by someone’s finger! Relays are electromagnetic switches that can be activated by voltage in this way and in days gone by were actually used to implement logic!   

Consider a third situation.  We want a burglar alarm which will alarm if a burglar forces EITHER a door OR a window OR BOTH (It could even cope with two burglars at once!). Both our door and window sensors both give LOGIC 1 when forced.  The logic gate to do this job is called an OR gate. 

OR

OR symbol

OR symbol

Figure 7.6

Note the distinctive shape of the OR GATE SYMBOL in figure 7.6. A good memory aid is to think of the word AR(RO)W which contains OR and describes the arrow head shape!

 

 

 

 

 

Figure 7.7 The truth table of an OR gate

INPUT

OUTPUT Q

A

B

A OR B

0

0

0

1

0

1

0

1

1

1

1

1

 

 

Boolean algebra:      

 

Q = A + B      

 

 

Switch circuit diagram for OR gate

Figure 7.8 Switch circuit diagram for OR gate

Four other types of Logic gate are also available. Try to dream up sensor or alarm situation input situations where these might be useful yourselves.  The first of these is the NAND gate NAND standing for NOT AND, it is rather like having an AND gate with a NOT gate connected to its output.   

 

NAND

Note shape is like AND but with a small negation circle or ‘bubble’ on the output.

 

 That is, the output is 1 when NOT (A AND B are 1), as shown in the truth table.

 

 

Switch circuit diagram of NAND gateFigure 7.9 Switch circuit of NAND gate

INPUT

OUTPUT

A

B

A NAND B

0

0

1

 1

0

1

 0

1

1

  1

1

0

 Figure 7.10 Truth Table NAND GATE

 

Switch circuit diagram of NAND gate. Note this time normally closed push swithces are used.

 

Note how the truth table outputs are the opposites (NOTS) of the AND GATE TABLE.

 

Boolean algebra:   

 

                                                                  ____

    Q = A . B               

 

(Q equals A AND B all bar.)

 

 

NOR GATE

Similarly, the NOR gate is the NOT of an OR gate. That is, the output is 1 only when both inputs are 0, as shown in the truth table.

 

INPUT

OUTPUT Q

A

B

A NOR B

0

0

1

1

0

0

0

1

0

1

1

0

Switch circuit diagram of NOR gate

Figure 7.11 Switch circuit diagram of NOR gate

 

 

Figure 7.12 Truth Table NOR gate 

 

           

Boolean algebra:      

 

                                           _____

                                   Q = A + B       

 

(Q equals A OR B all bar.)

 

We say ‘all bar’ when the bar is over the whole term.

 

 

 

XOR and XNOR gates

These are the only other logic gates we will meet - XOR (exclusive-OR) and XNOR (exclusive-NOR).

INPUT

OUTPUT Q

A

B

A XOR B

0

0

0

0

1

1

1

0

1

1

1

0

The XOR is a ‘stricter’ version of the OR gate. Rather than all  owing the output to be 1 when either one or both of the inputs are 1, an XOR gate has a 1 output only when only one input is 1. Thus, it has the truth table shown to the right. This can also be interpreted (for a two-input gate) as “Output= LOGIC 1 , when the inputs are different”.

Figure 7.13 Truth Table XOR

 

 

XOR  Boolean Algebra:      

      

Q = A Ĺ  B    

 

(Q equals A EXOR B.)

 

XNOR GATE

INPUT

OUTPUT Q

A

B

A XNOR B

0

0

1

1

0

0

0

1

0

1

1

1

XNOR is an inverted version of the XOR gate. Thus, it has the truth table shown to the right. This can also be interpreted as

“ Output =Logic 1 when the inputs are same”. Its other name is the PARITY GATE because it outputs 1 when inputs come in equal pairs.

Figure 7.14 Truth Table XNOR

Boolean algebra:   

 

                                                                         _____     

Q = A Ĺ  B    

 

(Q equals A EXNOR B.)

 

 

 

                                               

 

 

 

 

 

The simple logic gates above can also be combined to form more complicated Boolean logic circuits. Logic circuits are often classified in two groups: combinatorial logic, in which the outputs are instant continuous-time functions of combinations at the inputs, and sequential logic, in which the outputs depend on information stored by the circuits as well as on the inputs and information may move fast or more slowly in a step-wise manner through the system. We will meet Combinatorial Logic later in this Chapter.

Some aspects of sequential logic will be dealt with elsehwere in the book.   

An alternative summary of the ‘electronic’ action of the common logic families can be seen in the table, FIGURE 7.15.

 

 

OR

Any high input will drive the output high

NOR

Any high input will drive the output low

AND

Any low input will drive the output low

NAND

Any low input will drive the output high

 

 

 

Figure 7.15 LOGIC SUMMARY

TABLE

 

 

Introduction to Combinatorial Logic: Making Gates from NAND gates

It is more economical in cost, power consumption and space to make circuits from just one kind of chip since logic chips contain 4 or 6 logic gates and many circuits are made up of just NAND gates.  Let us look how:

Figure 7.16 NAND gate

The two inputs of a NAND gate connected together make the NAND gate into a NOT gate, see figure 7.16

In figure 7.17 the output of a NAND gate is inverted by the NOT gate to produce the output of an AND gate. 

Figure 7.17 NAND and NOT in series

Figure 7.18  NAND/NOT Combination Truth Table 

A

B

C

Q

0

0

1

0

0

1

1

0

1

0

1

0

1

1

0

1

Now look at the circuit in figure 7.19

 

Figure 7.19 Three  NAND CIRCUIT 

By working through logically and finding what the intermediate outputs C and D are,

you should be able to solve for Q.

 

 

 

Try working the other way round; look at the truth table in figure 7.20.

 

A

B

X

Y

Q

0

0

1

1

0

0

1

1

1

0

1

0

1

1

0

1

1

0

1

1

Two NAND gates used to simulate the AND gate. The truth table shows how this happens the second NAND gate acts as an

 

inverter because one input is held at logic 1

 

Figure 7.20 Two NAND Truth Table 

Now try to draw the logic diagram.  It is important you master this, you will be tested on these concepts in you’re a level exam. You will notice that there are two ways to make a NAND gate act as an Inverter .One is as in this example by holding one of its inputs at Logic 1. This can be done by connecting it directly to the +ve supply rail. The second way is by connecting both inputs of the NAND GATE together.    

Introduction to Boolean algebra

Boolean algebra does the same job as a truth table, but is briefer to use and has symbols.  A Boolean expression tells us what condition will give an output of 1.

In Boolean algebra it is traditional but not essential to refer to the output logic level of a gate as a capital letter Q.

For our NOT gate  Image Preview the Boolean expression is:

 

    Figure 7.21 NOT Boolean

The symbol Ā is pronounced “A-bar”, and means that the state Q is opposite to the state Q.  So the statement says “Q is equal to NOT A”.  This means that the output Q is logic 1 when A is logic 0. 

Remember if you are not sure of this you can check the NOT truth table in figure 7.2.

AND GATE BOOLEAN

For an AND gate the Boolean expression is:

  Figure 7.22 AND Boolean

The dot between the A and the B mean that both A AND B have to be 1 for Q to be 1.  The expression is pronounced, “Q equals A dot B”.  Remember the equivalent truth table is:

A

B

Q

0

0

0

1

0

0

0

1

0

1

1

1

 

For the OR gate the Boolean expression is:

    Figure 7.23 OR Boolean

This is pronounced, “Q is equal to A OR B” and remember the truth table is:

A

B

Q

0

0

0

1

0

1

0

1

1

1

1

1

 

 

 

Practical Logic Gates

Perhaps the most common family of Logic Gates in use by Electronics Engineers today is the 7400 series of TTL I.C.’S (transistor/transistor logic integrated circuits). This family of logic operates from a +5 Volt D.C. supply rail and there are to be found multiple logic gates provided inside each I.C. Package. The I.C. packages, sometimes affectionately called just CHIPS, after the notion of the silicon chip, themselves contain multiple gates You are not obliged to use all the gates in any one package if your circuit design does not call for this, but it is advisable to connect all inputs of unused gates to 0 volts, sometimes referred to as Earth or Ground.         

 

The 7400 chip, containing four NAND's. The two additional contacts supply power (+5 V) and connect the ground.   Figure 7.24 Logic gate 14 Pin DIL

 

The example shown above is the SN 7400N quad NAND gate. Such packages are known as 14 pin D.I.L (as you can see there are two pairs of seven pins in a parallel line).

You will not be asked to recall manufactures I.C. numbering systems or pin connection numbers in any A-level examination.    It is necessary however to be able to use manufacturers’ catalogues and data sheets for practical and project work. Note how pin1 of the I.C. is always located BELOW the left of the edge dimple when looking down on the chip from above. In some I.C.S it   is also marked with a brown or black spot.  

Although we have said that logic 0 is equivalent to 0volts and logic 1 to a high voltage or full supply voltage, different families of logic chips interpret practical voltages in different ways. Besides TTL logic it is possible you may also meet CMOS.   The table shows how the two different families interpret voltages at their INPUT terminals:

Technology

L voltage

Logic 0

H voltage

Logic 1

Notes

CMOS

0V to VCC/2

VCC/2 to VCC

VCC = supply voltage

Usually 5-15 volt.

TTL

0V to 0.8V

2V to VCC

VCC is 4.75V to 5.25V

Figure 7.25 Table of CMOS and TTL operating voltages

Common Basic Logic ICs

CMOS

TTL

Function

4001

7402

Quad two-input NOR gate

4011

7400

Quad two-input NAND gate

4049

7404

Hex NOT gate (inverting buffer)

4070

7486

Quad two-Input XOR gate

4071

7432

Quad two-input OR gate

  4077

74266

Quad two-input XNOR gate

4081

7408

Quad two-input AND gate

 

 

Figure 7.26

CMOS logic ICs, including gates with more than two inputs, are described in maufacturers’ catalogues as  4000 series.

You may find the table above very useful if you are contemeplating using Logic I.C.’S in your Course work. Although only two input gates have been dealt with here it is possible to get gates with more inputs for instance 3 and 4 input AND and OR gates are quite common. You might be able to relaise they would be useful in a more sophistaicated burglar alram with multiple input sensors. The exception is of course the NOT gate which only ever has one input!   

REVIEW

·         Logic operates with only 2 states or levels, known as Binary.  Logic 0 = 0volts, Logic 1 is equivalent to +ve supply rail or greater than some fraction of it depending on logic family.  

·         Basic logic gates are NOT, AND, OR , NAND, NOR, EX-OR AND EX-NOR.

·         Basic logic gates can be described by symbols, thruth tables and Boolean algebra expressions.  You must commit their functions to memory.

·         Combinations of gates can be made to replace single gates.

·         Combinations of NAND gates are very useful.

·         The most common logic families are TTL and CMOS.

·         Logic chips contain multiple gates

·         Unused inputs must be grounded

·         Logic gates may have two or more inputs except for NOT gates which have only one.

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER EIGHT:  TRANSDUCER DRIVER SUBSYSTEMS AND CURRENT AMPLIFIERS

In Chapter Seven we saw   how Logic gates may be used amongst other things to provide an output related in someway to inputs from one or more voltages or sensors, as may be required in a burglar alarm for example. We also talked of the output Q from a Logic being either Logic 1 or Logic 0. We can see how the presence of a voltage output (Logic1) might be used to theoretically be used to activate a lamp or alarm.   However, is a logic gate strong enough in practice to activate a powerful alarm bell?

The answer is no!  Logic gates cannot give out very high currents only a few tens of milliamps at the most. A powerful alarm bell may take several amps to operate.

The solution is to employ an extra sub-system known as a transducer driver or current amplifier. We have two main choices. Either we can use a three terminal electronic device called a bipolar transistor or an even more efficient device called a MOSFET (metal oxide silicon field effect transistor).

The Bipolar Transistor

 

Go to fullsize imageGo to fullsize imageAssorted transistors

EnlargeFigure 8.1 Bipolar tansistors

The diagrams show some typical transistors.  The one on the left is a NPN transistor and has been positioned over a drawing of its circuit symbol.

 

 

 

The transistor is a three terminal solid state semiconductor device that can be used for amplification, switching and  voltage stabilization.

TRANSISTOR ACTION

A Bipolar Transistor essentially consists of a pair of PN Junction Diodes that are joined back-to-back. This forms a sort of a sandwich where one kind of semiconductor is placed in-between two others. There are therefore two kinds of bipolar sandwich, the NPN and PNP varieties. The three layers of the sandwich are conventionally called the Collector, Base, and Emitter. The reasons for these names will become clear later once we see how the transistor works.

Figure 8.2 Transistor structure and symbols

Some of the basic properties exhibited by a Bipolar Transistor are immediately recognizable as being diode-like. However, when the ‘filling’ of the sandwich is fairly thin some interesting effects become possible that allow us to use the Transistor as an amplifier or a switch. To see how the Bipolar Transistor works we can concentrate on the NPN variety. Most A-level syllabuses only deal with circuits using NPN transistors but you will not be penalized if you use a PNP transistor in your coursework!



 
The diagram above shows the energy levels in an NPN transistor when there are no  externally applying any voltages. We can see that the arrangement looks like a back-to-back pair of PN Diode junctions with a thin P-type filling between two N-type slices of ‘bread’. In each of the N-type layers conduction can take place by the free movement of electrons in the conduction band. In the P-type (filling) layer conduction can take place by the movement of the free holes in the valence band. However, in the absence of any externally applied electric field, we find that depletion zones form at both PN-Junctions, so no charge wants to move from one layer to another.

Figure 8.4 Biased Collector-Base junction

 

 



Looking at figure 8.4, we can see what happens when we apply a moderate voltage between the Collector and Base parts of the transistor. The polarity of the applied voltage is chosen to increase the force pulling the N-type electrons and P-type holes apart. (i.e. we make the Collector positive with respect to the Base.) This widens the depletion zone between the Collector and base and so no current will flow. In effect we have reverse-biased the Base-Collector diode junction. The precise value of the Base-Collector voltage we choose doesn’t really matter to what happens provided we don’t make it too big and blow up the transistor! So for the sake of example we can imagine applying a 10 Volt Base-Collector voltage.

 

If we apply a tiny forward bias to the base emitter junction, big changes will happen.

 



The relatively small Emitter-Base voltage, figure 8.4 , whose polarity is designed to forward-bias the Emitter-Base junction ‘pushes’ electrons from the Emitter into the Base region and sets up a current flow across the Emitter-Base boundary. Once the electrons have managed to get into the Base region they can respond to the attractive force from the positively-biased Collector region. As a result the electrons which get into the Base move swiftly towards the Collector and cross into the Collector region. Hence we see a Emitter-Collector current whose magnitude is set by the chosen Emitter-Base voltage we have applied. To maintain the flow through the transistor we have to keep on putting ‘fresh’ electrons into the emitter and removing the new arrivals from the Collector. Hence we see an external current flowing in the circuit.

The precise value of the chosen Emitter-Base voltage isn’t too important to our argument here, but it does determine the amount of current we’ll see. For the sake of example we’ve chose half a volt although the generally accepted figure for turn on voltage is 0.6-.7 volt.  Remember silicon diodes?  Since the Emitter-Base junction is a PN diode we can expect to see a current when we apply forward voltages of this sort of size. In practice with a Bipolar transistor made using Silicon we can expect to have to use an Emitter-Base voltage in the range from around a half volt up to almost one volt. Higher voltages tend to produce so much current that they can destroy the transistor!

It is worth noting that the magnitude of the current we see isn’t really affected by the chosen Base-Collector voltage. This is because the current is mainly set by how easy it is for electrons to get from the Emitter into the Base region. Most (but not all!) the electrons that get into the Base move straight on into the Collector provided the Collector voltage is positive enough to draw them out of the Base region. That said, some of the electrons get ‘lost’ on the way across the Base. This process is illustrated  below:

Figure 8.5 Some electrons fall into hole

 

 



As we can see from figure 8.5, some of the free electrons crossing the Base encounter a hole and ‘drop into it’. As a result, the Base region loses one of its positive charges (holes) each time this happens. If we didn’t do anything about this we’d find that the Base
potential would become than the Emitter Current more negative (i.e. ‘less positive’ because of the removal of the holes) until it was negative enough to repel any more electrons from crossing the Emitter-Base junction. The current flow would then stop.

To prevent this happening we use the applied Emitter-Base voltage to remove the captured electrons from the Base and maintain the number of holes it contains. This has the overall effect that we see some of the electrons which enter the transistor via the Emitter emerging again from the Base rather than the Collector. For most practical Bipolar Transistors we keep the base region part of the sandwich really narrow and so only about 1% of the free electrons which try to cross Base region get caught in this way. Hence we see a Base Current, IB, which is typically around one hundred times smaller
, IE.

 

   Figure 8.6 Current gain (Beta) view of transistor

 



Viewed from the outside world we can describe the transistor’s behavior in terms of a Current Gain, Beta. This is defined in terms of the ratio of the number of electrons which manage to cross the transistor to those which get caught. We can now treat the transistor as a Current Amplifier since when we put ‘in’ (i.e. into the Base) a current, IB, we get ‘out’ (i.e. from the Emitter and Collector) a current, IC or IB, which is much larger and whose value we can control by altering IB.  We are now in the business of being able to use the transistor as a switch or current amplifier.

Figure 8.7 Conventional view of transistor



This leads us to the conventional view of Bipolar Transistors as they are represented in most electronics text books. The diagram above shows two changes: We now refer the Collector potential to the Emitter (VCE) rather than to the Base, and we now represent the current in conventional terms - passing from positive to negative. Since the precise Collector voltage doesn’t have much effect on the currents, moving the place we reference it from isn’t very important and this new view is more convenient in practice. Changing to conventional (positive to negative) current flow allows us to fit in with the normal view of electronics. Note also that, for simplicity, we can normally assume that the values of the Collector and Emitter currents are essentially identical since they only differ by a percent or so.

By remembering that the Base-Emitter is a forward biased diode junction and taking the above description into account we can formulate two rough ‘rules of thumb’ for the behavior of a Bipolar Transistor when using it as an amplifier, etc. A more precise picture is got at by looking up the current gain HFE in a manufacturers’ catalogue. These vary from about 20 -1000. They are generally lower for power transistors and higher for small signal low current transistors. 

 

·         The Base-Emitter voltage, VBE will always be about half to 0.7 volt.

·         The currents, IE = IC = 100×IB

·          More accurately IC = HFE  x IB

 

Types of transistor

NPN and PNP transistor symbols

Figure 8.8

Transistor circuit symbols

As we have seen there are two types of standard transistors, NPN and PNP, with different circuit symbols. The letters refer to the layers of semiconductor material used to make the transistor. Most transistors used today are NPN because this is the easiest type to make from silicon. This page is mostly about NPN transistors and if you are new to electronics it is best to start by learning how to use these first.

The leads are labeled base (B), collector (C) and emitter (E).     Below: Figure 8.9

                                                                                                      
 

 

transistor currentsPractical Transistor currents

Figure 8.9 illustrates the fact that there is no need to use two batteries as in our theoretical explanation. Properly chosen resistors do the trick. The diagram shows the two current paths through a transistor. You can build this circuit with two standard 5mm red LEDs and any general purpose low power NPN transistor (typical manufactures’ codes being; BC108, BC182 or BC548 for example).

As we have seen from the theory, the small base current controls the larger collector current.

When the switch is closed, a small current will flow into the base (B) of the transistor. It is just enough to make LED B glow dimly. The transistor amplifies this small current to allow a larger current to flow through from its collector (C) to its emitter (E). This collector current is large enough to make LED C light brightly.

When the switch is open no base current flows, so the transistor switches off the collector current. Both LEDs are off.

·         Key Point A transistor amplifies current and can be used as a switch.

This arrangement where the emitter (E) is in the controlling circuit (base current) and in the controlled circuit (collector current) is called common emitter mode. It is the most widely used arrangement for transistors so it is the one to learn first.
                                                                                                             Figure 8.10             

Functional model of NPN transistor

Functional model of an NPN transistor

You may have found the operation of a transistor difficult to understand in terms of its internal structure. If so, it may be more helpful to use the functional model figure 8.10:

·         The base-emitter junction behaves like a diode.

·         A base current IB flows only when the voltage VBE across the base-emitter junction is 0.7V or more.

·         The small base current IB controls the large collector current Ic.

·         Ic = hFE × IB   (unless the transistor is full on and saturated)
hFE is the current gain (strictly the DC current gain), a typical value for hFE is 100 (it has no units because it is a ratio)

·         The collector-emitter resistance RCE is controlled by the base current IB:

    • IB = 0   RCE = infinity   transistor off
    • IB small   RCE reduced   transistor partly on
    • IB increased   RCE = 0   transistor full on (‘saturated’)

Additional notes:

·         A resistor is needed in series with the base connection to limit the base current IB and prevent the transistor being damaged.

·         Transistors have a maximum collector current Ic rating.

·         The current gain hFE can vary widely, even for transistors of the same type!

·         A transistor that is full on (with RCE = 0) is said to be ‘saturated’.

·         When a transistor is saturated the collector-emitter voltage VCE is reduced to almost 0V.

·         When a transistor is saturated the collector current Ic is determined by the supply voltage and the external resistance in the collector circuit, not by the transistor’s current gain. As a result the ratio Ic/IB for a saturated transistor is less than the current gain hFE.

·         The emitter current IE = Ic + IB, but Ic is much larger than IB, so roughly IE = Ic.

 

Darlington pair

Figure 8.11

Darlington pair

This is two transistors connected together so that the current amplified by the first is amplified further by the second transistor. The overall current gain is equal to the two individual gains multiplied together:

Darlington pair current gain, hFE = hFE1 × hFE2
(hFE1 and hFE2 are the gains of the individual transistors)

This gives the Darlington pair a very high current gain, such as 10000, so that only a tiny base current is required to make the pair switch on.

Figure 8.12 Darlington Pair as a touch switch

 

Using a transistor as a switch to control large currents 

When a transistor is used as a switch it must be either OFF or fully ON. In the fully ON state the voltage VCE across the transistor is almost zero and the transistor is said to be saturated because it cannot pass any more collector current Ic. The output Protection diode for a relaydevice switched by the transistor is usually called the ‘load’.

 The power developed in a switching    transistor is very small:

·          

·         Figure 8.12 Transistor relay driver with protection diode

 

·         In the OFF state: power = Ic × VCE, but Ic = 0, so the power is zero.

 

 

·         In the full ON state: power = Ic × VCE, but VCE = 0 (almost), so the power is very small.

This means that the transistor should not become hot in use and you do not need to consider its maximum power rating. The important ratings in switching circuits are the maximum collector current Ic(max) and the minimum current gain hFE(min). The transistor’s voltage ratings may be ignored unless you are using a supply voltage of more than about 15V.   A much larger current can be controlled or switched by the relay contacts.

Protection diode

If the load is a motor, relay or solenoid (or any other device with a coil) a diode must be connected across the load to protect the transistor (and chip) from damage when the load is switched off. The diagram shows how this is connected ‘backwards’ so that it will normally NOT conduct. Conduction only occurs when the load is switched off, at this moment current tries to continue flowing through the coil and it is harmlessly diverted through the diode. Without the diode no current could flow and the coil would produce a damaging high voltage ‘spike’ in its attempt to keep the current flowing.

When to use a relay to drive an output device

Relay, photograph © Rapid Electronics

Relay, photograph © Rapid Electronics

Figure 8.13

 

Relays

  

Transistors cannot switch AC or high voltages (such as mains electricity) and they are not usually a good choice for switching large currents (> 5A). In these cases a relay will be needed, but note that a low power transistor may still be needed to switch the current for the relay’s coil! Relays use an electromagnetic coil to move the poles of a switch when powered. There are three pairs of connections known as common, normally open and normally closed.

 

Advantages of relays:

·         Relays can switch AC and DC, transistors can only switch DC.

·         Relays can switch high voltages, transistors cannot.

·         Relays are a better choice for switching large currents (> 5A).

·         Relays can switch many contacts at once.

Disadvantages of relays:

·         Relays are bulkier than transistors for switching small currents.

·         Relays cannot switch rapidly; transistors can switch many times per second.

·         Relays use more power due to the current flowing through their coil.

·         Relays require more current than many chips can provide, so a low power transistor may be needed to switch the current for the relay’s coil.


Connecting a transistor to the output from a chip

Most chips cannot supply large output currents so it may be necessary to use a transistor to switch the larger current required for output devices such as lamps, motors and relays. The 555 timer chip which we shall meet soon is unusual because it can supply a relatively large current of up to 200mA which is sufficient for some output devices such as low current lamps, buzzers and many relay coils without needing to use a transistor.

A transistor can also be used to enable a chip connected to a low voltage supply (such as 5V) to switch the current for an output device with a separate higher voltage supply (such as 12V). The two power supplies must be linked, normally this is done by linking their 0V connections. In this case you should use an NPN transistor.

A resistor RB is required to limit the current flowing into the base of the transistor and prevent it being damaged. However, RB must be sufficiently low to ensure that the transistor is thoroughly saturated to prevent it overheating, this is particularly important if the transistor is switching a large current (> 100mA). A safe rule is to make the base current IB about five times larger than the value which should just saturate the transistor.

Choosing a suitable NPN transistor

The circuit diagram shows how to connect an NPN transistor; this will switch on the load when the chip output is high. To get the opposite action, with the load switched on when the chip output is low (0V) you can use a PNP transistor.

 

The procedure below explains how to choose a suitable switching transistor.

NPN transistor switch

Figure 8.14 NPN transistor switch
(load is on when chip output is high)

 
Using units in calculations
Remember to use V, A and ohmor
V, mA and kohm.

The transistor’s maximum collector current Ic(max) must be greater than the load current Ic.

load current Ic =  

supply voltage Vs

load resistance RL

The transistor’s minimum current gain hFE(min) must be at least five times the load current Ic divided by the maximum output current from the chip.

hFE(min)  >   5 ×  

  load current Ic  

max. chip current

Choose a transistor which meets these requirements and make a note of its properties: Ic(max) and hFE(min).
Technical data for some popular transistors is available in manufacturers’ catalogues.  

 

KEY POINTS

1.      Calculate an approximate value for the base resistor:

RB =  

Vc × hFE

   where Vc = chip supply voltage
  (in a simple circuit with one supply this is Vs)

5 × Ic

2.      For a simple circuit where the chip and the load share the same power supply (Vc = Vs) you may prefer to use: RB = 0.2 × RL × hFE

3.      Then choose the nearest standard value for the base resistor.

4.      Finally, remember that if the load is a motor or relay coil a protection diode is required.

 

 

 

 

Worked Example
The output from a 4000 series CMOS chip is required to operate a relay with a 100ohm coil.
The supply voltage is 6V for both the chip and load. The chip can supply a maximum current of 5mA.

1.      Load current = Vs/RL = 6/100 = 0.06A = 60mA, so transistor must have Ic(max) > 60mA.

2.      The maximum current from the chip is 5mA, so transistor must have hFE(min) > 60 (5 × 60mA/5mA).

3.      Choose general purpose low power transistor BC182 with Ic(max) = 100mA and hFE(min) = 100.

4.      RB = 0.2 × RL × hFE = 0.2 × 100 × 100 = 2000ohm. so choose RB = 1k8 or 2k2.

5.      The relay coil requires a protection diode.


 

Transistor inverter (NOT gate)

As we saw in Chapter 7, inverters (NOT gates) are available on logic chips but if you only require one inverter it is usually as easy to use the circuit given in figure 8.15. The output signal (voltage) is the inverse of the input signal:

 

 

 

 

 

 

 

  • When the input is high (+Vs) the output is low (0V).
  • When the input is low (0V) the output is high (+Vs).

Figure 8.15 NPN Bipolar as a NOT GATE

Any general purpose low power NPN transistor can be used. For general use RB = 10kohm and RC = 1kohm, then the inverter output can be connected to a device with an input impedance (resistance) of at least 10kohm such as a logic chip or a 555 timer (trigger and reset inputs).

If you are connecting the inverter to a CMOS logic chip input (very high impedance) you can increase RB to 100kohm and RC to 10kohm, this will reduce the current used by the inverter.

The NPN transistor as an audio amplifier

The arrangement shown in figure 8.16 is often called the common emitter amplifier because the input voltage to the transistor appears between the base & emitter, and the output voltage appears between the collector & emitter — i.e. the emitter terminal is shared by (or ‘common to’) the input and output.

Note. , , and are the voltages between each of the transistor base, collector, and emitter terminals and the ‘ground’ (zero volts). They aren't the same thing as or which are the voltages from base-to-emitter and collector-to-emitter more usually associated with manufactures’ specifications.  The diagram also shows the input and output signal AC voltages, and . These aren't equal to and because the 0·1F capacitors block any d.c. connection between these potentials.) If puzzled see section of this book on Capacitors.

 

Figure 8.16 Class A Common Emitter Amplifier

It could actually be VERY complicated to work out all the resistor values if we followed the rigorous mathematical route to deal with both the D.C. and A.C. conditions in the circuit.     However the same old rule of thumb conditions apply to the transistor which we have met previously. The base bias resistors shown in figure 8.16 must be chosen to satisfy point (1) below.  That is the transistor must be slightly turned on that is conducting some D.C current all the time. This is known a class A.

  1. The base-emitter voltage will always be about 0·6 Volts (or ­0·6 for a PNP transistor).
  2. The current gain (the value) will be a few hundred.
  3. The large value means that , so we can assume that

 

image:Electronic_Amplifier_Class_A.pngFigure 8.17

 

 

 

In figure 8.17 only a skeleton cirucit is shown.   We can see how the output waveform is a perfectly ampliifed replica of the input.   In a Class A circuit, the transistor   is biased such that the device is always conducting to some extent, and is operated over the most linear portion of its characteristic curve (known as its transfer characteristic or transconductance curve). Because the device is always conducting, even if there is no input at all, power is wasted. This is the reason for its efficiency is quite low.  The input A.C. signal merely adds to and subtracts from the base bias.  The output signal V out  merely adds to and sutracts from Vc.  In the simplest case  Re is used to limit the current through the transistor to stop it getting thremal runaway.

 

 

MOSFETS.

 

If output currents larger than 1A are needed and high speed switching is desired  which draws virtually no current from the logic gate’s output,  then a high power transducer driver can be built using a MOSFET (metal oxide field effect transistor). 

Like bipolar transistors FET's have three legs but they are called the gate, source and drain.   Unlike bipolar transistors however MOSFET's have very high input impedance and require only a very small gate current to operate. In the true sense of the word they a voltage operated rather the current operated devices.  depletion mode. IGFET is a related, more general term meaning insulated-gate field-effect transistor, and is almost synonymous with "MOSFET", though it can refer to FETs with a gate insulator that is not oxide. Some prefer to use "IGFET" when referring to devices with polysilicon gates, but most still call them MOSFETs.

 

Usually the semiconductor of choice is silicon, but some chip manufacturers, most notably IBM, have begun to use a mixture of silicon and germanium (SiGe) in MOSFET channels. Unfortunately, many semiconductors with better electrical properties than silicon, such as gallium arsenide, do not form good gate oxides and thus are not suitable for MOSFETs.

The gate terminal is a layer of polysilicon (polycrystalline silicon; why polysilicon is used will be explained below) placed over the channel, but separated from the channel by a thin insulating layer of what was traditionally silicon dioxide, but more advanced technologies used silicon oxynitride. When a voltage is applied between the gate and source terminals, the electric field generated penetrates through the oxide and creates a so-called "inversion channel" in the channel underneath. The inversion channel is of the same type — P-type or N-type — as the source and drain, so it provides a conduit through which current can pass. Varying the voltage between the gate and body modulates the conductivity of this layer and makes it possible to control the current flow between drain and source.  Devices where a gate voltage enhances the channel are called Enhancement mode and devices where the gate voltage pinches off the channel and stops current flow are called Depletion Mode

 

 

Figure 8.18 Mosfet as a transducer driver

 

 Inductive Switching Issues

The switching of inductive loads can be very hazardous for the health of the switching device. While mechanical switches can cope with the arcing between the contacts at the expense of operating life, a semiconductor device will almost certainly be killed by the large voltage transient at turn off. The simplest method to solve this problem is to use a commutating, clamp diode or protection diode across the inductive component. The diagram below shows the layout of a diode clamped coil with MOSFET switch.

 

 Figure 8.19

When the switch is conducting, the diode is reverse bias and therefore no current exists in the diode branch. If the MOSFET is turned off quickly, the collapsing magnetic flux of the coil induces a voltage in the coil which tries to maintain the current. The faster the current is switched off, the larger is the induced voltage. Without a commutating or protection diode the induced voltage could reach several hundreds or even thousands of volts, certain death for the MOSFET, if the pulse exceeds the rated avalanche energy. Basically the commutating diode provides a low resistance path for the induced voltage to drive the current. The voltage only has to rise to a level which is enough to reach the conducting voltage of the diode, usually around 1V. This keeps the MOSFET happy and ready for its next switching action. While this is certainly an effective means of limiting the turn off transient voltage, it isn't necessarily the best in terms of turn off speed. Ideally we want the current in the coil to turn off as quickly as possible. The simple commutating diode is sufficient for an A-level understanding but in reality is some distance from the ideal goal. If we want the current to decay faster we need to let the induced voltage reach a higher value. The absolute maximum we can allow it to rise depends on the voltage rating of the device. Suppose we are using a 60V MOSFET and a 40V supply, the largest induced voltage allowable is then 20V. One possibility is to connect a resistor in series with the diode. The specific value would need to be determining according to the coil current at turn off, the supply voltage, and the maximum device voltage. Another would be to use a zener voltage clamp across the MOSFET.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER NINE: SIMPLE OUTPUT DEVICES

 

In reality output devices are simply chosen for the job in hand.

 

With an alarm system you may want a visible warning for the deaf, i.e. a bright strobing lamp of some sort and you may want a loud audible siren, bell or buzzer. 

 

To create movement as say in robot or model aircraft the output device will be called  an actuator and may be  motor. Motors come in various types which will be discussed later in this book.   For more powerful movement hydraulic actuators may be needed.

 

With an amplifier you may want headphones or a loudspeaker as an output device.

 

With an on –off warning light for a piece of equipment or a low battery voltage indicator a  single LED (Light Emitting diode) will suffice .

 

With a clock or timer or counter you may want a seven segment LED display or an LCD display. 

 

With a more sophisticated information system such as a motorway warning gantry you may want a dot matrix display.  

 

The purpose of this Chapter then is to look at the construction and operation of output devices which in turn relates to how they must be interfaced, that is connected to the previous stage, and driven.   

 

 

 

 

Filament bulbs

 

Connecting filament bulbs or lamps is easy, they simply act as resistive loads and the maximum current they consume is worked out by considering their resistance when cold.   So provided the output driver device or sub-system you employ can deliver this current there is no problem in interfacing the device.

 

 

 

 

 

Figure 9.1 BULB

 

 

 

Bulbs are relatively easy to use. A bulb will be rated according to the maximum safe voltage and the current that will flow at this voltage. A bulb rated at 6 V, 0.06A will have a resistance of 100 ohms when it is working at normal brightness.

 

 

 

The input terminal would connect to the collector of a NPN or Drain of a MOSFET driver.

 

 

 

Electric Bells.

When the switch is pushed closed the circuit is completed and current flows through the coil. The iron striker is attracted to the electromagnet and strikes the bell.As the striker moves towards the bell, the contact is broken. Current stops flowing through the coil which loses its magnetism. The spring returns the striker to its original position which makes a new contact and so electricity flows again. Back to the start and the cycle repeats itself.   The bell will continue to ring as long as the switch held closed.   The bell is an inductive load and must be interfaced according to the Electric Bell

Figure 9.2 Electric Bell

 

methods described in Chapter 8 for such loads.

 

 

 

Buzzers

Buzzers come in several different types. Depending on the type will depend on the interfacing.  Figure 9.3 shows an ageing D.C buzzer, alongside its modern counterpart, both of which operate on a similar principle to the electric bell.   A.C. buzzers are also possible.  D.C. Buzzers must be treated as inductive loads.   A.C. Buzzers must be powered through a relay.

 

 Go to fullsize image

 

Figure 9.3 Buzzers ancient and modern

 

 

 

 

 

Buzzers based on vibrating piezoelectric elements are also possible, see figure 9.3.

A   transistor circuit to drive such a buzzer is shown in figure 9.4.

 

 

 

Piezo transducer

Figure 9.4

 

Piezo transducer

piezo transducer symbol

circuit symbol

Piezo transducers are output transducers which convert an electrical signal to sound. They require a driver circuit (such as a 555 astable) to provide a signal and if this is near their natural (resonant) frequency of about 3kHz they will produce a particularly loud sound.

Piezo transducers require a small current, usually less than 10mA, so they can be connected directly to the outputs of most ICs. They are ideal for buzzes and beeps, but are not suitable for speech or music because they distort the sound. They are sometimes supplied with red and black leads, but they may be connected either way round. PCB-mounting versions are also available. Piezo transducers can also be used as input transducers for detecting sudden loud noises or impacts, effectively behaving as a crude microphone

 

 

 

Fig 9.5  A Piezo-buzzer

Figure 9.6 Circuit to drive piezo-buzzer from Logic source.

 

 

Integrated or Complete Audible Warning Devices (CAWD)

 

Besides bells and buzzers, these days a large range of audio warning devices is available which have their own integral circuitry capable of producing a large variety of high level sounds up to in some cases > 120 decibels, in other words almost ear splitting sound!   You should always refer to the manufacturers’ data sheet for connection of such devices which are often polarity and voltage conscious.

 

The circuits in these devices often use a combination of logic gates and mosfets  to produces very high voltage 200-300 volt short duration pulses which are sent to specially reinforced piezo-electric sounder elements.  Conventional loudspeakers cannot stand such high voltages. 

Dynamic Loudspeaker Principle

A current-carrying wire in a magnetic field experiences a magnetic force perpendicular to the wire. In practice the wire is wrapped into a coil attached to a stiffened paper cone which then vibrates back and forth in sympathy with the induced movement. See figure 9.7

 

.

Figure 9.7 Loudspeaker Construction and principle

 

Figure 9.8 Actual loudspeaker loudspeaker

 

 Loudspeakers, figure 9.8, are output transducers which convert an electrical signal to sound. Usually they are called 'speakers'. They require a driver circuit, such as a 555 astable or an audio amplifier, to provide a signal. There is a wide range available, but for many electronics projects a 300mW miniature loudspeaker is ideal. This type is about 70mm diameter and it is usually available with resistances of 8ohm and 64ohm. If a project specifies a 64ohm speaker you must use this higher resistance to prevent damage to the driving circuit.

Most circuits used to drive loudspeakers produce an audio (AC) signal since sounds, voices and music are essentially time varying fluctutations it is necessary as we have seen for amplifiers to separate out these currents and voltages present. Alternating components from any quiescent or standing D.C. which is combined with a constant DC signal. The DC will make a large current flow through the speaker due to its low resistance, possibly damaging both the speaker and the driving circuit. To prevent this happening a large value electrolytic capacitor is connected in series with the speaker, this blocks DC but passes audio (AC) signals. See capacitors

Loudspeakers may be connected either way round except in stereo circuits when the + and - markings on their terminals must be observed to ensure the two speakers are in phase.

Correct polarity must always be observed for large speakers in cabinets because the cabinet may contain a small circuit (a 'crossover network') which diverts the high frequency signals to a small speaker (a 'tweeter') because the large main speaker is poor at reproducing them.

Miniature loudspeakers can also be used as a microphone and they work surprisingly well, certainly well enough for speech in an intercom system for example.
loudspeaker symbol Figure 9.9 speaker circuit symbol

 

 A simple amplifier to boost the audio line out from a computer is shown in figure 9.10 , note how the loudpseaker is A.C. coupled to the circuit through a 470 micro-farad capacitor.

 

schematic

 

Figure 9.10 Computer audio amplifier

 

 

We will revist audio amplifiers in a later section of this book, see filters and push-pull output stages.

 

LEDS (Light Emitting Diodes)

Light emitting diodes or LEDs are polarized devices and must be connected the right way round in a circuit. Since the maximum voltage to be applied across an LED is about 2V they almost always have a resistor connected in series. The value of the resistor is calculated from the voltage of the power supply and the current required by the LED.

LEDs come in three main colours: red, yellow and green. Blue LED's are available but are very expensive. There can be bought in a wide range of sizes and shapes - look at suppliers’ catalogues for more details

 

Figure 9.11 LED symbol.

 

 

Example:   LED    Circuit symbol:   LED circuit symbol

Function

LEDs emit light when an electric current passes through them. They are much more efficient than filament bulbs and require less current generally about 10-20 mA.

Connecting and soldering

LEDs must be connected the correct way round, the diagram is labeled a or + for anode and k or - for cathode (yes, it really is k, not c, for cathode!). The cathode is the short lead and there may be a slight flat on the body of round LEDs. If you can see inside the LED the cathode is the larger electrode (but this is not an official identification method).

LEDs can be damaged by heat when soldering, but the risk is small unless you are very slow. No special precautions are needed for soldering most LEDs.

Testing an LED

Never connect an LED directly to a battery or power supply!
It will be destroyed almost instantly because too much current will pass through and burn it out.

LED colours

 

 

Figure 9. 12 Coloured LEDS

 

 

For quick testing purposes a 1kohm resistor is suitable as a current limiter for most LEDs if your supply voltage is 12V or less. Remember to connect the LED the correct way round!  The flat on its body is the negative or cathode connection.

 

Colours of LEDs

LEDs are available in red, orange, amber, yellow, green, and blue and white. Blue and white LEDs are much more expensive than the other colours.

The colour of an LED is determined by the semiconductor material, not by the colouring of the 'package' (the plastic body). LEDs of all colours are available in uncoloured packages which may be diffused (milky) or clear (often described as 'water clear'). The coloured packages are also available as diffused (the standard type) or transparent.

Tri-colour LEDs

Tri-colour LED

 

 

 

 

 

Figure 9.13

Tricolour LED

 

 

 

The most popular type of tri-colour LED has a red and a green LED combined in one package with three leads. They are called tri-colour because mixed red and green light appears to be yellow and this is produced when both the red and green LEDs are on.

The diagram shows the construction of a tri-colour LED. Note the different lengths of the three leads. The centre lead (k) is the common cathode for both LEDs, the outer leads (a1 and a2) are the anodes to the LEDs allowing each one to be lit separately, or both together to give the third colour.

Bi-colour LEDs

A bi-colour LED has two LEDs wired in 'inverse parallel' (one forwards, one backwards) combined in one package with two leads. Only one of the LEDs can be lit at one time and they are less useful than the tri-colour LEDs described above.

 

Sizes, Shapes and Viewing angles of LEDs

LEDs are available in a wide variety of sizes and shapes. The 'standard' LED has a round cross-section of 5mm diameter and this is probably the best type for general use, but 3mm round LEDs are also popular.

Round cross-section LEDs are frequently used and they are very easy to install on boxes by drilling a hole of the LED diameter, adding a spot of glue will help to hold the LED if necessary. LED clips are also available to secure LEDs in holes. Other cross-section shapes include square, rectangular and triangular.

As well as a variety of colours, sizes and shapes, LEDs also vary in their viewing angle. This tells you how much the beam of light spreads out. Standard LEDs have a viewing angle of 60° but others have a narrow beam of 30° or less.

 

 

 

LED resistor circuit

 

 

 

 

Figure 9.14 Calculating an LED resistor value

 

 

 

Exam Topic

 

An LED must have a resistor connected in series to limit the current through the LED, otherwise it will burn out almost instantly.

The resistor value, R is given by:

R = (VS - VL) / I

VS = supply voltage
VL = LED voltage (usually 2V, but 4V for blue and white LEDs)
I = LED current (e.g. 20mA), this must be less than the maximum permitted

If the calculated value is not available choose the nearest standard resistor value which is greater, so that the current will be a little less than you chose. In fact you may wish to choose a greater resistor value to reduce the current (to increase battery life for example) but this will make the LED less bright.

For example

If the supply voltage VS = 9V, and you have a red LED (VL = 2V), requiring a current I = 20mA = 0.020A,
R = (9V - 2V) / 0.02A = 350ohm, so choose 390ohm (the nearest standard value which is greater).

Working out the LED resistor formula using Ohm's law

Ohm's law says that the resistance of the resistor, R = V/I, where:
  V = voltage across the resistor (= VS - VL in this case)
  I = the current through the resistor

So   R = (VS - VL) / I

 

In practice LEDS will often be driven direct by small transistors, logic or timer I.C.S.

555 and 556 output sinking and sourcing

Figure 9.15

Driving a LED

 

 

 

 

 

 

 

7 Segment  Displays

LED displays are packages of many LEDs arranged in a pattern, the most familiar pattern being the 7-segment displays for showing numbers (digits 0-9). The pictures below illustrate some of the popular designs:

Bargraph display, photograph © Rapid Electronics

7-segment display, photograph © Rapid Electronics

Starburst display, photograph © Rapid Electronics

Dot matrix display, photograph © Rapid Electronics

Bargraph

7-segment

Starburst

Dot matrix

Figure 9.16 Various LED Displays

Pin connections of LED displays

7-segment display pin connections, photograph © Rapid Electronics

Figure 9.17 Pin connections diagram
for 7 segment display  

There are many types of LED display and a supplier's catalogue should be consulted for the pin connections. The diagram on the right shows an example from a manufactures’ catalogue; like many 7-segment displays, this example is available in two versions: Common Anode (SA) with all the LED anodes connected together and Common Cathode (SC) with all the cathodes connected together. Letters a-g refers to the 7 segments, A/C is the common anode or cathode as appropriate (on 2 pins). Note that some pins are not present (NP) but their position is still numbered.

 

 

Exercise

 

Try to work out for yourselves which segments need to be illuminated to make numbers 0-9. Assume the device has a common cathode. Which boxes need a logic1 in the grid?

 

 

 

1

2

3

4

5

6

7

8

9

0

a

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

 

 

 

 

 

c

 

 

 

 

 

 

 

 

 

 

d

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

f

 

 

 

 

 

 

 

 

 

 

g

 

 

 

 

 

 

 

 

 

 

 

Figure 9.18 7 Segment Exercise

 

 

 

 

Solenoid

A solenoid consists of a coil of wire around a ferrous core. Solenoids are similar to relays but instead of bringing about electrical switching they can bring about linear mechanical movement which may or may not be of the latching kind depending on the precise mechanical arrangement. This is because it converts the electrical signal into linear kinetic energy.

 

 

 

Because the solenoid is an inductive component it needs a protection diode in the same manner as the other inductive devices discussed.

 

Motors

A d.c. motor converts the electrical signal into rotational kinetic energy. Details of the construction of d.c. motors can be found in most Physics textbooks. Before connecting these devices to the outputs from processing subsystems (we call this interfacing) it is necessary to know the working voltage and the maximum current drawn by the motor. This will enable the correct choice of driver to be made.

 

Figure 9.19   

 

 

Some d.c. motors tend to be "noisy" - this is particularly true of cheap motors. The noise referred to is not sound but electrical noise. Inside the motor there is a part called the commutator which rotates against conductors called brushes. 

The commutator is made up of a series of separate sectors with insulation between them and, as the brushes pass from one sector to another, there is a switching of current. 

 

This rapid switching causes voltage spikes to appear on the power lines and this can disturb the working of the rest of the circuit. If electronic methods of suppression (usually a resistor in series with the motor and a capacitor across the terminals of the motor) are not successful, it may be necessary to use a separate power supply for the motor and switch it on through a relay.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 10:  CAPACITORS AND TIMING SUB-SYSTEMS 

 

Imagine we build a burglar alarm. We might want the alarm siren to sound a series of beeps or whistles or warbles that stop after a given period. How would we do it?

 

We can use a special subsystem known as a 555 Timer IC which can be configured as either a pulse generator (Astable) or Timer (Monostable).

 

In order to understand how these sub-systems work one must first understand something about an electronic component known as a capacitor.   

 

unpolarised capacitor symbol

unpolarised capacitor symbol
 

polarised capacitor symbol

polarised capacitor symbol

Capacitance

Capacitance (symbol C) is a measure of a capacitor's ability to store charge. A large capacitance means that more charge can be stored. Capacitance is measured in farads, symbol F. However 1F is very large for practical purposes, so prefixes as in figure 2.1 (multipliers) are used to show the smaller values, 

  • µ (micro) means 10-6 (millionth), so 1000000µF = 1F
  • n (nano) means 10-9 (thousand-millionth), so 1000nF = 1µF       Figure 10.1           
  • p (pico) means 10-12 (million-millionth), so 1000pF = 1nF          Capacitor   
                                                                                                           symbols

 

Charge and Energy Stored

The amount of charge (symbol Q) stored by a capacitor is given by:

 

Charge,   Q = C × V

  where:

Q = charge in coulombs (C)
C = capacitance in farads (F)
V = voltage in volts (V)

When they store charge, capacitors are also storing energy:

Energy,   E = ˝QV = ˝CV˛    where E = energy in joules (J).

Note that capacitors return their stored energy to the circuit. They do not 'use up' electrical energy by converting it to heat as a resistor does. The energy stored by a capacitor is much smaller than the energy stored by a battery so they cannot be used as a practical source of energy for most purposes, although very large banks of high voltage capacitors can be charged for use in heart defibrillators, for example.

 

Capacitive Reactance Xc

Capacitors oppose A.C. current flow a little bit like resistors oppose D.C. flow. Capacitive reactance (symbol Xc) is a measure of a capacitor's opposition to AC (alternating current). Like resistance it is measured in ohms,ohm, but reactance is more complex than resistance because its value depends on the frequency (f) of the electrical signal passing through the capacitor as well as on the capacitance, C. Also reactance can’t be measured on a simple D.C. ohmmeter.

 

 

Capacitive reactance,   Xc =  

   1   

  where:  

Xc = reactance in ohms (ohm)
f    = frequency in hertz (Hz)
C   = capacitance in farads (F)

 

2pifC

The reactance Xc is large at low frequencies and small at high frequencies. For steady DC which is zero frequency, Xc is infinite (total opposition), hence the rule that capacitors appear to pass AC but block DC.

For example a 1µF capacitor has a reactance of 3.2kohm for a 50Hz signal, but when the frequency is higher at 10kHz its reactance is only 16ohm.  We will meet these ideas again when we consider audio filters.

.

 

capacitors in series and parallelCapacitors in Series and Parallel                    

Combined capacitance (C) of
capacitors connected in
series:  

 1 

  =  

 1 

+

 1 

+

 1 

+ ...

 

 

 

 

C

C1

C2

C3

 

Combined capacitance (C) of
capacitors connected in
parallel:  

C = C1 + C2 + C3 + ...

 

Figure 10.2 Capacitors in series and parallel

The above formulae are often found in exam data sheets.  If you are good at fractions you will see that a short cut if you have just two capacitors in series is called the product over sum rule

C= C1XC2/ (C1+C2)

 

Two or more capacitors are rarely deliberately connected in series in real circuits, but it can be useful to connect capacitors in parallel to obtain a very large capacitance, for example to smooth a power supply.

KEY POINT Note that these equations are the opposite way round for resistors in series and parallel.

 

Charging a capacitor

When a capacitor is connected straight to a battery or power supply it charges

 

instantaneously but the charging can be slowed down by resistor.

 

The capacitor (C) in the circuit diagram is being charged from a supply voltage (Vs) with the current passing through a resistor (R). The voltage across the capacitor (Vc) is initially zero but it increases as the capacitor charges. The capacitor is fully charged when Vc = Vs. The charging current (I) is determined by the voltage capacitor chargingacross the resistor (Vs - Vc):

Charging current, I = (Vs - Vc) / R   (note that Vc is increasing) The capacitor (C) in the circuit diagram is being charged from a supply voltage (Vs) with the current passing through a resistor (R).

At first Vc = 0V so the initial current, Io = Vs / R

 

 

                                                                      Figure 10.3 Capacitor charging circuit

 

Vc increases as soon as charge (Q) starts to build up (Vc = Q/C), this reduces the voltage across the resistor   and therefore reduces the charging current. This means that the rate of charging becomes progressively slower.

time constant  = R × C

  where:  

time constant is in seconds (s)
R = resistance in ohms (ohm)
C = capacitance in farads (F)

Example Calculations:
If R = 47kohm and C = 22µF, then the time constant, RC = 47kohm × 22µF = 1.0s.
If R = 33kohm and C = 1µF, then the time constant, RC = 33kohm × 1µF = 33ms.

A large time constant means the capacitor charges slowly. Note that the time constant is a property of the circuit containing the capacitance and resistance; it is not a property of a capacitor alone.

Graphs showing the current and
voltage for a capacitor charging

time constant = RC

charging current

Figure 10.4 Current in a charging capacitor

The time constant is the time taken for the charging (or discharging) current (I) to fall to 1/e of its initial value (Io). 'e' is the base of natural logarithms, an important number in mathematics (like pi). e = 2.71828 (to 6 significant figures) so we can roughly say that the time constant is the time taken for the current to fall to 1/3 of its initial value.

After each time constant the current falls by 1/e (about 1/3). After 5 time constants (5RC) the current has fallen to less than 1% of its initial value and we can reasonably say that the capacitor is fully charged, but in fact the capacitor takes for ever to charge fully!

 

 

Time

Voltage

Charge

 

 

 

0RC

0.0V

  0%

0.69RC

                         4.5V

50%

1RC

5.capacitor charging voltage7V

63%

 

 

 

2RC

7.8V

86%

 

 

 

3RC

8.6V

95%

 

 

 

4RC

8.8V

98%

 

 

 

5RC

8.9V

99%

 

 

 

The bottom graph shows how the voltage (V) increases as the capacitor charges. At first the voltage changes rapidly because the current is large; but as the current decreases, the charge builds up more slowly and the voltage increases more slowly.

Because of the mathematics involved it is easier to remember just key points on the charging curve most examinations only call for these, which have been highlighted in yellow.  For instance after 0.69 Time constants or 0.69 RC 50 % of total charge is reached or the

                                                    Figure 10.5 Voltage in a charging capacitor 

 

capacitor has charged to exactly half  the supply voltage. After one time constant (RC), the capacitor has charged to  63% of total charge or supply voltage.

After 5 time constants (5RC) the capacitor is almost fully charged with its voltage almost equal to the supply voltage. We can reasonably say that the capacitor is fully charged after 5RC, so this figure of 5RC is needed for exam recall, although really charging continues for ever (or until the circuit is changed).


                                                      

 

Discharging a capacitor

Graphs showing the current and
voltage for a capacitor discharging

time constant = RC

capacitor charging current

capacitor discharging voltage

The top graph shows how the current (I) decreases as the capacitor discharges. The initial current (Io) is determined by the initial voltage across the capacitor (Vo) and resistance (R):

Initial current, Io = Vo / R.

Note that the current graphs are the same shape for both charging and discharging a capacitor. This type of graph is an example of exponential decay.

Key points discharge curve.

·         To ˝ charge or ˝ terminal voltage in 0.69RC seconds

·         To 37% (100-63) of charge or terminal voltage in RC seconds

·         To zero in 5RC second

                                                                        Figure 10.6 Discharging a capacitor

 

Where we might use a capacitor.

  • For ‘AC Coupling’ between stages of an audio system and to connect a loudspeaker.
  • Filtering - for example in the tone control of an audio system, see later
  • Tuning - for example in a radio system, see later
  • Storing energy - for example in a camera flash circuit.

 

 

Practical Capacitors

 

As we have seen capacitors store electric charge. They are used with resistors in timing circuits because it takes time for a capacitor to fill with charge. They are used to smooth varying DC supplies by acting as a reservoir of charge. They are also used in filter circuits because capacitors easily pass AC (changing) signals but they block DC (constant) signals.

 

Three prefixes (multipliers) are used, µ (micro), n (nano) and p (pico):

  • µ means 10-6 (millionth), so 1000000µF = 1F
  • n means 10-9 (thousand-millionth), so 1000nF = 1µF
  • p means 10-12 (million-millionth), so 1000pF = 1nF

Values of capacitors are often harder to find because there are many types of capacitor with different labeling systems compared with simple resistor codes!  In a good electronics lab a capacitance meter is thus a useful tool.  

Capacitors split into two groups, polarised and unpolarised. Each group has its own circuit symbol.

 

Polarised capacitors (large values, 1µF +)

Examples:   electrolytic capacitors     

 

Figure 10.7 Polarised or electrolytic capacitors

Electrolytic Capacitors

Electrolytic capacitors are polarised and they must be connected the correct way round, at least one of their leads will be marked + or -. They are not damaged by heat when soldering.

There are two designs of electrolytic capacitors; axial where the leads are attached to each end (220µF in picture) and radial where both leads are at the same end (10µF in picture). Radial capacitors tend to be a little smaller and they stand upright on the circuit board.

It is easy to find the value of electrolytic capacitors because they are clearly printed with their capacitance and voltage rating. The voltage rating can be quite low (6V for example) and it should always be checked when selecting an electrolytic capacitor. If the project parts list does not specify a voltage; choose a capacitor with a rating which is greater than the project's power supply voltage. 25V is a sensible minimum for most battery circuits.

Tantalum Bead Capacitors

Tantalum bead capacitors are also polarised and have low voltage ratings like electrolytic capacitors. They are expensive but very small, so they are used where a large capacitance is needed in a small size.

Modern tantalum bead capacitors are printed with their capacitance and voltage in full. However older ones use a colour-code system which has two stripes (for the two digits) and a spot of colour for the number of zeros to give the value in µF. The

tantalum bead capacitors

 

standard colour code is used, but for the spot, grey is used to mean × 0.01 and white means × 0.1 so that values of less than 10µF can be shown. A third colour stripe near the leads shows the voltage (yellow 6.3V, black 10V, green 16V, blue 20V, grey 25V, white 30V, pink 35V).

For example:   blue, grey, black spot   means 68µF
For example:   blue, grey, white spot   means 6.8µF
100nF capacitorFor example:   blue, grey, grey spot   means 0.68µF

 

1nF capacitorUnpolarised capacitors (small values, up to 1µF)

Examples:   small value capacitors  

  Circuit symbol:   capacitor symbol

 

Figure 10.8 Non-polarised capacitors.

Small value capacitors are unpolarised and may be connected either way round. They are not damaged by heat when soldering, except for one unusual type (polystyrene). They have high voltage ratings of at least 50V, usually 250V or so. Many small value capacitors have their value printed but without a multiplier, so you need to use experience to work out what the multiplier should be!

For example 0.1 means 0.1µF = 100nF.

Sometimes the multiplier is used in place of the decimal point:
For example:   4n7 means 4.7nF.

 

 

 

Capacitor Number Code

A number code is often used on small capacitors where printing is difficult:

  • the 1st number is the 1st digit,
  • the 2nd number is the 2nd digit,
  • the 3rd number is the number of zeros to give the capacitance in pF.
  • Ignore any letters - they just indicate tolerance and voltage rating.

For example:   102   means 1000pF = 1nF   (not 102pF!)

For example:   472J means 4700pF = 4.7nF (J means 5% tolerance).

Colour Code

Colour

Number

Black

0

Brown

1

Red

2

Orange

3

Yellow

4

Green

5

Blue

6

Violet

7

Grey

8

White

9

10nF and 220nF capacitorsCapacitor Colour Code

A colour code was used on polyester capacitors for many years. It is now obsolete, but of course there are many still around. The colours should be read like the resistor code, the top three colour bands giving the value in pF. Ignore the 4th band (tolerance) and 5th band (voltage rating).

For example:

    brown, black, orange   means 10000pF = 10nF = 0.01µF.

Note that there are no gaps between the colour bands, so 2 identical bands actually appear as a wide band.

polystyrene capacitor

                                                                         Figure 10.9 Capacitor color code

For example:

    wide red, yellow   means 220nF = 0.22µF.

Polystyrene Capacitors

This type is rarely used now. Their value (in pF) is normally printed without units. Polystyrene capacitors can be damaged by heat when soldering (it melts the polystyrene!) so you should use a heat sink (such as a crocodile clip). Clip the heat sink to the lead between the capacitor and the joint.

 

Real capacitor values (the E3 and E6 series)

You may have noticed that capacitors are not available with every possible value, for example 22µF and 47µF are readily available, but 25µF and 50µF are not!

Why is this? Imagine that you decided to make capacitors every 10µF giving 10, 20, 30, 40, 50 and so on. That seems fine, but what happens when you reach 1000? It would be pointless to make 1000, 1010, 1020, 1030 and so on because for these values 10 is a very small difference, too small to be noticeable in most circuits and capacitors cannot be made with that accuracy.

To produce a sensible range of capacitor values you need to increase the size of the 'step' as the value increases. The standard capacitor values are based on this idea and they form a series which follows the same pattern for every multiple of ten.

The E3 series (3 values for each multiple of ten)
10, 22, 47, then it continues 100, 220, 470, 1000, 2200, 4700, 10000 etc.
Notice how the step size increases as the value increases (values roughly double each time).

The E6 series (6 values for each multiple of ten)
10, 15, 22, 33, 47, 68, then it continues 100, 150, 220, 330, 470, 680, 1000 etc.
Notice how this is the E3 series with an extra value in the gaps.

The E3 series is the one most frequently used for capacitors because many types cannot be made with very accurate values.

Silvered Mica Capacitors 

For real precision work usually in the pico-farad ranges of capacitance, silvered mica capacitors are employed. The dielectric or insulating material in these capacitors is the naturally occurring mineral material mica. The electrodes are silver plated or sputtered directly onto the mica.   

 

Variable capacitors

variable capacitor symbol

Variable Capacitor Symbol

variable capacitor

Figure 10.10 Variable Capacitor

Variable capacitors are mostly used in radio tuning circuits and they are sometimes called 'tuning capacitors'. They have very small capacitance values, typically between 100pF and 500pF (100pF = 0.0001µF). The type illustrated usually has trimmers built in (for making small adjustments - see below) as well as the main variable capacitor.

Many variable capacitors have very short spindles which are not suitable for the standard knobs used for variable resistors and rotary switches. It would be wise to check that a suitable knob is available before ordering a variable capacitor.

Variable capacitors are not normally used in timing circuits because their capacitance is too small to be practical and the range of values available is very limited. Instead timing circuits use a fixed capacitor and a variable resistor if it is necessary to vary the time period.


Trimmer capacitors

trimmer capacitor symbol

Trimmer Capacitor Symbol

trimmer capacitor

Trimmer Capacitor
Figure 10.11  

Trimmer capacitors (trimmers) are miniature variable capacitors. They are designed to be mounted directly onto the circuit board and adjusted only when the circuit is built.

A small screwdriver or similar tool is required to adjust trimmers. The process of adjusting them requires patience because the presence of your hand and the tool will slightly change the capacitance of the circuit in the region of the trimmer!

Trimmer capacitors are only available with very small capacitances, normally less than 100pF. It is impossible to reduce their capacitance to zero, so they are usually specified by their minimum and maximum values, for example 2-10pF.

Trimmers are the capacitor equivalent of presets which are miniature variable resistors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 555 Timer Sub-systems

 

We can go on to see how RC time constants are employed in two major sub-systems using the 555 Timer I.C.


The 555 timer IC was first introduced around 1971 by the Signetics Corporation as the SE555/NE555 and was called "The IC Time Machine" and was also the very first and only commercial timer IC available. It provided circuit designers with a relatively cheap, stable, and user-friendly integrated circuit for both monostable and astable applications and more than 30 years on continues to do so! Since this device was first made commercially available, a myriad of novel and unique circuits in addition to theses two basic sub-systems have been also been  developed using 555’s and presented in several trade, professional, and hobby publications.

 

 

   

 

555 circuit symbol

 

 

Figure 10.12 IC Pin connection, layout and circuit symbol 555 Timer

 

 

 The 555, in fig. 10.12 above, comes in two packages, either the round metal-can called the 'T' package or the more familiar 8-pin DIP 'V' package. About 20-years ago the metal-can type was pretty much the standard (SE/NE types). The 556 timer is a dual 555 version and comes in a 14-pin DIP package, the 558 is a quad version with four 555's also in a 14 pin DIP case.

 

 


Fig. 3, 555 Block Diagram 




 

Figure 10.13
Inside the 555 timer.

 

 

 

 

 

 

 

Inside   the 555timer   figure 10.13, are the equivalent of over 20 transistors, 15 resistors, and 2 diodes, depending of the manufacturer. The figure shows the equivalent circuit, in block diagram, providing the functions of control, triggering, level sensing or comparison, discharge, and power output. Some of the more attractive features of the 555 timer are: Supply voltage between 4.5 and 18 volt, supply current 3 to 6 mA, and a Rise/Fall time of 100 nSec. It can also withstand quite a bit of abuse, its output can sink or source up to 250mA with up to a 15 volt supply!

The action of the timer is all down to the 2 internal comparators (see chapter 11) so that when the trigger input Pin 2 falls below 1/3rd Vs the device is triggered and the output goes high, like a latching switch.   The output can be made to go low again when the threshhold input Pin6 goes above 2/3rds Vs. Thus use of certain RC networks on these input pins allows either single timing pulses (monostable) or continuous pulses (astable) to be generated.

 

 

 

EXAM TOPIC

In more detail actions at the various pins pertinent to exam knowledge can be summarized as follows:

 

Trigger input: when < 1/3 Vs ('active low') this makes the output

high (+Vs). It monitors the discharging of the timing capacitor in an astable circuit. It has a high input impedance > 2Mohm.

Threshold input: when > 2/3 Vs ('active high') this makes the output low (0V)*. It monitors the charging of the timing capacitor in astable and monostable circuits. It has a high input impedance > 10Mohm.
* providing the trigger input is > 1/3 Vs, otherwise the trigger input will override the threshold input and hold the output high (+Vs).

Reset input: when less than about 0.7V ('active low') this makes the output low (0V), overriding other inputs. When not required it should be connected to +Vs. It has an input impedance of about 10kohm.

Control input: this can be used to adjust the threshold voltage which is set internally to be 2/3 Vs. Usually this function is not required and the control input is connected to 0V with a 0.01µF capacitor to eliminate electrical noise. It can be left unconnected if noise is not a problem.

The discharge pin is not an input, but it is listed here for convenience. It is connected to 0V when the timer output is low and is used to discharge the timing capacitor in astable and monostable circuits.

 

The astable (EXAM Topic)

The 555 astable, or oscillator, subsystem uses a 555 timer IC to provide an output signal that constantly switches between high and low states. It is effectively a pulse subsystem provided good control over the output signal.

The 555 astable is based on the 555 timer IC. The time that the output signal is high is known as the mark of the pulse. The time that the output signal is low is known as the space of the pulse. 

A mark/space ratio is used to show how much longer the mark time is compared to the space time. 

 

A typical astable circuit diagram feeding a buzzer output device is shown  in figure 10.14.

 

 

 

Figure 10.14 555 Astable

 

In the basic arrangement is shown above, R1, R2 and C1 are external components whose values fix the frequency of the stream of continuous square wave pulses produced automatically at the output (pin 3).

The period T of the approximate square wave is given by

T = 0.7 (R1+2R2) C1

Where again T is in seconds if R is in Megohms and C is in microfarads.

The frequency f = 1/T

The duty cycle or mark to space ratio is the ratio of the time the output is on divided by the time the output is off. For a true square wave this is 1. If you look carefully at the pin out diagram and circuit you will see that the timing capacitor charges through both R1 and R2 and discharges through R2 only. This means that a rectangular wave is produced unless R1 is very small in comparison to R2. In practice we cannot make R1 less than about 1K or the 555 will burn out.

Choosing R1, R2 and C1

555 astable frequencies

C1

R2 = 10kohm
R1 = 1kohm

R2 = 100kohm
R1 = 10kohm

R2 = 1Mohm
R1 = 100kohm

0.001µF

68kHz

6.8kHz

680Hz

0.01µF

6.8kHz

680Hz

68Hz

0.1µF

680Hz

68Hz

6.8Hz

1µF

68Hz

6.8Hz

0.68Hz

10µF

6.8Hz

0.68Hz
(41 per min.)

0.068Hz
(4 per min.)

R1 and R2 should be in the range 1kohm to 1Mohm. It is best to choose C1 first because capacitors are available in just a few values.

  • Choose C1 to suit the frequency range you require (use the table as a guide).
  • Choose R2 to give the frequency (f) you require. Assume that R1 is much smaller than R2 (so that Tm and Ts are almost equal), then you can use:

R2 = 

  0.7  

f × C1

  • Choose R1 to be about a tenth of R2 (1kohm min.) unless you want the mark time Tm to be significantly longer than the space time Ts.
  • If you wish to use a variable resistor it is best to make it R2.
  • If R1 is variable it must have a fixed resistor of at least 1kohm in series
    (this is not required for R2 if it is variable).

 

 

 

 

Astable operation Exam Topic

 

 

555 astable operation

 

 

 

 

  

 

Figure 10.15 Astable timing diagram

 

 

With the output high (+Vs) the capacitor C1 is charged by current flowing through R1 and R2. The threshold and trigger inputs monitor the capacitor voltage and when it reaches 2/3Vs (threshold voltage) the output becomes low and the discharge pin is connected to 0V.

The capacitor now discharges with current flowing through R2 into the discharge pin. When the voltage falls to 1/3Vs (trigger voltage) the output becomes high again and the discharge pin is disconnected, allowing the capacitor to start charging again.

This cycle repeats continuously unless the reset input is connected to 0V which forces the output low while reset is 0V.

An astable can be used to provide the clock signal for circuits such as counters.

A low frequency astable (< 10Hz) can be used to flash an LED on and off, higher frequency flashes are too fast to be seen clearly. Driving a loudspeaker or piezo transducer with a low frequency of less than 20Hz will produce a series of 'clicks' (one for each low/high transition) and this can be used to make a simple metronome.

An audio frequency astable (20Hz to 20kHz) can be used to produce a sound from a loudspeaker or piezo transducer. The sound is suitable for buzzes and beeps. The natural (resonant) frequency of most piezo transducers is about 3kHz and this will make them produce a particularly loud sound.


Duty cycle

The duty cycle of an astable circuit is the proportion of the complete cycle for which the output is high (the mark time). It is usually given as a percentage.

For a standard 555/556 astable circuit the mark time (Tm) or Time High must be greater than the space time (Ts) or Time Low, so the duty cycle must be at least 50%:

Duty cycle  =  

    Tm    

 = 

 R1 + R2 

Tm + Ts

R1 + 2R2

Figure 10.16 Astable Duty Cycle.

 

Duty cycles

 

 

 

 

 

 

555 astable circuit with diode across R2

Figure 10.17 555 Astable circuit with diode across R2

Practical Hint: to achieve a duty cycle of less than 50% a diode can be added in parallel with R2 as shown in the diagram. This bypasses R2 during the charging (mark) part of the cycle so that Tm depends only on R1 and C1:

Tm = 0.7 × R1 × C1   (ignoring 0.7V across diode)
Ts  = 0.7 × R2 × C1   (unchanged)

Figure 10.18  Duty cycle with diode  =  

    Tm    

 = 

  R1  

Tm + Ts

R1 + R2

Use a signal diode such as 1N4148.

 

 

THE 555 MONOSTABLE EXAM TOPIC

  
 

 

 

Figure 10.19  555 Monostable

 

The 555 monostable subsystem figure 10.19 provides an output signal that stays high for a period of time before returning to low. It is able to provide a range of time delays up to about 20 minutes with reasonable accuracy. In practice the timing resistor at the discharge pin should be no higher than 1M and the timing capacitor at the threshold pin no higher than 1000 microfarads otherwise leakage currents may dominate and the timing pulse may never reach an end. In other words the circuit would stay latched on. 

 The 555 monostable is based on the 555 timer IC. A single pulse is generated by the monostable when it is triggered by a negative-going input pulse, such as that produced by the push switch connected to the trigger input. Once triggered the output remains high for the timed period. This time period can be calculated using the formula:

T= 1.1 R x C    KEY EQUATION  

 where R is in M ohms and C is in µF

 

Monostable operation Exam Topic

555 monostable operation

 

 

 

 

 

 

 

 

Figure  10.20 Monostable Timing Diagram Exam Topic

The timing period is triggered (started) when the trigger input (555 pin 2) is less than 1/3 Vs, this makes the output high (+Vs) and the capacitor C1 starts to charge through resistor R1. Once the time period has started further trigger pulses are ignored.

 

The threshold input (555 pin 6) monitors the voltage across C1 and when this reaches 2/3 Vs the time period is over and the output becomes low. At the same time discharge (555 pin 7) is connected to 0V, discharging the capacitor ready for the next trigger.

The reset input (555 pin 4) overrides all other inputs and the timing may be cancelled at any time by connecting reset to 0V, this instantly makes the output low and discharges the capacitor. If the reset function is not required the reset pin should be connected to +Vs.

power-on reset or trigger circuit

Figure 10. 21 Power-on reset or
trigger circuit

Power-on reset or trigger

It may be useful to ensure that a monostable circuit is reset or triggered automatically when the power supply is connected or switched on. This is achieved by using a capacitor instead of (or in addition to) a push switch as shown in the diagram.

The capacitor takes a short time to charge, briefly holding the input close to 0V when the circuit is switched on. A switch may be connected in parallel with the capacitor if manual operation is also required.

 

Driving other subsystems (practical aspects)

 

For simplicity, the astable and monostable are shown here driving buzzers but it should be remembered they can be allowed to drive any number of other subsystems such as logic or output drivers or other output devices, provided they are corrected interfaced.  

Remember this IC. Can sink or source up to 200 mA. This is more than most chips and it is sufficient to supply many output transducers directly, including LEDs (with a resistor in series), low current lamps, piezo transducers, loudspeakers (with a capacitor in series), relay coils (with diode protection) and some motors (with diode protection). The output voltage does not quite reach 0V and +Vs, especially if a large current is flowing.

 

 

555 and 556 output sinking and sourcing    Figure 10.22 Sinking and sourcing

 

To switch larger currents you can connect a transistor.

The ability to both sink and source current means that two devices can be connected to the output so that one is on when the output is low and the other is on when the output is high. The top diagram shows two LEDs connected in this way..

Loudspeakers

A loudspeaker (minimum resistance 64ohm) may be connected to the output of a 555 or 556 astable circuit but a capacitor (about 100µF) must be connected in series. The output is equivalent to a steady DC of about ˝Vs combined with a square wave AC (audio) signal. The capacitor blocks the DC, but allows the AC to pass as explained in capacitor coupling. connecting a loudspeaker to 555 and 556 outputs   Figure 10.23 Speaker connection

Piezo transducers may be connected directly to the output and do not require a capacitor in series.

Relay coils and other inductive loads

Like all ICs, the 555 and 556 must be protected from the brief high voltage 'spike' produced when an inductive load such as a relay coil is switched off. The standard protection diode must be connected 'backwards' across the the relay coil as shown in the diagram.

However, the 555 and 556 require an extra diode connected in series with the coil to ensure that a small 'glitch' cannot be fed back into the IC. Without this extra diode monostable circuits may re-trigger themselves as the coil is switched off! The coil current passes through the extra diode so it must be a 1N4001 or similar rectifier diode capable of passing the current, a signal diode such as a 1N4148 is usually not suitable

 

555 and 556 output protection    Figure 10.24 Driving Relays

Example Circuits

The 555 is such a versatile I.C. it has been considered worthy of including a few unusual example circuits which some of you might consider incorporating in some way into course works.

Edge-triggering                                           

edge-trigger circuit

Figure 10.25 Edge-triggering circuit

If the trigger input is still less than 1/3 Vs at the end of the time period the output will remain high until the trigger is greater than 1/3 Vs. This situation can occur if the input signal is from an on-off switch or sensor.

The monostable can be made edge triggered, responding only to changes of an input signal, by connecting the trigger signal through a capacitor to the trigger input. The capacitor passes sudden changes (AC) but blocks a constant (DC) signal. For further information please see the page on capacitance. The circuit is 'negative edge triggered' because it responds to a sudden fall in the input signal.

The resistor between the trigger (555 pin 2) and +Vs ensures that the trigger is normally high (+Vs).

555/556 Inverting Buffer or NOT gate

555 buffer circuit

Figure 10.26 555  as a NOT gate or inverting buffer

NOT gate symbol

Revision NOT gate symbol

The buffer circuit's input has a very high impedance (about 1Mohm) so it requires only a few µA, but the output can sink or source up to 200mA. This enables a high impedance signal source (such as an LDR) to switch a low impedance output transducer (such as a lamp).

It is an inverting buffer or NOT gate because the output logic state (low/high) is the inverse of the input state:

  • Input low (< 1/3 Vs) makes output high, +Vs
  • Input high (> 2/3 Vs) makes output low, 0V

When the input voltage is between 1/3 and 2/3 Vs the output remains in its present state.

 

Strictly speaking this circuit is more like a Schmitt trigger because its intermediate input region is a deadspace where there is no response, a property called hysteresis, it is like backlash in a mechanical linkage.

If high sensitivity is required the hysteresis is a problem, but in many circuits it is a helpful property. It gives the input a high immunity to noise because once the circuit output has switched high or low the input must change back by at least 1/3 Vs to make the output switch back, see  Figure 10.31 and Schmitt Triggers .

Figure 10.27 Power Alarm Power Alarm

 

This circuit figure 10.27 can be used as a audible 'Power-out Alarm'. It uses the 555 timer as an oscillator biased off by the presence of mains line-based DC voltage. When the line voltage fails, the bias is removed, and the tone will be heard in the speaker. R1 and C1 provide the DC bias that charges capacitor Ct to over 2/3 voltage, thereby holding the timer output low (as you learned previously). Diode D1 provides DC bias to the timer-supply pin and, optionally, charges a rechargeable 9-volt battery across D2. And when the line power fails, DC is furnished to the timer through D2. A line base voltage is one derived from am mains power supply, see power supplies. 

Tilt Switch   

Figure 10.28 Tilt Switch

 Actually figure 10.28 is really a alarm circuit, it shows how to use a 555 timer and a small glass-encapsulated mercury switch to indicate 'tilt'. The switch is mounted in its normal 'open' position, which allows the timer output to stay low, as established by C1 on start-up. When S1 is disturbed, causing its contacts to be bridged by the mercury blob, the 555 latch is set to a high output level where it will stay even if the switch is returned to its starting position. The high output can be used to enable an alarm of the visual or the audible type. Switch S2 will silent the alarm and reset the latch. C1 is a ceramic 0.1uF (=100 nano-Farad) capacitor.

 
Metronome

Fig. 10.29 Metronome

 

Figure 10.28 Essentially shows a variable frequency astable, a Metronome is a device used in the music industry. It indicates the rhythm by a 'toc-toc' sound which speed can be adjusted with the 250K potentiometer. It is very handy if you learning to play music and need to keep the correct rhythm up.   

Audio oscillator 

If you want a simple audio oscillator you can experiment with the metronome circuit by reducing the capacitor value. Inserting a Morse key in series with the power lead or speaker lead will give you a Morse code practice oscillator. 

 

    

CW Monitor    

Fig. 10.30 CW Monitor

 

Any of you who are licensed radio amateurs may be interested in the circuit shown in figure 10.30.

 This circuit monitors the Morse code 'on-air' via the tuning circuit and diode detector (see radio receivers) hook-up to pin 4 (the reset pin) and the short wire antenna. The 100K potentiometer controls the tone-pitch. The circuit is effectively an astable pulsing in the audio frequency range . When there is no signal present pin 4 is on zero volts and the astable output is permanently reset to zero (no output). When the detector receives a Morse signal a positive voltage is put on the reset pin and the astable pitch is allowed to sound in the speaker. It will therefore sound in sympathy with the incoming signal. You might like to experiment with this circuit as a mobile phone or mobile mast detector as well!  

 


Schmitt Trig.    

Fig. 10.31 Schmitt Trigger

 Figure 10.31 shows a simple, but effective circuit. It cleans up any noisy input signal in a nice, clean and square output signal. In radio control (R/C) it will clean up noisy servo signals caused by r.f. interference by long servo leads. As long as R1 equals R2, the 555 will automatically be biased for any supply voltage in the 5 to 16 volt range.: It should be noted that there is a 180-degree phase shift, see amplifiers . This circuit also lends itself to condition 60-Hz sine-wave reference signal taken from a 6.3 volt AC transformer before driving a series of binary or divide-by-N counters, see counters. The major advantage is that, unlike a conventional multivibrator type of squarer which divides the input frequency by 2, this method simply squares the 60-Hz sine wave reference signal without division.


 

The following circuits are examples of how a 555 timer IC assist in combination with another Integrated Circuit. Again, don't be afraid to experiment. Unless you circumvent the min and max parameters of the 555, it is very hard to destroy. Just have fun and learn something doing it.

555 Two-tone experiment

Fig. 10.32 Two-Tones

 The purpose of the experiment shown in figure 10.32 is to wire two 555 timers together sequentially to create a 2-note tone. If you wish, you can use the dual 556 timer ic.

Coin Toss

Fig. 10.33 Coin Toss

 

The electronic 'Heads-or-tails' coin toss circuit is basically a Yes or No decision maker when you can't make up your mind yourself. The 555 is wired as a Astable Oscillator, driving in turn, via pin 3, the 7473 flip-flop, see latches, flip flops, counters etc.  When you press S1 it randomly selects the 'Heads' or 'Tails' led. The LEDS flash rate is about 2 KHz (kilo-Hertz), which is much faster than your eyes can follow, so initially it appears that both LEDS are 'ON'. As soon as the switch is released only one led will be lit.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER 11  OPERATIONAL AMPLIFIERS AND COMPARATORS.

Previously we saw how light and dark sensor circuits could provide high or low outputs that could drive logic sub-systems, similarly for high or low temperature detectors. But what if twilight were applied to our sensor or a medium temperature?  

The output voltage would be intermediate between high and low and the logic system would be confused.  Comparators are subsystems which enable us to get a good logic signal output from virtually any analogue system input by means of usually one i.c. known as an operational amplifier and a reference voltage input, usually adjustable and obtained form a potential divider sub-system.  

We have seen amplifiers using transistors. (ICs) called operational amplifiers or op amps often have about 20 or 30 transistors inside them and their inputs work on a principle which is known as a long tailed pair or current mirror (this is beyond the scope of an A level text so we will not expand on it here. . They are called ``operational'' amplifiers, because they can be used to perform arithmetic operations (addition, subtraction, multiplication) with signals. In fact, op amps can also be used to integrate (calculate the areas under) and differentiate (calculate the slopes of) signals.

\includegraphics{lab4-opamp.eps}

Figure 11.1 A circuit model of an operational amplifier (op amp) with open loop gain $A$ and input and output resistances $R_{in}$and$R_{out}$.

A circuit model of an operational amplifier is shown in Figure 11.1 The output

voltage of the op amp is linearly proportional to the voltage difference between non inverting and inverting  input terminals $v_+ - v_-$by a factor of the gain$A$. However, the output voltage is limited to the range$-V_{CC} \leq v \leq V_{CC}$, where $V_{CC}$is the supply voltage specified by the designer of the op amp. The range $-V_{CC} \leq v \leq V_{CC}$is often called the linear region of the amplifier, and when the output swings to $V_{CC}$or $-V_{CC}$, the op amp is said to be saturated. An ideal op amp has infinite gain ($A = \infty$), infinite input resistance ( $R_{in} = \infty$), and zero output resistance.

 

 

 

Real Op Amps 

 

 

These have an open loop gain of about 100000 times. Their output voltage is therfore

given by  the following equation:

V_\mathrm{out} = (V_+ - V_-) \cdot G_\mathrm{openloop}

 

This means that for all but a tiny voltage difference (a few microvolts) between the non- inverting and inverting input terminals the output will saturate. However with a real op-amp, saturation occurs at 2 or 3 volts lower than the supply rail voltage. 

                                                             

 

 

 

 

 

T   Figure 11.2 Op-amp circuit symbol

he usual circuit symbol for an op-amp is: Diagram of op-amp pinoutswhere:

·      V+: non-inverting input

·      V: inverting input

·      Vout: output

·      VS+: positive power supply (sometimes also VDD, VCC, or VCC + )

·      VS−: negative power supply (sometimes also VSS, VEE, or VCC − )

 

The power supply pins are (VS+ and VS−) . The positions of the inverting and non-inverting inputs may be reversed in diagrams where appropriate; the power supply pins are not commonly reversed.

Connecting an Op Amp

Op amps with 8 pin Dual in Line Packages such as the LM741 should be connected to a breadboard as shown here. The notch is at the top of the op amp, with pins counted counterclockwise from the upper left corner.

Figure 11.3 741 Pin out

The Comparator

This setup is used to determine which input signal is greater. When the inputs are equal, there is no output. When the inverting input is greater, the op amp becomes saturated and output voltage is equal to the voltage of the power supply the op amp is connected to. When the non inverting input is greater, the output voltage is equal to the negative voltage supply, or the negative of the positive supply if connected to ground. Comparators are often used in analog to digital conversions.

Figure 11.4 Comparator

In an absolutely ideal case when the tow inputs are equal there should be no output voltage whatsoever.  In practice there may be a tiny voltage known as the offset.

This can be put right using an offset null control. The recommended circuit for balancing out the input offset is quite simple, as shown here. The offset null pins (1 and 5) give direct access to the 1K emitter resistors in the input stage, and the offset null circuit is simply a 10K potentiometer connected between them, with its slider connected to the negative power supply. This is equivalent to putting a 5K resistance in parallel with each of the 1K resistors inside the IC. The difference is that we can vary the external resistances by adjusting the potentiometer, until the voltage offset becomes zero.

Comparator action and circuits; exam topic

 An op-amp, used without any limiting feedback, will amplify the difference between the inputs by the open loop gain. As the open loop gain is assumed to be very large then even a very small difference between the inputs will result in the output saturating. The output saturating means that the output voltage gets as close to the supply voltage as it is able to. For example, if a standard 741 is used with ±15v power supplies then the output voltage will either be +13v or -13v unless the inputs are within a few microvolts of each other

 

Figure 11.5 Op amp saturation

In effect the op-amp is comparing the two inputs and giving an output that shows which of the inputs is bigger ... hence the op-amp is acting as a comparator

If the Non-inverting input is greater than the Inverting input then the output is positive, if the Inverting input is greater than the Non-inverting input then the output is negative

V+ > V- gives Vout > 0v

V- > V+ gives Vout < 0v

The comparator is useful for detecting when an input goes above or below a certain pre-determined value. In this sense the analogue input voltage is converted into a digital state - either on or off - and so a comparator is a simple 1 bit ADC!! Alternatively, in a simple sense, a comparator is bit like a voting system  its  output an indicator of whichever input ‘wins’.

 

Comparator used as a temperature sensor

The circuit diagram shows a comparator used to determine when the temperature goes above or below a threshold temperature

comparator

Figure 11.6 Comparator with temperature sensor 

  • The potential divider forms a voltage reference input sub-system by fixing the non-inverting input at some pre-determined voltage. This "reference" voltage is determined by the values of the resistors used in the potential divider. If a variable reference voltage is required, to set a variable temperature threshold, then a potentiometer can be used instead of the fixed potential divider.
  • The inverting input derives a voltage from a potential divider that has a thermistor as one of its resistors and so the voltage at the inverting input varies with temperature. If the temperature increases then the resistance of the thermistor decreases and the voltage at the inverting input increases
  • When the temperature is low, the voltage at the non-inverting input is higher than that at the inverting input and the output is positive. Current flows from the 741 (current sourcing) and through the green LED causing it to light
  • As the temperature raises, the voltage at the inverting input rises and the instant it is greater than the reference voltage at the non-inverting input, the output becomes negative. Current flows from 0v and into the output of the 741 (current sinking) causing the red LED to light

 

 

 Comparator used as a light level detector

The circuit below shows a comparator used to detect light level. When the light level passes some pre-determined threshold then the output changes state

light level detector

 

Figure 11.7 Comparator with light sensor

  • A variable resistor is used to set the threshold voltage at the inverting  input
  • When the light level is high, the resistance of the LDR is low and so the voltage at the non inverting is low, therefore the output is low
  • Note that the op-amp uses the 12v and 0v supplies, not the ±12v supplies and so the minimum output voltage is 0v (or 2v in reality)
  • When the light level falls, the resistance of the LDR rises and so does the voltage at the non inverting input. This causes the output to go high when the voltage on the non inverting input is greater than the voltage on the inverting input.
  • The point at which the output changes state can be set using the variable resistor  


 Comparator used as a range indicator; Practical Topic

The circuit below shows two comparators used to detect when the input voltage is within a given range

range detector

 

Figure 11.8 Range detector

  • When the input voltage is low, the inverting inputs of both op-amps are below the non-inverting inputs. Both outputs are positive and so there is no voltage difference across the LED and it does not light.
  • When the input voltage is high, the inverting inputs of both op-amps are above both the non-inverting inputs. Both outputs are negative and again there is no voltage difference across the LED and it does not light.
  • When the input voltage is between the two threshold voltages determined by the three resistors in the potential divider chain, the output of the upper op-amp is positive and the output of the lower op-amp is negative and so current flows through the LED and it lights to show that the input voltage is within the range required.

This simple circuit could be the basis of many projects where both upper and lower thresholds are required. If the input voltage is temperature dependent for instance then the output tells you when it is neither too hot nor too cold ... useful for anything from a baby’s room to beer making! Other possibilities exist if the input voltage is dependent on some other factor such as light level or time etc, etc.

 

Gain bandwidth product and Frequency Response

An op-amp has a very high gain, but only at dc and low frequencies. As frequency increases, the gain drops off steeply (usually at usuallyat6 dB per octave or 20dB per decade). Remember that dB = 20*log (Vo/Vi) so 20 dB is the same as a voltage ratio of 10:1. The output voltage falls by a factor of ten when the frequency rises by a factor of ten.


If you don’t like the maths just remember that due to the frequency compensation, the 741's voltage gain falls rapidly with increasing signal frequency. Typically down to 1000 at 1 kHz, 100 at 10 kHz, and unity at about 1MHz. To make this easy to remember we can say that the 741 has a gain-bandwidth product of around one million (i.e. 1 MHz as the units of frequency are Hz).

 ..\gifs\op-freq.gifFigure 11. 9 Gain –bandwidth

The gain-bandwidth product is a constant value for any point on the sloping part of the curve shown here. It is typically about 1 MHz for a 741.

It follows from the above that if we had some way of controlling or reducing the gain we might be able to use amplifiers over a wider frequency range. With op-amps this is done using negative feedback.  We can then go on to think about how might use op-amps as audio frequency amplifiers and sound mixers.

Op-amps With Negative Feedback

 

There are several basic ways in which an op-amp can be connected using negative feedback to stabilize the gain and increase frequency response.

 The large open-loop gain of an op-amp creates instability because a small noise voltage on the input can be amplified to a point where the amplifier is driven out of the linear region.

 Open-loop gain varies between devices.

 Closed-loop gain is independent of the open-loop gain.

Closed-Loop voltage gain, Acl

 It is the voltage gain of an op-amp with external feedback.

 Gain is controlled by external components.

 

Figure 11.10 Noninverting Amplifier

http://www.electronic-factory.co.uk/wp-content/op%20amp8.JPG

 

 

  Input signal is applied to the non-inverting input.

 The output is applied back to the inverting input through feedback (closed loop) circuit formed by the input resistor Ri and the feedback resistor Rf.  This creates a negative feedback.

 The two resistors create a voltage divider, which reduces Vout and connects the reduced voltage Vf to the inverting input.  The feedback voltage is:

Vf = Ri/(Ri + Rf)Vout

 The difference between the input voltage and the feedback voltage is the differential input to the op-amp.

 

 

This differential voltage is amplified by the open loop gain, A, to get Vout­.

Vout­ = A(Vin – Vf)

 Let B = Ri/(Ri + Rf). Thus Vf = BVout and

Vout = A(Vin – BVout)

Manipulate the expression to get:

Vout = AVin - AolBVout

Vout + ABVout = AolVin

Vout(1 + AB) = AolVin

Overall Gain = Vout/Vin = A/(1 + AB)

 

Since AolB >> 1, the equation above becomes:

 

Vout/Vin = Aol/(AolB) = 1/B

 

 Thus the closed loop gain of the noninverting (NI) amplifier is the reciprocal of the attenuation (B) of the feedback circuit (voltage-divider).

A(NI) = Vout/Vin = 1/B = (Ri + Rf)/Ri

 

Finally:

A(NI) = 1 + Rf/Ri

 

 Notice that the closed loop gain is independent of the open-loop gain.

 

 

 

 

Example

 

Determine the gain of the amplifier circuit shown below. The open loop gain of the op-amp is 150000.

http://www.electronic-factory.co.uk/wp-content/op%20amp9.JPG

Solution

This is a non-inverting amplifier op-amp configuration. Therefore, the closed-loop voltage gain is

A(NI) = 1 + Rf/Ri = 1 + 100 /4.7  = 22.3

 

 

Voltage-Follower (VF)

 

 Output voltage of a noninverting amplifier is fed back to the inverting input by a straight connection.

 The straight feedback has a gain of 1 (i.e. there is no gain). The closed-loop voltage gain is 1/B, but B = 1. Thus, the A(VF) = 1.

 It has very high input impedance and low output impedance.

 

 

 

Figure 11.12 Voltag Follower

http://www.electronic-factory.co.uk/wp-content/op%20amp10.JPG

Inverting Amplifier (I)

 

 The input signal is applied through a series input resistor Ri to the inverting input.

 The output is fed back through Rf to the same input.

 The non-inverting input is grounded.

http://www.electronic-factory.co.uk/wp-content/op%20amp11.JPG

Figure 11.13 Inverting Amplifier with negative Feedback 

 

 For finding the gain, let’s assume there is infinite impedance at the input (i.e. between the inverting and non-inverting inputs).

 Infinite input impedance implies zero current at the inverting input.

 If there is zero current through the input impedance, there is NO voltage drop between the inverting and non-inverting inputs.

 Thus, the voltage at the inverting input is zero!

 The zero at the inverting input is referred to as virtual earth (ground).

http://www.electronic-factory.co.uk/wp-content/op%20amp12.JPG

Figure 11.14 Virtual earth

 

 Since there is no current at the inverting input, the current through Ri and the current through Rf are equal:

Iin = If.

 The voltage across Ri equals Vin because of virtual ground on the other side of the resistor. Therefore we have that

Iin = Vin/Ri.

 

 Also, the voltage across Rf equals –Vout, because of virtual ground. Therefore:

 

If = -Vout/Rf

     Since If = Iin, we get that:

-Vout/Rf = Vin/Ri

 Or, rearranging,

Vout/Vin = -Rf/Ri

 So,

A(I) = -Rf/Ri

 Thus, the closed loop gain is independent of the op-amp’s internal open-loop gain.

 The negative feedback stabilizes the voltage gain.

 The negative sign indicates inversion.

 

 

 

 

Figure 11.15 Op Amp Summing Amplifier

 

http://ecircuitcenter.com/Circuits/opsum/image002.gif

                            The summing amplifier is a handy circuit enabling you to add several signals together. What are some examples? If you're measuring temperature, you can add a negative offset to make the display read "0" at the freezing point. On a precision amplifier, you may need to add a small voltage to cancel the offset error of the op amp itself. An audio mixer is another good example of adding waveforms (sounds) from different channels (vocals, instruments) together before sending the combined signal to a recorder. It can also be used as a 3-bit D/A Converter.

Just remember that the circuit also inverts the input signals. Not a big deal. If you need the opposite polarity, put an inverting stage with a gain of -1 after the summing amplifier.

 

Summing Action

The summing action of this circuit is easy to understand if you keep in mind the main "mission" of the op amp. It's a simple one: keep the potential of the negative terminal very close to the positive terminal. In this case, keep the negative terminal close to 0V (virtual ground). Thus the op amp essentially holds one leg of R1, R2 and R3 to a 0V potential. This makes it easy to write the currents in these resistors.

I1 = V1 / R1;    I2 = V2 / R2;   I3 = V3 / R3

 So what's the current I flowing in RF? Using Kirchoff’s Law, we get

I = I1 + I2 + I3

Finally, notice that one leg of RF is also kept at 0V. So the output becomes Vo = -RF x I. Combining these pieces of information, we have a simple description of the amplifier

Vo = - RF (V1 / R1  +  V2 / R +  V3 / R3)

      = - (V1 · RF / R1 +  V2 · RF / R2  +  V3 · RF / R3 )

As you can see, the gain for each input is controlled by its single resistor: K1 = -RF/R1  K2 = -RF/R2  and K3 = -RF/R2.

Thus if RF=R1=R2=R3 then the output would be -( V1+V2+V3)

 


The  Differential Amplifier

\includegraphics{lab4-differential.eps}

Figure 11.16: Differential amplifier circuit.

A differential amplifier circuit is shown in Figure 

\begin{displaymath}
V_{out} = -\frac{R_2}{R_1} (V_1 - V_2).
\end{displaymath}

 

Uses

  • drive loudspeakers
  • amplify radio frequency energy before feeding to the antenna
  • drive DC motors. Both speed and direction can be controlled.

Source Followers

To boost current signals form op-amps, source followers are often used.

  • The N Channel FET provides power amplification for the positive part of the AC input.
  • The P Channel FET provides power amplification for the negative part of the AC input.
  • The voltage gain is 1
  • No output coupling capacitor is needed (avoiding the use of a physically big component). Single ended (not push pull) amplifiers need a big output coupling capacitor.
  • When there is no input, neither MOSFET is conducting. This saves energy. Single ended amplifiers consume power even when there is no input.
  • When there is an AC input, each MOSFET is conducting for only 50% of the time.

Cross Over Distortion

This simple push –pull circuit suffers from cross over distortion.

The red trace is the input signal. The blue trace is the output.

MOSFET Push Pull Amp.gif

MOSFET Push Pull Amp XOD.gif

 

Figure 11.17 Mosfet Push –pull with cross-over distortion

  • Quite a large input voltage is needed to turn on the FETs, 2 to 4 Volts.
  • This has an unwanted side effect. The output is 2 to 4 volts less than the ideal case.
  • A positive potential will turn on the top N Channel FET.
  • A negative potential will turn on the bottom P Channel FET.
  • Small potentials close to zero will turn on neither FET.
  • This causes severe cross over distortion, most noticeable with quiet music.
  • The amplifier works fairly well for potentials greater than +/- 2 to 4 volts but hardly works at all for lower potentials.

 

 

 

Bias the MOSFETs

A solution to cross-over distortion is to bias the mosfets so they are conducting all the time.

This diagram shows simple biasing using diodes and resistors. 0.7 Volts is lost across the diodes so the output will be lower than expected compared with using ideal components. It is possible to use LEDs. In this case about two Volts will be lost.

MOSFET Push Pull Amp Biased.gif

Figure 11.18 Mosfet Push-pull stage with Bias

Adjustable Bias and Quiescent Current

Bias may be refined by additional voltage divider resistors, adjustable so that both MOSFETS are just on the point of turning on. A small quiescent current (the current flowing when there is no input signal).

 

Use Negative Feedback

In addition to biasing, negative feedback further improves or eliminates cross-over distortion. 

  • This circuit uses both biasing and negative feedback to improve performance.
  • The LEDs have two volts across them. This helps to reduce cross over distortion. This is an unusual way of biasing the MOSFETs but it works.
  • The MOSFETS are included in the feedback path.
  • The Op Amp voltage follower uses a higher power supply voltage. This allows the MOSFET source follower outputs to swing over a larger range of voltages.

MOSFET Push Pull Amp Biased 3.gif

Figure 11.19 Mosfet Amplifier with bias and negative feedback

  • This circuit has a voltage gain of 1 but a much higher power gain (power_out / power_in).
  • The Op amp output potential will be just right to ensure that Vout = Vin
  • Negative feedback is being used to correct for errors in the output.
  • The operational amplifier is wired up as a voltage follower so Vout should track Vin exactly.
  • Cross over distortion is minimised.

Push Pull Advantages

  • Don't need a large coupling capacitor between the output and the speaker.
  • In other types of amplifier, this capacitor limits the low frequency response (high pass filter).

Push Pull Disadvantages

MOSFETs have good high frequency properties. Usually this is an advantage but it makes it easy to build an oscillator capable of high power outputs. The oscillations are likely to be outside the range of human hearing but still able to overheat and destroy speakers, usually the tweeters. Careful design is needed.

Saturation, Clipping, Limiting

Another form of distortion is known as saturation distortion or clipping.

This is when the amplifier cannot produce output voltages that are larger than the power supply voltages. If the input is too big, the amplifier output will increase until it is nearly equal to the supply voltage. After that the output voltage cannot rise any more. The red trace below shows the input. The blue trace shows the amplifier output. The MOSFETs have saturated. The sine wave input is clipped. The amplifier output is limited (by the power supply voltage).

MOSFET Push Pull Clipping.gif

RMS Output Power

  • The power supply is 20 Volts.
  • An 8Ω speaker is being used.
  • Decide whether to use 20V (ideal) or 18V (real life) in the calculation. If the exam question does not make it clear which one to use, just say whether you are doing the ideal or real life calculation. Below, the ideal calculation is shown.

Vrms = 0.7 x Vpeak

 

Power = Vrms2 / R

 

Power = (20 x 0.7)2 / 8

 

Power = 24.5 Watts

Power audio ICs

 

As an alternative to discrete components such as op-amps and mosfets power amplifier ICs can be utilized in radio receivers, hifi’s and AM modulators    

TDA2005 - 20 Watt Class B Amplifier

Tda 2005 ICThe TDA2005 is a class B dual audio power amplifier specifically designed for car radio applications. Power booster amplifiers capable of driving very low impedance loads (down to 1.6ohm) can be designed easily using this device with high current capability (up to 3.5 A).

 

TDA1013B - 4W Audio Power Amplifier

Tda 1013 ICThe TDA1013B is an integrated audio amplifier circuit with DC volume control in a 9 lead single inline plastic package. The wide supply voltage range makes this circuit ideal for applications in mains and battery fed devices such as record players and television receivers. This device requires only a few external components offering stability and performance.

 

LM386 - Low Voltage Audio Power Amplifier

LM 386 ICLM386 is an audio power amplifier IC designed for use in low voltage consumer applications. The gain is internally set to 20, but the addition of an external capacitor resistor between pins 1 - 8 will increase the gain to any value from 20 to 200. The output automatically biases to one half of the supply voltage. The quiescent power drain is small, only 24 mW when operating from a 6V supply, making the LM386 ideal for battery operation.

 

TDA2040 - Hi-Fi 20W Audio Power Amplifier IC

TDA 2040 ICThe TDA2040 is a good quality class AB audio power amplifier in Pentawatt package. Provides 22W output power (with d = 0.5%) at Vs = 32V/4ohm. The IC provides high output current and has very low cross-over and harmonic distortion. The device incorporates a thermal shut-down system and an efficient short circuit protection system, automatically limiting the dissipated power to keep the working point of the output transistors within their safe operating area.

 

TDA2003 - 10W Car Radio Audio Power Amplifier

TDA 2003 ICThe power amplifiers constructed with TDA 2003 need a very low number of external components. The IC provides high output current capability (up to 3.5A) with a very low harmonic and cross-over distortion. A completely safe operation is guaranteed due to the efficient protection against AC and DC short circuits between all pins and ground, load dump voltage surge (up to 40V), thermal over-range and fortuitous open ground.