Superposition Theorem - Basic Electronics - College Algebra Course Manual

Superposition theorem is one of those strokes of genius that takes a complex subject and simplifies it in a way that makes perfect sense. A theorem like Millman's certainly works well, but it is not quite obvious why it works so well. Superposition, on the other hand, is obvious.

The strategy used in the Superposition Theorem is to eliminate all but one source of power within a network at a time, using series/parallel analysis to determine voltage drops (and/or currents) within the modified network for each power source separately. Then, once voltage drops and/or currents have been determined for each power source working separately, the values are all "superimposed" on top of each other (added algebraically) to find the actual voltage drops/currents with all sources active. Let's look at our example circuit again and apply Superposition Theorem to it:

Since we have two sources of power in this circuit, we will have to calculate two sets of values for voltage drops and/or currents, one for the circuit with only the 28 volt battery in effect. . .

When re-drawing the circuit for series/parallel analysis with one source, all other voltage sources are replaced by wires (shorts), and all current sources with open circuits (breaks). Since we only have voltage sources (batteries) in our example circuit, we will replace every inactive source during analysis with a wire.

Analyzing the circuit with only the 28 volt battery, we obtain the following values for voltage and current:

Analyzing the circuit with only the 7 volt battery, we obtain another set of values for voltage and current:

When superimposing these values of voltage and current, we have to be very careful to consider polarity (voltage drop) and direction (electron flow), as the values have to be added algebraically.

Applying these superimposed voltage figures to the circuit, the end result looks something like this:

Currents add up algebraically as well, and can either be superimposed as done with the resistor voltage drops, or simply calculated from the final voltage drops and respective resistances (I=E/R). Either way, the answers will be the same. Here I will show the superposition method applied to current:

Once again applying these superimposed figures to our circuit:

Quite simple and elegant, don't you think? It must be noted, though, that the Superposition Theorem works only for circuits that are reducible to series/parallel combinations for each of the power sources at a time (thus, this theorem is useless for analyzing an unbalanced bridge circuit), and it only works where the underlying equations are linear (no mathematical powers or roots). The requisite of linearity means that Superposition Theorem is only applicable for determining voltage and current, not power!!! Power dissipations, being nonlinear functions, do not algebraically add to an accurate total when only one source is considered at a time. The need for linearity also means this Theorem cannot be applied in circuits where the resistance of a component changes with voltage or current. Hence, networks containing components like lamps (incandescent or gas-discharge) or varistors could not be analyzed.

Another prerequisite for Superposition Theorem is that all components must be "bilateral," meaning that they behave the same with electrons flowing either direction through them. Resistors have no polarity-specific behavior, and so the circuits we've been studying so far all meet this criterion. The Superposition Theorem finds use in the study of alternating current (AC) circuits, and semiconductor (amplifier) circuits, where sometimes AC is often mixed (superimposed) with DC. Because AC voltage and current equations (Ohm's Law) are linear just like DC, we can use Superposition to analyze the circuit with just the DC power source, then just the AC power source, combining the results to tell what will happen with both AC and DC sources in effect. For now,

Appendix

C H A P T E R

+ + + +

A-1 The Bread Board

A-2 Soldering

A-3 PCB Making

A-3 Schematic Diagram of the DC Power Supply

A-4 Block Diagram Of a Power Supply

A-5 Block Diagram Of aTelevision Set

A-6 Block Diagram of a cell phone model

You will build your circuits on the terminal strips by inserting the leads of circuit components into the contact receptacles and making connections with 22-26 gauge wire. There are wire cutter/strippers and a spool of wire in the lab. It is a good practice to wire +5V and 0V power supply connections to separate bus strips.

Usi

Using the Breadboard ng the Breadboard ng the Breadboard ng the Breadboard (Socket Board)(Socket Board)(Socket Board) (Socket Board)

The bread board has many strips of metal (copper usually) which run underneath the board. The metal strips are laid out as shown below.

These strips connect the holes on the top of the board. This makes it easy to connect components together to build circuits. To use the bread board, the legs of components are placed in the holes (the sockets). The holes are made so that they will hold the component in place. Each hole is connected to one of the metal strips running underneath the board.

Each wire forms a node. A node is a point in a circuit where two components are connected. Connections between different components are formed by putting their legs in a common node. On the bread board, a node is the row of holes that are connected by the strip of metal underneath.

The long top and bottom row of holes are usually used for power supply connections.

The rest of the circuit is built by placing components and connecting them together with jumper wires. Then when a path is formed by wires and components from the positive supply node to the negative supply node, we can turn on the power and current flows through the path and the circuit comes alive.

For chips with many legs (ICs), place them in the middle of the board so that half of the legs are on one side of the middle line and half are on the other side.

Soldering iron

Soldering iron is a necessary instrument when you solder. Solder is hardening in a normal temperature, but solder can melt easily by using the soldering iron and the parts and wiring materials can be fixed to the printed wiring board(PWB). The important piont is temperature of the soldering iron. For soldering, it needs to become the temperature of the object(PWB, parts, wire etc) to solder melting temperature. However, the temperature of soldering iron must not be too high. The electronic component gets damage with high temperature. So, you need to solder in a short time.

Sometimes, the loose contact of soldering occurs. It is difficult to confirm only by looking at. When the temperature of the object is not enough, the loose contact will be occured.

At the end of assembling of the electronic circuit, you need to check the soldered contact with circuit tester etc.

Electric power

Electric power (Cal (Cal (Calorific value is decided with this) (Calorific value is decided with this)orific value is decided with this) orific value is decided with this)

There are various kind of soldering irons. I am using 3 kinds of soldering irons.

25W type

I am usually using this type. This type is convenient when solder the parts on PWB.

80W type

I use this type when I solder the parts to thick copper plate. In case of thick copper plate, the heat is easy to escape and the temperature rise is difficult.

15W type

I use this type for the part which is easy to break by the heat. Usually, 25W type is enough.

The tip of iron

The soldering is done at the tip of iron. So, the tip of iron is very important. There is the type that the tip of soldering iron is made of copper stick. But I don't recommend that type.

Because, the copper stick rusts easily by heat and it becomes difficult to convey heat. Also the tip of copper stick melts with solder. It becomes difficult to sloder. I recommend the one that is using a special metal for tip. It is difficult to rust and melt. The tip of iron must keep clean. When it get dirty, it becomes difficult to convey heat.

There are many shape of tips. The tip which fit to the DIP type IC is used to remove the ICs. All of the solder on the pins can be melt at same time then it easy to remove the IC. I do not have such kind of soldering iron. Usually the soldering iron is heated by electricity. However, there is the soldering iron heated by gas. It is convenient to carry.

Soldering iron stand

The soldering iron becomes high temperature. Therefore it can't be placed on the desk directly. The stabilized soldering iron stand is necessary.

When making the electronic circuit, sometime I forgot the existence of soldering iron, because I have devoted to the parts, wiring etc. It was serious when I noticed, desk was burning.

You need to choose the iron stand with appropriate weight which can hold iron stably.Also you need to choose the iron stand that fit the form of iron.

Usually I wipe the tip of iron with moistened sponge. Therefore I use the iron stand with the place for sponge. This is your taste.

Solder

The solder is the alloy of lead and tin.

As for good solder, the containment rate of tin is high. The finish of soldering is beautiful. The price is a little bit high.

There are several kinds of solder, solder wire( thread form solder ) is convenient for electronic circuit making.

This solder wire is doing the structure of the pipe and flux is included inside. Flux melts together with the solder and the solder becomes easy to attach to the component leads.

Solder pump

This is the tool that can be absorbed the melted solder with the repulsion power of the spring that was built in with the principle of the piston.

The usage is shown below.

Pushe down the knob of the upper part of the pump against to spring until it is locked.

Melt the solder of the part that wants to absorb solder with iron. Apply the nozzle of the pump to the melted solder part.

Push the release knob of pump.

Then the plunger of the pump is pushed up with the power of spring and solder is absorbed inside the pump.

You need to do this operation quickly, otherwise the part gets damage by the heat. A little practice is needed.

Desoldering wire

This is made of thin copper net wire like a screen cable in a coaxial cable.

Like water inhales to cloth, the solder is absorbed to the net wire by a capillary tube phenomenon.

The usage is shown below.

Apply the desoldering wire to the part that wants to take solder. Apply the soldering iron from the top and Melt the solder.

The melted solder is absorbed to desoldering wire with a capillary tube phenomenon. At this time you absorb solder while shifting desoldering wire.

When the solder can not be removed in the once, remove repeatedly while shifting the desoldering wire.

There are several kinds of width of desoldering wire. I am using the one with 2mm width.

Making PWB

When assembling an electronic circuit, a board is needed on which the components can be mounted and wired together.

Mainly, I use the universal prined wiring board (PWB) for assembling the circuit. But I will explain about instruments that makes the printed board.

When you make the high frequency circuit, you need to consider the wiring length and the route of wiring etc.

Therefore when you make the high frequency circuit ( radio, high speed CPU etc. ), you need to make the printed wiring board.

In other countries, they are refered to as "Printed Circuit Boards," or PCBs.

The printed board is doing the structure which stuck copper leaf on insulation board such as the epoxy material of glass or the epoxy material of paper or the material of bakelite. The copper leaf becomes a wiring part. There are 2 kinds of types in the printed board. They are single-sided printed board and double sided printed board.

To make the printed wiring board, leaving the necessary(wiring part) place of the copper leaf, the unnecessary(insulate part) place is lost. This work is called Etching

There are several method to make the printed board.

Fundamentally the copper leaf is melted with the solution of the Ferric Chloride. The mask pattern is used to leave the wiring part.

You can write the mask pattern directly on negative printed board with oily ink. Some ink is melted by solvent, then you had better to check beforehand.

Even this method is good in the case that you make only 1 sheet.

This time, I will introduce the method using positive exposure printed board as negative printed board. The sensitizer has been applied on negative printed board. The nature of the sensitizer when hit the light changes. Lighted part of sensitizer can melt to the developer and the part not lighted does not melt.

The mask is made with the black color ink where the part that you want to leave the copper leaf. ( positive mask )

Dissolve the copper leaf is called Etching.

Etching liquid

This is the solution of the Ferric Chloride(FeCl3·H2O).The Ferric Chloride is not the toxic substance, play thing, dangerous article that were regulated with the laws but the liquid that the copper of the printed board dissolved by the etching becomes a waste fluid regulation object.(in case of Japan) Even if it is a little it pours to sewerage and also do not bury during the soil. Processing medicine that is attached to etching liquid without fail is used or it must process it in the waste fluid processing place of the specialty. When liquid is attached to the clothes it is never able to take it.

Do the attention to handling sufficiently, because the clothes have changed color. ( My experiences )

Avoid contact with eyes.

This is a mini drill that makes holes for mounting the parts on the printed board. For most of parts like resistor, cpacitor, the size of hole is about 0.6 mm.

Flux

The copper foil after removing the sensitizer becomes clean, but sheet copper is becoming bare condition then oxidization begins right away. Flux needs to be applied thinly to prevent oxidization. When flux is applied, you can make the copper leaf in clean condition forever. Also, you can carry out soldering easily.

INTRODUCTION TO ELECTRONICS...1

Section 1.1 Electronics Safety ... 1

Section 1.2 Applications of Electronics ... 3

Job titles... 4

Exercise 1. Electronics safety comprehension exam... 5

RESISTORS ...6

Section 2.1 Types of Resistors... 7

Carbon film resistors... 7

Metal film resistors ... 8

CDS Elements... 8

Other Resistors ... 9

Thermistor ( Thermally sensitive resistor )... 9

Section 2.2 Resistor color code ... 10

Exercise 2. Resistor Color Codes... 12

Section 2.3 The Ohmmeter ... 13

Zero Resistance... 13

Using the Ohmmeter... 14

Ohmmeter Ranges ... 14

Ohmmeter Safety Precautions ... 15

Section 2.4 The Multimeter... 15

Multimeter Controls... 16

Multimeter Scales ... 16

Parallax Error... 17

Multimeter Safety Precautions... 18

Laboratory Experiment 1 Using the Ohmmeter ... 19

Variable Resistors... 20

Rheostats and Potentiometers ... 20

Section 2.6 Rating of Resistors ... 22

Section 2.7 Resistor Troubles ... 22

Section 2.8 Resistor Connections... 23

Series Combinations of Resistors ... 23

Exercise 4 Resistors in Series ... 26

Parallel Resistors ... 27

Parallel Resistors - A Point to Remember ... 27

Exercise 5 Resistors in Parallel ... 28

Combinations of Resistors - Series/Parallel Circuits ... 29

Exercise 5 Resistors in Parallel ... 31

OHM'S LAW ...36

Section 3.4 PARALLEL CIRCUIT... 43

Section 3.5 Series - Parallel Circuits ... 46

Section 3.6 Voltmeters... 49

How to Use a Voltmeter ... 49

Section 3.7 Ammeters ... 53

Ammeter Connected in Series ... 53

Effect on the Circuit being Measured ... 54

Ammeter Sensitivity ... 55

Ammeter Ranges ... 55

Range Selection ... 57

Ammeter Safety Precautions ... 58

Exercise 3. Problem Sets on Ohm’s Law... 59

Solutions to Exercise Number 3... 65

COMMON ELECTRONIC DEVICES ...73

Section 4.1 Transformer ... 73

Construction... 73

Transformer Core... 74

Section 4.2 Switch and Fuse... 75

Fuse... 75

How to select a fuse in a circuit ... 76

Laboratory Experiment 3 Transformer Switch and Fuse Testing ... 79

Section 4.3 Semiconductor Diodes ... 80

Introduction ... 80

REVIEW:... 83

Section 4.4 Meter check of a diode ... 83

REVIEW:... 86

Section 4.5 Rectifier circuits ... 87

Laboratory Experiment 4 Diode Biasing ... 90

Section 4.6 Capacitors ... 91

The unit of measurements of capacitance ... 91

Schematic symbols of a capacitor... 92

Laboratory Experiment 5 Capacitor Action ... 93

Section 4.7 Different types of capacitors... 94

Electrolytic Capacitors (Electrochemical type capacitors) ... 94

Tantalum Capacitors ... 95

Ceramic Capacitors... 95

Multilayer Ceramic Capacitors ... 96

Polystyrene Film Capacitors ... 96

Electric Double Layer Capacitors (Super Capacitors) ... 96

Polyester Film Capacitors... 97

Mica Capacitors ... 98

Metallized Polyester Film Capacitors... 98

Variable Capacitors ... 98

Characteristics of Capacitors ... 99

Capacitor Connections... 100

Laboratory Experiment 6 Filtered Rectifier Circuits ... 101

Section 4.8 Transistors ... 102

Introduction ... 102

REVIEW:... 103

Section 4.9 Meter check of a transistor... 104

REVIEW:... 108

OTHER TECHNIQUES OF SOLVING VOLTAGE AND CURRENT VALUES .109

Section 5.1 Voltage divider circuits... 109

Linear Potentiometer Construction ... 113

REVIEW:... 116

Section 5.2 Kirchhoff's Voltage Law (KVL) ... 116

REVIEW:... 125

Section 5.3 Current divider circuits ... 126

REVIEW:... 129

Section 5.4 Kirchhoff's Current Law (KCL)... 129

REVIEW:... 131

Section 5.5 Thevenin's Theorem... 131

REVIEW:... 135

Section 5.6 Norton's Theorem ... 136

REVIEW:... 139

Section 5.7 Thevenin-Norton Equivalencies... 139

REVIEW:... 141

Section 5.8 Superposition Theorem... 141

REVIEW:... 145

APPENDIX ...146

The Breadboard... 147

Etching liquid ... 152 Battery driven mini drill ... 153 Flux ... 153

In document Basic Electronics - College Algebra Course Manual (Page 141-157)