brushing up circuits

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from the online learning library series of

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UpBrus hingA Review of Circuits

In todays fast-paced automation environment, filled with multi-featured

mechatronic components, keeping your electrical knowledge sharp is

paramount. If your electrical toolbox could use an upgrade, a primer on

of the basics may be in order and this handy Review of Circuits eBook

is here to help. Included are concise illustrated reviews of Ohms law, eddy

currents, transistor basics, and thermocouple phenomena including Joules

law and the Seebeck, Peltier, and Thomson effects. Equivalent circuits and

semiconductor physics are also detailed in a colorful formats, along with a

fresh look at LEDs and how they work.

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A Review of Circuits table of contents

A message from our sponsor

UpBrus hing

4Ohms Law: George Ohm discovered that in certain materials, current and voltage are directly proportional, related by resistance.6Thermoelectric effects: It takes a lot of energy to dislodge a neutron or proton from an atom, but electrons are out the door with the slightest nudge. A small voltage, a tiny amount of heat, or the impact of a few photons is all it takes, especially in metals.

12Eddy currents: A changing magnetic field induces circulating currents in a conductor. These currents, called eddy currents, stem from emfs caused by magnetic flux changes.

16 Equivalent circuit models: Designers use mathematical models to predict how electrical systems will behave. The details expressed by these models, like significant digits in an equation, go as deep as the analysis requires.

18Semiconductor device physics: Chip designers are concerned with electron movements in crystals and the holes they leave behind, how each moves, and the effects of one type outnumbering another in different regions of a crystal.

20The making of LEDs: What is the structure of LEDs, and how do they emit light? All ICs, including LEDs, are basically sourced from P-N junctions. A P-N junction is made of N and P-type semiconductors doped with different impurity.

Read more about this proliferating technology.

Industrial Technology students at Pleasantville High School, in Pleasantville, Iowa, have spent the last three years building a multi-mirror solar array. Instructor and mentor Frank Vanderpool championed the project from its inception.

Sunlight is focused on a solar heat exchanger positioned at the focal point of the array. Water is warmed and then piped indoors to a storage tank and radiator where it is used to heat the room, before circulating back to the solar heat exchanger to be reheated.

The array consists of 96 one-foot-square mirrors positioned in a 10x10 array. The hinged array/exchanger assembly is fitted with wheels so it can track the sun with both altitude and azimuth motions during each day. Two SureStep stepping systems from AutomationDirect power these two axes of motion via custom gearboxes designed and built by the students.

Three simple photo-resistors enclosed in narrow tubes, each with a slit facing skyward, are used as sunlight detectors to monitor the suns position. The tubes are aimed slightly away from the angle of the array. When sunlight reaches the bottom of the tubes and excites the photo-resistor, it signals a need to move the array to keep alignment with the sun.

A DirectLOGIC PLC accepts

AutomationDirect components put to good use:

Solar array by Pleasantville High School students

discrete inputs from the sunlight detectors and uses that information to control the motion of the two stepper systems. Additional logic in the PLC is used to position the array on cloudy days so that if/when the clouds dissipate the array is positioned to begin its automatic operation. The PLC controls the flow of water and controls a pump inside the storage tank. Analog inputs allow monitoring of temperatures in additional locations. Based on the various temperatures, the PLC opens and closes a valve to regulate the flow of water through the loop, and most importantly to stop the flow of water if the array is not producing heat for some reason (perhaps a cloud is blocking the sunlight).

On a sunny day, results can be more than impressive. On several occasions, the water has boiled and pressurized steam (measured at over 104C) has caused problems such as blown hoses. Today, the students have resolved those issues and water temperatures in the storage tank average about 165-180F even on moderately sunny days. They routinely heat the shop exclusively with solar energy.

Frank Vanderpool is understandably proud of what his students have achieved thus far. He reports, The project has been, and continues to be, a wonderful learning experience for all of the students involved.

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UpBrushingOhms law

I n 1827, George Simon Ohm, a German physicist, published a paper titled, The Galvanic

Circuit Investigated Mathematically. Here,

Ohm described a series of experiments in which he measured and analyzed

current and voltage through and across various conductive materials. He concluded that in certain

materials, current and voltage were directly

proportional, related by a constant, resistance, the

unit of which is the ohm ().

According to Ohms law, the voltage V across a current-carrying resistor is the product of the current I and

resistance R; V = RI. The corresponding power P dissipated by the resistor is found by substituting V = RI in the standard power

equation P= VI, yielding P = (RI)I = I2R.

PIV

V2

I

V R

RI2R

VR

PV

PR

V2P

PI

PIRI2

VI

PR

Ohms law relationships

A resistor is an electrical component often used to limit current or reduce source voltage powering a load.

Industrial applications for resistors big, tough ones are quite common, running the gamut from dynamic braking on adjustable-speed drives to reduced-voltage (soft) starting on ac motor-driven conveyors, hoists, pumps, and mill stands.

They also include current or torque-limited starting and stopping on equipment powered by dc motors.

Series connection

The equivalent resistance REs of two or more resistors connected in series is the sum of the individual resistances.

REs = R1s + R2s + ... RNs

Series resistance

REs

R1s R2s RNs

The equivalent resistance REp of two or more resistors connected in parallel is the reciprocal of the sum of the reciprocals of each resistance.

REp = 1/(1/R1p + 1/R2p + ... 1/RNp)

Parallel resistance

REp R1p R2p RNp

Parallel connection

Resistors at work

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In 1834, French physicist Jean C. A. Peltier discovered the inverse of the Seebeck effect: A current passing through the junctions formed by two dissimilar metals or semiconductors creates a thermal gradient, causing one junction to heat while the other cools.

The Peltier effect is employed in solid-state heat pumps, also known as thermoelectric coolers.

Cest hot!

Currentsource

Heatproducing

Heatabsorbing

Hot

Cool

e- e-

e-

e-e-

More on Peltier on page 10 ...


UpBrushing

Thermoelectric effectsAnyone whos taken a hands-on course in electric circuits knows that resistors warm when conducting current. The amount of heat is proportional to the product of the resistance and the square of the current.

This relationship, known as Joules Law, was discovered in the 1800s by James Joule, an English physicist.

Other scientists studying thermoelectricity at the time include Seebeck, Peltier, and Thomson. Their findings that certain materials convert electric energy directly into heat and vice versa are now employed in everything from submarines to spacecraft to automobiles.

Peltier effect

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The open-circuit voltage of a dissimilar-metal junction is a function of junction temperature and the composition of the two metals. The voltage, called the Seebeck voltage, is proportional to the change in temperature. The proportionality constant is known as the Seebeck coefficient.

This circuit may look familiar; its a standard thermocouple used to measure temperature.

A thermopile is essentially a series connection of many thermocouples. It can be used to power small electrical loads, such as lamps, dc motors, and solenoids, provided the junctions on opposite sides of the wires are kept at different temperatures.

Heat to voltage converter

Metal A

Metal BV = f(T)

Themoelectric effectsUpBrushing

In 1821, German physicist Thomas J. Seebeck discovered a measurable voltage along a metal conductor, hot on one end, cool on the other. The voltage is on the order of several millivolts per degree C of temperature gradient.

This effect, named after its discoverer, is also observed across the junctions of a circuit formed by two metals, where one junction is hotter than the other.

Electrons move from the hot to the cold end of a metal bar, producing a voltage. The voltage is proportional to the temperature gradient as well as fundamental material properties.

Seebeck effect

Voltage

Was ist das voltage?

Hot

Cool

e-

e-

e-e-e-

e- e-e-

e-

e-

Seebeck voltage at work

Seebeck discovered that a pair of wires (made of different metals) joined at both ends makes a magnetic needle move if the two junctions are

held at different temperatures. Needle deflection indicates charge flow, or the presence of current.

Reversing the temperatures changes the currents direction.

Charge pumpCurrent

Metal A

Metal B

Metal A

It takes a lot of energy to dislodge a neutron or proton from an atom, but electrons are out the door with the slightest nudge. A small voltage, a tiny amount of heat, or the impact of a few photons is all it takes, especially in metals.

Thermal and electrical energy, in particular, work hand-in-hand, one enhancing the effect of the other, as several 19th-century scientists discovered. Three scientists, in fact, made names for themselves Seebeck, Peltier, and Thomson observing different (thermoelectric) properties of metals exposed to heat and cold.


Gumption junction

Thermoelectric cooling

Metal A

Metal A

Metal B

Metal B

+

e-

Peltier emf

In 1854, William Thomson discovered that a temperature gradient across a conductor causes electrons to flow. In some metals, the electrons flow from hot to cold (copper, for example); in other metals, such as iron, the electrons flow from cold to hot. The thermally induced current is actually a net charge flow due to the fact that electrons at different energy levels move at different velocities. The flow is also accompanied by a buildup of space charge across the conductor, and hence an electromotive force (emf) or voltage.

Hot to trot

+

+

+

e-

e-

e-

-

-

-

Scottish scientist William Thomsons discovery put another way: A current-carrying conductor subject to a temperature gradient will absorb or give off heat depending on the material and the polarity of the current.

Thomson showed that unlike Joule or resistive heating, which is not reversible, the heating mechanism he discovered changes sign with a

change in the direction of current.

Peltier effect

Put a bowling ball on a steep hill, and down it rolls. Likewise, put an electron on a voltage slope and you get an electrical current.

A dissimilar-metal junction provides just such a gradient known as the Peltier emf (electromotive force) the result of the difference in average electron energy levels (Fermi levels) in the two materials.

The greater the difference in potential or emf, the more energy released or absorbed as the electrons cross the junction.

A few years after Seebecks discovery, J. C. A. Peltier, in 1834, found that at the junction of two metals carrying a small current, the temperature goes up or down depending on the direction of current and the difference in the Fermi levels of the two materials.

If the velocity of electrons below the Fermi energy (or chemical potential) is higher than that of those above the Fermi level, the junction absorbs heat.

The heat is consumed providing energy to lift the electrons up and over the barrier presented by the junction.

Such thermoelectric cooling is widely used in military as well as commercial applications. Submarines, for example, use solid-state thermoelectric (TE) cooling to eliminate compressor noise. Guidance systems employing heat-seeking infrared detectors also use TE coolers.

Peltier effect

-

Forcing a current through a conductor, cold at one end and hot on the other, causes a transverse heat flow. Changing the direction of the current, as William Thomson discovered, reverses the flow of heat. Thomson, by the way, is also known as Lord Kelvin, after whom the Kelvin temperature scale is named.

Heat crossing

Thomson effect

e-

e-

e-

e-

Currentsource

How's this for a wee effect?Cool end

Hot endAbsorbs(or emits)

heat



(Magnetic) Eddy currents

Action...

Reactive force

Eddy current field

A changing magnetic field induces circulating currents in a conductor. These currents, called eddy currents, stem from emfs caused by magnetic flux changes. Moving the conductor through a static field produces similar results.

Time-varying magnetic field

Eddy currents

Eddy currents produce fields of their own which oppose and weaken the applied field. These fields also exert a reactive force on the conductor in a direction opposing the original motion. These observations are generally referred to as Lenzs law.

Applied field

...Reaction

Faradays law

Direction of motion

Induced voltage

Applied fieldFaraday discovered he could

induce a voltage in a conductor by moving it through a magnetic

field. This voltage, called an electromotive force or emf, also

develops when a conductor is placed in a time-varying

field. Faradays law is typically expressed as emf = -d/dt, where

= magnetic flux and t = time.

Oscillator CoilProximity sensors often work by inducing eddy currents in conductive targets.

Reactive field

Excitation field

Direction of motion

Eddy currents

A special circuit, called an eddy current killed oscillator, is used in certain types of inductive proximity sensors. The circuit

oscillates at its natural frequency until the reactive field from a conductive target

changes the reluctance of the circuit, killing the large-amplitude oscillations.

Proximity sensors

UpBrushing



Oscillator amplitude drops when a target nears the sensor, changing the reluctance and hence natural frequency of the magnetic circuit.

Target present

Amplitude

Effect of target

Frequency

Applied fieldReactive forces from

eddy currents resist motion.

Though not as common as some of the other applications, eddy currents also play a role in damping vibration.

The damping action stems from the fact that eddy currents produce reactive forces that oppose causal motion.

Vibration damping

No applied field

Induction heating

Resistive losses generate heat.

Magnetic field induces current in the conductor.Eddy currents do most of the work

in inductive heating and cooking. The amount of heat they produce is proportional to the square of the current times the resistance, I2R.

Reducing eddy currents with laminations

Eddy currents confined to long, thin laminates.

High-resistance path limits induced current, lowering the I2R loss.

Reactive fields from opposing currents on inner laminate surfaces cancel.

If youre designing a motor or transformer, the last thing you want is eddy currents circulating in the iron core.

Besides wasting energy as heat, their reactive fields reduce the flux powering the device. One way to avoid this is to use an iron core consisting of laminated layers rather than a solid material.

Perimeter current components are the only ones that contribute to the reactive field, minimizing flux loss.

More on Eddy currents




Thevenins theoremThevenins theorem, based on superposition,

reduces linear circuits to equivalent models consisting of a voltage source in series with a resistor. Thevenins equivalents are useful when analyzing power systems and other circuits where the load resistance may change.

To find a circuits Thevenin source voltage vT, replace the load resistor with an open circuit. The open-circuit voltage vOC is simply vT because no voltage drops across RT when i = 0. To find the Thevenin equivalent resistance RT, remove all power sources and calculate the total resistance across the load terminals.

A Thevenin equivalent circuit model places a

voltage source in series with a resistance. When

the load is replaced with an open circuit, the

output voltage equals the Thevenin voltage.

Superposition reduces ac, as well as combined ac and dc source circuits by turning off all independent sources (except one) and finding the circuits output with that one

turned on.

Repeating for each indepen-dent source and adding in-

dividual outputs determines the total output.

SuperpositionOne of the most powerful tools when modeling

electrical circuits is superposition. The principle, which applies to any linear system consisting of multiple energy sources, allows the effect of each source to be analyzed independently. Summing the effects of the individual sources working alone produces the net effect of all sources acting together. The condition of linearity means simply that all variables in the system are proportionally related (no exponents, powers, or roots).

Isolating power sources in an electrical circuit is accomplished by turning off all independent voltage and current sources except the one of interest. All current sources are replaced with open circuits (representing zero current), while all voltage sources are replaced by short circuits (zero voltage). With all sources removed, remaining components in the circuit are more easily simplified to series/parallel impedance combinations.

RN

Sourcei

isciN

The Norton equivalent circuit model places a current source

in parallel with a resistance.

Nortons theoremNortons theorem, related to Thevenins, states

that a complex linear circuit can reduce to an equivalent current source and parallel resistor.

This is the dual of Thevenins theorem, where instead of voltage, equations focus on current relationships. As such, the first step is finding the source current iN by replacing the load with a short and calculating current through it. Here, iN = iSC because source current is diverted through the short circuit load.

To find the equivalent resistance RN, remove all power sources and calculate total resistance at the load.

Designers often use mathematical models to predict how mechanical and electrical systems will behave. The details expressed by these models, like significant digits in an equation, go only as deep as the analysis requires.

Determining how gears convert torque, for example, is satisfied with a simple model, usually just two parameters (gear ratio and efficiency). Predicting how a gear will behave under stress, on the other hand, calls for a more complex model, typically of finite-element resolution.

In the electrical domain, models follow a similar order. The model of an ac motor drive, for instance, doesnt need to include every last component to predict how the current and voltage output will power its intended load. In fact,

all thats needed is a single voltage or current source and an equivalent resistor a simple combination that can represent many complex, multi-source circuits.

Equivalent circuit models+

RT

Source

vT

i

vOC

+

vO3+

R

R

R

Shortcircuits

vS3

+


Doping

Diffusion and drift


Successfully designing diodes and other semiconductor circuits depends on an understanding of the physical processes taking place at the atomic level. Chip designers are especially concerned with electron movements in crystals and the holes they leave behind, how each moves, and the effects of one type outnumbering another in different regions of a crystal. These processes contribute to the construction and operation of integrated circuits used in such products as cell phones, microwaves, and motion controllers.

When fabricating integrated circuits, one of the most common doping methods is ion implantation. Ion implanters produce ions, charged particles, and accelerate them with an electric field. These ions strike the silicon surface

and penetrate to varying depths. How deeply they embed in the crystal depends on the ion beams energy, which is controlled by the accelerating field voltage. Varying the beam current (flow of ions) controls the density,

or number, of ions implanted.

Boron implant

Photoresist

n+ n+ SiO2

p-substrate n-well

Polysilicongate

Doping alters carrier (charged particle) concentration in semiconductor

materials. Silicon regions doped with mostly electrons are n-type; mostly

holes, p-type.

Decelerationground extension

Dual-slitextractionelectrode

Beam tunnel

Electronconfinementbeam guide

Analyzer magnetedge focusing

Flag Faraday

Plasmaelectronflood (xenon)

Wafer

High-current implanters produce beam currents up to 25 mA. The greater the current, the faster the implantation. With faster

implantation, fabs output more wafers per hour.

Semiconductor device physicsCarriers move through silicon crystals via diffusion and drift.

Diffusion is the movement of particles from an area of high

concentration to low concentration and is caused by thermal agitation.

Drift results when an electric field is applied across a crystal,

superimposing a small velocity that accelerates free carriers. Holes drift

in the direction of the electric field, while electrons drift opposite the

electric field.

+

++

+

++

++ + +

n-well

SiO2

p-n junction

Oxide

p-type substrate

p-n junctionp-type substrate

+

++

+

++

++ +

n-well

SiO2

Oxide

E

If the electron concentration is greater in one part of a crystal

than another, electrons will diffuse to the region with fewer

electrons. (The same holds true for holes.) With drift, holes move

in the direction of the electric field, E, and electrons in the other

direction.

Semiconductor diodes are the simplest electronic devices, consisting of p and n-type silicon. At room temperature, thermal ionization breaks the silicons covalent bonds, freeing electrons from their parent atom. The positive charges (holes) left behind are quickly filled by electrons from nearby atoms in a process called recombination.

n-type siliconp-type silicon

p-n junction Rendez-vous

The point where two oppositely charged semiconductor regions meet is known as a p-n junction. At all times, free electrons and holes are present in equal magnitude, number, and concentration.

Doping involves adding impurity atoms to a semiconductor crystal to change its electrical properties. Adding a phosphorous atom to silicon, for example, introduces a free electron (one not shared in a covalent bond) making the silicon more n-type (mostly negatively charged carriers).

In this case, phosphorous is a donor atom. Adding boron to silicon, on the other hand, produces p-type (mostly positively charged carriers) material because each boron atom uses one silicon electron to complete its covalent bond. Here, boron is classified as an acceptor atom.

In the real world



The structure of LEDsUpBrushing

While energy production and distribution have always been a challenge, today it is increasingly urgent to reduce power consumption and lighting is no exception. Light-emitting diodes or LEDs provide an alternative to conventional lighting for consuming less power, lower

thermal dissipation, and longer life. In fact, LED products are already spurring evolution in lighting, and it is anticipated that power LEDs will lead the way in combining high intensity and efficiency. So what is the structure of LEDs, and how do they emit light?

(Photons)

PN junction

Vforward

Anode

Cathode

Iforward(Electrons)

visible

Electric

al model of an LED

How LEDs emit light All ICs, including LEDs, are basically sourced from P-N junctions. A P-N junction is made of N and P-type semiconductors doped with different impurity.

See the tic-tac-toe-looking image, left: Free electrons and holes, initially intended to meet across a junction, result in a depletion zone. The zone blocks charge flow (or current) and so, a suitably directed voltage is needed by the two ends of the P-N junction (forward bias) to overcome blocking force. (The wrong direction makes the depletion zone wider.)

An LED is a P-N junction semiconductor diode that emits photons when forward-biased, and it occurs when minority carriers recombine with carriers of the opposite type in a diodes bandgap.

The electrical module of LED emitting light wavelength

varies, primarily with the semi-conductor materials used,

because the bandgap energy varies with different semicon-

ductors.

Approximating white sunshine is the ultimate goal of much artifical lighting. White LEDs may soon replace incandescent and fluorescent lamps, as they match the coloring of these old technologies, but with better efficiency.

Blue lighting has been key in the development of white LED manufacturing. The first blue LED was produced in RCA Laboratories in 1971 after experimentation with doping and materials. However, it had poor output, so it wasnt until the 1990s that blue LEDs achieved the efficiency and technological maturity required for commercialization.

Making white light with LEDsOriginal source

Inspired material/phosphor Principle

Blue LED InGaN/YAGBlue light from InGaN + yel-low light from YAG inspired by the blue light = white light

Blue LED InGaN/ PhosphorWhite light from RGB Phos-phor inspired by the blue light from InGaN

Blue LED ZnSeBlue light from the layer + yel-low light from ZnSe substrate = white light

Ultraviolet LED

InGaN/PhosphorWhite light from RGB Phos-phor inspired by ultraviolet light from InGaN

Blue, yellow/green LED

InGaN GaPEncapsulating two chips of complementary color to build white LED

Blue, Green, Red LED

InGaN AlInGaPEncapsulating three chips respectively emitting RGB light to build white LED

Multi-color LED

InGaN GaP AlIn-GaP

Encapsulating multiple chips falling in the whole visible spectrum to build white LED

Lightings holy grail: White light

Today, primary-color LEDs mix red, green, and blue to produce white light, mainly for custom low-volume applications. Di, tri, and tetrachromatic multi-colored white LEDs vary in color stability, color rendering capability, and luminous efficacy. Dichromatic white LEDs have the best luminous efficiency, but the least accurate color rendering. Tetrachromatic white LEDs exhibit excellent color rendering, but often shine dimly. Trichromatic white LEDs are in between, having both good luminous efficiency and fair color rendering capability.


LED s

tructure

Top bond wire Die mounted inreflective cavity

Translucent case

Post

Anvil

22 CIRCUITS eBook Sponsored by AUTOMATIONDIRECT

Producing color LEDMaterials ColorAlGaAs Red and infrared

AlGaP Green

AlGaInP Orange-red, orange, yellow, green

GaAsP Red, orange-red, orange, and yellow

GaP Red, yellow and green

LED development began with infrared and red light emitting devices made from gallium

arsenide.

Advances in materials science have made it

possible to produce many colors of light. These colors

can be generated from various materials, made up from a small group of

semiconductive elements.

Pick a bin: Grading LEDs

Binning is used to grade and classify power LED products. Essentially, it subdivides the huge variety of LEDs into grades based on luminous flux, forward voltage, dominating wavelength, and correlated color temperature. For manufacturers and end users, binning reduces cost and ensures certain levels of quality.

Materials ColorGaN Green, pure green (or emerald green), and blue;

also white (if with AlGaN Quantum Barrier)

InGaN Near ultraviolet, bluish-green, blue

SiC as substrate Blue (under development)

ZnSe Blue

AlN, AlGaN, AlGaInN Near to far ultraviolet

LED ch

ip 0.25 mm

Emission area

Top contact metallization

0.25

mm

0.1mm

Structure of an LED LEDs are composed of a die, a lead frame to hold the die, and encapsulation epoxy, which surrounds and protects the die and

disperses light. The die is bonded

with conductive epoxy into a recess in

one half of the lead frame called the anvil due to its shape. The recess in the anvil is shaped

to project the radiated light. The dies top contact is wire bonded to the other lead frame terminal, the post. LED dies or chips are processed in wafer form similar to silicon integrated circuits, and broken into dice.

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brushing up circuits

Documents

eddy currents

equivalent circuits

circulating currents

solar heat exchanger

handy review of circuits

electrical systems

multimirror solar array

10x10 array