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ENS 100: Introduction to Engineering
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First through sixth editions, copyright © 1994-1999 by John K. Bennett;
Seventh edition, August 2000, copyright © 2000 by James F. Young;
Rice University, Houston, Texas
Permission is hereby granted to reproduce and to distribute verbatim copies of this document in whole or
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Other than verbatim copies with copyright notice intact, no part of this document may be reproduced in
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on this document is not granted, and requires written consent.
Substantial portions of this document are derived from The 6.270 Robot Builder's Guide, Copyright ©
1992 by Fred G. Martin, with the permission of the author. Please see the Acknowledgements for
additional contributors and information.
The M.I.T. Department of Electrical Engineering and Computer Science and the M.I.T. Media Laboratory,
who sponsored the development of the original 6.270 class technology, have agreed to unrestricted and
free distribution of the robotics technology described in the course documentation for the 6.270 class,
including their printed circuit board artwork and software programming environment. The Department of
Electrical Engineering and the George R. Brown School of Engineering at Rice University have agreed to
similar unrestricted distribution of the ELEC 201 class technology developed at Rice. While the material
has not been placed in the public domain (it is still copyrighted), this means that any individual or
organization can use the material for whatever purposes they desire. Our mutual hope is that people will
use this work in the spirit of GNU software, which is distributed freely and is supported largely by a
community of interested users. Corrections and suggestions for improvement are most welcome.
The ELEC 201 Notes is no longer printed, except for the Assembly Manual. PostScript versions or LaTeX
source code for the various chapters are available by request from:
James F. Young
Electrical & Computer Engineering Department
Rice University, MS-366
PO Box 1892
Houston, TX 77251
[email protected]
1
Basic Mechanics
The branch of physics that deals with the action of forces on matter is referred to as mechanics. All
considerations of motion are addressed by mechanics, as well as the transmission of forces through the
use of simple machines.
Describing motion involves more than just saying that an object moved three feet to the right. The
magnitude and direction of the displacement are important, but so are the characteristics of the object's
velocity and acceleration. To understand these concepts, we must examine the nature of force. Changes
in the motion of an object are created by forces.
Forces
Whether a force is the push of a motor or the pull of gravity or muscles, the important characteristics are
the magnitude and direction of the force, and the mass and previous state of motion of the object being
affected. By pushing on a moving car, one can either cause it to gain speed or come to a stop, depending
on which direction the force is applied, and that same force applied to a feather would be expected to
more drastically affect the motion of the feather.
It is common practice to determine the expected changes in motion that an object will experience
due to a particular force with the aid of a "free body" diagram. A diagram can tell us at a glance in which
direction we would expect an object to accelerate or decelerate. A free body diagram shows all of the
forces acting on an object, even if their effects are balanced out by another force. We will use free body
diagrams to consider different situations involving the lamp that you find at your lab station (Figure 3.1).
One force that always acts on the lamp is gravity. This familiar force would accelerate the lamp
downward toward the center of the earth if left unchallenged. However, when the lamp is placed on a
table it does not move downward because the table holds it up. The lamp is pushing down on the table
and the table is pushing up on the lamp. This pair of forces is an action-reaction pair: equal and opposite
forces acting on two different objects in contact. The reaction force from the table is called the normal
force because this force is oriented normal (perpendicular) to the surface of the table. The arrows
representing the forces are labeled. The symbols over the labels remind us that the forces are vector
quantities and that the direction in which the force is applied is important. The length of the force vector
should be proportional to their magnitudes.
In Figure 3.1 the lamp was represented by a simple dot. We assumed that the lamp was rigid and
that a downward force applied at one particular spot on the lamp would yield the same result as a similar
downward force applied at a different place on the lamp. Actually, in order for a force of equal magnitude
and direction to affect an object's motion in the same manner it must be applied along the same line of
action as the original force (see Figure 3.2. If the original force had been a tug on a string tied to the lamp,
then it makes sense that grabbing the string at a different distance away from the lamp to tug should not
make a difference provided that the direction and magnitude do not change.
Friction
The normal force from the table's surface is a reaction force only. Without the downward force on the
table from the object resting its weight on the surface, the normal force does not exist. This type of
behavior is also descriptive of frictional forces.
Friction is opposition to motion, so if nothing is trying to move there will be no friction. However,
friction will be present when motion is attempted, even if the object is not yet moving. There are two
different types of friction: static, which acts before the object begins to move, and dynamic, which acts
after the object begins moving. Static friction is usually stronger than dynamic friction.
2
Figure 3.1: Free Body Diagrams
Friction occurs because the surfaces in contact are not smooth. The small ridges on the different
surfaces catch, and in order for the objects to move, these ridges must be broken off or the object must
ramp up and over the obstructions. By adding a lubricant between the two layers, it is possible to "float"
one layer high enough to miss some of the obstructions to motion. At an atomic level, cold joints may
form where the atoms from one object's surface may form weak bonds with the atoms on the surface of
the other object. These bonds must also be broken in order for the object to move. All of this resistance to
motion is called friction. Friction is very important because it not only inhibits motion, friction also makes
motion possible.
Torque
To understand the importance of using a line of action when considering a force, think of a yard stick
which has been pinned at the center. The yard stick is free to pivot around its center, so a downward
force applied at different places (and thus through different lines of action) will yield different results.
Pressing down directly over the pivot does not cause the stick to move or rotate, while pressing down at
one end causes the stick to rotate about the pivot. By pressing down at the end, we have applied a torque
to the stick and have caused it to rotate.
3
Figure 3.2: Line of Action
Figure 3.3: "Close Up" of surfaces in contact
4
Figure 3.4: Illustrating Torque
A torque is a force applied at a distance from a pivot. When describing torques, one must include
magnitude, direction, and perpendicular distance from the pivot. For torques the line of action is a circle
centered on the pivot. As torque is a product of force and distance, one may be "traded" for the other. By
applying more force closer to the pivot, one may produce the same torque. This concept of "trading"
distance traveled/applied for force experienced/applied is key to many simple machines.
Simple Machines
Complex machines are made up of moving parts such as levers, gears, cams, cranks, springs, belts, and
wheels. Machines deliver a certain type of movement to a desired location from an input force applied
somewhere else. Some machines simply convert one type of motion to another type (rotary to linear).
While there is a seemingly endless variety of machines, they are all based upon simple machines. Simple
machines include inclined planes, levers, wheel and axle, pulleys, and screws.
It is important to remember that all machines are limited in their efficiency. No machine is 100
percent efficient in its efforts, so the mechanical advantaged gained must be considered worthwhile of the
extra energy that will be required to accomplish the job.
The Inclined Plane
In an inclined plane the force required to raise an object a given distance is decreased by increasing the
distance over which that force must be applied. Imagine lifting something twice your weight to a 4 foot
high shelf. Now imagine rolling the same mass up a gently sloping surface. The latter would be much
easier. Inclined planes are commonly put to use in cutting devices and often two inclined planes are put
back to back to form a wedge. In a wedge forward movement is converted into a parting movement acting
perpendicular to the face of the blade (see Figure 3.6). A zipper is simply a combination of two lower
wedges for closing and an upper wedge for opening (Figure 3.6).
Figure 3.5: Inclined Plane
5
Figure 3.6: The Inclined Plane at Work
Levers
A lever has three points of interest: the fulcrum, the load, and the effort. The fulcrum is the point around
which the lever pivots rotationally. The load is what we wish to manipulate with the lever, and the load is
described by magnitude, direction, and position relative to the fulcrum. The effort also has a magnitude,
direction, and position with respect to the fulcrum. A lever is commonly used to change the direction of
movement, and to trade the magnitude of the effort for the distance over which the effort is applied.
As shown in Figure 3.7, there are three different classes of levers defined by the relative positions
of the fulcrum, effort, and load. A first class lever has the fulcrum positioned between the effort and the
load. Examples of first class levers include: a balance, a crow bar, and scissors. In a second class lever
the load is placed between the fulcrum and the effort. Examples of second class levers include: a
wheelbarrow, a bottle opener, and a nutcracker. Third class levers place the effort between the fulcrum
and the load. Examples of a third class lever are a hammer, a fishing rod, and tweezers. Most machines
that employ levers use a combination of several levers, often of different classes.
6
Figure 3.7: Classes of Levers
The Wheel and Axle
In both levers and the inclined plane, you gain in force what you lose in distance traveled. With wheels
and axles the same is true; the movement of the wheel is converted to a shorter but more powerful
movement at the axle. The wheel and axle can be thought of as simply a circular lever, as shown in
Figure 3.8. Many common items rely on the wheel and axle such as the screwdriver, the steering wheel,
the wrench, and the faucet.
Gears and Belts
A wheel and axle assembly becomes especially useful when gears and belts are brought into the picture.
Gears can be used to change the direction or speed of movement, but changing the speed of rotation
inversely affects the force transmitted. A small gear meshed with a larger gear will turn faster, but with
less force. There are four basic types of gears: spur gears, rack and pinion gears, bevel gears, and worm
gears. Spur gears are probably the type of gear that most people picture when they hear the word. The
two wheels are in the same plane (the axles are parallel). With rack and pinion gears there is one wheel
and one rack, a flat toothed bar that converts the rotary motion into linear motion. Bevel gears are also
known as pinion and crown or pinion and ring gears. In bevel gears, two wheels intermesh at an angle
changing the direction of rotation (the axles are not parallel); the speed and force may also be modified, if
desired. Worm gears involve one wheel gear (a pinion) and one shaft with a screw thread wrapped
7
around it. Worm gears change the direction of motion as well as the speed and force. Belts work in the
same manner as spur gears except that they do not change the direction of motion.
Figure 3.8: The Wheel and Axle
In both gears and belts, the way to alter speed and force is through the size of the two interacting
wheels. In any pair, the bigger wheel always rotates more slowly, but with more force. This "tradeoff"
between force and speed comes from the difference in the distance between the point of rotation and the
axle between the two wheels. On both the big and the small gear, the linear velocity at the point of
contact for the wheels is equal. If it was unequal and one gear were spinning faster than the other at the
point of contact then it would rip the teeth right off of the other gear. As the circumference of the larger
gear is greater, a point on the outside of the larger gear must cover a greater distance than a point on the
smaller gear to complete a revolution. Therefore the smaller gear must complete more revolutions than
the larger gear in the same time span. (It's rotating more quickly.) The force applied to the outer surface
of each wheel must also be equal otherwise one of them would be accelerating more rapidly than the
other and again the teeth of the other wheel would break. The forces of interest however are not the
forces being applied to the outer surfaces of the wheels, but rather the forces on the axles. Returning to
the concept of levers, we know that the distance at which the force is applied affects the force yielded,
and a wheel and axle works like a lever. Equal forces are being applied to each wheel, but on the larger
wheel that force is being applied over a greater distance. Thus for the larger wheel the force on the axle is
greater than the force on the axle for the smaller wheel.
Cams and Cranks
Both cams and cranks are useful when a repetitive motion is desired. Cams make rotary motion a little
more interesting by essentially moving the axle off-center. Cams are often used in conjunction with a rod.
One end of the rod is held flush against the cam by a spring. As the cam rotates the rod remains
stationary until the "bump" of the cam pushes the rod away from the cam's axle.
Cranks convert rotary motion into a piston-like linear motion. The best examples of cranks in
action are the drive mechanism for a steam locomotive and the automobile engine crankshaft. In a crank,
the wheel rotates about a centered axle, while an arm is attached to the wheel with an off-centered peg.
This arm is attached to a rod fixed in a linear path. A crank will cause the rod to move back and forth, and
if the rod is pushed back and forth, it will cause the crank to turn. On the other hand, cams can move their
rods, but rods cannot move the cams. Cams can be used to create either a linear repetitive motion such
as the one illustrated in Figure 3.9, or a repetitive rotational motion such as the one shown in Figure 3.15.
Pulleys
Pulleys can be used to simply change the direction of an applied force or to provide a force/distance
tradeoff in addition to a directional change, as shown in Figure 3.10. Pulleys are very flexible because
8
they use ropes to transfer force rather than a rigid object such as a board or a rod. Ropes can be routed
through virtually any path. They are able to abruptly change directions in three-dimensions without
consequence. Ropes can be wrapped around a motor's shaft and either wound up or let out as the motor
turns.
Figure 3.9: Cams and Cranks
Figure 3.10: Pulleys
Ropes also have the advantage that their performance is not affected by length. If a lever arm
was extremely long, then it would be unable to handle the magnitude of forces that a shorter version
could withstand. In a lever, to move a given distance next to the fulcrum, the end of the lever must move
a distance proportional to its length. As the length of the lever increases, it becomes more likely that the
lever will break somewhere along its length.
Figure 3.11 illustrates how a compound pulley `trades' force for distance through an
action/reaction force pair. In a double pulley, as the rope passes over the pulley the force is transmitted
9
entirely but the direction has changed. The effort is now pulling up on the left side of the bottom pulley.
Now, for a moment forget that the end of the rope is tied to the bottom of the top pulley. The mechanics
are the same if the rope is fixed to the ceiling. The important thing is that the end of the rope is immobile.
The effort is once again transmitted entirely as the rope passes over the bottom pulley and there is a
direction change. The end of the rope is attached to the ceiling so the rope is pulling down on the ceiling
with the force of the effort (and half of the force of the load). We assume that the ceiling holds up, so this
must mean that there is a force balancing out this downward force. The ceiling pulls up on the rope as a
reaction force. This upward force is equal to the effort and now there is an upward force on the right side
of the bottom pulley. From the perspective of a free-body diagram the compound pulley system could be
replaced by tying two ropes to the load and pulling up on each with a force equal to the effort.
Figure 3.11: How Compound Pulleys Work
The disadvantages of pulleys, in contrast to machines that use rigid objects to transfer force, are
slipping and stretching. A rope will permanently stretch under tension, which may affect the future
performance of a device. If a line becomes slack, then the operation of a machine may change entirely.
Also, ropes will slip and stick along pulley wheels just like belts. One solution to the problems associated
with rope is to use chain. Chain is pliable like rope, and is able to transfer force through many direction
changes, but the chain links are inflexible in tension, so that the chain will not stretch. Chains may also be
made to fit on gears so that slipping is not a problem.
The Screw
The screw is basically an inclined plane (see Figure 3.12) wrapped around a cylinder. In an inclined
plane, a linear force in the horizontal plane is converted to a vertical "lifting" force. With a screw, a rotary
force in the horizontal plane is converted to a vertical "lifting" force.
When a wood screw is turned, the threads of the screw push up on the wood. A reaction force
from the wood pushes back down on the screw threads and in this way the screw moves down even
10
though the force of turning the screw is in the horizontal plane. Screws are known for high friction, which
is why they are used to hold things together.
Figure 3.12: The Screw
Inertia
Inertia is a property of all matter: a resistance to changes in motion. To be clear, a change in motion is not
just beginning to move from a stop. Slowing down, speeding up, and changing direction are all changes in
motion. The only way to change a object's motion is to apply a force to that object. A book slid across a
table only comes to a stop because of the frictional forces acting on it. Inertia is proportional to mass, so a
more massive object is more difficult to move or stop than a lighter one (even on a frictionless surface).
Figure 3.13: Flywheel
11
Rotational Inertia
Just as a book slides until a force opposes its motion, a disc will spin until its rotation is opposed by some
force. This property is aptly named rotational inertia. One of the most common applications of rotational
inertia is shown in Figure 3.13. Many children's toys use rotational inertia. In friction-drive cars, the child
pushes the car forward several times to set an internal flywheel in motion. When the car is put down, the
flywheel is still spinning and the car moves. This is an interesting way to store energy -- in kinetic, rather
than potential format. Rotational inertia is also used to avoid changes in motion for such objects as record
players, where it is important to rotate at a constant speed. A flywheel could conceivably be used to store
energy to keep an ELEC 201 robot operating after its motors were required to be shut off.
Springs
A favorite device for storing potential energy is the spring. Everything from clocks to catapults make use
of springs. There are two distinctive forms of springs: the familiar coil and the bending bar. A common use
for springs is to return something to its original position. A more interesting application is to use them to
measure force -- springs in scales. The third use is to store energy. All springs perform all three functions
all of the time, but specific devices are built to exploit certain functions of the spring.
A coil spring works for more or less the same reason as a bar spring, it's just in a different shape.
To understand a spring, one must zoom in to the microscopic level where molecules interact. Molecules
are held together in rigid bodies because of electromagnetic forces. Some of these forces are repulsive,
and some of them are attractive. Normally they balance out so that the molecules are evenly spaced
within an object; however, by bending a bar, some molecules are forced farther apart and others are
shoved closer together. Where the molecules have been spread out, the attractive forces strive to return
the original spacing. Where molecules have been forced together, the repulsive forces work to return the
object to the original shape.
Figure 3.14: Bar Spring
12
Rubber Bands
A rubber band is just a kind of spring. A rubber band is slightly more versatile than a metal spring
because of its flexibility, just as pulleys are more versatile than their rigid cousin the lever. Rubber bands
also prove useful in the case of repetitive motions. Rather than turning a motor forward then backwards
then forwards and so on, one could make use of a cam and a rubber band to allow the motor to always
turn in one direction. Look at the assembly in Figure 3.15 for an example.
Figure 3.15: Using a Cam and a Rubber Band
.
Counterweights
Counterweighting is a necessary evil in constructing even a simple robot. Examples of common
counterweights are shown in Figure 3.16. If a robot that has been traveling along at high speed suddenly
comes to a halt, there is danger of the robot overturning if the location of the robot's center of mass has
not been well placed. The ELEC 201 robots carry around a fairly massive battery, and its placement
within the robot's structure is important. When an arm extends, the robot should remain stable. This is
accomplished through the use of counterweights.
Figure 3.16: Some Common Counterweights
13
Counterweighting might also prove useful to raise a bin carrying blocks. Rather than committing
an entire motor to raising a bin, a set of counterweights known to be heavier than the bin plus contents
could be suspended until the time when the bin should rise. Of course if a motor was used to take care of
the counterweights then no motors have been saved. A motor could be used for more than one task if a
mechanical transmission (see Figure 8.15) was employed. Another solution would be to use the high
current LED outputs to operate a solenoid.
14
Basic Electronics
The goal of this chapter is to provide some basic information about electronic circuits. We make the
assumption that you have no prior knowledge of electronics, electricity, or circuits, and start from the
basics. This is an unconventional approach, so it may be interesting, or at least amusing, even if you do
have some experience. So, the first question is ``What is an electronic circuit?'' A circuit is a structure that
directs and controls electric currents, presumably to perform some useful function. The very name
"circuit" implies that the structure is closed, something like a loop. That is all very well, but this answer
immediately raises a new question: "What is an electric current?" Again, the name "current" indicates that
it refers to some type of flow, and in this case we mean a flow of electric charge, which is usually just
called charge because electric charge is really the only kind there is. Finally we come to the basic
question:
What is Charge?
No one knows what charge really is anymore than anyone knows what gravity is. Both are models,
constructions, fabrications if you like, to describe and represent something that can be measured in the
real world, specifically a force. Gravity is the name for a force between masses that we can feel and
measure. Early workers observed that bodies in "certain electrical condition" also exerted forces on one
another that they could measure, and they invented charge to explain their observations. Amazingly, only
three simple postulates or assumptions, plus some experimental observations, are necessary to explain
all electrical phenomena. Everything: currents, electronics, radio waves, and light. Not many things are so
simple, so it is worth stating the three postulates clearly.
Charge exists
We just invent the name to represent the source of the physical force that can be observed. The
assumption is that the more charge something has, the more force will be exerted. Charge is measured in
units of Coulombs, abbreviated C. The unit was named to honor Charles Augustin Coulomb (1736-1806)
the French aristocrat and engineer who first measured the force between charged objects using a
sensitive torsion balance he invented. Coulomb lived in a time of political unrest and new ideas, the age
of Voltaire and Rousseau. Fortunately, Coulomb completed most of his work before the revolution and
prudently left Paris with the storming of the Bastille.
Charge comes in two styles
We call the two styles positive charge, +, and (you guessed it) negative charge, - . Charge also comes in
lumps of 1.6 ×10-19C, which is about two ten-million-trillionths of a Coulomb. The discrete nature of charge
is not important for this discussion, but it does serve to indicate that a Coulomb is a LOT of charge.
Charge is conserved
You cannot create it and you cannot annihilate it. You can, however, neutralize it. Early workers observed
experimentally that if they took equal amounts of positive and negative charge and combined them on
some object, then that object neither exerted nor responded to electrical forces; effectively it had zero net
charge. This experiment suggests that it might be possible to take uncharged, or neutral, material and to
separate somehow the latent positive and negative charges. If you have ever rubbed a balloon on wool to
make it stick to the wall, you have separated charges using mechanical action.
Those are the three postulates. Now we will present some of the experimental findings that both led to
them and amplify their significance.
Voltage
First we return to the basic assumption that forces are the result of charges. Specifically, bodies with
opposite charges attract, they exert a force on each other pulling them together. The magnitude of the
force is proportional to the product of the charge on each mass. This is just like gravity, where we use the
term "mass" to represent the quality of bodies that results in the attractive force that pulls them together
(see Fig. 4.1).
15
Figure 4.1: Opposite charges exert an attractive force on each other, just like two
masses attract. External force is required to hold them apart, and work is
required to move them farther apart.
Electrical force, like gravity, also depends inversely on the distance squared between the two
bodies; short separation means big forces. Thus it takes an opposing force to keep two charges of
opposite sign apart, just like it takes force to keep an apple from falling to earth. It also takes work and the
expenditure of energy to pull positive and negative charges apart, just like it takes work to raise a big
mass against gravity, or to stretch a spring. This stored or potential energy can be recovered and put to
work to do some useful task. A falling mass can raise a bucket of water; a retracting spring can pull a
door shut or run a clock. It requires some imagination to devise ways one might hook on to charges of
opposite sign to get some useful work done, but it should be possible.
The potential that separated opposite charges have for doing work if they are released to fly
together is called voltage, measured in units of volts (V). (Sadly, the unit volt is not named for Voltaire, but
rather for Volta, an Italian scientist.) The greater the amount of charge and the greater the physical
separation, the greater the voltage or stored energy. The greater the voltage, the greater the force that is
driving the charges together. Voltage is always measured between two points, in this case, the positive
and negative charges. If you want to compare the voltage of several charged bodies, the relative force
driving the various charges, it makes sense to keep one point constant for the measurements.
Traditionally, that common point is called "ground."
Figure 4.2: Like charges exert a repulsive force on each other.
External force is required to hold them together, and work is
required to push them closer.
16
Early workers, like Coulomb, also observed that two bodies with charges of the same type, either
both positive or both negative, repelled each other (Fig. 4.2). They experience a force pushing them
apart, and an opposing force is necessary to hold them together, like holding a compressed spring. Work
can potentially be done by letting the charges fly apart, just like releasing the spring. Our analogy with
gravity must end here: no one has observed negative mass, negative gravity, or uncharged bodies flying
apart unaided. Too bad, it would be a great way to launch a space probe. The voltage between two
separated like charges is negative; they have already done their work by running apart, and it will take
external energy and work to force them back together.
So how do you tell if a particular bunch of charge is positive or negative? You can't in isolation.
Even with two charges, you can only tell if they are the same (they repel) or opposite (they attract). The
names are relative; someone has to define which one is "positive." Similarly, the voltage between two
points A and B , VAB , is relative. If VAB is positive you know the two points are oppositely charged, but you
cannot tell if point A has positive charge and point B negative, or visa versa. However, if you make a
second measurement between A and another point C, you can at least tell if B and C have the same
charge by the relative sign of the two voltages, VAB and VAC to your common point A. You can even
determine the voltage between B and C without measuring it: VBC = VAC - VAB. This is the advantage of
defining a common point, like A, as ground and making all voltage measurements with respect to it. If one
further defines the charge at point A to be negative charge, then a positive VAB means point B is positively
charged, by definition. The names and the signs are all relative, and sometimes confusing if one forgets
what the reference or ground point is.
Current
Charge is mobile and can flow freely in certain materials, called conductors. Metals and a few other
elements and compounds are conductors. Materials that charge cannot flow through are called insulators.
Air, glass, most plastics, and rubber are insulators, for example. And then there are some materials called
semiconductors that, historically, seemed to be good conductors sometimes but much less so other
times. Silicon and germanium are two such materials. Today, we know that the difference in electrical
behavior of different samples of these materials is due to extremely small amounts of impurities of
different kinds, which could not be measured earlier. This recognition, and the ability to precisely control
the "impurities" has led to the massive semiconductor electronics industry and the near-magical devices it
produces, including those on your RoboBoard. We will discuss semiconductor devices later; now let us
return to conductors and charges.
Figure 4.3: Two spheres with opposite charges are connected by a conductor,
allowing charge to flow.
Imagine two oppositely charged bodies, say metal spheres, that are being held apart, as in
Fig. 4.3. There is a force between them, the potential for work, and thus a voltage. Now we connect a
conductor between them, a metal wire. On the positively charged sphere, positive charges rush along the
wire to the other sphere, repelled by the nearby similar charges and attracted to the distant opposite
charges. The same thing occurs on the other sphere and negative charge flows out on the wire. Positive
17
and negative charges combine to neutralize each other, and the flow continues until there are no charge
differences between any points of the entire connected system. There may be a net residual charge if the
amounts of original positive and negative charge were not equal, but that charge will be distributed evenly
so all the forces are balanced. If they were not, more charge would flow. The charge flow is driven by
voltage or potential differences. After things have quieted down, there is no voltage difference between
any two points of the system and no potential for work. All the work has been done by the moving
charges heating up the wire.
The flow of charge is called electrical current. Current is measured in amperes (a), amps for short
(named after another French scientist who worked mostly with magnetic effects). An ampere is defined as
a flow of one Coulomb of charge in one second past some point. While a Coulomb is a lot of charge to
have in one place, an ampere is a common amount of current; about one ampere flows through a 100
watt incandescent light bulb, and a stove burner or a large motor would require ten or more amperes. On
the other hand low power digital circuits use only a fraction of an ampere, and so we often use units of
1/1000 of an ampere, a milliamp, abbreviated as ma, and even 1/1000 of a milliamp, or a microamp, µa.
The currents on the RoboBoard are generally in the milliamp range, except for the motors, which can
require a full ampere under heavy load. Current has a direction, and we define a positive current from
point A to B as the flow of positive charges in the same direction. Negative charges can flow as well, in
fact, most current is actually the result of negative charges moving. Negative charges flowing from A to B
would be a negative current, but, and here is the tricky part, negative charges flowing from B to A would
represent a positive current from A to B. The net effect is the same: positive charges flowing to neutralize
negative charge or negative charges flowing to neutralize positive charge; in both cases the voltage is
reduced and by the same amount.
Batteries
Charges can be separated by several means to produce a voltage. A battery uses a chemical reaction to
produce energy and separate opposite sign charges onto its two terminals. As the charge is drawn off by
an external circuit, doing work and finally returning to the opposite terminal, more chemicals in the battery
react to restore the charge difference and the voltage. The particular type of chemical reaction used
determines the voltage of the battery, but for most commercial batteries the voltage is about 1.5 V per
chemical section or cell. Batteries with higher voltages really contain multiple cells inside connected
together in series. Now you know why there are 3 V, 6 V, 9 V, and 12 V batteries, but no 4 or 7 V
batteries. The current a battery can supply depends on the speed of the chemical reaction supplying
charge, which in turn often depends on the physical size of the cell and the surface area of the
electrodes. The size of a battery also limits the amount of chemical reactants stored. During use, the
chemical reactants are depleted and eventually the voltage drops and the current stops. Even with no
current flow, the chemical reaction proceeds at a very slow rate (and there is some internal current flow),
so a battery has a finite storage or shelf life, about a year or two in most cases. In some types of
batteries, like the ones we use for the robot, the chemical reaction is reversible: applying an external
voltage and forcing a current through the battery, which requires work, reverses the chemical reaction
and restores most, but not all, the chemical reactants. This cycle can be repeated many times. Batteries
are specified in terms of their terminal voltage, the maximum current they can deliver, and the total
current capacity in ampere-hours.
You should handle batteries carefully, especially the ones we use in this course. Chemicals are a
very efficient and compact way of storing energy. Just consider the power of gasoline or explosives, or
the fact that you can play soccer for several hours powered only by a slice of cold pizza for breakfast.
Never connect the terminals of a battery together with a wire or other good conductor. The battery we use
for the RoboBoard is similar to the battery in cars, which uses lead and sulphuric acid as reactants. Such
batteries can deliver very large currents through a short circuit, hundreds of amperes. The large current
will heat the wire and possibly burn you; the resulting rapid internal chemical reactions also produce heat
and the battery can explode, spreading nasty, reactive chemicals about. Charging these batteries with too
large a current can have the same effect. Double check the circuit and instructions before connecting a
battery to any circuit. More information on batteries can be found in Chapter 7.
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Circuit Elements
Resistors
We need some way to control the flow of current from a voltage source, like a battery, so we do not melt
wires and blow up batteries. If you think of current, charge flow, in terms of water flow, a good electrical
conductor is like big water pipe. Water mains and fire hoses have their uses, but you do not want to take
a drink from one. Rather, we use small pipes, valves, and other devices to limit water flow to practical
levels. Resistors do the same for current; they resist the flow of charge; they are poor conductors. The
value of a resistor is measured in ohms and represented by the Greek letter capital omega. There are
many different ways to make a resistor. Some are just a coil of wire made of a material that is a poor
conductor. The most common and inexpensive type is made from powdered carbon and a glue-like
binder. Such carbon composition resistors usually have a brown cylindrical body with a wire lead on each
end, and colored bands that indicate the value of the resistor. The key to reading these values is given in
Chapter 2.
There are other types of resistors in your robot kit. The potentiometer is a variable resistor. When
the knob of a potentiometer is turned, a slider moves along the resistance element. Potentiometers
generally have three terminals, a common slider terminal, and one that exhibits increasing resistance and
one that has decreasing resistance relative to the slider as the shaft is turned in one direction. The
resistance between the two stationary contacts is, of course, fixed, and is the value specified for the
potentiometer. The photoresistor or photocell is composed of a light sensitive material. When the
photocell is exposed to more light, the resistance decreases. This type of resistor makes an excellent light
sensor.
Ohm's Law
Ohm's law describes the relationship between voltage, V , which is trying to force charge to flow,
resistance, R , which is resisting that flow, and the actual resulting current I . The relationship is simple
. Thus large voltages and/or low resistances produce large
and very basic:
currents. Large resistors limit current to low values. Almost every circuit is more complicated than just a
battery and a resistor, so which voltage does the formula refer to? It refers to the voltage across the
resistor, the voltage between the two terminal wires. Looked at another way, that voltage is actually
produced by the resistor. The resistor is restricting the flow of charge, slowing it down, and this creates a
traffic jam on one side, forming an excess of charge with respect to the other side. Any such charge
difference or separation results in a voltage between the two points, as explained above. Ohm's law tells
us how to calculate that voltage if we know the resistor value and the current flow. This voltage drop is
analogous to the drop in water pressure through a small pipe or small nozzle.
Power
Current flowing through a poor conductor produces heat by an effect similar to mechanical friction. That
heat represents energy that comes from the charge traveling across the voltage difference. Remember
that separated charges have the potential to do work and provide energy. The work involved in heating a
resistor is not very useful, unless we are making a hotplate; rather it is a byproduct of restricting the
current flow. Power is measured in units of watts (W), named after James Watt, the Englishman who
invented the steam engine, a device for producing lots of useful power. The power that is released into
the resistor as heat can be calculated as P=VI , where I is the current flowing through the resistor and V is
the voltage across it. Ohm's law relates these two quantities, so we can also calculate the power as
The power produced in a resistor raises its temperature and can change
its value or destroy it. Most resistors are air-cooled and they are made with different power handling
capacity. The most common values are 1/8, 1/4, 1, and 2 watt resistors, and the bigger the wattage
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rating, the bigger the resistor physically. Some high power applications use special water-cooled
resistors. Most of the resistors on the RoboBoard are 1/8 watt.
Combinations of Resistors
Resistors are often connected together in a circuit, so it is necessary to know how to determine the
resistance of a combination of two or more resistors. There are two basic ways in which resistors can be
connected: in series and in parallel. A simple series resistance circuit is shown in Figure 4.4.
Figure 4.4: Two Resistors in Series
Determining the total resistance for two or more resistors in series is very simple. Total resistance
equals the sum of the individual resistances. In this case, RT=R1+R2 . This makes common sense; if you
think again in terms of water flow, a series of obstructions in a pipe add up to slow the flow more than any
one. The resistance of a series combination is always greater than any of the individual resistors.
The other method of connecting resistors is shown in Figure 4.5, which shows a simple parallel
resistance circuit.
Figure 4.5: Two Resistors in Parallel
Our water pipe analogy indicates that it should be easier for current to flow through this
multiplicity of paths, even easier than it would be to flow through any single path. Thus, we expect a
parallel combination of resistors to have less resistance than any one of the resistors. Some of the total
current will flow through R1 and some will flow through R2, causing an equal voltage drop across each
resistor. More current, however, will flow through the path of least resistance. The formula for total
resistance in a parallel circuit is more complex than for a series circuit:
RT={1{1R1}+{1R2}...+{1Rn}}
(1)
Parallel and series circuits can be combined to make more complex structures, but the resulting
complex resistor circuits can be broken down and analyzed in terms of simple series or parallel circuits.
Why would you want to use such combinations? There are several reasons; you might use a combination
to get a value of resistance that you needed but did not have in a single resistor. Resistors have a
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maximum voltage rating, so a series of resistors might be used across a high voltage. Also, several low
power resistors can be combined to handle higher power. What type of connection would you use?
Capacitors
Capacitors are another element used to control the flow of charge in a circuit. The name derives from
their capacity to store charge, rather like a small battery. Capacitors consist of two conducting surfaces
separated by an insulator; a wire lead is connected to each surface. You can imagine a capacitor as two
large metal plates separated by air, although in reality they usually consist of thin metal foils or films
separated by plastic film or another solid insulator, and rolled up in a compact package. Consider
connecting a capacitor across a battery, as in Fig. 4.6.
Figure 4.6: A simple capacitor connected to a battery through a resistor.
As soon as the connection is made charge flows from the battery terminals, along the wire and
onto the plates, positive charge on one plate, negative charge on the other. Why? The like-sign charges
on each terminal want to get away from each other. In addition to that repulsion, there is an attraction to
the opposite-sign charge on the other nearby plate. Initially the current is large, because in a sense the
charges can not tell immediately that the wire does not really go anywhere, that there is no complete
circuit of wire. The initial current is limited by the resistance of the wires, or perhaps by a real resistor, as
we have shown in Fig. 4.6. But as charge builds up on the plates, charge repulsion resists the flow of
more charge and the current is reduced. Eventually, the repulsive force from charge on the plate is strong
enough to balance the force from charge on the battery terminal, and all current stops. Figure 4.7 shows
how the current might vary with time for two different values of resistors. For a large resistor, the whole
process is slowed because the current is less, but in the end, the same amount of charge must exist on
the capacitor plates in both cases. The magnitude of the charge on each plate is equal.
Figure 4.7: The time dependence of the current in the circuit of
Fig. 4.6 for two values of resistance.
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The existence of the separated charges on the plates means there must be a voltage between
the plates, and this voltage be equal to the battery voltage when all current stops. After all, since the
points are connected by conductors, they should have the same voltage; even if there is a resistor in the
circuit, there is no voltage across the resistor if the current is zero, according to Ohm's law. The amount of
charge that collects on the plates to produce the voltage is a measure of the value of the capacitor, its
capacitance, measured in farads (f). The relationship is C = Q/V , where Q is the charge in Coulombs.
Large capacitors have plates with a large area to hold lots of charge, separated by a small distance,
which implies a small voltage. A one farad capacitor is extremely large, and generally we deal with
microfarads ( µf ), one millionth of a farad, or picofarads (pf), one trillionth (10-12) of a farad.
Consider the circuit of Fig. 4.6 again. Suppose we cut the wires after all current has stopped
flowing. The charge on the plates is now trapped, so there is still a voltage between the terminal wires.
The charged capacitor looks somewhat like a battery now. If we connected a resistor across it, current
would flow as the positive and negative charges raced to neutralize each other. Unlike a battery, there is
no mechanism to replace the charge on the plates removed by the current, so the voltage drops, the
current drops, and finally there is no net charge left and no voltage differences anywhere in the circuit.
The behavior in time of the current, the charge on the plates, and the voltage looks just like the graph in
Fig. 4.7. This curve is an exponential function: exp(-t/RC) . The voltage, current, and charge fall to about
37% of their starting values in a time of R ×C seconds, which is called the characteristic time or the time
constant of the circuit. The RC time constant is a measure of how fast the circuit can respond to changes
in conditions, such as attaching the battery across the uncharged capacitor or attaching a resistor across
the charged capacitor. The voltage across a capacitor cannot change immediately; it takes time for the
charge to flow, especially if a large resistor is opposing that flow. Thus, capacitors are used in a circuit to
damp out rapid changes of voltage.
Combinations of Capacitors
Like resistors, capacitors can be joined together in two basic ways: parallel and series. It should be
obvious from the physical construction of capacitors that connecting two together in parallel results in a
bigger capacitance value. A parallel connection results in bigger capacitor plate area, which means they
can hold more charge for the same voltage. Thus, the formula for total capacitance in a parallel circuit is:
CT=C1+C2...+Cn ,
(2)
the same form of equation for resistors in series, which can be confusing unless you think about the
physics of what is happening.
The capacitance of a series connection is lower than any capacitor because for a given voltage
across the entire group, there will be less charge on each plate. The total capacitance in a series circuit is
CT={1{1C1}+{1C2}...+{1Cn}}.
(3)
Again, this is easy to confuse with the formula for parallel resistors, but there is a nice symmetry
here.
Inductors
Inductors are the third and final type of basic circuit component. An inductor is a coil of wire with many
windings, often wound around a core made of a magnetic material, like iron. The properties of inductors
derive from a different type of force than the one we invented charge to explain: magnetic force rather
than electric force. When current flows through a coil (or any wire) it produces a magnetic field in the
space outside the wire, and the coil acts just like any natural, permanent magnet, attracting iron and other
magnets. If you move a wire through a magnetic field, a current will be generated in the wire and will flow
through the associated circuit. It takes energy to move the wire through the field, and that mechanical
energy is transformed to electrical energy. This is how an electrical generator works. If the current through
a coil is stopped, the magnetic field must also disappear, but it cannot do so immediately. The field
represents stored energy and that energy must go somewhere. The field contracts toward the coil, and
the effect of the field moving through the wire of the coil is the same as moving a wire through a
stationary field: a current is generated in the coil. This induced current acts to keep the current flowing in
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the coil; the induced current opposes any change, an increase or a decrease, in the current through the
inductor. Inductors are used in circuits to smooth the flow of current and prevent any rapid changes.
The current in an inductor is analogous to the voltage across a capacitor. It takes time to change
the voltage across a capacitor, and if you try, a large current flows initially. Similarly, it takes time to
change the current through an inductor, and if you insist, say by opening a switch, a large voltage will be
produced across the inductor as it tries to force current to flow. Such induced voltages can be very large
and can damage other circuit components, so it is common to connect some element, like a resistor or
even a capacitor across the inductor to provide a current path and absorb the induced voltage. (Often, a
diode, which we will discuss later, is used.)
Inductors are measured in henrys (h), another very big unit, so you are more likely to see
millihenries, and microhenries. There are almost no inductors on the RoboBoard, but you will be using
some indirectly: the motors act like inductors in many ways. In a sense an electric motor is the opposite of
an electrical generator. If current flows through a wire that is in a magnetic field (produced either by a
permanent magnet or current flowing through a coil), a mechanical force will be generated on the wire.
That force can do work. In a motor, the wire that moves through the field and experiences the force is
also in the form of a coil of wire, connected mechanically to the shaft of the motor. This coil looks like and
acts like an inductor; if you turn off the current (to stop the motor), the coil will still be moving through the
magnetic field, and the motor now looks like a generator and can produce a large voltage. The resulting
inductive voltage spike can damage components, such as the circuit that controls the motor current. In
the past this effect destroyed a lot of motor controller chips and other RoboBoard components. The
present board design contains special diodes that will withstand and safely dissipate the induced voltages
-- we hope.
Combinations of Inductors
You already know how inductors act in combination because they act just like resistors. Inductance adds
in series. This makes physical sense because two coils of wire connected in series just looks like a longer
coil. Parallel connection reduces inductance because the current is split between the several coils and the
fields in each are thus weaker.
Semiconductor Devices
The Truth About Charge
Our statements above about charge are not wrong, but they are simple and incomplete. In order to
understand how semiconductor devices work one needs a more complete description of the nature of
charge in the real world. Charge does not exist independently; it is carried by subatomic particles. For this
discussion we will be concerned primarily with electrons, which carry a negative charge of 1.6 × 10-19 C ,
the minimum amount of charge that can exist in isolation. At least, no one has found any smaller amount
than this fundamental quantum of charge.
Electrons are one component of atoms and molecules. Atoms are the building blocks out of which
all matter is constructed. Atoms bond with each other to form substances. Substances composed of just
one type of atom are called elements. For example, copper, gold and silver are all elements; that is, each
of them consists of only one type of atom. More complex substances are made up of more than one atom
and are known as compounds. Water, which has both hydrogen and oxygen atoms, is such a compound.
The smallest unit of a compound is a molecule. A water molecule, for example, contains two hydrogen
atoms and one oxygen atom.
Atoms themselves are made up of even smaller components: protons, neutrons and electrons.
Protons and neutrons form the nucleus of an atom, while the electrons orbit the nucleus. Protons carry
positive charge and electrons carry negative charge; the magnitude of the charge for both particles is the
same, one quantum charge, 1.6 ×10-19 C. Neutrons are not charged. Normally, atoms have the same
number of protons and electrons and have no net electrical charge.
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Figure 4.8: Structure of an Atom
Electrons that are far from the nucleus are relatively free to move around under the influence of
external fields because the force of attraction from the positive charge in the nucleus is weak at large
distances. In fact, it takes little force in many cases to completely remove an outer electron from an atom,
leaving an ion with a net positive charge. Once free, electrons can move at speeds approaching the
speed of light (roughly 670 million miles per hour) through metals, gases and vacuum. They can also
become attached to another atom, forming an ion with net negative charge.
Electric current in metal conductors consists of a flow of free electrons. Because electrons have
negative charge, the flow of electrons is in a direction opposite to the positive current. Free electrons
traveling through a conductor drift until they hit other electrons attached to atoms. These electrons are
then dislodged from their orbits and replaced by the formerly free electrons. The newly freed electrons
then start the process anew. At the microscopic level, electron flow through a conductor is not a steady
stream, like water flowing from a faucet, but rather a series of short bursts.
Figure 4.9: A Simple Model of Electron Flow
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Silicon
Semiconductor devices are made primarily of silicon (silicon's element symbol is "Si"). Pure silicon forms
rigid crystals because of its four valence (outermost) electron structure -- one Si atom bonds to four other
Si atoms forming a very regularly shaped diamond pattern. Figure 4.10 shows part of a silicon crystal
structure.
Figure 4.10: A Silicon Crystal Structure
Pure silicon is not a conductor because there are no free electrons; all the electrons are tightly
bound to neighboring atoms. To make silicon conducting, producers combine or "dope" pure silicon with
very small amounts of other elements like boron or phosphorus. Phosphorus has five outer valence
electrons. When three silicon atoms and one phosphorus atom bind together in the basic silicon crystal
cell of four atoms, there is an extra electron and a net negative charge. Figure4.11 shows the crystal
structure of phosphorus doped silicon.
Figure 4.11: Silicon Doped with Phosphorus
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This type of material is called n-type silicon. The extra electron in the crystal cell is not strongly
attached and can be released by normal thermal energy to carry current; the conductivity depends on the
amount of phosphorus added to the silicon.
Boron has only three valance electrons. When three silicon atoms and one boron atom bind with
each other there is a "hole" where another electron would be if the boron atom were silicon; see Fig. 4.12.
This gives the crystal cell a positive net charge (referred to as p-type silicon), and the ability to pick up an
electron easily from a neighboring cell.
Figure 4.12: Silicon Doped with Boron
The resulting migration of electron vacancies or holes acts like a flow of positive charge through
the crystal and can support a current. It is sometimes convenient to refer to this current as a flow of
positive holes, but in fact the current is really the result of electrons moving in the opposite direction from
vacancy to vacancy.
Diodes
Both p-type and n-type silicon will conduct electricity just like any conductor; however, if a piece of silicon
is doped p-type in one section and n-type in an adjacent section, current will flow in only one direction
across the junction between the two regions. This device is called a diode and is one of the most basic
semiconductor devices.
A diode is called forward biased if it has a positive voltage across it from from the p- to n-type
material. In this condition, the diode acts rather like a good conductor, and current can flow, as in
Fig. 4.13.
There will be a small voltage across the diode, about 0.6 volts for Si, and this voltage will be
largely independent of the current, very different from a resistor.
If the polarity of the applied voltage is reversed, then the diode will be reverse biased and will appear
nonconducting (Fig. 4.14). Almost no current will flow and there will be a large voltage across the device.
The non-symmetric behavior is due to the detailed properties of the pn-junction. The diode acts
like a one-way valve for current and this is a very useful characteristic. One application is to convert
alternating current (AC), which changes polarity periodically, into direct current (DC), which always has
the same polarity. Normal household power is AC while batteries provide DC, and converting from AC to
DC is called rectification. Diodes are used so commonly for this purpose that they are sometimes called
rectifiers, although there are other types of rectifying devices. Figure 4.15 shows the input and output
current for a simple half-wave rectifier. The circuit gets its name from the fact that the output is just the
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positive half of the input waveform. A full-wave rectifier circuit (shown in Figure 4.16) uses four diodes
arranged so that both polarities of the input waveform can be used at the output.
Figure 4.13: A Forward Biased Diode
Figure 4.14: A Reverse Biased Diode
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Figure 4.15: A Half-Wave Rectifier
Figure 4.16: A Full-Wave Rectifier
The full-wave circuit is more efficient than the half-wave one.
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The Microprocessor and Memory
At the most primitive level, a computer consists of a microprocessor, which executes instructions, and a
memory, for storing those instructions (as well as other data).
Figure 5.1: Diagram of Microprocessor and Memory
Figure 5.1 is a block diagram of the microprocessor and memory, showing four types of wires that
connect the two:
Address Bus
These wires are controlled by the microprocessor to select a particular location in memory for reading or
writing. The RoboBoard uses a memory chip that has 15 address wires. Since each wire has two states (it
can be a digital one or a zero), 2 to the 15th power locations are possible. 215 is precisely 32,768
locations; thus, the system is said to have "32K" of memory (1K = 1024 bytes).
Data Bus
These wires are used to pass data between the microprocessor and the memory. When data is written to
the memory, the microprocessor drives the data bus; when data is read from the memory, memory drives
the bus.
In our example (and in the RoboBoard), there are eight data wires (or bits). These wires can
transfer one of 28, or 256, different values per transaction. The data size of 8 bits is commonly referred to
as a byte. (This jargon gets worse; a data size of 4 bits is frequently referred to as a nybble.)
Read/Write Control Line
This single wire is driven by the microprocessor to control the function of the memory. If the read/write
control line is asserted as a logical one, i.e., ``true'', then the memory performs a ``read'' operation. If it is
asserted as a logic zero, i.e., ``false'' then the memory performs a ``write'' operation. (The relationship
between logic level and voltage level can vary, depending on the implementation. For example, with the
exception of some of the serial port circuitry, a logical ``zero'' on the RoboBoard corresponds to a voltage
level near 0 volts, and a logical ``one'' on the RoboBoard corresponds to a voltage level near 5 volts.)
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Memory Enable Control Line
This wire, also called the E clock, connects to the enable circuitry of the memory. When the memory is
enabled, it performs either a read or write operation as determined by the read/write line.
Multiplexing Data and Address Signals
Figure 5.2: Block Diagram of Microprocessor and Memory with Latch
Things are a little more complex with the particular microprocessor that is used in the RoboBoard,
the Motorola 68HC11. On the 68HC11, the eight data bus wires take turns acting as address wires as
well.
When a memory location is accessed (for reading or writing), the data wires act first as address
wires, transmitting the eight lower-order bits of the address. Then they function as data wires, either
transmitting a data byte (for a write cycle) or receiving a data byte (for a read cycle). All of this happens
very fast -- 2 million times per second on the RoboBoard.
This kind of split-personality bus is referred to as a multiplexed address and data bus. The
memory needs help to deal with a multiplexed address/data bus, provided by an 8-bit latch. This chip (the
74HC373) performs the function of latching, or storing, the 8 address values so that the memory will have
the full 15-bit address available for reading or writing data.
Figure 5.2 shows how the latch is wired. The upper 7 address bits are normal, and run directly
from the microprocessor to the memory. The lower 8 bits are the multiplexed address and data bus.
These wires connect to the inputs of the latch and also to the data inputs of the memory.
An additional signal, the Address Strobe output of the microprocessor, tells the latch when to grab
hold of (latch) the address values from the address/data bus.
When the full 15-bit address is available to the memory (7 bits direct from the microprocessor and 8 bits
from the latch), the read or write transaction can occur. Because the address/data bus is also wired
directly to the memory, data can flow in either direction between the memory and the microprocessor.
The entire process -- transmitting the lower address bits, latching these bits, and then the read or
write transaction with the memory -- is orchestrated by the microprocessor. The E clock, the Read/Write
line, and the Address Strobe line perform in tight synchronization to make sure these operations happen
in the correct sequence and within the timing capacities of the actual chip hardware.
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