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					                                      Basics of Electronics
                                              S.K. Tewksbury
                               Dept. of Electrical and Computer Engineering
                                      Stevens Institute of Technology
                                            Hoboken, NJ 07030
                                              (201) 216-5623



Contents                                                        pated for routine appearing within the next 10-
                                                                20 years. This article provides an introduction to
1 The ”Electrons” in Electronics                       1        some of the basic concepts involved in electron-
                                                                ics, including concepts used to create computers,
2 Insulators, Conductors, and Semi-
                                                                to create mobile telephone, to create video games
  conductors                        3
                                                                systems, to create control systems for space craft,
3 Voltage, Current, and Resistors                      4        to create high speed data networks to move in-
                                                                formation easily, to create advanced features in
4 Electrical Power Distribution and                             automobiles, and so forth. In many of these
  Switches                          5                           cases, the main theme seen by the consumer is
                                                                a rapid advance from today’s electronic systems
5 Electronically Controlled Switches                   6        to far more powerful electronic systems within
                                                                the short time of a couple of years. Video games
6 Digital (Logic) Circuits                             7
                                                                which began with a simple bouncing of a ball
7 Analog Circuits                                      9        have grown rapidly to similarly priced systems
  7.1 Amplifiers Using Voltage Depen-                            today providing attractive 3-D animation con-
      dent Resistance . . . . . . . . . .              9        trolled from a joystick. A personal computer
  7.2 Filters Using Frequency Depen-                            purchased just a few years ago is already obso-
      dent Resistances . . . . . . . . .              10        lete, with new personal computers providing so
                                                                much more performance (at about the same cost
8 Looking Ahead                                      11         as the earlier computer) that entirely new and
                                                                more powerful software programs can be used
1       The ”Electrons” in Electronics                          easily by the general public. This rate of im-
                                                                provement is due in part to continuing advances
The impact of electronic products and services                  in the capabilities of microelectronics, a tech-
on our homes, jobs, entertainment, transporta-                  nology which fabricates millions of transistors
tion, medical care, communications, and many                    on a sliver of silicon crystal about the size of
others has increased dramatically over the past                 your fingernail. The amount of electronic cir-
20 years, with truly fantastic capabilities antici-             cuitry on such “chips” doubles about every 18
    0
                                                                months, with this doubling continuing for many
     This basic review of electronics was developed ini-
                                                                more years. These advances will continue into
tially for Grolier’s World Book of Knowledge but required
complete redevelopment to match the age group of chil-          the 21st century, creating a world forecast by sci-
dren targeted by that publication.


                                                            1
                     Bound electron            Free                                         Free          Replacement
  Nucleus with                                                  Electrons                (to move)         electrons
                    orbiting nucleus         electron
   positively                                                    leaving                 electrons          entering
charged protons




                                                                                           Electron flow


                                                                                     +     Battery    Ð
                  (a)                  (b)
                                                               Current I equal to
Figure 1: (a) Normal atom with electrons orbit-                 flow of charge
                                                                                            (a)
ing the nucleus. (b) An electron “escaping” from
orbit and becoming free to move in material.                                                             Conductor
                                                                                                      (zero resistance)
                                                                                Current I = V/R


ence fiction writers in which electronics becomes
as dominant as our physical environment on our
routine lives.                                                    Resistance R
      The word“electronics” highlights the role of
electrons. As shown in Figure 1a, all atoms con-                            +                     Ð
                                                                                    Voltage V
sist of a nucleus, a tight core of protons (with
                                                                                          (b)
positive electrical charge) and neutrons, acting
like a miniature planet around which electrons              Figure 2: (a) Flow of free electrons in bar when
(with negative electrical charge) circle in orbit.          a voltage is applied. (b) Circuit representation
Since all matter is composed of atoms, the elec-            of (a).
trons used for electronics are everywhere. How-
ever, those electrons orbiting the nucleus of an
atom are not very useful since they are stuck               as in digital cameras and in solar cells.
(“bound”) to the nucleus by powerful forces and                   The free electrons can be encouraged to
we can’t move them from one place (e.g., a wall             flow in a desired direction if a force can be ap-
socket) to another (e.g., a radio).                         plied to those electrons. This force can be pro-
      However, there are various ways in which              vided by applying a voltage across two ends of
an electron, bound to an atom’s nucleus, can es-            material bar, as illustrated in Figure 2a, where
cape from the atom as shown in Figure 1b, much              a 9 volt battery has been used to provide the
like a spaceship being launched into space. Once            force. It could also be provided from an electrical
launched away from the atom, these free elec-               socket in your room (in this case 110 volts). The
trons can wander freely and be moved. For some              strength of the voltage is measured in the units
materials, the electrons are all strongly bound             of “volts,” much as a person’s weight is measured
to the nucleus and very few electrons can launch            in units of pounds. The voltage across the bar
into free space. For other materials, an electron           causes the electrons to flow to the left and out of
can escape from its orbit relatively easily, lead-          the bar, entering the positive terminal of the bat-
ing to many free electrons in the material. Light           tery. The same number of electrons flows from
can also “knock” an electron off its atomic site,            the negative terminal of the battery into the left
providing free electrons which can be detected,             side of the bar so that the number of free elec-

                                                        2
trons in the bar does not. This leads to a flow of
free electrons from the battery, through the ma-
terial, and back into the battery. Each electron         Large force
carries its elementary charge qe = −1.6 × 10−19                        Small force   Large flow
                                                                                                  Small flow
coulombs, where a “coulomb” is the unit of elec-
trical charge. The amount of charge leaving the
bar of material in one second is called as the               +   Voltage Ð               +   Voltage Ð
electrical current, which is measured in units of                  V                           V
amperes (amps for short). In Figure 2a, the di-
rection of current is opposite to the direction of                 (a)                        (b)
flow of electrons because the electrons carry neg-        Figure 3: Dependence of resistance on shape. (a)
ative, rather than positive charge.                      Different lengths, with larger force causing more
      The circuit representation corresponding to        current to flow. (b) Different cross sections, with
Figure 2a is shown in Figure 2b. where the bar           larger cross section providing more current flow.
is represented as a resistor (discussed later) and
the lines to the battery are metal conductors.
                                                          Insulators (extremely large resistance): These
                                                             are materials such as glass in which very few
                                                             electrons have been able to escape from the
2   Insulators, Conductors, and Semicon-
                                                             atoms, with negligible numbers of electrons
    ductors
                                                             emerging from a glass bar when a voltage
There are various ways to increase the current               is applied. In such materials, the resistance
through the bar of material. We can simply in-               is nearly infinite. Plastic handles on screw-
crease the voltage, causing the free electrons to            drivers with metal tips help avoid getting a
flow faster through the bar. We can also change               shock when the tip is contacting a voltage
the shape of the bar, as illustrated in Figure 3.            by preventing current from flowing in the
If Figure 3a, the force is greater on electrons in           handle.
the shorter bar. In Figure 3b, the force is the           Conductors (extremely small resistance): In
same in both bars but the “pipe” is larger in the           the case of metals such as aluminum and
upper case.                                                 copper, the electron density is very high.
      We can also use a material with a larger              Even a very small voltage will cause a huge
number of free electrons per unit volume (i.e.,             current to flow though a metal bar. In such
a higher “density” of free electrons), leaving the          materials, the resistance is nearly zero. Met-
voltage unchanged. The larger the density of free           als such as copper are used for electrical
electrons in the bar in Figure 2a, the larger the           wiring since current flows so easily through
current (and the less resistance to current flow).           them.
The resistance, measured in units of ohms, is
used to determine the current for a given voltage,        Semiconductors (adjustable resistance): The
with the current equal to the voltage divided by            most commonly used semiconductor is sili-
the resistance. The current flowing in the bar ob-           con, an element which is very common (sand
tained by dividing the voltage by the resistance,           on the beach is silicon dioxide). In a crys-
as shown in Figure 2b).                                     talline form of pure silicon, there are very
      The four main classes of electronic material          few free electrons. However, there are some
are summarized as follows.                                  impurity atoms which, if added to the crys-

                                                     3
    tal, provide atoms from which a free electron           V power
    is virtually certain to have been launched                                                  RA     RB Current Vout
    into the free electron state. In this case,                                               (ohms) (ohms) (amps) (volts)
    the electron density can be adjusted as de-                                                10      10          0.5      5




                                                                        RA




                                                                                     Case 1
    sired, merely by adding the correct num-                                                   100    100         0.05      5
    ber of impurity atoms. There are also im-




                                                        Current
                                                                                              1000    1000        0.005     5
    purity atoms which capture (grab) an elec-
    tron from a neighboring silicon atom, leav-                                                100    100         0.05      5
    ing a silicon atom missing an electron. Such




                                                                                     Case 2
                                                                             V out             10     190         0.05     9.5
    “missing electrons” (called holes can also




                                                                        RB
    move in the semiconductor, acting like elec-                                               190     10          0.5     0.05

    trons but having positive rather than nega-
                                                                                               100     10         0.09     0.9




                                                                                     Case 3
    tive charge.
                                                                                               100    1000        0.0095   9.5
 Resistors: The term “resistor” does not repre-
   sent a material in the usual sense but rather                  (a)                                       (b)
   the behavior of the material when a voltage          Figure 4: (a) Two resistors placed in series. (b)
   is applied. For example, although the fila-           Table illustrating changes in current and voltage
   ment of a light bulb is a conductor, using an        for resistor pair.
   extremely thin wire leads to considerable re-
   sistance. A powder of carbon granules pro-
   vides another example. Current flows from
   granule to granule only through the points           current and voltage. This power dissipation cor-
   where the grains contact one another, es-            responds to the generation of heat, one of the
   sentially establishing a very narrow region          reasons why electronics can become hot and the
   through which the electrons can flow. If one          way in which electric stoves generate heat and
   “squeezed” the powder of carbon, the con-            light bulbs generate light.
   tact regions between grains would increase                 Figure 4 shows two resistors connected to
   and the current would also increase. In fact,        one another, with current flowing through both.
   this is the way telephone microphones were           This combination will be discussed extensively
   made, with the sound pressure when talking           later. Since the current flows through both resis-
   into the telephone changing the pressure on          tors, the current is given by the voltage divided
   the carbon powder, changing its resistance           by the sum of the resistances. However, the volt-
   and therefore changing the current flowing            age across each resistor is the product of the cur-
   through the powder.                                  rent and the resistance of the resistor. The table
                                                        in Figure 4 shows some of the useful variations,
3   Voltage, Current, and Resistors                     including adjusting the current while maintain-
                                                        ing the same output voltage, adjusting the out-
In Figure 2b, the current I through the resis-          put voltage while maintaining the same current,
tor with resistance R is related to the voltage V       and finally changing both the current and volt-
across the resistor by I = V /R. If a current I         age by holding one resistance fixed and switching
is flowing through the resistor, then the voltage        the other between a larger and a smaller resis-
across the resistor is V = I × R. There is also         tance. This latter case will be used to describe
a power dissipation given by the product of the         logic circuits and other electrical circuits.

                                                    4
          Fuse

 "Hot"
                       Wall           Switch                    Switch
 Wire




                                                                                         To other plugs and
                      socket           OFF                       ON




                                                                                              switches
     Fuse Box




     "Return"
      Wire
                                                 (a)




    Vpower




                                                                                        To other circuits
                                                               Switch




                                                                          Electronic
                         Electronic




                                               Electronic



     Power




                                                                           Circuit
                                                Circuit
                          Circuit




     Supply

    Ground Return

                                                 (b)

Figure 5: Connection of electrical power. (a) Household wiring, with plugs and switches. (b)
Electronic system wiring with direct and switched connection of power to circuits.


4     Electrical    Power      Distribution  and embedded in the battery voltage, a clock run-
      Switches                                    ning on a battery must use some local oscillation
                                                  which only approximates time (and battery op-
The electric power in your home, provided by erated clocks must be readjusted from time to
some power company, provides 110 volts of volt- time).
age. However, this is not a constant voltage but        The oscillating voltage used for household
rather a voltage which oscillates smoothly be- power is called AC, for “alternating current.”
tween +110 volts and -110 volts, completing one Many of the signals used in electronics are also
oscillation cycle every 1/60th second. This cor- AC signals, including the signal from a micro-
responds to a frequency of 60 cycles each second phone, the signal used to transmit radio signals,
(60 Hertz). This rate of 60 Hertz is maintained etc. The constant voltage provided by batteries
with great precision, ensuring that over long pe- is called DC, for ‘direct current.” Constant volt-
riods of time there will be precisely 60 oscilla- ages are often used to power electronic systems
tions. This is why an electric clock plugged into (e.g., power a computer, a radio, etc.). The “cur-
the wall maintains the time precisely. A battery, rent” in AC and DC merely reflects the fact that
on the other hand, provides a constant voltage the current changes similarly to the voltage.
(for example, 9 volts). Since there is no “time”        Figure 5a shows a typical portion of the


                                                        5
wiring in your home. A similar scheme, shown in                switch on your radio operates similarly, ei-
Figure 5b, is used for distributing DC voltages                ther allowing current to flow into the radio
within electronic systems such as television sets,             or breaking the connection and preventing
airplane electronic control systems, automobiles,              current from entering the radio.
etc. The current is supplied by the “hot” wire
                                                     Figure 6 illustrates the use of a different
in Figure 5a and by the voltage source labeled
                                               kind of switch to control a light bulb from two
Vpower in Figure 5b. The current is returned by
                                               separate switches (S1 and S2). In Figure 6a, the
the “return” wire in Figure 5a and by the line
                                               two switches set to allow current to flow from the
labeled “ground return” (and represented by the
                                               “hot” wire through A1 to A2 and into the light.
triangle of lines) in Figure 5b. A fuse in the
                                               In Figure 6b. Switch 2 is changed, with no path
household current supply line “blows” when the
                                               for current to flow from the “hot” wire to the
current flowing exceeds a limit, preventing fires
                                               light. In Figure 6c. switch 1 is then changed,
due to excessive power dissipation (product of
                                               creating a path for current through B1 and B2
current and voltage). Household wiring also uses
                                               and causing the light to turn ON. This actually
a third wire called “Ground” (not shown in Fig-
                                               corresponds to a logic function, namely: if both
ure 5a). This third wire is actually connected to
                                               switches are ON (up position) or both are OFF
a metal stake or pipe in the ground near your
                                               (down position), the light is ON; otherwise the
house to ensure that the voltage of the electrical
                                               light is OFF. The switches in your home may be
boxes and appliances is the same as “the ground
                                               wired such that if one switch is ON and the other
on which you are standing.”
                                               is OFF, the light is lit; otherwise the light is OFF
 Power connection: When you “plug” your ra- (corresponding to a change in Figure 6 such that
   dio into a wall socket, you are connecting A1 is connected to B2 and B1 is connected to
   your radio to the the 110 volts provided at A2, rather than as shown).
   the wall plug. When you connect the power
   wires in a computer to a disk drive unit, 5 Electronically Controlled Switches
   you are providing the voltages and currents
                                               Rather than pushing the light switch with your
   needed to operate the disk drive.
                                               finger, perhaps you’d like to shout “Lights ON”
 Power Switches: The light switch allows you
                                                         "return"        "hot"           "return"        "hot"        "return"        "hot"
   to turn off the power to a light bulb. The
   hot wire enters one side of the switch and                                       S1                           S1                              S1
   exits the other side, continuing to one ter-                     A1         B1                   A1     B1                    A1         B1
   minal of the light(s). The other light termi-
                                                                    A2         B2                   A2      B2                   A2         B2
   nal connects to the return wire which con-
                                                                                    S2                           S2                              S2
   nects directly to the overall return wire as
   shown. When the switch is ON, current
   flows through the light’s filament and the
   light lights (the power dissipated in the fil-
                                                                         (a)                         (b)                              (c)
   ament of the light bulb causes it to glow
   “white hot”, much like a hot electric stove           Figure 6: Two switches controlling a single light.
   element “glows” red when hot). When the               (a) Initial settings with the light ON. (b) Switch
   switch is OFF, there is no path for the               2 changed and the light is OFF. (c) Next, switch
   current to flow to the light. The power                1 is changed and the light is ON.

                                                     6
             +5V                                               States   Voltage   Condition   Binary    Switch
                                                                                               Digit
                                   Vout
                                                            State 1      +5V        True         1       ON
         R                                                  State 2      0V         False        0       OFF
                                  5V
                           Vout
                                                                        Table 1: Binary variables.
             a
Switch




                       c                                   voltage (a quick change that can be used to am-
         R*                 Vin
                  b                                        plify voltages,as discussed later).
                                  0V                  Vin
                                   0V     2.5V   5V        6     Digital (Logic) Circuits

                                                           Digital electronic circuits are circuits in which
                 (a)                       (b)
                                                           the voltages can have one of two values (e.g.,
Figure 7: Basic electronic switch. (a) Switch,             +5V and 0V). The circuit in Figure 7 can be
with resistance R∗ controlled by voltage Vin , in          viewed as a digital circuit in the following sense.
series with a fixed resistance R. (b) Dependence            If the input voltage is 0V (actually any voltage
of output voltage Vout on control voltage Vin .            between 0V and about 2V), the output voltage
                                                           is +5V. Similarly, if the input voltage is +5V
                                                           (actually any voltage between about +3V and
and “lights OFF” to control your lights. In this           +5V), then the output voltage is 0V. The two
case, you’ll need an electronic system which can           states (0V and +5V) are called binary states, i.e.,
recognize your speech (and such systems exist)             having only two values. When using binary elec-
and an electronic switch that can be turned ON             tronic circuits, we can interpret the two voltages
and OFF with an electronic voltage. These elec-            in various ways, as indicated in Table 1, namely
tronic switches are a fundamental part of elec-            as true/false conditions, as binary numbers 1 and
tronic circuits.                                           0, or as ON/OFF states. The digital circuit in
      The basic electronic switch, illustrated by          Figure 7 is a digital inverter circuit, changing
the shaded oval in Figure 7a, is a “three terminal         the input state into the other state (e.g., “true”
device.” Two of the terminals (‘a” and “b”) are            into “false” and vice-versa, “1” into “0” and vice-
the path through which the current flows and the            versa, and “ON” into “OFF” and vice versa).
third (“c”) is the control voltage which controls          We will use “1” and “0” to represent all of these
that current. The electronic switch is essentially         cases in the discussion below.
a voltage controlled resistor, with the control                  Basic binary logic circuits are based on ta-
voltage establishing either a very high resistance         bles giving the output for a given set of inputs.
or a very low resistance. The dependence of the            Table 2 gives four simple examples of 2-input
output voltage Vout on the control voltage Vin is          logic functions. The use of the word “logic”
shown in Figure 7b and corresponds to the resis-           is helpful in understanding the meaning of the
tance being very large when the control voltage            terms “AND”, “OR”, etc. Letting “1” (“0”) cor-
is 0V and very small when the control voltage is           respond to a statement being true (false) the ex-
5V, illustrating the use of a pair of resistors dis-       ample logic functions are as follows.
cussed earlier (Figure 4). The resistance changes
quickly at control voltages near 2.5V, leading to           AND: If conditions A and B are both true
the quick change in Vout as Vin changes near that             (also +5V, binary 1, ON) then the conclu-

                                                       7
     Inputs             Outputs
     A B       AND    OR XOR        XNOR                            +5V
     0 0        0      0    0         1
     0 1        0      1    1         0                    A         T1
     1 0        0      1    1         0
     1 1        1      1    0         1                    B         T2

Table 2: AND, OR, Exclusive OR (XOR), and                                                    +5V
                                                                          R = AND
Exclusive NOR (XNOR) logic functions for in-
puts A and B.
                                                                                A       T1         T3    A*
                                                                    (a)
    sion (output) is true (also +5V, binary 1,                                  B
                                                                    +5V                 T2         T4    B*
    ON). Otherwise the conclusion is false (also
    0V, binary 0, OFF).

 OR: If either condition A OR condition B is           A       T1          T2       B              R = XNOR
   true, then the conclusion is true. Otherwise,
   the conclusion is false.
                                                                          R = OR             (c)
 XOR (exclusive OR): If the conditions A and
   B are different, then the conclusion is true.
   Otherwise the conclusion is false.                               (b)

  XNOR (inverse of XOR): If the conditions A Figure 8: Use of transistors to perform logical
     and B are either both true or both false, functions. (a) AND function. (b) OR function.
     then the conclusion is true. Otherwise the (c) Exclusive Or (XOR) function.
     conclusion is false. Note that this corre-
     sponds to the two light switches in Figure
                                                          Arithmetic can be performed by logic cir-
     6.
                                                    cuits by using the binary number representation.
      Figure 8 shows electronic circuits which can Digit of a binary number has the two possi-
realize these 2-input binary logic functions (the ble values of 0 and 1 (much like the digits of
asterisk indicates the complement of the vari- a decimal number have the ten possible values
able (e.g., ifA = 0 then A∗ = 1 and if A = 1 of 0, 1, 2, . . . , 9). When using a decimal number
then A∗ = 0). In the case of the AND circuit such as 523, this is interpreted as being 5 hun-
in Figure 8a, both transistors T1 and T2 must dreds, 2 tens and 3 ones, with the progression
be ON to establish a low resistance (compared ones -¿ tens -¿ hundreds -¿ thousands ... your
to the resistor to ground) and an output volt- normal way of counting. Binary numbers use
age equal to +5V. In the OR circuit of Figure the progression ones -¿ twos -¿ fours -¿ eights -¿
8b, either transistor T1 or T2 being ON estab- sixteens (powers of 2 rather than powers of 10).
lishes a low resistance to +5V and an output of The binary numbers with values zero, one, two,
+5V. If a transistor is OFF, its resistance is very and three are 00, 01, 10, 11. For example, the
large (compared to the fixed resistor to ground) binary number 11 corresponds to 1 twos and 1
and the output voltage is 0V. Figure 8c shows ones equaling three. The binary number 01 cor-
the XNOR function, corresponding the to light responds to 0 twos and 1 ones equaling one.
switch configuration shown earlier in Figure 6.            Table 3 illustrates the addition of two bi-

                                                   8
       Binary       Binary        Decimal                                                 0.2V
                                                                           5V
       Inputs     Addition           Sum




                                                          Output voltage
                                                                           4V
       A B       Carry Sum        of A & B
                                                                           3V
       0   0       0       0         zero                                                               3V
                                                                           2V
       0   1       0       1         one
                                                                           1V
       1   0       0       1         one
       1   1       1       0         two                                   0V
                                                                                0V     2.4V      2.6V            5V
    Table 3: Truth table for binary addition                                                        Input voltage

                                                          Figure 9: Use of transistor to amplify a small
nary digits A and B. When added, the result may           changing input voltage centered at a DC bias
include a carry. In the case of binary numbers,           voltage.
the addition of 8 (8 ones) and 7 (7 ones) gives
15 (1 tens and 5 ones), with the “1” in the result
“15” having to be added to the “tens” column of           the signals in analog systems varies from very
digits. Table 3 shows the “sum” (result of addi-          low frequencies (e.g., brain waves) to high fre-
tion for the “ones” contribution) and the “carry”         quencies in the megahertz range (“mega” cor-
(result of the addition for the “twos” contribu-          responds to a million) to very high frequencies
tion) using the same approach. The value of               in the gigahertz range (“giga” corresponds to a
the result of adding A and B is also shown in             billion).
the table. Comparing the entries for the carry                  Analog circuits manipulate these analog
in Table 3 to the entries for logic functions in          signals for a variety of reasons and generally in-
Table 2, it is seen that the carry output is the          volve amplification of small electronic voltages,
AND logic function of A and B and that the                elimination of voltage components with various
sum output is the XOR logic function. The digi-           frequencies, and conversion of signals at one fre-
tal circuits in Figure 8a and b generate the carry        quency to signals at another frequency (e.g., mu-
and sum results. More complex digital circuits            sic with frequencies ranging from a few hertz to
are readily designed, including addition of large         several thousand hertz changed to frequencies in
numbers, multiplication, division, and other op-          the megahertz range for FM radio transmission).
erations and providing the basis for calculators
and for computers.                                        7.1               Amplifiers Using Voltage Dependent
                                                                            Resistance
7   Analog Circuits
                                                          In Figure 11, the input/output voltage charac-
Whereas the digital signals seen in digital cir-          teristic of the simple transistor/resistor circuit
cuits are considered to change between two dis-           in Figure 7 has been expanded in the region of
tinct voltage levels in time, analog signals change       input voltages where the output voltage changes
continuously in amplitude in time. Analog sig-            rapidly between 0V and +5V. As shown, a small
nals often represent physical conditions such as          change of the input voltage of 0.2 volts leads to a
temperature, the acoustic pressure of speech, the         change of 3 volts at the output, an amplification
intensity of light, etc. The conversion from the          by a factor of 15.
physical phenomenon to an electrical signal cor-                However, there are always variations in
responding to that phenomenon is performed by             the detailed input/output voltage behavior of a
elements called transducers. The frequency of             given transistor, making amplification with sim-

                                                      9
                             Rb                                     Voltage
                                                                     +V
            Rf                                                                       Conductor       Voltage
                        +                                  Charge Q
                                                                                                      +V
                                                            + + +         +      +   +
      vin               -
                                               vout
                                   Amplifier                        Insulator
                                                                                                               C
                            (a)                             Ð   Ð     Ð      Ð   Ð   Ð
                                                                                         Conductor
                              Rb
                 Gain =
                              Rf                                       (a)                             (b)

                 vout                                   Figure 11: Capacitor. (a) The structure. (b)
                  vin                                   Symbol (parallel lines) for capacitor in circuit.

                            (b)

Figure 10: (a) Use of negative feedback through         which is zero at zero frequency and increases as
resistors to set the gain of the overall circuit. (b)   the frequency increases. The term “impedance”
Amplification of a small signal to obtain a larger       is generally used, rather than resistance, to de-
signal.                                                 scribe this frequency-dependent resistance.
                                                              Figure ??a illustrates the physical structure
                                                        of a capacitor, consisting of two metal plates sep-
ple transistors unpredictable. Negative feedback
                                                        arated by an insulator (the insulator preventing
techniques, such as illustrated in Figure 10 make
                                                        the flow of any DC current from one plate to the
use of a very high gain amplifier (using for ex-
                                                        other. The capacitor stores a charge Q given by
ample basic transistor amplifiers of the general
                                                        the product of the voltage across the capacitor
type shown in Figure 11) with a feedback resistor
                                                        and the capacitor’s capacitance C. Figure ??b
Rb connecting the output of the inverting ampli-
                                                        illustrates the use of the capacitor for computer
fier to its input. In this manner, the gain of the
                                                        memory, with the left switch to “charge” the ca-
overall circuit depends only on the ratio of the
                                                        pacitor to a voltage of either +5V (logic 1) or
feedback resistance and the input resistance Rf ,
                                                        0V (logic 0) and the right switch used to read
masking variations in the gain of the amplifier
                                                        whether the charge state of the capacitor. Tens
without such feedback.
                                                        of millions of such capacitors are placed on sili-
                                                        con chips to provide today’s computer memory
7.2   Filters Using Frequency Dependent
                                                        (DRAM). Here, the use of capacitors to eliminate
      Resistances
                                                        signals with particular frequencies (i.e., filtering
Capacitors (with capacitance C measured in              out particular frequencies) is considered.
farads) and inductors (with inductance L mea-                 Again, we draw on the pair of connected
sured in henries) are commonly used in elec-            resistors shown earlier in Figure 4 to illustrate
tronic circuits. The capacitor behaves like a re-       the use of capacitors in analog circuits. In this
sistor with a resistance which is infinite at zero       case, the frequency dependence of the resistance
frequency and decreases towards zero as the fre-        causes a circuit to behave differently for low and
quency increases. The inductor (basically a coil        high frequencies. In Figure 12a, the current en-
of wire) behaves like a resistor with a resistance      tering the capacitor is limited by the resistor, re-

                                                      10
                                                                   1
                                        Low Pass Filter                   Low
 (a)      Vin              Vout                             Vout
                                                                       Frequencies
                                                            V in
                                                                   0
                                                                                          Frequency ->


                                                                   1
                                       High Pass Filter                                  High
                                                            Vout
(b)      Vin               Vout                                                       Frequencies
                                                            V in
                                                                   0
                                                                                           Frequency ->

                                        Bandpass Filter            1
        Vin                         Vout                    Vout
  (c)
                                                            V in
                                                                   0
                                                                              f1             Frequency ->
                                                                                     f2

Figure 12: Use of R-C networks to “filter” out frequencies. (a) Low pass filter, passing low frequency
signals (below frequency f2 ) and eliminating higher frequencies. (b) High pass filter, passing high
frequency signals (above frequency f1 ) and eliminating lower frequencies. (c) Band-pass filter,
passing frequencies between f1 and f2 and eliminating lower and higher frequencies.


quiring some time for the capacitor to charge up      8   Looking Ahead
to the input voltage. Low frequency input signals
appear directly at the output (since the capaci-
                                                      The progression of silicon CMOS circuits has
tor’s resistance at low frequencies is very large).
                                                      been estimated by a consortium of US industry
At higher frequencies, the capacitor’s resistance
                                                      (the Semiconductor Industries Association). In
is very low and the capacitor does not have time
                                                      the year 2007, it is estimated that a single chip
to charge to the input voltage. This leads to
                                                      of silicon crystal will provide 64 Gigabits of data
the low pass filter function shown, passing low
                                                      storage. Each bit corresponds to storage of either
frequencies input signals but deleting high fre-
                                                      a 1 or a zero. Eight bits (called a byte) can rep-
quency signals. In Figure 12b, the positions of
                                                      resent 256 different things, for example all the
the capacitor and resistor have been reversed,
                                                      letters (upper and lower case) of the alphabet,
with the result that only high frequency input
                                                      numbers between 0 and 9, symbols such as “$”,
signals are passed to the output (i.e., the high
                                                      “?”, “#”, etc. A “giga” something means a bil-
pass filter shown). A low pass and a high pass
                                                      lion. Each of the single chips of silicon therefore
filter can be combined to create a bandpass fil-
                                                      will be able to store 8 billion letters, numbers
ter as shown in Figure 12c. The frequencies f1
                                                      and characters. A single page of this encyclo-
and f2 shown can be varied merely by varying
                                                      pedia contains about 500 words or about 2000
the capacitances. For example, the bandpass fil-
                                                      letters. In this case, each of those silicon chips
ter in Figure 12c can be “tuned” by changing
                                                      could hold about 4 million pages of this ency-
the capacitance to select a given station on your
                                                      clopedia. This will be the smallest amount of
radio.
                                                      memory which will be available for your personal
                                                      computer. In addition, the computer chips will
                                                      also become far more powerful, with a computer

                                                   11
chip in the year 2007 capable of performing as
much as would require 60 computers in 1998.
One of the most exciting aspects of electronics
is the steady evolution towards more powerful
electronics placed in a very small sized crystal.
Certainly, by the year 2007 you will be able to
carry a card in your wallet as powerful as today’s
most powerful computers.




                                                 12

				
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