Chapter 2
Aspects of Technology
Now that we have covered some elements of physics in Chapter 1 we can continue with our
survey of basic concepts by touching on a number of topics from analog electronics. We concentrate here on describing the large-scale technology of circuit elements, on how they are
constructed. We review what is meant by an analog waveform, an analog filter, the transistor
amplifier and the operational amplifier. We shall see how a transistor or an operational amplifier
can be used as a gate, in preparation for our discussion of digital electronics in Chapter 3.
Energy Sources
The Chemical Cell
The most common small-scale source of electrical
energy is the chemical cell. Chemical cells are constructed from various materials, usually of two chemically dissimilar substances, called a cathode and an
anode, separated by a liquid or a paste medium called
electrolyte. The anode serves as a source of electrons
which are driven by chemical action through the
electrolyte to the cathode. Thus the anode takes on a
positive potential, the cathode a negative potential.
An example is the carbon-zinc type whose internal
structure is drawn in Figure 2-1.
intended. Cells are connected in series and in parallel
to form batteries of 9 volts, 12 volts etc., capable of
delivering various currents (Figure 2-2).
Figure 2-2. At the top are shown common consumer type
chemical cells of 1.5V. The batteries (bottom) of 6 and 9V
consist of two or more cells connected in series or in parallel
and encapsulated in a single convenient container.
Figure 2-1. Internal structure of the carbon-zinc cell.
A chemical cell is designed to produce an electromotive force (emf) of 1.5 volts and to have a size and a
shape appropriate to the device for which it is
Cells and batteries are designed to have a charge capacity expressed in ampere-hours (Ah) or milliamperehours (mAh). Capacities for typical cell types are
listed in Table 2-1. The larger the current drawn from
a battery the shorter is its lifetime. Charge capacity is
roughly related to the amount of chemical mass in the
cell and therefore indirectly to the cell’s volume. A cell
for a digital watch or a hearing aid might be tiny
whereas a battery in a nuclear submarine might be as
large as an average refrigerator. Research is being
2-1
Aspects of Technology
carried out in major corporations like Union Carbide,
Sony and others to produce cells of ever-increasing
capacity and lifetime.1
Table 2-1. Charge Capacities of Some Cell Types.2
Type
D
C
AA
AAA
Description
Gen Purpose
Gen Purpose
General
Heavy Duty
Elements
Carbon-Zn
Carbon-Zn
Carbon-Zn
Zn Chloride
Capacity
1500
700
300
120
Example Problem 2-1
Cell Lifetime
Ordinary flashlights use D cells. A fresh D cell has a
typical charge capacity of 1500 mAh. If 25 mA are
drawn from the cell continuously, how long in hours
should the cell last?
Solution:
The number of milliampere-hours can be written I x
t, where I is in mA and t is in hours. Thus
t = 1500 mA-hours/25 mA = 60 hours.
The D cell should be expected to last 60 hours.
solar cell has a lifetime that, in principle, is infinite.
The physics of the silicon solar cell is basically the
physics of the PN junction diode that we have discussed in Chapter 1. We shall concentrate here on the
practical uses of the cell as an alternative source of
power and the practical details of its power output for
various light and load conditions.
Each silicon solar cell (Figure 2-3) can convert solar
energy directly into electrical energy by a process
called photovoltaic conversion. Essentially a large-area
PN junction diode, the cell is made from two pieces of
silicon fused together. One piece is doped so as to yield
an excess of free electrons (N type) while the other is
doped so as to yield a deficiency of free electrons or
an excess of holes (P type). One layer of the cell is
made thin enough to enable photons of light to penetrate to the junction and there to interact with free
electrons. A free electron, in absorbing a photon,
acquires enough energy to take part in electrical conduction. This means that the number of minority
charge carriers in each semiconductor type increases
—holes in the P-material and free electrons in the Nmaterial. These carriers, if they reach the junction
before recombining, cross the junction in response to
the cross-junction electric field. Once across the junction they are free to move through an external circuit
and deliver power to a load.
The Power Supply
Next to the chemical cell the most common source of
electrical energy in a laboratory is a power supply.
Basically, a power supply converts the input from the
mains at 110 V AC to some DC voltage at a (possibly
variable) DC current. One such instrument you will
use in this course is the Agilent Model E3640A programmable power supply. This supply can be made
to function as a voltage source or as a current source.
More details on this instrument can be found in
Appendix A.
metal
annular
ring
metal
base
plate
P-TYPE SILICON
N-TYPE SILICON
electrodes
Figure 2-3. The disk-shaped silicon solar cell.
The Solar Cell
The solar cell is a less common source of electrical
energy than is the chemical cell, though its importance
increases daily. Many hand calculators used by students today are powered by solar cells. In contrast to
the chemical cell, the solar cell, by its name, derives
energy not from the dissociation of chemicals, but
from sunlight or the ambient light in buildings. The
2-2
A single cell is typically able to deliver about 0.5 volt
to an open circuit (called the open circuit voltage VOC)
and a certain maximum current to a shorted load
(called the short circuit current ISC). To form a practical
power source, a number of cells must be connected in
series to form arrays with voltage outputs of 6, 9, 12
volts, and so forth, and in parallel to give a desired
Aspects of Technology
output current. Most arrays have a flat geometry, consistent with the need to capture maximum sunlight.
Some are fabricated on a glass substrate and are
fragile while others are made on a metallic backing
and are flexible, enabling them to be bent into convenient shapes and to be used in demanding applications
as in pleasure boats and spacecraft. Connecting a solar
array to a circuit is simple—you connect the array to
the circuit with two wires.
Though we have described a silicon solar array as a
power source, the power it can deliver is relatively
low; it is therefore not often used in a stand-alone
way. Most often it functions as a trickle charger for a
higher-power primary source like a lead-acid battery
or a gell-cell. Under normal conditions the battery
supplies power to the main load (house wiring, etc)
and is independent of the array. When convenient
(during periods of non-usage), the battery is
recharged by being disconnected from the main load
and connected to the array.
Silicon solar arrays are commonly described by
three parameters: the maximum power, PMAX, they can
deliver to a load of a common type (like a lead-acid
battery), the open circuit voltage, VOC, and the short
circuit current, ISC. These parameters are quoted for the
array for one full sun, which is the illumination
received in an outdoor position on the equator at high
noon on a summer day.
This curve is obtained by connecting the array to a
load resistor and then graphing I as a function of V as
the resistance is changed. You can see that as the load
resistance increases the output current decreases.
Superimposed on the figure is the output power P
(the product of I and V). P goes through a maximum
for a certain V and therefore also for a certain resistance R. R is equal to the array’s internal resistance.
Thus maximum power is obtained from an array
when it is connected to a load whose resistance is
equal to the internal resistance of the array.
The Selenium Photocell
The selenium photocell functions in practice much
like a solar array in that it converts solar energy into
electrical energy. The advantage of selenium photovoltaic cells over other cells is that their response is
very close to that of the human eye. Their efficiency as
energy converters of the total spectrum is not as high
as other photocells, and so they are not used as
sources of energy as are solar cells.
Figure 2-5 shows the cross-section of an idealized
barrier-layer selenium photocell. The steel support
plate “A” provides the rear (positive) contact, and
carries a layer of metallic selenium “B”, which is a few
hundreds of a millimeter in thickness. “C” is a thin
transparent electrically-conductive layer applied by
cathodic sputtering; it is reinforced along its edge by a
sprayed on negative contact ring “D” and protected
from damage by lacquering. The rear support of the
photocell is protected from corrosion by a metallic
spray coating “E”; this also improves electrical
contact.
IV Characteristic of a Solar Cell
Many of the properties of a silicon solar cell or array
are described by its IV characteristic curve (Figure 24).
200
1600
Maximum Power
180
1200
Output Current (mA)
140
120
1000
100
800
80
600
60
400
40
Open Circuit Voltage Voc
20
200
0
Output Power (mW)
Short Circuit Current Isc
160
A
B
C
D
1400
E
Figure 2-5. Cross-section of a selenium photocell.
12
11
10
Output Voltage (V)
9
8
7
6
5
4
3
2
1
0
0
Figure 2-4. A typical IV characteristic for a solar cell (or
array) subject to some level of illumination. The power goes
through a maximum in the “knee” region of the current.
This kind of photoelectric cell is used chiefly for light
meters, exposure meters, and other devices involving
light. They are usually specified by curves of closedcircuit current versus illumination in lux.
2-3
Aspects of Technology
The Thermocouple
A thermocouple is a junction of two dissimilar metals,
like copper and constantan, that produces an open
circuit voltage that depends on the temperature. The
effect is called the thermoelectric or Seebeck effect , named
after Thomas Seebeck who discovered it in 1821. The
voltage, though small, is measurable with a highquality digital multimeter, or if amplified by a signal
conditioner or amplifier. Thermocouples, being made
of wire, are very rugged and inexpensive and can
operate over a wide range of temperature, and also to
a high temperature.
Since the Seebeck voltage is so small, a thermocouple is impractical for use as a source of electrical
energy; but as a temperature sensor it works very
well. In general, the emf V is observed to depend nonlinearly on temperature T. However, if the temperature change ∆T is small enough then V follows a
linear relationship
V = s∆T ,
[2-1]
where ∆T is the temperature difference between the
junction temperature and a reference temperature and
s is the Seebeck coefficient (temperature coefficient) of
the particular thermocouple combination.
Many different thermocouple combinations have
been found to be useable in this way (Table 2-2). A
combination is chosen for its sensitivity (temperature
dependence) and temperature range (Figure 2-6).
Figure 2-6. Response curves for various thermocouple combinations. Some are more common than others, for example,
CR-AL, Fe-CN, and Cu-CN.
Of all of these combinations types K and J are the
most used in undergraduate science laboratories. You
will likely be using a type K in this course. If you do
use a thermocouple to measure temperature you must
take special precautions to provide a temperature
reference and to calibrate the combination correctly.
Alternatively, you can use a thermocouple with a
special signal conditioner. These issues we postpone
for Chapter 6.
Piezoelectricity
Table 2-2. Standard Thermocouple Types and Useful Temperature Ranges.
Letter
Designation
Type K
Type J
Type T
Type E
Type S
Type R
2-4
Metals
Chromel/Alumel
Iron/Constantan
Copper/Constantan
Chromel/Constantan
Pa/Pa 10% Rhodium
Pa/Pa 13% Rhodium
Approx Temp
Range (˚C)
–200 to 1250
0 to 750
–200 to 350
–200 to 900
0 to 1450
0 to 1450
When certain crystalline materials (such as Rochelle
salt or quartz) and ceramics (such as barium titanante)
are deformed, a voltage develops across them. This
phenomenon is called the piezoelectric effect. The force
or pressure on a piezoelectric material produces a
voltage that is directly proportional in sign and magnitude to the applied stress. Common piezoelectric
devices are the buzzer and pressure sensor. We
discuss these further in Chapter 6.
Aspects of Technology
Resistors
Arguably, most resistors to be found in consumer electronic devices today are made from semiconductor materials and exist in the form of monolithic integrated circuits (ICs). A treatment of
the subject would take us into areas of technology and engineering that lie beyond the intended
scope of these notes.3 We confine our attention here to discrete large-scale resistor types that you
might encounter in a research project in the science lab.
Carbon Composition Type
A large-scale discrete resistor can be made from virtually any conductor, from copper to carbon. However,
most resistors are fabricated from a section of wire cut
to a certain calculated length or an amount of carbon
compressed to a certain shape and dimension, cylindrical being the most common in consumer electronics. A cut-away view of the carbon composition type
is drawn in Figure 2-7.
ten. The fourth band gives the manufacturer’s tolerance. The tolerance is the manufacturer’s estimate of
the uncertainty in the resistance, based on quality
control employed at the factory. An example in
reading a color code is given in Example Problem 2-2.
Example Problem 2-2
Reading a Color Code
A resistor has color bands in the order: grey, red,
yellow and silver. What is the resistance?
Solution:
The numbers corresponding to the colors are: 8, 2, 4
and 10%. According to the code the resistance is:
(82 x 104 ± 10%) ohms.
Figure 2-7. A cutaway view of a carbon composition resistor.
Color Code
The resistance value of a carbon composition resistor
is indicated by a color code painted in four bands on
the resistor’s body (Table 2-3).
Table 2-3. Resistor Color Code
Bands 1, 2, 3
Black
0
Brown
1
Red
2
Orange 3
Yellow 4
Green
Blue
Violet
Grey
White
5
6
7
8
9
Band 4
Gold
Silver
No Color
5%
10%
20%
Beginning with the band closest to one end of the
resistor, they give, respectively, the first significant
digit, the second significant digit, and the multiple of
In this example the manufacturer guarantees that if
the resistance is measured with a reputable instrument, the result will fall within ±10%, or ±8 x 104 Ω, of
the value specified by the color code. Resistors of 1 %
and 0.5 % tolerance are available at higher cost.
Power Rating
A resistor can transfer only so much heat to the surrounding air at room temperature before undergoing
an unacceptable change in resistance. Carbon composition resistors are rated as to the maximum power
they can dissipate without the resistance drifting outside the tolerance range. The ratings most commonly
available off the shelf are 1/8, 1/4, 1/2, 1, 2, 5, and 10
watts. The rating is largely a factor of the resistor’s
volume and surface area (Figure 2-8).
The larger the surface area the greater the power
dissipation. Should a manufacturer’s rating be
exceeded a resistor can heat up sufficiently to selfdestruct. Forced air cooling increases the effective
power dissipation.
Higher-power resistors are also available, though
they are not often called for in modern low power
2-5
Aspects of Technology
devices. These resistors are nearly always wirewound and have a large surface area. Other types of
resistors are the carbon film and metal film types that
are designed to produce low levels of electrical noise.
Much research is under way to develop smaller,
stabler and electrically “quieter” resistors from new
materials.
2W
1W
1/2 W
1/4 W
Figure 2-8. Examples of resistors having the same resistance
but different body sizes and power ratings.
The Fuse
A fuse (Figure 2-9) is a resistor that is actually a safety
element placed in series with a device to protect it
from electrical and/or heat damage. It can be found
in nearly every consumer electronic device as well as
in the AC mains.
this case the fast-blow fuse provides a better measure
of protection. The functionality of higher-power fuses
is effected by devices called circuit breakers.
Temperature Dependence of Resistance
The resistance of many materials is observed to
depend on temperature in a way that can be described
by the following empirical function:
RT 2 = RT1 [1 +α ( T2 – T1 )] ,
…[2-2]
where T1 and T 2 are temperatures. The proportionality
factor α is called the temperature coefficient of resistance.
α is a characteristic of the material of which the resistor is made and varies between about 2 x 10–2 ˚C –1 and
2 x 10–5 ˚C–1 for various materials (Table 2-4). Notice
that all of the coefficients listed in the table are positive with the exception of carbon. This means that as
the temperature increases, the resistance of carbon
decreases.
Table 2-4. Temperature Coefficients of Various Materials.
Material
Nickel
Copper
Silver
Iron
Platinum
Mercury
Carbon
Coefficient
6.7 x 10–3
4.3 x 10–3
4.1 x 10–3
4.0 x 10–3
3.9 x 10–3
9.9 x 10–4
–7.0 x 10–4
Figure 2-9. Two types of fuse, fast and slow blow.
Platinum Resistance Thermometer (PRTD)
The active element in a fuse is usually a metal strip,
which is designed to melt if certain conditions are
exceeded. If the strip melts, the circuit is opened and
the device in series with the fuse is protected from
electrical damage. Fuses are rated according to
current and voltage, though it is the power delivered
the fuse element that heats it to the melting point.
Fuses are categorized as of the slow-blow or fastblow variety. The fast-blow variety is the quicker reacting of the two. Sensitive equipment can sometimes be
damaged if the fuse rating is exceeded only briefly. In
The resistance of any material depends on temperature. This means that any material can, in principle,
serve as a temperature sensor. If the resistance can be
accurately measured and if the material’s α value is
known, then the temperature can be calculated.
Alternatively, for a special material like platinum,
the temperature can be obtained from standard tables
of resistance (see the file PRTD.dat). This is the theory
of operation of the Platinum Resistance Temperature
Detector (PRTD).
Platinum is a metal ideally suited for the sensing of
temperature because its resistance is stable and
repeatable at high temperatures and in harsh environ-
2-6
Aspects of Technology
ments. We shall return to this subject in Chapter 6.
The Thermistor
A thermistor is in essence a thermal resistor, a resistor
whose resistance changes with temperature more
dramatically than is adequately described by eq[2-2].
For example, the resistance-vs-temperature response
of a typical commonly-available thermistor, the Radio
Shack type #271-110, is shown in Figure 2-10.
Thermistor Type RS#271-110
150
T (degC)
100
50
0
-50
0
1.10 5
2.10 5
where T is the absolute temperature, R is the resistance and A, B and C are constants to be determined
in a curvefit process. We discuss the thermistor in
more detail in Chapter 6, along with the fitting of
eq[2-3] in Appendix F.
The Strain Gauge
The strain gauge, as its name implies, is a device for
measuring strain. The strain is determined from the
change that occurs in the device’s resistance. It is in
essence a long section of wire firmly fixed to a
support (Figure 2-11). If the support is bent or
strained then the wire element is stretched a small
amount, causing its resistance to change (in
accordance with eq[1-3]). Since the change in
resistance is very small, the strain gauge is almost
always used in conjunction with a null-detection
circuit involving a Wheatstone bridge (described
below). We shall return to the strain gauge in Chapter
6.
3.10 5
R (Ohms)
Figure 2-10. Resistance vs temperature of a Radio Shack
#271-110 thermistor.
Thermistors are made from a variety of materials, that
include evaporated films, carbon or carbon compositions, ceramic-like semiconductors of oxides of
copper, cobalt, manganese, magnesium, nickel,
titanium or uranium. Thermistors can be molded or
compressed into various clever shapes to fit a wide
range of applications. These devices have a resistance
change characteristic of 4 to 6%/˚C with generally a
negative temperature coefficient (NTC). Thermistors
made of barium or strontium titanate ceramics have a
positive temperature coefficient (PTC).
As can be seen from Figure 2-10, the resistance of a
thermistor depends on temperature in a highly nonlinear way. The dependence can be approximated
empirically by the so-called Steinhart-Hart equation:
1
3
= A + Bln ( R) + C( ln( R)) ,
T
…[2-3]
Figure 2-11. Structure of a strain gauge.
The Photoresistor
A broad range of materials have a resistance that
depends on the intensity of light falling on them. The
most well-known examples are cadmium sulphide
(CdS) and cadmium selenide (CdSe). The composition
of a cadmium sulphide photocell, deliberately designed to exploit this property is illustrated in crosssection in Figure 2-12.
2-7
Aspects of Technology
The Voltage Divider
Active region
(photoconductive
material)
λ
Ohmic
contact
Ohmic
contact
λ
Figure 2-12. Construction of a CdS photocell and its circuit
symbol.
One application of resistors connected in series is the
voltage divider (Figure 2-14a). In the figure, a voltage
source is shown connected across three series resistors
(any number of resistors greater than one would suffice for our argument). The node between each resistor is connected to a terminal of a rotary switch. By
manually positioning the switch on the terminals A,
B, or C three fractions of the applied voltage V can be
made to appear as the output voltage Vout.
The resistance R of a CdS photocell is observed to
depend on light intensity according to an empirical
relationship of the form:
R = RoI – K ,
R1
[2-4]
R2
V
where Ro (Ω) is a constant, I (fc) is the intensity of light
and K is a constant which is less than 1. Figure 2-13
shows the resistance of a cell with R o = 2000 Ω and K =
0.75 plotted on a log-log graph. Clearly, this kind of
dependence makes the CdS cell an obvious sensor of
light intensity. We shall return to this device in
Chapter 6.
R3
(a)
C
V
Resistance (Ω)
CdSPhotocell.dat
A
B
Vout
Vout
(b)
Figure 2-14. A voltage divider activated by a rotary switch
(a) and a voltage divider in the form of a potentiometer (b).
10 4
When the switch is at A,
10 3
Vout = V ,
10 2
10 1
10 -2
10 -1
10 0
10 1
10 2
and when at B,
Vout =
R2 + R3
V,
R1 + R2 + R3
and when at C,
Vout =
R3
V.
R1 + R2 + R3
10 3
Intensity (fc)
Figure 2-13. Log-log plot of resistance vs light intensity for
the Radio Shack type 276-1657 CdS photocell.
This divider gives discrete values of Vout. If continuous values are desired then a special, variable, resistor
called a potentiometer may be substituted (Figure 2-14b
and 2-15).
The potentiometer is equipped with a wiper, indicated by the arrow (connected to the center tap in Figure
2-15), that can be moved continuously over a carbon
2-8
Aspects of Technology
element or a series of closely-spaced wire windings. In
this way more precise values of Vout can be chosen
than is possible with the rotary switch. The potentiometer was in fact widely used as an audio volume
control in legacy consumer electronics. Similar
devices called potentiometer actuators are used as
position sensors in robotics (discussed in more detail
in Chapter 6).
The Current Divider
Two resistors connected in parallel (Figure 2-16) form
a current divider. It is useful to have a formula for I1 or
I2 in terms of the “input current” I.
R1
I1
R2
I2
I
+
–
V
Figure 2-16. Two resistors connected in parallel.
Let us solve for I1 . The same voltage V that appears
across the resistor combination appears across R 1 .
Thus we can write
Figure 2-15. Examples of potentiometers, a single (top) and
dual (bottom). The center tap of each set of three pins connects to the wiper. These controls are largely obsolete.
Example Problem 2-3
Voltage Divider
A circuit like the one shown in Figure 2-14 has a
source of 10 V and two resistors in series, R 1 = 100 Ω
and R2 = 200 Ω. What is the voltage drop across R 2?
Solution:
According to the treatment of the previous section
the voltage is given by
V2 =
R2
200Ω
x10V =
x10V
R1 + R2
100Ω+ 200Ω
=6.67 V.
so that
V=I
R1R2
= I1 R1,
R1 + R2
I1 = I
R2
.
R1 + R2
…[2-5]
This circuit enables us to obtain the current we desire,
I1 , from an available current I.
Example Problem 2-4
Current Divider
In the circuit shown in Figure 2-16, you are given
that I = 1 A, R 1 and R 2 are 100 Ω and 200 Ω respectively. What is the current through R 1?
Solution:
According to eq[2-5],
I1 =
R2
200
x1 =
x1
R1 + R2
100 + 200
=2/3 A.
The available current is 1 ampere, but only 2/3
ampere flows through R1.
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Aspects of Technology
The Wheatstone Bridge
A Wheatstone bridge is a diamond shaped arrangement of resistors (Figure 2-17).
R1
V
a
Rv
A
b
Rx
R2
circuit must be used with a voltage source and an
instrument whereby the voltage (or the current flow)
between points a and b can be measured.
Often the circuit is employed as a “null detector”,
that is, Rv is varied until the ammeter connected
between a and b reads zero. The sensitivity of the
bridge is thus a function of the sensitivity of the
ammeter, and therefore can be quite high.
You should be able to show that if the reading on
the ammeter is zero (when the bridge is said to be
balanced) then the following relationship between Rx
and Rv applies:
Rx =
Figure 2-17. A Wheatstone bridge.
A Wheatstone bridge has desireable electrical properties and is found in a number of sensor circuit
designs. R1 and R2 are usually fixed resistors, often of
high precision, which are mounted on the sensor
board itself or in the controlling electronics. Rx is the
sensing element or “unknown” in the form of a
thermistor, a strain gauge, or other resistance sensor.
Rv is a resistor whose resistance can be varied. This
R2
Rv .
R1
…[2-6]
Thus if the bridge is balanced by varying Rv, then the
unknown Rx can be calculated.
Wheatstone bridges are often used with sensors
(such as the strain gauge discussed earlier) which
produce a very small change in a sensed variable. This
very small change then results in a deviation from the
null condition which, if the ammeter is sensitive
enough, is easily detected and to high precision.
Capacitors
For reasons of space, we restrict our attention to large-scale non-IC capacitor types.
General
As we have seen in Chapter 1 a capacitor is modelled
as a set of parallel metal plates. Practical large-value,
capacitors are made by sandwiching a dielectric
between two thin metal plates and then rolling the
assembly into a tubular shape (Figure 2-18).
Figure 2-18. A fixed-value tubular capacitor.
2-10
The dielectric can be of almost any non-conductive
material, paper, plastic, oil, glass or even air. A
capacitor’s capacitance value is often printed on the
capacitor’s body.
Specifications
Capacitors, like resistors, are categorized in a number
of different ways: for example, the frequency and
voltage range over which they are to be used, whether
they are of polar or non-polar type (more on this
below), and the materials of their manufacture.
Generally, a capacitor is used either in a power
application at low frequencies (60 Hz), in an audio
frequency application (≤ 20 kHz) or a radio frequency
application (MHz region). The capacitor used in the
smoothing section of a power supply is of a large
value (greater than 1 µF) and is often of the polar or
Aspects of Technology
electrolytic type. Non-polar capacitors with values of
order 0.001 to 0.01 µF are usually used at audio frequencies, and capacitors with values less than 0.001 µF
are usually used at radio frequencies. This usage is
largely determined by the capacitor’s impedance
(Chapter 1).
Polarized Capacitors
Power or electrolytic capacitors made from aluminum
and tantalum are “polarized”. This means that the
polarity markings on the capacitor’s body must be
observed when placing the capacitor into a circuit.
The positive terminal of the capacitor must be connected to the higher potential in the circuit. If this is not
observed, the capacitor may break down. Also, a
polarized capacitor requires a polarizing (DC) voltage
and cannot withstand a reverse current; it cannot be
used in a situation in which a DC voltage is absent
and/or in which an existing AC voltage reverses the
capacitor’s polarity. All other capacitor types are nonpolar. More details on capacitors are listed in Table 25.
Table 2-5. Fact sheet on commonly-used non-IC capacitors.
TYPE
TYPICAL
VALUE RANGE
TYPICAL
TOLERANCE
APPLICATIONS &
CHARACTERISTICS
Aluminum
Electrolytic
0.68 - 200, 000 µF
– 10 % - + 75 %
Power-supply filtering, bypass, coupling.
Used where large values are needed.
Tantalum
Electrolytic
0.001 - 1000 µF
5 - 20 %
Bypass, coupling, decoupling. Very stable,
long life
Ceramic
1pF - 2.2 µF
5 - 30 %
Transient decoupling, bypass. Value changes
with frequency and temperature.
Mica
1 pF - 1 µF
1 - 30 %
Timing, Oscillator, and AF circuits.
Very stable.
Polypropylene
1 pF - 10 µF
2 - 10 %
Blocking, bypass, coupling, and timing circuits.
Filter, noise suppression.
Good for audio through UHF.
Polyester
(Mylar)
0.001 - 10 µF
5 - 20 %
Blocking, filtering, transient suppression. Good
for audio. Small size with medium stability.
Paper
0.001 - 10 µF
10 - 20 %
General purpose. Large size, low cost, medium
stability, and poor moisture characteristics.
Polystyrene
51 pF - 0.15 µF
1-5%
Timing and tuned circuits. Small capacitance
change with temperature. Excellent stability.
Good in audio circuits.
Capacitors in Sensors
A few words are in order about the use of capacitors
as sensing elements. One clever example is the patented Humicap sensor manufactured by Vaisala Inc.
(Figure 2-19) for measuring relative humidity. The
basic principle of humidity measurement is the same
in both the HUMICAP® and INTERCAP® sensors.
The dielectric in these sensors is a thin polymer film
that either absorbs or exudes water vapour as the
relative humidity of the ambient air rises or falls.
Figure 2-19. The Vaisala Humicap humidity sensor.
2-11
Aspects of Technology
As the dielectric constant of the capacitor changes so
does the capacitance. The capacitance is measured by
the electronics of the instrument and converted to a
humidity reading. We have a few more details on this
type of sensor in Chapter 6 since it is used in the
UTSC weather station.
Inductors
We confine our attention here to large-scale non-IC types of inductors.
Inductors, Chokes and Coils
An inductor is modelled as a coil of wire wound on a
support or a form (Figure 2-20). The form may be of
magnetic material, non-magnetic, or even non-existent
(the inside of the coil being air). You may recall from
Chapter 1 that the interesting property of an inductor
is its inductance. Inductance is the property responsible for producing an emf across the coil when the
current through the coil is made to change with time.
Figure 2-20. An inductor of the simplest geometry is one
that is wound on a circular toroidal shaped form. Because of
its efficiency, this kind of inductor with an iron form is
commonly used in the low pass filter section of the power
supplies of high quality audio amplifiers.
Specifications published for inductors usually give the
Q value, test frequency, and current rating. The Q
value indicates how sharp the response of the coil is
when resonating at the test frequency. The current
rating is the amount of current the wire making up
the coil can safely carry without self-destructing. (The
wire making up the coil can be of various gauges.)
Inductor Forms
The type of form on which a coil is wound affects a
coil’s inductance and frequency response. Iron forms
or cores are used at low frequencies (up to 100 kHz).
Coils used at frequencies up to 30 MHz are usually
space-wound (air core) or wound on cores made of
ferrite (iron filings epoxy-bound). Coils used above 30
MHz are usually wound on non-ferrous materials
such as brass or copper to minimize power losses to
eddy currents. Two iron core types are illustrated in
Figure 2-22.
The terms “inductor”, “choke”, and “coil” are often
used interchangeably in electronics jargon. But an
inductor called a coil is usually intended to resonate or
peak at a certain frequency, while a choke is intended
to attenuate (i.e., “choke”) a group of frequencies
(Figure 2-21). (For the meaning of these terms see the
discussion of the filter later in this chapter.)
Figure 2-22. A selection of inductor types: chokes (top) and
iron cores (bottom).
Figure 2-21. Examples of chokes and coils.
2-12
Aspects of Technology
The Transformer
A transformer is a special type of inductor consisting
of two coils. The coils are wound close together but in
such a way as to be electrically insulated from each
other. One coil is called the primary winding, the other
the secondary. The normal use of a transformer is to
obtain a desired AC voltage across the secondary
from an available AC voltage applied across the
primary. A transformer works in this way because of
an effect called mutual induction. If the two coils are
close enough together the magnetic flux produced by
the current in coil 1 passes through coil 2 and vice
versa. Thus a changing current in coil 1 induces an
emf across coil 1 and across coil 2.
In order for mutual induction to occur a means
must exist to enable the flux produced by the current
in coil 1 to pass through coil 2. This is called “flux
linkage”. Linkage is achieved by placing the coils
close together, by interleaving the coils (winding them
together) or by using a closed loop of some magnetic
material like iron to guide the flux. The diagram of a
toroidal core transformer is drawn in Figure 2-23a.
The circuit symbol for a transformer is drawn in
Figure 2-23b.
Primary
Coil 1
i1
Secondary
Coil 2
B
n1
n2
+
v1
L1
(a)
v2
L2
–
magnetic material for flux loop
+
i1
n1
n2
source v1
–
i2
L2
v2 =
n2
v.
n1 1
…[2-7]
If n 2 /n 1 is greater than 1 then v2 is greater than v1 , i.e.,
the voltage across the secondary exceeds the voltage
across the primary—thus the source of the name
transformer. This kind of transformer is called a step
up transformer. If n2 /n 1 is less than 1 then v2 is less
than v1 and the situation is reversed; the transformer
is a step down type.
As we have stated, a transformer is placed in a circuit to obtain a desired AC voltage from an available
one. The most commonly available AC voltage is the
115 volts supplied by the AC mains. Transformers are
therefore the first stage in most consumer devices that
obtain their power from the mains. As well, the AC
mains voltage is derived from high-voltage lines with
step down transformers. This topic in “high power” is
beyond the intended scope of these notes.
Transformers are very non-ideal devices; because of
eddy current losses, they tend to lose energy to heat
and they tend to distort current waveforms. They are
therefore to be avoided in modern circuit designs
wherever possible. Indeed, in modern low-power
mostly digital consumer devices they are rarely to be
seen at all.
+
v2 load
L1
The Transformer Equation
A working relationship exists between the AC voltages appearing across the primary and secondary
windings of an ideal transformer. (An ideal transformer is one in which no energy is lost to heat.) If v1
and v2 are the voltages developed across primary and
secondary, and if the windings have n 1 and n 2 turns of
wire, respectively, then it can be shown that
(b)
–
mean that the coils are wound in the same
sense, i.e., clockwise or counterclockwise
Figure 2-23. An ideal transformer (a) is given the circuit
symbol (b).
Example Problem 2-5
Transformer
A transformer like the one shown in Figure 2-23 has
its primary connected to the 115V AC mains. If the
number of turns in the primary and secondary are
1000 and 500, respectively, what is the voltage to be
expected across the secondary?
Solution:
According to the treatment of the previous section
the voltage is given by
2-13
Aspects of Technology
Vsec ondary =
nsec ondary
500
x115V =
x115V
nprimary
1000
= 57.5 V.
The transformer is a step-down type.
The Inductor in Sensors
An inductor is often part of a sensor whose function is
to count something. An example is the rain gauge
(discussed in more detail in Chapter 6). The active
element in a rain gauge is a spoon or a cup in which
the rain drops. The handle of the spoon is balanced on
a pivot so that once the spoon fills with water it tips
out. A magnet is attached to the handle end of the
spoon. As the spoon tips the magnet comes into
contact with the end of an inductor. The inductor’s
inductance rises suddenly, causing a change to occur
in the emf across the inductor. This brief change of
emf is registered as an electrical pulse which is then
counted.
An Analog Waveform Revisited
In a science lab an analog waveform can be produced
by a signal generator (Figure 2-24). By analog waveform is meant a waveform that is a continuous function of time. An analog waveform has the property
that at any instant of clocktime it has a definite value
of displacement or voltage. Or in other words,
between any two clocktimes it has an infinite number
of displacement or voltage values. Most waveforms
we encounter in our everyday lives are analog in
nature. The sounds that we hear with our ears are
continuously-varying waves of air pressure. The
voltage signal we obtain from the wall sockets in our
homes and labs is an analog waveform. The “real
world” is arguably an analog one.
Figure 2-24. The output from a signal generator has an analog waveform. 4
2-14
From its beginning, analog electronics was focussed
on the issues of routing an analog signal from one
point to another in a circuit without distorting the signal in any way, that is, by introducing changes in
amplitude or phase. The difficulties achieving this to
the satisfaction of the consumer was one of the things
to drive the digital revolution in the audio industry.
The waveform we have chosen here as an example
is a pure sinusoid, a special case. Analog waveforms
may in general consist of a number of superposed
sinusoids, in other words, a number of components.
One example of a waveform consisting of the superposition of 1 kHz and 2 kHz components is shown in
Figure 2-25. Audio waveforms that we hear every day
consist of a wide range of frequencies and amplitudes,
all changing in complicated ways with time.
Figure 2-25. A waveform consisting of two component waveforms of frequency 1 kHz and 2 kHz.
Aspects of Technology
DTMF
A practical application of waveforms consisting of
two components, or tones, is in the Dual Tone Multiple
Frequency (DTMF) method of conveying information
via the telephone line. This application we literally
hear every day, every time we use a telephone.
In spite of the digital revolution, telephony is an
analog medium at heart (because speech is analog?).
Digital information (e.g., a telephone number) is sent
over a telephone line as a two-tone signal. Each
character on the keypad of a telephone has its own
combination of two-tone signals (Table 2-6). Dual
tones are decoded by special ICs in routing equipment. Some instruments, in particular the Telulex
Model SG-100/A signal generator (described in Appendix 1) is equipped with the firmware to perform
this decoding.
It sometimes happens that when complex waveforms pass through a system some components are
modified in amplitude and phase more than others. A
system which selectively modifies components of
waveforms is called a filter. Filters appear again and
again in sensors and signal conditioning circuitry.
That brings us to the next section where we examine
filters in detail.
Table 2-6. Dialing Digits and their associated dualtone
frequencies.
Keypad Character
0
1
2
3
4
5
6
7
8
9
*
#
A
B
C
D
Frequencies
941 Hz and 1336 Hz
697 Hz and 1209 Hz
697 Hz and 1336 Hz
697 Hz and 1477 Hz
770 Hz and 1209 Hz
770 Hz and 1336 Hz
770 Hz and 1477 Hz
852 Hz and 1209 Hz
852 Hz and 1336 Hz
852 Hz and 1477 Hz
941 Hz and 1209 Hz
941 Hz and 1477 Hz
697 Hz and 1633 Hz
770 Hz and 1633 Hz
852 Hz and 1633 Hz
941 Hz and 1633 Hz
2-15
Aspects of Technology
The Analog Filter
Filters exist in many places in electric circuits, in forms that are intended and those that are not.
Any circuit that consists of a resistor and a capacitor, or a resistor and an inductor in close
proximity, can serve as an analog filter. A filter is really a frequency selective attenuator, in the sense
that it alters the frequency makeup of a waveform by changing the amplitude and/or phase of a
range of frequency components of the waveform, leaving other frequency components unchanged. A filter that does not amplify, which we discuss here is called a passive filter. A filter that does
amplify is called an active filter. We shall discuss these kinds of filters (called amplifiers) later in
this chapter.
The Impedance Divider
Thus dividing eq[2-8b] by [2-8a] we get
The story of filters begins with the idea of the
impedance divider. We have seen in Chapter 1 how a
voltage divider can be made from two series resistors.
The equivalent in AC circuits is two series impedances Z 1 and Z 2 (Figure 2-26).
system
G=
…[2-9]
G in fact is what is known in mathematics as a complex number. This is because Z 1 and Z 2 are themselves
complex numbers (Chapter 1). But if the form of Z 1
and Z 2 are known then |G| and the phase angle φ can
be calculated. Let us consider an example.
Z1
vin
vout
Z2
=
.
vin Z 1 + Z 2
The RC Low Pass Filter
Z2
vout
Replacing Z1 in Figure 2-26 with a resistance R and Z2
with a capacitance C, the circuit reduces to Figure 227. The system is called an RC filter.
vin
Figure 2-26. In its most general form a filter can be thought
of as an impedance divider.
R
C
vout
Figure 2-27. An RC low pass filter.
In electronics jargon the circuit is called a four-terminal
network. There are four terminals—two inputs and
two outputs. The circuit can also be regarded as a
system (within the dashed rectangle). The input voltage vin is the stimulus applied to the system and the
output voltage vout the response. We can quantify this
circuit’s effect on the input by finding the ratio of the
output voltage to input voltage and the phase angle
between the two signals. This ratio, which we shall
call G, can be measured with a DMM, the phase angle
φ with an oscilloscope.
The input and output voltages are:
and
2-16
vin = i( Z1 + Z2 ) ,
…[2-8a]
vout = iZ2 .
…[2-8b]
In a rigorous mathematical treatment, we would deal
with G as a complex number. To avoid this, we
bypass the mathematics and simply state the results.
The absolute value of G, |G|, is given by
1
,
1+ ω 2 R 2 C2
…[2-10a]
φ(ω ) = ArcTan(–ωRC) .
…[2-10b]
| G(ω)|=
and
These expressions are functions of the angular frequency ω. φ is the angle the output voltage leads the
input voltage. To examine the frequency dependence
of these functions more carefully, we have plotted
Aspects of Technology
them in log-log graphs (Figures 2-28).
With study, the meaning of Figures 2-28 should be
evident. Low frequency components of the input
signal are transferred to the output without change in
amplitude or phase. But high frequency components
are both attenuated and phase shifted. This is just the
kind of action performed by a filter—in this case, a low
pass filter. Even if the circuit in Figure 2-27 were, in
fact, invisible to you, you could still infer the equivalent circuit from measurements of the responses
|G(ω)| and φ(ω). Let us see in the following example
problem how to interpret filter response curves in
detail.
Example Problem 2-6
Interpreting the Effect of a Filter on a Signal Applied
to it
You are given that a signal consists of the sum of
sinusoids of 1000 Hz and 10000 Hz of equal
amplitude. The signal is input to the low pass filter
whose response curves are shown in Figures 2-28.
Describe the signal to be expected at the filter’s
output.
Solution:
From a study of the curves we can make the
following predictions:
Gain vs Frequency
At a frequency of 1000 Hz,
• |G|, the ratio of the output to the input signal,
should be about 0.9
• φ should be about –0.25 radians (–14 degrees)
At a frequency of 10000 Hz,
• |G| should be about 0.3
• φ should be about –1.25 radians (–72 degrees)
Gain G
1.0
0.5
0.0
10 0 10 1 10 2 10 3 10 4 10 5 10 6
Log Frequency (Hz)
Phase Shift vs Frequency
0.5
Radians
0.0
-0.5
-1.0
-1.5
-2.0
10 0 10 1 10 2 10 3 10 4 10 5 10 6
Log Frequency (Hz)
Figure 2-28. Plots of |G| and φ from eqs[2-10] for the RC
low pass filter. Here C= 4.7 µF and R = 10 Ω.
The conclusion to be drawn is that the 1000 Hz
signal should be affected very little by the filter; at
the output its amplitude should be reduced by about
10% and retarded in phase by about 14 degrees. The
filter’s effect on the 10000 Hz signal should be
greater. The 10000 Hz signal should have its output
reduced by a factor of 70% and be retarded in phase
by 1.25 radians, or approximately 72 degrees.
Clearly, the filter should selectively attenuate and
phase shift the 10000 Hz signal more than the 1000
Hz signal.
We have assumed in this discussion that the capacitor
is perfectly ideal and therefore dissipates no energy to
heat. In a real capacitor, however, some energy will
inevitably be lost, meaning that the curves for a real
RC filter will deviate to a lesser or greater extent from
what is shown in Figures 2-28.
We shall take up this subject again in Appendix C
where we show how a computer application can be
used to measure |G| and φ. Our next topic is the
subject of diodes.
2-17
Aspects of Technology
Diodes
We have described in Chapter 1 some of the physics of the semiconductor diode. Diodes are
fabricated as a junction of P- and N-type semiconductor materials, with the type of semiconductor determining how the diode is used. Diodes made from germanium and silicon are mostly
used as rectifiers and signal detectors. Diodes made from exotic materials such as GaAsP and
others are used as light detectors and sources. All diodes are tested by manufacturers and sold
with specifications as to the maximum voltage and current they can sustain.
Rectifier/Signal Diodes
band. A selection of specifications for a few of these
diode types is listed in Table 2-6. The peak inverse
voltage (PIV) is the maximum reverse voltage the
diode can sustain without suffering electrical breakdown. The forward current If is the maximum current
the diode can sustain in the forward direction and the
forward voltage drop is the corresponding voltage
drop across the diode.
Diodes designed for rectification or signal detection
purposes are made of germanium or silicon and packaged much like resistors but without the color code.
The body is commonly black and of a size consistent
with the current-handling capability (larger size for
larger currents). The cathode end of the body is
usually indicated by a rounding of the body or by a
Table 2-6. Selected specifications for a number of rectifier/signal diodes @25 ˚C that you will most likely encounter in this
course. We have included the generic type number (in the form 1N#) and the Radio Shack catalog number where known.
Type
RS#
1N34
Description
Ge signal
Vmax
(V)
1.0
PIV
(V)
60
If max
(A)
0.05
Ir max
@ PIV (µA)
30
1N60
Ge signal
1.0
50
0.03
40
Si rectifier
50
35
6
25
Si rectfier
1.6
50
1
10
Si rectifier
1
1000
2.5
1
Vf AV
(V)
0.9
276-1661
1N4001
276-1101
276-1114
Of the two diode types, the germanium diode has the
advantage of an intrinsically lower forward voltage
drop (typically 0.3 volts as compared with 0.7 volts for
silicon). This low forward voltage drop results in a
low power loss and more efficient diode, making it
superior in many ways to silicon. This lower voltage
drop becomes important in very low signal environments (signal detection from audio to FM frequencies)
and in low level logic circuits. The disadvantage of the
germanium diode is its larger leakage current for
reverse voltages (Figure 1-38). This makes the silicon
diode the diode of choice for rectification.
2-18
The Photodiode
A special type of silicon diode, related to the solar cell
and called a photodiode, is especially designed to detect
light. It is usually much smaller than a solar cell,
sometimes as small as the head of a pin. A photograph showing a number of photodiode products is
reproduced in Figure 2-29.
The photodiode has a very fast response time, often
of the order of nanoseconds. It is used reversedbiased. In this mode the current which flows across
the junction is linearly proportional to the intensity of
the light striking the diode (described in Chapter 1
Aspects of Technology
and shown in Figure 1-27). A simple circuit employing a photodiode in a light intensity meter is drawn in
Figure 2-30.
Figure 2-29. A selection of photodiodes.
diodes are fabricated from semiconductor compounds
such as Gallium Nitride, Indium Phosphide (InP),
Gallium Phosphide (GaP), Gallium Arsenide (GaAs),
and Gallium Arsenide Phosphide (GaAsP). An LED is
designed to emit light of a specific color when forward biased, mostly red or green, but sometimes
other colors, such as yellow, blue and white.
LEDs are used as replacements for incandescent
lamps, in indicator devices of all kinds ranging from
ON/OFF indicators to large billboard displays in
subways. We shall spend a few moments here on the
LED because you will be using an LED indicator box
in your study of the RS-232 interface (Appendix B).
An LED, unlike a rectifier diode, is encapsulated in
a transparent covering. When the LED is forward
biased by a voltage equal to or greater than the turnon voltage, the diode emits light. Information regarding typical LEDs is given in Figure 2-31. Specifications
for a selection of LEDs are listed in Table 2-7.
I
LED symbol
LED
case
Figure 2-30. A simple light intensity meter using a photodiode. As the intensity of the light increases the resistance
of the diode decreases and the current detected increases.
anode
cathode
anode
(b)
(a)
Vin
In addition to the usual specifications published for
diodes, photodiodes are described by a responsivity
factor R defined as follows:
I = RP ,
where I is the measured photocurrent (A) flowing
through the diode and P is the optical power (W)
incident on the diode. R depends on the wavelength.
The wavelength response characteristics depend on
the material from which the photodiode is made
(silicon or other materials), details of the diode fabrication process, and the optical filter, if any, between
the light sensor and the active photodiode surface.
The Light-Emitting Diode (LED)
As its name implies, a light emitting diode (LED) is a
PN diode especially designed to emit light. It is relatively inexpensive, efficient, consumes far less power
than an incandescent lamp and has a long life. These
cathode
R
LED
(c)
Figure 2-31. Information on LEDs, package (a), circuit
symbol (b) and circuit (c).
The anode of an LED is identified by the longer of the
two lead wires (a). An LED can pass only a small
current (typically 20 mA) without self-destructing. For
this reason an LED is nearly always used with a series
current-limiting resistor (c). If Vin is of the order of 6V
then the current limiting resistor R should be about
220 Ω. Some LEDs are designed for use with a 5 volt
source and have the current limiting resistor built-in.
2-19
Aspects of Technology
Table 2-7. Specifications for a selection of LEDs @25 ˚C that you will most likely encounter in this course.
Type
RS#
276-310
Description
Wide Angle
red LED
Yellow
Jumbo LED
276-022
Vmax
(V)
5.2
PIV
(V)
If max
(A)
Vf AV
(V)
2.1
P max
(mW)
Peak Wavelength (nm)
697
2.8
4.1
0.1
1.9
130
590
0.025
2.1
75
Green
LED
Amplification
We have seen in Chapter 1 that a carbon composition resistor continuously radiates or dissipates
heat energy to the surrounding air. Most circuit elements dissipate heat in a similar way—
including the capacitor and inductor— because they all possess some amount of resistance. In
other words, capacitors and inductors are not ideal elements. For this reason most circuit designs
require some amplification or boosting of voltage, current or power to offset losses of energy.
What is an Amplifier?
The idea of an amplifier is illustrated in Figure 2-32. A
signal of amplitude Vin is applied to a system and has
its amplitude increased to a value Vout. This process
takes energy. The energy is drawn from a source like
a battery or a power supply. Amplification should be
thought of as a process in which a smaller signal
controls a larger signal and not like an image being
magnified by a magnifying lens. The “amp” in the
figure can be a transistor or an operational amplifier.
Energy
from
supply
peak, or peak-to-peak values. φ is the angle, in radians
or degrees, that the output signal leads or lags the
input signal. To give an example, Figure 2-33 shows
the input and output signals for an amplifier with a
gain of 10 and a phase shift of 180 degrees.
Vout
Vin
amp
Figure 2-32. The idea of amplification. An input signal controls the energy drawn from a power supply so as to give
rise to an output signal increased in amplitude.
Amplifiers are described by the same parameters used
for a filter: the gain G and phase shift φ. G is the ratio
of the output to input voltages expressed as rms,
2-20
Figure 2-33. A screen save from a TekTDS210 digital oscilloscope. At the top is shown the input signal (on CH1) applied to an inverting opamp of the type shown in Figure 245. At the bottom is shown the output (on CH2). The gain
is 10 since the ratio of the peak-to-peak values of CH2 to
CH1 (5.04V/504mV) is 10 and the phase shift is 180 degrees since the output is inverted with respect to the input.
Aspects of Technology
Amplifiers to be Described
Two of the most popular discrete amplifier devices in
use today are the bipolar junction transistor (BJT) and
the field effect transistor (FET). The integrated circuit
(IC) type of amplifier called the operational amplifier
(opamp) is even more important in a practical sense
than is the BJT and FET since it so easy to use and
figures in thousands if not millions of applications.
We shall therefore discuss in the next section the BJT
only briefly in anticipation of spending most of our
time on the opamp. All of the signal conditioning
circuits reproduced in Chapter 6 use opamps.
The Transistor Amplifier
The two most important transistor types are the bipolar junction transistor (BJT) and the field effect
transistor (FET). The latter was the first to be invented but the former was the first to be widely
adopted by the electronics industry. Except for special applications today, discrete transistors
have largely been replaced by ICs. And the few examples of discrete transistors to be found today
are largely FETs. Therefore we begin our discussion of transistors with the BJT, not because it is
state-of-the-art, but because in many respects it is a natural advance on PN junction technology.
The Bipolar Junction Transistor
We discuss here the bipolar junction transistor (for
convenience we shall just use the word transistor). A
transistor can be used to amplify an AC signal as well
as a DC signal, but before it will work at all, it must
first be “prepared” with certain DC voltages set up
between its terminals or DC currents made to flow
through its body. We begin, therefore, with the issue
of DC preparation or bias and defer until later a
discussion of the response of the transistor to an AC
signal. 5
Classes
There are two general classes of transistor: the NPN
and the PNP. Both classes are made from germanium,
silicon and more exotic materials like gallium
arsenide. Both classes consist of three sections of
doped semiconductor arranged in a kind of sandwich
(Figure 2-34). These sections are called the collector,
the base and the emitter, and are each provided with
an electrical connection. The origin of the nomenclature NPN and PNP should be clear from the order of
the sections in the figure.
To make our task of explaining how a transistor
works as easy as possible we can think of both classes
as having the same geometry. 6 The base is the center
material, the collector and emitter are the outer
materials. The base is lightly doped, the emitter and
collector are more heavily doped. (For an explanation
of doping see Chapter 1.) And the emitter is more
heavily doped than the collector. The two classes
differ in the direction the current flows—into the base
terminal of the NPN and out of the base terminal of
the PNP. Current flows from collector to emitter
through the NPN and in the reverse direction
through the PNP. We shall focus on the NPN class in
our discussion here, though the PNP class is of equal
importance.
collector base
C
N P
IC
emitter
E
N
C
base
B
E
IB
emitter
E
P N P
B
C
B
collector
IC
C
(a)
E
B
IB
(b)
Figure 2-34. Composition and circuit symbol of bipolar
junction transistors: NPN class (a) and PNP class (b).
Electrical Characteristics of the NPN Transistor
To make a transistor work, two external DC voltages
must be applied to it (Figure 2-35). These voltages
may be derived from two separate power sources, as
is implied in the figure, or from a single source. Thus
there are two loop currents: a base current IB induced
by the voltage VBE between the base and emitter and a
collector current IC induced by the voltage VCE between collector and emitter. IC is typically two orders
of magnitude larger than IB and VCE is much larger
2-21
Aspects of Technology
than VBE .
germanium and 0.7 V for silicon) and the basecollector junction reverse biased by a few volts.
VCE
IC
C
N
P
N
B
E
–
+
IB
VBE
Figure 2-35. Biasing of an NPN transistor.
Recalling our study of the PN junction diode in
Chapter 1 you should recognize (Figure 2-36) that the
base emitter junction functions like a PN diode. The
purpose of the base-emitter voltage VBE is to turn on
the base-emitter junction, that is, to reduce the resistance of that junction to a low value, thereby allowing
a collector current to flow. Alternatively, the resistance of the base-emitter junction would be so high as
to reduce the flow of the collector current IC to a point
where the transistor could not function as intended.
Transistor Characteristics
Much of a transistor’s electrical behavior is summarized in its families of characteristic curves. One family
is called the collector characteristics (Figure 2-37). These
curves show how the collector current depends on
the collector-emitter voltage when the base current is
held constant at various values. To function as a linear amplifier, a transistor must be operated in a state
represented by a point on the graph where the variables depend linearly on one other. This range, called
the plateau region, is where the collector current is
directly proportional to the base current and is relatively independent of small changes in the collectoremitter voltage. In this region the transistor can be
modelled as a current source in series with a diode
(Figure 2-38).
IC
IB3
IB2
IB1
Plateau region
VCE
IC
VCE
IC
IC
N
P
N
E
IB
C
B
+
IB
Figure 2-37. The family of IC vs VCE curves of a typical BJT.
C
IC = β IB
–
VBE
Figure 2-36. An attempt to illustrate how a small baseemitter current in a transistor (bottom loop) controls a
much larger collector-emitter current (top loop).
= hFE IB
B
VPN
E
Figure 2-38. Model of a typical NPN transistor.
The base-emitter junction works as a kind of valve.
Small variations in VBE (and therefore in IB) produce
small changes in the base-emitter resistance, which in
turn cause large variations in IC. Small variations in IB
causing large variations in IC is “amplification in
action”.
Thus an NPN transistor is normally operated with the
base-emitter junction forward biased (0.3 volts for
2-22
The three currents in a transistor, IB , IC and IE are
proportional to one another in the following way:
IC = αI E ,
= βIB = hFE IE ,
…[2-9]
Aspects of Technology
where α and β, which are approximately constant, are
called the alpha- and beta-parameters. α and β are
themselves related by
β=
α
.
1– α
…[2-10]
Typically β is about 99 and α about 0.99. These numbers show that the ratio IC/IB is large, implying that
the transistor can be used to amplify current. Since
VCE/VBE is also large (at least for some configurations
as we shall show in the next section), the transistor
can be used to amplify voltage.
Transistor Configurations
Since a transistor has three electrical terminals, a signal can be applied between any pair of its terminals
three different ways. This leads to three configurations (Figure 2-39). The two terminals on the left in
each figure represents the input, the two terminals on
the right the output. One terminal is common to both
input and output. The configurations are therefore
called the common emitter (CE), the common base (CB)
and the common collector (CC).
C
C
C
in
B
out
in
out
B
E
E
Common emitter, CE
Common collector, CC
(a)
(b)
E
E
out
B
B
In order to design a working amplifier based on one
of these configurations the transistor must be properly biased, as we have already stated. This means that
the transistor must be operated in an electrical state
characterized by values of IB, IC and VCE making up a
point in the plateau region of the collector curves
(Figure 2-37). Only in this region does the amplifier
function linearly with the collector current being
directly proportional to the base current and more-orless independent of the collector-emitter voltage. A
point in this region is also far removed from a state in
which maximum current flows through the transistor,
the so-called “saturated” state (corresponding to VCE
= 0) or a state in which no current flows through the
transistor at all, the state of “cut off” (corresponding
to IC = 0). This point is called an operating or quiescent point. To do this, we must add external resistors,
capacitors, etc., to the transistor to effect the necessary
current limiting. This topic would take us into what is
usually covered in a course in electronics and beyond
the intended scope of these notes. In the event that
you have to use a transistor circuit in this course the
circuit diagram will be given.
The Phototransistor
C
in
• The CE amplifier has both current and voltage
gain. It is used as a general purpose amplifier.
• The CC amplifier has current gain but a voltage
gain of only unity (VBE ~ 0.6 V so VEC/VBC ~ 1). It
is used as a coupling stage when high input impedance and low output impedance are required.
• The CB amplifier has voltage gain but a current
gain of only unity (IC/IE ~ 1). It is used in high
frequency circuits since the capacitance linking
output to input is small.
(c)
Common base, CB
Figure 2-39. The configurations of an NPN transistor: common emitter (CE), common collector (CC), and common
base (CB). For simplicity, we have omitted external components from the diagrams.
Each configuration has advantages and disadvantages that can be summarized in the following points.
Still on the subject of transistors, there is a transistor
that is especially constructed to allow light to penetrate to the base-emitter junction. It is used as a
detector of light. In this case it is the energy of the
light falling on the base (rather than an external
power supply) that provides the energy to induce a
collector current IC to flow across the base-emitter
junction. The greater the light intensity the greater the
collector current (Figure 2-40).
The collector current IC is observed to depend
directly on the light intensity Iλ in a relationship of
the form:
2-23
Aspects of Technology
IC ≅ h fe Iλ ,
where hfe is the current gain of the transistor (defined
in the previous section). There is no external
connection to the base (Figures 2-41). This device is
more sensitive than is a photodiode, but is slower to
react to changes in light intensity. We discuss this
device in more detail in Chapter 6.
I
Rs
V
Figure 2-41a. A simple light-intensity meter using a phototransistor.
unused
1k
I
0 - 1 mA
Figure 2-41b. A circuit for uswing a phototransistor like a
photodiode.
Figure 2-40. Collector characteristic curves for a typical
phototransistor.
2-24
This concludes our discussion of discrete amplifier
devices. We now move on in the next section to the
operational amplifier.
Aspects of Technology
The Operational Amplifier
The operational amplifier, or opamp for short, is a much easier device to employ in a circuit of
one’s own design than is a discrete transistor. For one thing, an opamp, unlike a transistor, needs
no bias. An opamp is fabricated as a single IC and is intended to be used like a black box.7 One
needn’t be concerned with its internal structure. One need only connect it correctly to a voltage
source, provide the appropriate feedback element (resistor, capacitor, whatever) and then ensure
that the signal applied to its input has an amplitude small enough not to induce unwanted
distortion in the output. Here we describe the properties of the opamp and how to construct
useful devices with it.
The Need to Know
The opamp is in many respects the goal of our review
of amplifier devices. Thousands of signal conditioning
circuits that are used with sensors employ opamps as
straight signal amplifiers, as filters or for other
purposes. It is useful to have a working knowledge of
opamps so as to better understand how sensor devices
do their job.
It is instructive for the user, whether student or professional engineer, to regard an opamp as an ideal
element first, then later as the real device that it is.
Therefore, we begin by explaining what is meant by
an ideal opamp and then consider the ideal opamp in
a number of what are called “linear” applications,
where the output is directly proportional to the input.
The Ideal OpAmp
A view of the bare bones of an opamp is drawn in
Figure 2-42. Shown is the opamp IC itself (the
triangle), the two signal inputs (“+” and “–“), the
output, the power supply lines V++ and V–– and the
ground line. (The power lines, most often ±15 volts
usually derived from the same power supply, are
nearly always omitted from circuit diagrams, and we
shall omit them from now on.)8 The equivalent circuit
of the ideal opamp IC itself is drawn in Figure 2-43.
reference
voltage
V+
V–
I+
I–
sample
voltage
V++ (+ 15 V)
+
A(jω)
–
Vout
= A (V+ – V– )
V– – (– 15 V)
Figure 2-42. Schematic of an opamp. The reference and
sample voltages can be applied to either input.
V+ I+
Ro
Vin
Ri
A (V+ – V– )
Vout
I–
V–
Figure 2-43. The equivalent circuit of an opamp IC. The
input resistance R i is very large, at least 1 MΩ, and the
output resistance R o is very small, of the order of ohms.
The opamp has two inputs, labelled “+” and “–“, and
one output. A ground line is common to them all.
Often, one or the other of the inputs is connected to
ground. If the “+” input is grounded and a signal is
applied between the “–“ input and ground, then the
output signal is inverted (or phase shifted by 180˚)
relative to the input. If the “–“ input is grounded and
a signal is applied between the “+” input and ground,
then the output signal is not inverted. For these reasons the “–“ and “+” inputs are called, respectively,
the inverting and non-inverting inputs.
Characteristics
An opamp has the important characteristic that its
output voltage Vout is proportional to the difference
between its input voltages (V+ – V– ). For this reason it
is said to have a differential input. Another characteristic is a very large gain when no feedback element is
in place (Figure 2-44). (A feedback element—resistor,
capacitor, whatever—is nearly always connected
between the output and one of the inputs.) The gain
without feedback is called the open loop gain.
As we have stated, over frequencies of interest, an
opamp behaves as a nearly ideal device. By this we
2-25
Aspects of Technology
mean it has an input resistance so high it can be
regarded as effectively infinite, and an output resistance so low it can be regarded as zero (Figure 2-43).
This means that an opamp can be described to a good
approximation by the following rules:
Rule 1: The input currents I+ and I– are zero
(a consequence of R i ≈ ∞ ).
RF
R1
S
–
Vi
Vin
+
(a)
Rule 2: The voltages V+ and V– are equal
(a consequence of Vin being very small).
RF
I1
Gain dB
100
open loop
Vin
closed loop
R 1 S I–
Io
Vi
Ri
Ro
– A Vi
(b)
Vout
Figure 2-45. An opamp with feedback (a) and its equivalent
circuit (b).
40
Vout = –AVi .
log f
Figure 2-44. Gain curves of a typical opamp with and without feedback.
These rules make up what is called the ideal amplifier
approximation. We shall see in what follows that these
rules are, indeed, approximations, and are not strictly
true. But by making them we can calculate many
useful properties of opamp circuits.
Thus before we look at the opamp from the point of
view of being a real device we study it in a number of
circuits we can analyze using the ideal amplifier
approximation.
The OpAmp With Feedback
One of the simplest opamp circuits for the beginner to
study is one that has a single input resistor R 1 and a
single feedback resistor R F (Figure 2-45a). The noninverting input is tied to ground and the input signal
Vin is applied between the inverting input and
ground.
The equivalent circuit of the amplifier is drawn in
Figure 2-45b. You should be able to see that this
circuit is just the circuit of Figure 2-43 with R 1 and R F
added. Since the inverting input is used here we can
write
2-26
Vout
…[2-11]
where A denotes the very large open-loop gain factor
and the “–“ sign indicates phase inversion. Summing
the currents flowing into node S we have
Vin – Vi Vout – Vi
+
– I− = 0 .
R1
RF
…[2-12]
Assuming I– = 0 (Rule 1) and substituting eq[2-12]
into eq[2-11] and expanding, we have
 1
1
1 
Vin
Vout 
+
+
 =– .
 RF AR1 ARF 
R1
Since A>>1 the second and third terms in parentheses
are negligible and can be dropped. Thus we are left
with
Vout
V
≈ – in
RF
R1
so that
G=
Vout
R
=– F.
Vin
R1
…[2-13]
This is the amplifier’s midband closed-loop gain. It is
Aspects of Technology
the midband gain in the sense of being the gain when
the frequency is neither very low nor very high—or
when the effects of frequency are negligible. Since Vi
= V+ – V– ≈ 0 the summing node S is at zero potential
or “virtual ground”.
We can calculate the input and output impedances
of the amplifier as a whole. Note that
Rin =
Vin
≅ R1 .
I1
…[2-14]
Detailed analysis would show that
Rout =
( R1 + RF )
AR1
Ro << Ro .
…[2-15]
The conclusion we draw is that the opamp with feedback in the above configuration has a large input impedance (equal to R 1 ) and a low output impedance
(much less than the output impedance of the opamp
itself). These are desireable characteristics.
Eq[2-13] is the DC closed-loop gain. The closed loop
gain curve is drawn in Figure 2-44 over a wide frequency range along with the open loop gain. The DC
closed loop gain is arbitrarily shown as 100 or 40 dB
(representative of the Motorola 741, a common opamp in many signal conditioning circuits). The closed
loop gain curve is flat out to a frequency at which it
meets the open loop gain curve. Clearly, feedback
enhances the amplifier’s frequency response or bandwidth and reduces its low frequency gain.
Noninverting Unity Gain Amplifier
One of the odder opamp circuits is one that has no
external components as such: the output is tied directly to the inverting input (Figure 2-46).
Vin = V+ = V– = Vout !
…[2-16]
Thus the gain is +1, and the output and input signals
are in phase. The circuit is technically known as a
voltage follower. The impedance between the noninverting input and ground is very high. This circuit
is typically used to match a device whose output
impedance is high to a device whose input impedance is low. Impedance matching is important in electronics. It is often (though not always) desired that
maximum power be transferred from one stage to
another, and this can only be achieved if the impedances are matched in this way.
Noninverting Amplifier with Gain
If we add two resistors to the previous circuit we get
the circuit in Figure 2-47.
+
–
Vin
R2
I
Vout
I– = 0 R
1
GAIN
10
100
1000
R1
1 kΩ
100 Ω
100 Ω
R2
bw
9 kΩ
100 kHz
9.9 kΩ
10 kHz
99.9 kΩ
1 kHz
RIN
400 MΩ
280 MΩ
80 MΩ
Figure 2-47. A noninverting amplifier with gain. Shown
below the figure are typical specifications for a Motorola
741.
According to Rule 1, I– = 0. The voltage at the inverting input is given by the voltage divider equation
+
Vin
Rule 2 we have:
–
Vout
V– =
R1
V
R1 + R2 out
= Vin ,
Figure 2-46. Noninverting unity-gain amplifier.
applying Rule 2. Thus the closed-loop gain is
Vin is applied to the non-inverting input. Applying
2-27
Aspects of Technology
G=
Vout R1 + R2
=
.
Vin
R1
I
…[2-17]
Thus the amplifier has gain but does not invert. The
input impedance is very high, as it was in the previous example. This circuit is typically used as a
general-purpose amplifier.
Inverting Amplifier With Gain
We briefly return to the inverting amplifier with gain
(reproduced in Figure 2-48). Typical values of external components are tabled below the figure.
I
R1
A
Vin
GAIN
1
10
100
1000
R2
–
G = – R2
R1
+
R1
10 kΩ
1 kΩ
1 kΩ
100 Ω
Vout
R2
bw
10 kΩ
1 MHz
10 kΩ 100 kHz
100 kΩ 10 kHz
100 kΩ 1 kHz
RIN
10 kΩ
1 kΩ
1 kΩ
100 Ω
Figure 2-48. Inverting amplifier with gain. Shown below
the figure are typical specifications for a Motorola 741.
G= –
Here
R2
.
R1
Current to Voltage Converter
The current to voltage amplifier (Figure 2-49) is a
variation of the inverting amplifier. Summing the
currents flowing into node A we have
so that
2-28
Vout – 0
= 0,
R
I=–
Vout
,
R
+
Vout = – RI
Figure 2-49. Current to voltage converter.
Vout = –IR .
and
…[2-19]
The output voltage is proportional to the input current. This function might look a little unusual, but the
circuit, called a current to voltage converter, is often
employed as a first stage in matching a sensor to
conditioning electronics (see Figure 6-13). Sensors
often have to be placed some distance from the controlling electronics and the connecting cables can be
quite long. To sidestep the voltage drop that would
otherwise occur in a long connecting cable the sensor
is designed as a current source. This means that at the
controlling end the current must be converted to a
voltage.
Sum Amplifier
With the circuit shown in Figure 2-50, signals can be
effectively added together. We can show that the
output voltage Vout is proportional to the algebraic
sum of the input currents.
…[2-18]
The amplifier has gain but inverts (shown by the
minus sign). The input impedance is essentially R 1.
I+
A
I
R
–
R1
RF
S
–
R2
V1
V2
+
Vout
Figure 2-50. A sum amplifier. This circuit is shown with
two inputs, but in principle could have any number of
inputs.
Summing the currents flowing into node S we have:
Aspects of Technology
V1 V2 Vout
+
+
=0.
R1 R2 RF
sum and difference amplifiers can be identified in
many signal conditioner circuits for sensors, as we
shall see in Chapter 6..
In the event that RF = R 1 = R 2 we have the simple
result:
Vout = – (V1 + V2 ) .
… [2-20]
The output equals the sum of the inputs (with inversion).
Difference Amplifier
The circuit of Figure 2-51 gives an output proportional to the difference between the two inputs.
Assuming an ideal opamp we neglect the currents
entering the inverting and non-inverting inputs. Thus
we can add the currents flowing into nodes A and B,
V1 – V–
V
– V–
+ out
R1
RF
Real OpAmps
We hope that with the examples we have chosen you
can appreciate the usefulness of the ideal amplifier
approximation. Though “not quite true” and leading
to expressions of gain that are “not quite correct” the
approximations are nevertheless good enough to
provide the functionality we need most of the time.
However, there are times when we need to take
account of how real opamps differ from the ideal. The
following list of parameters points out characteristics
and limitations of the typical opamp you should be
aware of:
… [2-21]
Ao (open loop voltage gain)
Typically 100,000 or 100 dB
V2 – V+
0 – V+
+
= 0.
R2
R3
… [2-22]
Vout = A(V+ – V– ) .
… [2-23]
Z in (input impedance)
Typically 1 MΩ for BJTs, 1 MMΩ for FETs. The larger
this number is the better.
Also
= 0 ,
Z out (output impedance)
Typically a few hundred ohms
A
V1
R1
Vx
V2
V–
V+
R2
–
IB (input bias current)
Typically a fraction of a µA for BJTs and a few picoA
for FETs. The smaller this number is the better.
RF
A
+
R3
Vout = A Vx
= A(V+ – V– )
B
Figure 2-51. A difference amplifier.
If we take for simplicity R 1 = R 2 = R F = R 3 (different
values lead to a weighting of the inputs), V+ and V–
can be eliminated from eqs[2-21], [2-22] and [2-23] to
give
2
Vout  1+  = V2 – V1 .
A
For A >> 1,
Vout = V2 – V1 .
VCC (supply voltage range)
Typical limits are ± 3 volts to ± 15 volts
VI (max) (input voltage range)
Typically 2 volts less than VCC
VIO (input-offset voltage)
Typically a few mV
fT (Transition Frequency)
The transition frequency is the frequency at which the
open loop gain curve falls to unity (or the frequency
at which Log(gain) = 0). For the 741 fT = 1 MHz. f T can
also be used as a gain-bandwidth product, i.e., f T = G
x bandwidth. Opamps with much larger fTs than the
741 have been on the market for some years.
Thus the circuit can be used to subtract signals. The
2-29
Aspects of Technology
Gain
At this stage you should be able to test your knowledge of opamps. Here is an example.
1000
Example Problem 2-7
Properties of an OpAmp
10
1
3
5
6
log f
Gain
bandwidth
fT
1
1 x 106
106
10
1 x 105
106
1000
1 x 103
106
Figure 2-52. The gain-bandwidth product of an opamp is a
constant. The data below the figure are for a typical
Motorola 741.
The opamp shown in Figure 2-54 may be considered
to be ideal. What is the gain to be expected of this
circuit? If the opamp’s fT is 1 x 10 6 Hz, what is the
bandwidth to be expected?
+
Vin
–
100 kΩ
Vout
200 kΩ
Slew Rate
An opamp is expected to faithfully reproduce the
swing or skew in the signal applied to it. But if the
frequency and amplitude of the input signal are large
enough then the output signal may not be able to
accurately follow the slew in the input (Figure 2-53).
This “inertia” or “lag” is quantified by engineers with
a parameter called the slew rate , expressed in volts per
second. Typical values are in the range 1 V/µs to 10
V/µs. One effect of slew rate limiting is that the bandwidth of the amplifier is greater for small input
signals than it is for large input signals.
50 kHz output
waveform
Vout
y
x
1 KHz output
waveform
Figure 2-53. The slew rate is given by y/x, where x is in µs
and y is in volts. The higher the frequency the greater the
slew rate limiting becomes apparent.
2-30
Figure 2-54. An op amp amplifier.
Solution:
The gain of the amplifier is given by eq[2-17] where
R 1 and R 2 are 200 kΩ and 100 kΩ, respectively. Thus
G = (200 kΩ + 100 kΩ)/200kΩ = 1.5.
The gain-bandwidth product, f T, is given as 1 x 106
Hz. Therefore the bandwidth to be expected is:
bw = f T/G = 1 x 106 /1.5 = 6.67 x 105 Hz.
This bandwidth is quite large, meaning that the
circuit could be used through the audio range of
frequencies and well beyond.
Aspects of Technology
The Idea of a Gate
As will be seen in Chapter 3, each bit in a binary number is physically implemented in the solid
state by a gate, a device whose output can exist in one of two states, one representing a “0”, the
other a “1”. The simplest gate is an ordinary switch, like a light switch, which can be manually set
to an ON position or an OFF position. An equivalent, semiconductor gate is a PN diode or
transistor, or even an opamp, as we shall see here.
Switch Gate
A gate in the form of a manual switch (Figure 2-55) is
the simplest kind of gate to understand.
R
V
R
HIGH
V volts
logic HIGH output.
On the other hand, if the voltage applied between
base and emitter equals or exceeds the base-emitter
turn on voltage, as shown in the circuit on the right,
then the base and collector currents are large, and the
collector-emitter voltage is therefore LOW (most of
the voltage V is dropped across R). The transistor is
said to be in a saturated state. The collector output is
therefore also at a logic LOW. Thus a logic HIGH
input results in a logic LOW output.
LOW
~ 0 volts
V
Figure 2-55. Gates in the form of manual switches.
The switch is connected in series with a resistor R and
a source of voltage V (the actual values of R and V are
not important to our argument). The output voltage
representing the logic state is taken across the switch.
When the switch is OPEN no current flows through R
or the switch and therefore the top of the switch is at
V volts, or a logic HIGH. When the switch is
CLOSED, current flows down through R and the
switch, and the output is at 0 volts, or a logic LOW.
Transistor Gate
The advantage of a transistor switch over a manual
switch is that the transistor switch is controlled by a
voltage (more accurately the base current) and, in
principle, can be made very fast. This functionality
can be achieved with the circuits of Figure 2-56. The
output voltage representing the output logic state is
taken between the collector and ground. If the voltage
applied between the base and emitter of the transistor
on the left is zero, or at least small—less than the
base-emitter turn-on voltage—then the base current is
zero and the collector current is very small; the
transistor is effectively non-conducting or “cut off”.
The collector output is therefore at a logic HIGH.
Here, a logic LOW (or an undefined logic) results in a
R
Floating
or
grounded
V
R
HIGH
V volts
V ≥ VPN
nonconducting
conducting
“OFF” Logic 1
“ON” Logic 0
LOW
~ 0 volts
Figure 2-56. Gates in the form of transistors.
OpAmp Gate
An opamp used as an open loop comparator can also
work as a switch (Figure 2-57). If Vin is positive by
more than a few hundreds of microvolts then Vout
rises more-or-less to the voltage of the positive power
supply (a logic HIGH). If on the other hand Vin is
negative by more than a few hundreds of microvolts
then Vout falls to the voltage of the negative power
supply (a logic LOW). This circuit more closely
resembles a voltage-controlled switch than the transistor switch since it requires a negligible current.
2-31
Aspects of Technology
+
Vin
–
As we have stated above one gate like the ones shown
here is required to “implement” each bit in a binary
number. We shall have more to say on this subject in
Chapter 3.
Vout
Figure 2-57. An opamp comparator can be used as a gate.
Remember, the power supply lines are not shown here.
IC Switching
Often in the sciences one is interested in controlling a relatively high-current device like an oven
or a motor from a computer. Special IC switches have been developed for these tasks. The
switches are usually controlled with a small current. This topic is included here because you will
be using some form of solid state switch in your project in this course.
The SCR
The Triac
Figure 2-58.
Figure 2-59.
2-32
Aspects of Technology
Practice Problems
1.
2.
A carbon composition resistor has color bands:
yellow, violet, red, silver
Express the resistance in standard form.
The following circuit has two resistors. Based on
the circuit values is it expected that one of the
resistors should eventually burn out? If so, which
one and why?
4.
The resistance of a photoresistor of R0 = 2000 Ω.
What is the light intensity in foot-candles?
5.
Show circuit of centre-tapped
Calculate peak and rms values.
6.
A sinusoidal waveform is described by the
following expression
transformer.
V = 5.0sin (2π60t ) Volts.
100 kΩ
1/4 W
100 V
3.
10 kΩ
1/2 W
Compute the current flowing through each
resistor in the following circuit.
What is
(i) the peak value of voltsge?
(ii) the peak-to-peak value of voltage?
(iii) the rms value of voltage?
(iv) the frequency in Hz?
7.
Two or three examples of opamp circuits.
Calculate gain etc.
3Ω
5V
6Ω
5Ω
2-33
Aspects of Technology
EndNotes for Chapter 2
1
For details on the cells and batteries available on today’s market see the Enercell Battery Guidebook (Master Publishing,
1990, 1985) available at many Radio Shack stores.
2
Cells are able to rejuvenate themselves slightly if run intermittently. These figures are for continuous use and are taken
from the reference in endnote 1.
3
Some electronics texts contain descriptions of various monolithic technologies that are employed in the manufacture of
small-scale resistors, capacitors and inductors. One of them is: R. Boylestad and L. Nashelsky, Electronic Devices & Circuit
Theory (Prentics-Hall, 5th Ed., 1992). See also the text in endnote 6.
4
The original signal represented by this display was analog. However, the signal shown here is actually a digital one since
it was sampled by a digital oscilloscope. The spacing between samples is so very small, however, that the representation is an
analog one to a good approximation.
5
In these notes we use the word “bias” in the manner in which it is actually used in the jargon of electronics. to denote a
DC voltage. The phrases “voltage bias”, “reverse bias” and “bias” all refer to a DC voltage.
6
For details on the structure and actual fabrication of a transistor you should consult a text on transistor technology. A
good beginning is A. C. Melissinos, Principles of Modern Technology (Cambridge U. Press 1990).
7
An opamp is formally described as a high gain differential DC coupled amplifier especially designed to be used with
feedback. Its equivalent circuit may include more than 20 transistors. A number of stages make up its internal structure, the
most important of which are a differential amplifier input (consisting of bipolar junction transistors or field effect transistors),
an intermediate gain stage and a push pull output stage. The gain of the basic opamp without feedback, referred to as the
open loop gain, is typically 103 to 10 6 . Being DC coupled, the opamp is useable from DC to an upper bound frequency set by
its structural design.
8
For historical reasons the discussion of the opamp in this section concerns the bipolar “work horse” opam, the 741. In
most of the sensor designs produced by Vernier Software the opamp of choice is the unipolar Texas Instruments TLC721.
2-34