EP 212 CIRCUIT ANALYSIS
INTRODUCTORY REMARKS FOR THE STUDENT
This part gives us brief information and general rules of laboratory work. It also
includes basic information of safety precautions, laboratory practice and laboratory report.
A-) LABORATORY RULES:
a) There are nine set in the circuit analysis laboratory room. If the student number is
higher than 18 then everybody has to choose a partner to perform the experiments
together with. Each pair will be given a group number. Nobody can change his
partner unless permission given by the instructor.
b) There should be no laud talking in the laboratory.
c) No smoking in the laboratory. If you must smoke ask for permission from your
laboratory instructor to go out into the hall.
d) No visitors are permitted in laboratory.
e) Bring your laboratory book each session.
f) Exactly, read the laboratory sheet and know procedure.
g) If an instrument in your set gets out of work, please inform the assistant or instructor.
h) No transfer of any equipment between the tables by the students.
i) During the experiments, some important precaution steps will be explained to you by
your assistant or instructor. If any point is not understood before you starting the
experiment please ask your assistant and instructor clearly.
j) Don’t supply the high voltage to the circuit from power supply.
k) Before leaving the laboratory please arrange everything in your set to the initial position.
B-) SAFETY PRECAUTIONS
a) Performing of an experiment requires a careful reading of laboratory manual, a clear
understanding of each step involved in the required procedure before its actual
performance and often a written, planned program (notes on references, rough outline
of proposed procedure, circuit to be investigated, if there are preliminary
calculations). Science organization is a guiding principle to be followed throughout
the preparation, performance and reporting of an experiment.
1
b) Always disconnect the power supply before connecting or charging to the your
circuit.
c) Be sure that the measuring instruments such as voltmeter, ammeter, etc. are
connected in correct places with sufficient ranges on the circuit. i.e., please pay
attention that the ammeter is not used in the voltmeter position and vice versa.
d) If the power supply is active on the circuit, an ohmmeter is never connected to this
circuit.
e) After the planning good experimental organization entails the neat assembly of the
circuits so that they may be easily visualized and checked, and the neat entering of
data with descriptive headings and complete information regarding meters and
apparatus used.
f) Make a rough plot of the data in the laboratory as soon as they have been taken,
whenever possible. If there are points out of line, they can be rechecked while the
apparatus is still set up.
g) The laboratory data sheet (notebook) is the record of what you did in the laboratory,
together with the result, calculations, and conclusion that may be drawn from your
experiments. The recording of data on separate pages of paper and copying it into
another notebook is possible.
h) If you must correct an entry in your notebook, draw a line through the incorrect entry,
and write a brief explanation of the correction.
i) The lab report must be turned in due the next lab period (usually the following week).
Late lab reports will not be accepted.
j) Before you leave the laboratory, you must have your instructor or assistant sign his
initials in your notebook. This says he is satisfied that you have cleaned up properly
and that the data is satisfactorily record in your notebook. No lab report will be
accepted without this signature.
k) Students are expected to do their own lab work and write their own lab reports.
l) Ratings of the components must be properly selected.
C-) LABORATORY REPORT:
a) All laboratory reports should be written to an A4 paper.
b) Each report should give sufficient information about the experiment.
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c) All pages should be numbered. The first page should contain course number and
name, all partners name, group number, course and laboratory instructors names,
laboratory report offering date, experiment no and also name of the experiment (see
Appendix G).
d) All reports must be written in pencil, ball-point pen, typewriter but only in the
headings colored pencil or ball-points are allowed.
e) Below is a brief outline of how your report should be kept:
At the top of second page:
a) Title of the experiment,
b) A short statement of the object of the experiment (simply its purpose),
c) The necessary theoretical calculations before coming to laboratory,
d) For step "b" and "c", you should read the experiment at home and complete
these steps before coming to lab,
e) Procedure, observation, and data. If the data is to be recorded in a chart, you
may use the data sheet that is giving at the end of this book (see Appendix H).
f) Calculations. Sometimes these must be done during the lab period; at other
times you will be permitted to complete them at home. It is suggested that
you do the rough calculations on a piece of scratch paper before making any
entries in your notebook.
g) Discussion (or results). Conclusion that may be drawn from the experiment,
possible sources of error (when applicable), and answers to the questions
asked in the discussion part.
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4
EP 212
DC CIRCUIT ANALYSIS
EXPERIMENT-1
COMMON LABORATORY INSTRUMENTS
1-) PURPOSE:
To study the uses of common electronic laboratory instruments, Digital Multimeter,
Avometer, Power Supply, Resistance Decade Box, Rheostat, Potentiometer, Circuit Board
and Digital Capacitance Meter.
2-) THEORY:
Although laboratory test equipments vary with each laboratory situation, there are
some basic equipments common to them all. Included in these equipments and common to
every laboratory are the voltmeter, ammeter, ohmmeter, and power supply (ac or dc). These
meters are used to measure voltage, current, and resistance and apply dc or ac voltages and
currents, respectively. Since it is often necessary to measure many different values of voltage,
current, and resistance, there is a need for several types of each meter covering many ranges
and accuracy of measurements. Two common types of multi-range and multifunction
instruments are the Digital Multimeter (DMM) and Avometer (AVO). The electronic DMM
and AVO can be used to measure voltage, current, and resistance over several ranges. The
accuracy of these equipments are generally ±3.0% or less depending on its cost. The details of
meter construction and how to make meter measurements are explained in many electronic
instrument books that are also available in library of Gaziantep University. Additionally, a
technical elective course (EP 485 Electronic Instruments and Measurement Techniques) has
been taught in this department to explain the related subjects about the electronic instruments.
Another important electronic instrument is the digital capacitance meter (DCM) that
is frequently used in circuit and analog-electronic experiments. Therefore a CM200 type
digital capacitance meter is present in the electronic laboratory of this department, Operation
principles and instructions of this instrument haven’t been given in this experiment (Ex.-1),
because the detailed explanations about this instrument have been given in Ex.-11.
2.1-) DIGITAL MULTIMETER (DMM)
This type of meter generally requires 220 Volt, 50 Hz and must be plugged into a line
source. It is a very popular tester because the digital readout is displayed automatically with
5
decimal point, polarity, and the unit, V, A, or
. Digital meters are generally easier to use
because they eliminate the human error that often occurs in reading different scales on an
analog meter. The Front Panel picture of an Escort EDM-2347 type digital Multimeter that is
used for circuit experiments in this department is shown in Figure 1.1. Another type of DMM
is also available in this laboratory. You can ask your laboratory assistants to receive it when
you need it. The necessary information about this instrument has been given in Appendix D.
Figure 1.1 : Front Panel picture of a Escort EDM-2347 type DMM.
The electrical specifications of Escort EDM-2347 type digital multimeter are:
a) (±) Direct Current (DC) Voltage range from 200 mV to 1000 Volt
b) Alternating Current (AC) Voltage range from 200 mV to 1000 Volt
c) DC current range from 200 A to 20 Ampere
d) AC current range from 200 A to 20 Ampere
e) Resistance range from 200 Ohms to 20 megaohms
f) Frequency range from 20 kHz to 200 kHz
Important Note: To measure voltage, the voltmeter test leads are connected across the two
points of potential difference. To measure current, the meter is connected as a series
component in the circuit. Similarly, when measuring resistance, the two leads are connected
across the resistance to be measured, but the power supply must be turned off. No power is
needed in the circuit being tested because the ohmmeter has its own internal battery.
6
2.1.1-) Precaution and Preparations for Measurements
a) Be sure the battery is correctly placed in the battery case and connected to the battery
snap (for adapter, output plug connected correct position).
b) Before making measurement check if function and range switches are set in correct
position.
c) Check the input terminal position for red test lead depending on measurement range.
d) Either one of the test lead should be taken off the circuit under test, when change the
measurement range.
e) Operate the instrument only in temperature 00C to 500C and less then 80% RH.
f) Pay carefully attention to the maximum rated voltage of each range and terminal.
g) When finished measurement; switch OFF the power. Be sure to remove the battery
when it is used for a long time to avoid a leakage problem.
h) Do not use or storage this instruments in a place of direct sunlight, high temperature,
and high humidity.
2.1.2-) Methods of Measurement
2.1.2.1-) DC-Voltage (DCV), AC-Voltage (ACV), AC-Voltage/dB Measurement
a) Connect black test lead into "COM" terminal.
b) Connect red test lead into "V- -
" terminal.
c) If measuring DCV, engage function push button "DC" and "V" on function scale.
d) If measuring ACV, engage function push button "AC" and "V" on function scale.
e) If measuring ACV/dB, engage function push button "AC" and "V" on function scale.
f) If measuring ACV/dB, engage function push button "AC" and "V" and "dB" on
function scale.
g) Determine the highest anticipated voltage in the range scale and press the
corresponding range push button.
h) Press power switch to "ON" position.
i) Connect test leads to measuring points and read the display value.
2.1.2.2-) DC-Current (DCA), AC-Current (ACA) Measurement
a) Connect black test lead into "COM" terminal.
b) Connect red test lead into "A" terminal for measurement up to 2 A, for measuring
current between 2 A and 20 A, connect test lead into "20 A" terminal.
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c) If measuring DCA, engage function push button "DC" and "A" on function scale.
d) If measuring ACA, engage function push button "AC" and "A" on function scale.
e) Determine the highest anticipated current on the range scale and press the
corresponding range push button.
f) Press power switch to "ON" position.
g) Connect test leads to measuring points and read the display value.
2.1.2.3-) Resistance Measurement
a) Connect black test lead to "COM" terminal.
b) Connect red test lead to "V- -
" terminal.
c) Engage function push button " " on function scale.
d) Determine the highest anticipated resistance on the range scale and press the
corresponding range push button.
e) Press power switch to "ON" position.
f) Connect test leads to measuring points and read the display value.
2.1.2.4-) Continuity Check by Buzzer
a) Connect black test lead to "COM" terminal.
b) Connect red test lead to "V- -
" terminal.
c) Engage function push button " " on function scale.
d) Simultaneously, engage range push button " " on range scale.
e) Press range switch at 2 k
or 200 k
or 20 M .
f) Press power switch to "ON" position.
g) Connect test leads to the circuit under test.
h) Built-in buzzer sounds, if the resistance of the circuit under test is less than 10 % of
the test range.
2.1.2.5-) Diode Check
a) Connect black test lead into "COM" terminal.
b) Connect red test lead into "V- -
" terminal.
c) Engage function push button " " on function scale.
d) Simultaneously, engage range push button " " on range scale.
e) Press power switch to "ON" position.
f) Connect test lead probes as follows.
8
g) When connected with polarity as shown in Figure 1.2.a, a forward current flow is
established and a good diode will produce a voltage reading on the display. For
example, a good silicon type diode should indicate a value between 0.500 V to 0.900
V on the display, if a value of 0.650 V was displayed for instance, the approximate
forward voltage would be 650 mV. If the diode under test is defective, "000" (short
circuit) or "1" (open circuit) will be displayed.
Red (+)
Black (-)
Black (-)
Red (+)
Figure 1.2.b
Figure 1.2.a
h) When connected as shown in Figure 1.2.b, a reverse check on the diode is made. If
the diode under test is good "1" will be displayed. If the diode under test is defective,
"000" (or other values) will be displayed; proper diode testing should include both
steps g and h as above.
i) The three diode test ranges are marked with a diode symbol and have enough open
circuit voltage to turn on silicon junction allowing the diode test. The 2 k
preferred for step g. Reading in 200 k
or 20 M
range is
range just indication whether diode
has turned on.
2.1.2.6-) Frequency Measurement
a) Select the range switch at the "Hz" function.
b) Connect black test lead to "COM" terminal and red to "V- -
" terminal.
c) Connect test leads to measuring points and read the display value.
d) Determine the highest anticipated Hz in the range scale and press the corresponding
range push button.
2.2-) AVOMETER (AVO)
This type of meter is portable and does not require any connection to the mains.
Because it is simple, compact, and portable, the AVO is probably more common. The cost of
a basic type of AVO is less than for a DMM. Also, where a change in V or I must be checked,
9
the AVO is more convenient. The Front Panel picture of a FT-303TR type Avometer that is
used in our laboratory is shown in Figure 1.3. The electrical properties of this type meter are:
Table 1.1: Electronic specifications of FT-303TR type AVO
DC VOLTAGE
AC VOLTAGE
DC CURRENT
RESISTANCE
Ranges:
0.3-3-12-30-120-3001200 Volt
1.5 Volt (for battery
check)
Accuracy at FSD:
±3 %
Sensitivity: 8 k /V
Ranges:
6-30-120-3001200 Volt
1.5 Volt (for battery
check)
Accuracy at FSD:
±4 %
Sensitivity: 8 k /V.
Ranges:
0.06-3-30 mA0.3 Amper
12 A on separate
input
Accuracy at FSD:
±3 %
Voltage Drop:
300 mV.
Ranges :
x 1-0.2 to 2 k ,
Midscale 20
x 10-2 to 20 k ,
Midscale 200
x 1 k-200 to 2 M ,
Midscale 20 k
x 10 k-2 k to 20 M ,
Midscale 200 k
Figure 1.3: The Front Panel picture of a FT-303TR type AVO.
2.2.1-) Operation of AVO
2.2.1.1-) Ohm Test
a) Plug the test leads into -COM and + terminals.
b) Place the range selector to the
range appropriate for the circuit to be tested.
c) Short the test leads and adjust the 0 ADJ until the pointer is placed to the zero
position of the
scale.
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d) Make sure that there is no voltage across the circuit to be tested.
e) Connect the test leads to the tested resistor and read the
scale.
2.2.1.2-) DCV Test
a) Plug the red test lead into the + terminal and the black lead into the -COM terminal.
b) Set the range selector to the DCV range appropriate for the circuit to be tested.
c) Connect the meter in parallel with the circuit being tested with the black test lead
on the negative side and the red lead on the positive side.
d) Read the tested value.
2.2.1.3-) ACV Test
a) Plug the red lead into the + terminal and the back lead into the -COM terminal.
b) Set the range selector to the ACV range appropriate for the circuit to be tested.
c) Connect the meter in parallel with the circuit being tested regardless its polarities.
d) Read the appropriate ACV scale.
2.2.1.4-) DCA Test
a) Plug the red test lead into the + terminal and the black lead into the -COM terminal.
(for DC 12 A test, red lead plugged into DC 12 +).
b) Set the range selector to the DCA range appropriate for the circuit to be tested.
c) Connect the tester in series with the circuit to be tested with the red test lead on the
positive side and the black lead on the negative side.
d) Read the tested value.
2.3-) POWER SUPPLY
Any instrument that produces voltage output continuously from its output terminals is
a voltage generator or simply power supply. The Front Panel representation of a PS2335B
type power supply that is present in this laboratory is shown in Figure 1.4.
2.3-1-) Front Panel :
A- Power switch.
B- Voltage potentiometer. This key adjusts the voltage value between 0-30 V by rotating it
clockwise (CW) or counter clockwise (CCW) direction.
C- If this LED is ON, the Power Supply is operating as a voltage source.
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D- Current potentiometer. This key adjusts the current value between 0-2 A by rotating it
clockwise (CW) or counter clockwise (CCW) direction.
E- If this LED is ON, the power supply is operating as a current source.
F- Digital screen to show adjusted voltage value.
G- Digital screen to show adjusted current value.
H- Positive (+) terminal of power supply
Ġ- Negative (-) terminal of power supply.
J- Ground terminal. This terminal is directly connected to the ground of power supply.
K- Two position key that adjusts the power supply in its dependent or un-dependent form.
L- Positive (+) terminal of constant 5V/3A source
M- Negative (-) terminal of constant 5V/3A source.
F1
G1
F2
K
G2
NEL
AMPER
VOLT
AMPER
VOLT
SĠMETRĠK
E1
E2
C1
BAĞIMSIZ
GÜÇ
BAĞIL KAYNAK
ANA KAYNAK
+
AÇIK
-
+
5V/3A
+
AKIM GERĠLĠM
GERĠLĠM AKIM
-
KAPALI
L
M
PS2000 DC GÜÇ KAYNAĞI
A
C2
B1
D1
H1
J1 I1
H2
J2
I1
D2
B2
Figure 1.4: The Front Panel representation of a PS2335B type power supply.
Before connection the power supply and circuit:
1) Take “K” key to “BAĞIMSIZ” position.
2) Adjust the voltage value up to your desired value between 0-30 V using voltage
potentiometer.
3) During the previous step, you can also restrict the current value by rotating the current
potentiometer.
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4) Connect the terminals of power supply to the circuit.
Important Note: Do not directly connect Positive (+) and Negative (-) terminals of power
supply (as a short circuit).
2.4-) DECADE RESISTANCE BOX (DB)
As shown in Fig.1.5, the decade box (Heathkit Model IN 17) is a variable typeresistor comprising many units of resistors for providing any one R within a wide range of
values. It can be considered as test equipment for trying different R-values in a circuit by
adjusting range dials of the box for which those units of resistors are connected in series.
Inside the box are six series strings of resistors, with one string for each dial switch.
1-) The first dial at the bottom right side connects in R of 1 to 9
2-) The second dial has units of 10 from 10 to 90
3-) The hundred dial has R of 100 to 900
. It is the units dial.
. It is the tens dial.
.
4-) The thousands dial has R of 1.000 to 9.000
5-) The ten-thousands dial has 10.000 to 90.000
.
.
6-) The last dial at the top left side has R of 100.000 to 900.000
Figure 1.5: Decade Resistance Box.
13
.
The six dial sections are connected in series with one another internally. Then any
value from 1 to 999.999
can be obtained. Note that the exact values are possible. As an
example, when all five dials are on 7, the total resistance R is equal to 777.777
.
2.6-) RHEOSTAT AND POTENTIOMETER:
These are variable resistances. A rheostat is a variable R with two terminals
connected in series with a load. The change in terminal resistance is obtained by sliding
contacts. They have high power dissipation capacity (a wattage rating high enough for the
maximum I when R is minimum). Thus they are useful in electricity and circuit laboratory.
They are often wire-wound variable resistors used to control relatively large values of current
in low-resistance circuits for AC power applications.
A potentiometer, generally called as a pot for short, has three terminals. The fixed
maximum R across the two ends is connected across a voltage source. Simply, sliding arm or
rotating moving contact is used to vary resistance between the center terminal and the ends.
The value of terminal resistance may be made to change linearly or in a logarithmic manner.
The other type of variable resistors can be wire-wound or the carbon type. In second
case, the control has performed by a circular disc, that is the carbon-composition resistance
element. It can be a thin coating on pressed paper or a molded carbon disc. Joined to the two
ends are the external soldering-lug terminals 1 and 3. The middle terminal is connected to the
variable arm that contacts the resistor element by a metal spring wiper. As the shaft of the
control is turned, the variable arm moves the wiper to make contact at different points on the
resistor element.
2.7-) CIRCUIT BOARD
The series circuit board is one of the most important electronic experimental tools
which practically allows to develop test circuit on it with definite accuracy. A schematic view
of one of the board is shown in Fig.1.6. Note that there are many differences between the
constructed boards by different firms.
1-) The diameter of interconnection wires must be between 0.3 and 0.8 mm.
2-) Connect positive (+) and negative (-) ends of the power supply (i.e. voltage source) to
terminals (A) and (B), respectively.
3-) There are at least 45 (or more) connection points (nodes) on each board. Each node has
five series interconnected holes with each other.
4-) Starting from the positive end of power supply set up the test circuit on the board. To do
this;
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a-) Insert one end of the circuit element (i.e. resistor) to one of the interconnected
holes in the node 1.
b-) Insert the other end of the circuit element to another node (i.e. node 10).
c-) The connected ends of the circuit elements on the circuit must be inserted on the
same node using the other holes.
d-) Following the above steps complete the circuit on the board.
C
E
D
5
10
15
20
25
30
35
40
45
5
10
15
20
25
30
35
40
45
A
B
Figure 1.6: A schematic view of a series type circuit board.
3-) EXPERIMENTAL PROCEDURE:
1. Adjust the six different voltages from your power supply and read these values by using
DMM and AVO.
Table 1.2
Applied Voltage
from
Power Supply
Measured value of voltage by
DMM
and
AVO
Percentage Difference between
Applied Voltage and
DMM
AVO
2. Set up the Figure 1.7 for current measurements. Adjust the power supply to 5 Volt.
Firstly connect to the circuit DMM ammeter and then AVO and change the value of
resistance from decade box. Read the value of current for each adjustment value of
decade box and repeat this step at least five times.
15
Ammeter
A
Q (DMM)
100
+ Power
- Supply
Decade
Box
Figure 1.7: Experimental circuit for current measurement.
Table 1.3
Adjusted value
of resistance
from Decade
Box
Measured Value
of Current by
DMM and AVO
Percentage
Difference between
by
DMM and AVO
4-) DISCUSSION
4.1-) What does it really mean when it is said that a meters has 5 % accuracy?
4.2-) Explain the difference between accuracy and sensitivity of an instrument?
4.3-) Why is the AVO meter provided with a mirror in the middle part of the scale?
4.4-) Is it possible to use the same scale on the 2, 10, 30, and 350 Volt range of AVO meter?
Explain.
4.5-) The ohm scale on your AVO meter is shown in logarithmic scale. Why? Explain it.
4.6-) What are the factors adversely affect the accuracy of a meter?
4.7-) Which readings obtained from AVO or DMM are more reliable?
4.8-) How does a potentiometer differ from a rheostat?
4.9-) Show, how can a potentiometer be used as a rheostat?
4.10-)How is a voltmeter and ammeter connected in a circuit?
4.11-)Should a voltmeter and an ammeter have very low or very high internal resistance.
Explain it.
4.12-)How is a DC Meter connected to a circuit in the correct polarity?
4.13-)How much current is required to give full-scale deflection of the needle of AVO meter
on a 30 mA scale?
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4.14-)Why must be careful to keep from short circuiting the output terminals of a power
supply?
4.15-)Why is it necessary to disconnect power supply from the circuit before measuring
resistance or in other words why must resistance never be measured in a current
carrying circuit?
4.16-) The standard test leads provided are not suitable for currents in excess of 6 amps.
Why?
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18
EP 212
DC CIRCUIT ANALYSIS
EXPERIMENT-2
COMPONENT IDENTIFICATION OF RESISTORS
1-) PURPOSE:
To study resistors and identification of them using Electronics Industries Association
(EIA) color code.
2-) THEORY :
2.1-) Component Identification:
The actual physical properties of resistors are out of scope of this experiment due to
unimportance of them in the network designs but the resistance value of resistors are always
important in network designs. The resistor’s resistance value can determined by simply twodifferent methods, 1-) directly measuring its resistance value by laboratory test equipments
(i.e. DMM or AVO) or 2-) its component identification. The components must be identified
as to their actual rated sizes. Some components are identified by printing their rated values on
the components themselves. Such as, carbon resistor uses color codes on it. Because, this type
of resistors are physically so small. Therefore, this experiment will deal only with carbon
resistors.
The color-coding has been standardized by EIA and is used throughout the industry to
identify many varieties of components. The use of bands or stripes is the most common
system for color-coding carbon resistors. Color bands are printed at one end of the resistors.
Each color listed is assigned with a number value as indicated below. These values are
standard and accepted throughout the industry.
Table 2.1
Color
Black
Brown
Red
Orange
Yellow
Green
Assigned
0
1
2
3
4
5
Multiplier
1
10
100
1.000
10.000
100.000
Color
Blue
Violet
Gray
White
Gold
Silver
No Band
19
Assigned
6
7
8
9
5% Tolerance
10% Tolerance
20% Tolerance
Multiplier
1.000.000
10.000.000
100.000.000
1.000.000.000
0.1
0.01
0.001
2.2-) Resistor Identification
a) Take a carbon resistor and note that it has at least four banded colors closely grouped
at one end of the resistor (see Fig.2.1). Hold the resistor so these bands are grouped to
your left. The resistance value can be read in this position. Read step (b) to help you
to determine resistor's resistance value.
b) Starting from left side, read the red band as two and write 2. This represents the first
significant color. The second orange band represents the second significant color of 3.
Now write 23. The third band represents the multiplier and from the above table this
indicates a multiplier of 10. Multiply 23 by 10 and the resistance value of the resistor
is R=230 Ohms.
1 st
significant
color
2nd sig.
color
3rd sig.
color
5% Tolerance = 230
Gold
101
Brown
3
Orange
Red
R=2
Tolerance
Figure 2.1: Resistor identification with its color codes.
c) Rather than multiplying by the third band, another method is simply to attach the
number of zeros represented by the third band. For example, the first two significant
colors were twenty-three and the third band represents the number 1. Simply affix one
zero to 23 and read 230
.
d) It should be noted that some resistors have five bands, instead of four. In this case, the
first three bands give three digits, followed by the decimal multiplier in the fourth
band and tolerance in the fifth band. These resistors have more precise values, with
tolerances of 0.1 to percent.
2-3-) Tolerance
The amount by which the actual R can be different from the color-coded value is the
tolerance, usually given in percent. The tolerance of the resistor is obtained from the fourth
band. This band may be either gold or silver. Gold represents a 5% tolerance and silver 10%.
20
For example, a 100 Ohm resistor with a gold fourth band has a plus or minus tolerance of
5%. If there is no color band for tolerance, it is 20 percent.
Example: Convert (±) 5% to a decimal
5 %/100 = (±) 0.05
Multiply (±) 0.05 x 100 Ohms = 5 Ohms
(+) Add 5 Ohms to 100 Ohms = 105 Ohms
(-) Subtract 5 Ohms from 100 Ohms = 95 Ohms
The 5% 100 Ohm resistor could have any resistance value between 95 and 105 Ohms
and still be classified as a 100 Ohm resistor.
The inexact value of carbon resistors is disadvantage of their economical
construction. They usually cost only about 10 to 50 cents each, or less in larger quantities. In
most circuits, though, a small difference in resistance can be tolerated.
2.4-) Resistors under 10
Resistors below 10
may be of the deposited film type or wire wound. Some of
these are usually printed with their resistance value on them. When resistors are below 10
the carbon type can be identified in the following manner:
This type of resistor has also four color bands but the third and fourth band are either
gold or silver (see Fig.2.2). The fourth band is the tolerance and the third band the multiplier.
Red
Orange
Gold
Gold
Example:
R=2
3
0.1
5% Tolerance = 2.3
Figure 2.2 : Resistor identification with its color codes below 10
.
2.5-) Wire-Wound-Resistors and Their Marking
In this construction, a special type of wire called resistance wire is wrapped around an
insulating core. The length of wire used and its specific resistivity determines the R of the
unit. Types of resistance wire include tungsten and manganin. Usually, wire-wound resistors
are big enough physically to have the R value printed on the insulating case. The tolerance is
generally 5 percent, except for precision resistors, which have a tolerance of 1 percent or
21
less. Some small wire-wound resistors may be color-coded with bands, however, like carbon
resistors. In this case, the first band is double the width of the others to indicate a wire-wound
resistor. This type of resistors is generally for high-current applications with low resistance
and appreciable power and they may have wattage ratings from 3 W up to 100 W or more.
2.5-) Wattage Rating
The two main characteristics of a resistor are its resistance R in ohms and its power
rating in watts, W. Resistors are available in a very wide range of R values, from a fraction
of an ohm to many megaohms. The power rating may be as high as several hundred watts
or as low as 1/10W. The R is the resistance value required to provide the desired I or IR
voltage drop. Also important is the wattage rating because it specifies the maximum power
the resistor can dissipate without excessive heat. Dissipation means that the power is
wasted as I2R loss, since the resultant heat is not used. Too much heat can make the resistor
burn. The wattage rating of the resistor is generally more than the actual power dissipation,
as a safety factor.
Most common in electronic equipments are carbon resistors that have wattage
ratings from 1/10 watt to 2 watts. These ratings are not identified on the components and
must be made by visual inspection of physical volume. During the current flowing, carbon
resistors are often quite warm, up to a maximum temperature of about 85 0C, which is
close to the 100 0C boiling point of water. Carbon resistors should not be so hot. If a
resistor becomes too hot because of excessive power dissipation, it can change appreciably
in resistance value or burn open.
The power rating is a physical property that depends on the resistor construction,
especially physical size. A larger physical size indicates a higher power rating and higher
wattage resistors can operate at higher temperatures. The 1/10 watt carbon resistor is the
smallest size and the 2 watt the largest. The 1/10 watt carbon resistor is about 174 inch
long and about 3/4 inch width and 5/16 inch in diameter. Since it is difficult to identify
wattage sizes, several wattage sizes should be observed during this experiment.
3-) EXPERIMENTAL PROCEDURE:
3.1-) Find the values of each resistor using its color-codes. List their values in ascending
order giving their tolerance in a table of the form.
22
Table 2.1
No
Colors
Value
by CC
Measured
Value by
DMM AVO
PD between CC and
DMM
1
2
3
4
5
3.2-) Measure the values of resistors using also AVO and DMM. Thus, again carefully read
necessary sections in experiment 1.
4-) DISCUSSION and CONCLUSION
4.1-) Identify the following resistors to the color-code.
1-) 1800 5%
4-) 27 10%
7-) 82
10%
2-) 1.5 M 5%
5-) 7.5 5%
8-) 100 k 20%
3-) 62 k 10%
6-) 220 k 20% 9-) 22 M 10%
4.2-) Identify the following resistors to the numerical values.
10-) 2.2 M 5%
11-) 250 10%
12-) 875 20%
1-) red-red-yellow-silver
6-) blue-red-black-gold
2-) gray-white-gold-silver
7-) green-blue-green-silver
3-) red-violet-blue
8-) green-black-gold-silver
4-) blue-gray-yellow-gold
9-) green-blue-orange-gold
5-) red-red-red-silver
10-) red-red-green
4.3-) What is the approximate physical size of a 1 Watt resistor?
4.4-) Is a 1000
1/2 Watt carbon resistor physically larger than a 10
1 Watt carbon
resistor? Explain.
4.5-) What possible sources of errors can cause the deviation in the resistance of resistors
given in Table 2.1?
4.6-) Compare the obtained and measured resistance values. If they are not same, explain
why. Which reading is more reliable?
4.6-) What can be the maximum and minimum resistance of a resistor which obtained from
color coded tolerance?
4.7-) Are the resistance obtained from the color-codes reliable for practice applications?
23
4.8-) Do the measured values of the resistors within the tolerance range that is indicated in
color code? If not, why not?
4.8-) Given the four resistors
(1) 100
, 0.25 W rating
(3) 500
(2) 1000
, 0.1 W rating
(4) 25
, 0.1 W rating
, 2 W rating
a-) which resistor has the maximum safe voltage and current
b-) which resistor has the least safe voltage and current
4.9-) Are the carbon type resistors operate above 100 0C? Why? Answer the same question
for wire-wound resistors.
4.10-)Draw the diagram for connecting two 1000
power rating of 2 W.
4.11-)Give your comments on the experiment.
24
1 W resistors to obtain 2000
with a
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-3
SIMPLE RESISTIVE NETWORKS
1-) PURPOSE:
To measure DC load-line (I-V) characteristic of various linear and non-linear
elements.
2-) THEORY
2.1-) Types of Resistor:
The simple resistive elements can be classified in two groups:
1) Linear Elements: Simple resistor, rheostat, etc...
2) Non-linear Elements: Light Bulb, Diode, Photo resistor, etc...
Also these two group elements may be either time-variant or time-invariant resistors.
Moreover, the resistance of linear elements (time-invariant resistors) can change with
temperature evolved internally owing to the current passing through them.
2.2-) Linear Resistive Elements:
Simply the linear resistive elements can be classified as:
a) Fixed Resistors (carbon-composition resistors, wire-wound resistors, film-type
resistors, cermet resistors). All these type of resistors considered here are linear,
means that they follow the Ohm’s relation. The resistance (R) values of these types of
resistors are not changed by applying voltage.
R
V
I
constant
(3.1)
b) Variable Resistors (i.e., decade box, potentiometer, rheostat, thermistor, varistor). See
Experiments-1 and -2 to obtain more information about linear resistive elements.
2.3-) Non-linear Resistive Elements:
The non-linear resistive elements may be classified in accordance to the effect of
temperature, light intensity, pressure, etc. The relation between terminal voltage and current
is non-linear. Simply the non-linear resistive elements are: Light Bulb, Junction Diode.
2.3.1-) Light Bulb: The I-V characteristic of a light bulb is shown in Figure 3.1.
25
I
V
Figure 3.1: The I-V characteristic of a light bulb.
Note that the I-V characteristic of a light bulb is not linear but it is symmetric with
respect to the origin. If the current is flowing in both direction on a resistor elements or its I-V
characteristic is symmetric with respect to the origin, this type of resistive elements are called
as bilateral components.
2.3.2-) Junction Diode: The I-V characteristic of a junction diode is shown in Figure 3.2.
I
V
I0
Figure 3.2: I-V characteristic of a junction diode.
As shown from Figure 3.2 that the I-V characteristic is not symmetric with respect to
the origin thus current is not symmetric with respect to origin thus current is not flowing in
both direction or a junction diode. Thus these types of resistive elements are called as not a
bilateral component.
2.4-) Load-Line Analysis of a Fixed Resistor :
The load-line analysis is a graphical method. The load line or I-V characteristic of a
fixed resistor is shown in Figure 3.3.
I
I
E
+ R
+
V
-1
1
tan
Slope
I
V
1
R
V
Figure 3.3: The circuit and I-V characteristic of a fixed resistor.
26
Now, consider the series combination of two different but linear fixed resistors R1 and R2
(R1<R2) as shown in Figure 3.4.a.
V1
+ I R1
Slope
+
V2
-
0
+ R2
E
1
R1
Slope
I
1
1
R2
2
V
(b)
(a)
Figure 3.4: (a) Circuit connection and (b) I-V characteristic of each fixed resistor (R1 and R2).
The current is the same both on the R1 and R2. The I-V characteristic of each resistor
is the same as fixed resistor (Figure 3.3). The I-V characteristic is shown in Figure 3.4.b. The
voltage axis (x-axis) provides identical scales for the variables V1 and V2. The slope of the
characteristic curve for the R2 is greater than R1. Thus in an I-V characteristic, the slope of a
characteristic depends on the value of R. Therefore, in series combination the total resistance
is greater than always R1 and R2. Then, to obtain I-V characteristic a series combination is
shown in Figure 3.5.
I
Slope
1
R1
Slope
I1
I2
1
R2
Slope
I0
V1
V2
V
1
R1
R2
V
3
Figure 3.5: Series Combination.
A similar procedure can be obtained graphically the I-V characteristics of R1 in
parallel with R2 (R1<R2). In this case, the total resistance is smaller than both R1 and R2, thus
the slope of parallel combination is greater than the other slopes as shown in Figure 3.6.
27
1
R1
Slope
I
I0
I0
E
R1
I1
+
-
+ R2
I2
+
V
-
1
R2
Slope
I2
I1
1
R2
1
R1
Slope
0
(a)
V0
Figure 3.6: Parallel Combination
V2
(b)
V1
V
3-) EXPERIMENTAL PROCEDURE:
Note: You can choose the value of the resistors between 50
3.1)
and 2 k for this experiment.
Obtain and draw the I-V characteristics of Figure 3.7 by changing the value of DC
Power Supply (E) to 0, 2, 4, 7 and 10 Volts, then read I and V in both cases.
A
I
V
+ R1
E
Figure 3.7
3.2)
Repeat 3.1. for Figure 3.8 and note the change in the I-V characteristics of Figure 3.8
from Figure 3.7.
A
I
R1
E
V
+
R2
Figure 3.8
3.3)
Repeat 3.1. for Figure 3.9 and again note the change in the I-V characteristics of
Figure 3.9 from Figure 3.8 and Figure 3.7.
A
E
I
R1
+ R2
Figure 3.9.
28
V
3.4)
Repeat 3.1. for Figure 3.10.
A
I
E
+
V
Figure 3.10.
3.5)
Repeat 3.1. for Figure 3.11.
R1
E
+ R3
R2
Figure 3.11.
3.6)
Measure the exact value of all used resistors using DMM.
4-) DISCUSSION and CONCLUSION:
4.1-) Find the values of all used resistors using I-V characteristics that you obtained in
previous section.
4.2-) The I-V characteristics of three resistors, R1, R2, and R3, are shown in Fig.3.12.
Superimpose on the same graph the I-V characteristics of the total resistance of R1, R2,
and R3
a-) in series and
b-) in parallel.
I
R1
R2
R3
V
Figure 3.12
4.3-) a-) Find the current through all branches in Fig.3.13 by means of circuit analysis
technique.
b-) Repeat step (a) by means of graphical analysis technique and explain how can you
apply this technique.
29
R1=500
E=20 V
R3=250
R2=1 k
Figure 3.13
4.4-) Explain the operational principle of a junction diode.
4.5-) Explain the mean of bilateral and non-bilateral components.
4.6-) Plot the graph showing the relationship between I and R for a constant voltage V. What
is the curve called?
4.7-) What can you say about the current through series and parallel circuit and voltage across
resistor in parallel and series circuit?
4.8-) From the following graph, Fig.3.14, determine the unknown values of R1 and R2.
I (mA)
Slope=1/R1+1/R2
350
250
200
Slope=1/(R1+R2)
150
100
50
5
15
10
Figure 3.14
20
25 V (Volt)
4.9-) Plot the I-V characteristics of the following circuits (Assume that I be as y-axes and V
be as x-axes). Assume that the diode is ideal.
+
I
E
-
+
I
V E
(a)
-
R
+
V
-
+
Figure 3.15
30
+
I
R
E
-
(b)
I
V1
(c)
D
E
-
(d)
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-4
+
KIRCHHOFF'S LAWS
1-) PURPOSE:
The purpose of this experiment is to verify Kirchhoff's Voltage and Current Laws and
to observe the validity of the principles of conservation of power in linear resistive networks.
2-) THEORY:
Any circuit can be solved by Kirchhoff’s laws because they do not depend on series
or parallel connections. Kirchhoff’s voltage law (KVL) states that “around any closed loop of
a network the algebraic sum of voltage drops is equal to the rises voltage”, or simply “the
algebraic sum of all voltages around any closed loop in an electric circuit is zero”, i.e.,
Vrises
Vdrops
(4.1)
n
i 1
Vi (around any closed loop) = 0
(4.2)
A junction where two or more currents merge is called a node. In Fig.4.1, the black
dot point represents a node for the currents I1 to I4. Consider all currents into a node as
positive and all currents directed away from that point as negative.
I1
I2
I3
I4
Figure 4.1: Representation a node
I2
I4
I1
I3
0
(4.3)
So, Kirchhoff's current law (KCL) states that “the algebraic sum of currents entering any
junction of a network must be equal to the algebraic sum of current leaving that junction”, or
simply “the algebraic sum of currents at a node is zero”, i.e.,
I enet ring
I leaving
(4.4)
n
i 1
Ii
0
(4.5)
In any linear resistive networks, the algebraic sum of energy delivered by active
sources must be equal to the energy absorbed by the elements of the network, i.e.,
Pdel
Pabs
31
(4.6)
3-) EXPERIMENTAL PROCEDURE:
3.1-) Connect the circuit shown in Figure 4.2 and then measure component voltages and
currents. Be careful with the polarities of measured quantities.
500
1k
E=12 V
2.2 k
100
1k
500
Figure 4.2
3.2-) Set up the circuit shown in Figure 4.3 and measure the current through each branch.
Is=6 mA
6
+mA
100
3.3 k
E=0 30 V
100
250
1k
2.2 k
Figure 4.3: Current divider circuit.
4-) DISCUSSIONS and CONCLUSIONS:
4.1-) Calculate all voltages and currents associated with each element in the circuit of Fig. 4.2
and Fig.4.3 using network analysis techniques. Indicate the actual direction of current
flow through each component as well as the polarity of voltage drops.
4.2-) Calculate the power supplied or delivered by each element. Compare the total power
absorbed by each component to the power by the source.
4.3-) Calculate the percentage differences of voltage and current between calculated and
measured values on each resistive elements in Fig.4.2 and Fig.4.3.
4.4-) Comment on the possible reasons for errors between calculated and measured results.
4.5-) Two resistors, R1 and R2, with a ratio of R1/R2=4 and a 40 V source are available.
a-) What is the voltage across each resistor when they are connected in series with the
source?
32
b-) What is the value of each of the resistors if the total current drawn from the 40 V
source 2 amp when the two resistors are connected in parallel with the source?
4.6-) Calculate loop voltages ABEF, BCDE, ACB, and ACDEF in the following circuit,
Fig.4.4.
250
100
A
B
100
250
E=15 V
C
100
500
F
E
D
Figure 4.4
4.7-) Show that Kirchhoff's current law is satisfied at nodes A, B, C, E and compare
calculated and measured currents at these nodes.
4.8-) Define a principle node.
4.9-) Using the Kirchhoff’s laws, derive the current and voltage divider equations.
33
34
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-5
WHEATSTONE-BRIDGE CIRCUIT
1-) PURPOSE:
To determine the resistance value of resistors using Wheatstone-Bridge Method.
2-) THEORY
A bridge circuit has four terminals, two for input voltage and two for output. The
purpose is to have a circuit where voltage drops can be balanced to provide zero voltage
across the output terminals, with voltage applied across the input. As shown in Fig.5.1, the
input terminals are a and d, with output terminals b and c. This particular circuit is called the
Wheatstone bridge and it measures the value of unknown resistance with a much higher
accuracy than that obtainable from DMM or color-codes. Runknown is the unknown resistance
in this circuit. If you use a Digital Multi Meter (DMM) for measuring the current between the
point b and c, when the circuit is not balance condition, the ammeter (DMM) measures
positive (+) or negative (-) current values. The value of R1 and R2 is known, then R3 is
adjusted so that the ammeter has a zero reading, then Runknown can be found in terms of R1, R2,
and R3. The bridge circuit is said to be balance when I=0 on the ammeter (DMM or also other
current measurable instruments, i.e. a galvonometer). At balance condition (null condition or
zero deflection), the voltage drop across Runknown must be equal to voltage across R3.
a
R2
R1
E
I1 b
A
R3
(DB)
c I2
Runknow
n
DB: Decade Box
d
Figure 5.1: The Wheatstone-Bridge circuit.
At balance condition, the current I1 and I2 is equal to each other. Then;
I1 R 1 I 2 R 2
I1R 3 I 2 R unknown
Dividing these two equations side by side
35
(5.1)
R1
R3
R2
(5.2)
R unknown
Then,
R 2R 3
R1
R unknown
(5.3)
Note that the equation takes on the form of
R unknown =
Product of adjacent arms
opposite resistor
(5.4)
Although this circuit can be used to measure the unknown resistance, the other types
of this circuit may be used to measure the impedance value of inductors and capacitance
value of capacitors if the excitation source (power supply) is alternating current. For example,
The Maxwell bridge and the Hay bridge circuits are used for inductance measurements,
whereas the Schering bridge circuit is used for capacitance measurements. The Wheatstone
bridge is used mainly for resistance measurements.
3-) EXPERIMENTAL PROCEDURE:
3.1-) Connect the circuit as shown in Figure 5.2 and set the current to zero on the ammeter
then measure the component currents and voltages on each resistance. Calculate the
value of the unknown resistance by using equation (3).
a
100
250
b
E=8 V
A
R3
(DB)
Figure 5.2
c
Runknow
n
d
3.2-) Connect the circuits as shown in Figure 5.3 and then Figure 5.4, and repeat steps 3.1.
a
a
500
2.2 k
A
b
E=8 V
c
E=8 V
Runknow
1k
R3
(DB)
n
A
b
Runknow
Figure 5.4. d
d
36
c
1k
n
Figure 5.3.
500
2.2 k
R3
(DB)
4-) DISCUSSIONS and CONCLUSIONS:
4.1-) Tabulate all calculated and measured branch currents and voltages obtained from
Fig.5.2, 5.3 and 5.4.
4.2-) Compare the value of unknown resistance in Parts 3 for Figure 5.3 and Figure 5.4.
4.3-) Name some of the factors which limit the measurement accuracy of the Wheatstone
bridge.
4.4-) Does the accuracy of the meter affect to the accuracy of the bridge? What would be your
suggestions to improve the accuracy?
4.5-) Explain the effect of series or shunt resistor connected with the meter on accuracy of the
measurement.
4.6-) What type of bridge circuit is best suited for measuring capacitance? Give brief
information about it.
4.7-) Can we measure resistance as low as 1
and as high as 1 M
with the Wheatstone
bridge? Explain the reasons for this limitation.
4.8-) Figure 5.5 shows another form of Whetstone bridge circuit. Find Rx, if the conditions
for bridge balance were achieved with R1=20
a
R1
b
Rx
R2
, R2=40
, and R3=60
A
c
d
R3
Figure 5.5
37
.
38
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-6
MESH AND NODAL ANALYSIS
1-) PURPOSE:
The purpose of this experiment is to verify experimentally the important circuit
analysis methods: Mesh and Nodal Analysis.
2-) THEORY:
2.1-) Mesh Analysis:
The terms mesh is derived from the similarities in appearance between the closed
paths of a network. Any closed path in a circuit is a loop. The first step is accomplished by
placing a loop current within each “window” of the network. A loop current is a branch
current only when it is the only loop current assigned to that branch. The number of loop
currents required is always equal to the number of windows of a planar network. However,
a network may appear to be non-planar. This network should be redrawn in planar form. If
the circuit isn’t drawn in planar form, the application of mesh analysis technique is not
possible to apply this circuit. The loop or mesh analysis method is based on systematic
application of KVL. Considering the circuit shown in Fig.6.1, a mesh analysis method is
applied as follows:
1-) Assign loop currents to each independent, closed loop in a clockwise (CW)
direction or counterclockwise (CCW) direction. But, the clockwise direction can
be chosen to establish uniformity. There are three loops in Fig.6.1, marked , ,
and .
2-) Indicate the polarities within each loop for each resistor as determined by the
assumed direction of the loop current. The polarity of a voltage source is
unaffected by the direction of the assigned loop currents.
3-) Apply Kirchhoff’s voltage law around each loop along the chosen direction to
establish required equations.
4-) If a resistor has two or more assumed currents through it, the total current through
the resistor is the assumed current of the loop in which Kirchhoff’s voltage law is
39
being applied, plus the assumed currents of the other loops passing through in the
same direction, minus the assumed currents through in the opposite direction.
5-) Write the mesh (loop) equations. The number of required equations is equal to the
number of chosen independent closed loops. In general, any n loops may be
considered to develop the required equations in n unknowns.
I1 R 1
I1 R 2
I3R 2
I1 R 4
I2R 4
I3R 3
I1 R 2
I3R 2
E2
I1 R 4
I2R 4
I2R 3
I2R 3
E1
I2R 5
I3R 3
0
(R 1
0
R2
R 4 I1
0
R 2 I1
(R 4
R 3I 2
R 3 ) I1
R 4I2
R 2 I3
E1
R3
R 5 )I 2
R 3I3
0
(R 2
R 3 )I 3
E2
(6.1)
6-) Solve the resulting simultaneous linear equations for the assumed loop currents
using Determinant Method (see appendix B).
E2
-
R1
E1
+
+
+
-
+
R2

+

+ R4
- +
- +
+ R3

+ R5
-
Figure 6.1
If current sources are present in the network to which mesh analysis is to be applied, all of
the current sources should convert voltage sources (see Appendix E to learn source
conversion).
Supermesh Currents : If a current source can not be converted to voltage source due
to non-parallel resistor across it, remove the current source from network (replacing
with its open equivalent circuit) and then apply Kirchhoff’s law to all the remaining
independent paths of the network using the mesh currents. Any resulting open
window, including two or more mesh currents, is said to be the path of a supermesh
current.
2.2-) Nodal Analysis :
A node is defined as a junction of two or more branches (see Ex.-4). The node
analysis method is based on systematic application of KCL. This method is quite general
technique and applicable to any kind of planar or non-planar network. The objective of
40
solving the network by this method is to determine the values of the voltages at the
different nodes. Voltage is the potential difference between two nodes. Considering the
circuit shown in Fig.6.2, nodal analysis method is applied as follows:
1-) Convert all voltage sources to their equivalent current source models. Current
source models are easier to deal with and more suitable for application of KCL at
the different nodes.
2-) Determine the number of nodes within the network.
3-) Pick a reference node, for convenience, the voltage of this reference node is taken
to be zero; in other words, this node could be assigned as the network ground
(with a notation G or symbol ┴, either temporarily or permanently if this node is
connected to the real ground. Label each remaining node with a subscripted value
of voltage: VA, VB, and so on.
4-) Apply Kirchhoff’s current law at each node, except the reference node.
5-) Write and then solve the resulting node equations resulting from node voltages.
VA
R1
VA VB
R2
VB VA
R2
VB
VA VB
R3
VA
R3
VB
R4
I1
(
1
R1
I2
1
R2
(
1
R2
1
)VA
R3
1
)VA
R3
(
(
1
R2
1
R2
1
)VB
R3
1
R3
I1
1
)VB
R4
I2
(6.2)
R2
VA
VB
R3
I1
R1
R4
I2
VG
Figure 6.2
Supernode: If any one voltage source between two nodes can’t be converted into
current source, it is replaced with its equivalent short-circuit, then apply Kirchhoff’s
current law to the previously defined nodes of the network. Any node including the
effect of elements tied only to other nodes is referred to as a supernode.
41
3-) EXPERIMENTAL PROCEDURE:
3.1-) Connect the circuit as shown in Figure 6.3, then measure component currents and nodevoltages VA, VB, and VC.
100
100
A
2.2 k
250
B
C
1k
500
500
8V
10 V
G
Figure 6.3
3.2-) Connect the circuit as shown in Figure 6.4 and then measure component currents and
node-voltages VA, VB, and VC.
A
1k
100
250
E=10 V
8V
B
500
C
250
G
Figure 6.4
4-) DISCUSSION and CONCLUSIONS:
4.1-) Using Mesh or Nodal Analysis technique, calculate all voltages and currents associated
with each element in the circuit of Fig. 6.3 and Fig.6.4. Indicate the actual direction of
current flow through each component as well as the polarity of voltage drops.
4.2-) Compare measured and calculated values, then calculate the percentage differences of
voltages and currents between calculated and measured values on each resistive
elements on Figure 6.3 and Figure 6.4.
4.3-) Using the Mesh Analysis technique, find the current through, then voltage across each
element of the network of Fig.6.5.
42
E2=10 V
100
100
250
500
I=10
mA
E1=15 V
Figure 6.5
4.4-) Using the nodal analysis technique, find the node voltages, then currents through each
element of the network of Fig.6.6.
1k
250
2.2 k
E=25 V
I=10
mA
500
250
Figure 6.6
4.5-) Using the nodal analysis technique, find the node voltages in the circuit shown in
Fig.6.7.
5
+
I=2 A
Ix
6
8
10
E1=5 V
5
E
+2=4 V
Figure 6.7
4.6-) Refer to the circuit shown in Fig.6.7 and decide whether general node or mesh analysis
techniques will lead to the solution for Ix most easily.
43
44
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-7
Y- (T- ) AND -Y( -T) CONVERSIONS
1-) PURPOSE:
The purpose of this experiment is to verify experimentally Y- (T- ) and
-Y( -T)
conversions.
2-) THEORY:
Circuit configurations are often encountered in which the resistors do no appear to be
in series or parallel. Under these conditions, it may be necessary to convert the circuit from
one form to another to solve for any unknown quantities if mesh or nodal analysis techniques
are not applied. Two circuit configurations that often account for these difficulties are the wye
(Y) and delta ( ), as shown in Fig.7.1. They are also referred to as the tee (T) and pi ( ). In
the analysis of these type networks, it is often helpful to convert a
to Y or vice versa. Either
it may be impossible to solve the circuit without the conversion, or the conversion makes the
solution simpler. The formulas for these transformation are derived from Kirchhofff’s laws.
RC
RC
R2
R1
RA
R1
RB
R2
R3
R3
RA
RB
Figure 7.1
In -Y conversion, “the each resistor of Y is equal to the product of the resistors in the
closest branches of the
divided by the sum of the resistors in the ”.
R1
R1
R3
RA
R BR C
RB RC
RA
R BR C
RB RC
(7.1)
R AR B
RA RB RC
or
RY
product of two adjacent R in
all R in
45
(7.2)
In Y- conversion, “the value of each resistor of the
is equal to the sum of the
possible product combinations of the resistances of the Y divided by the resistance of the Y
farthest from the resistor to be determined”.
RA
RB
RC
R 1R 2
R 2R 3
R1
R 1R 3
R 1R 2
R 2R 3
R2
R 1R 3
R 1R 2
R 2R 3
R3
R 1R 3
(7.3)
or
all cross products in Y
opposite R in Y
R
(7.4)
3-) EXPERIMENTAL PROCEDURE
3.1-) Set up the following circuit (Fig.7.2), then measure the total resistance between the
terminals (a) and (b).
a
1k
500
500
1k
250
250
b
Figure 7.2
3.2-) Now set up the equivalent of Fig.7.2 after the application of -Y conversion (Fig.7.3),
and measure the total resistance between the terminals (a) and (b).
a
1k
500
500
R1
R2
R3
b
Figure 7.3
46
4-) DISCUSSION and CONCLUSIONS
4.1-) Are the total resistance measured between the terminals (a) and (b) equal to each other?
Explain it.
4.2-) Firstly apply the necessary -Y or Y- conversion in below Fig.7.4, then find the source
current IS.
a
1k
Is
500
E=20 V
500
1k
250
250
b
Figure 7.4
4.3-) Is it necessary to apply -Y or Y- conversions to determine Is by means of Mesh or
Nodal Analysis Techniques.
4.4-) Derive the equations of -Y or Y- conversions starting from Kirchhoff’s law.
47
48
EP 212
DC CIRCUIT ANALYSIS
EXPERIMENT-8
SUPERPOSTITION THEOREM
1-) PURPOSE:
The purpose of this experiment is to verify experimentally one of the important
network theorem; Superposition.
2-) THEORY:
The superposition theorem can be used to find the solution to networks with two or
more sources that are not in series or parallel. The theorem states the following:
“In a network with two or more sources, the current through or voltage across any
resistor or source (simply any circuit element) is equal to the algebraic sum of the currents or
voltages produced independently by each source”
To consider the effects of each source independently requires that sources be removed
and replaced without affecting the final result. To remove a voltage source when applying
this theorem, the difference in potential between the terminals of the voltage source must be
set to zero (V=0 volt, short-circuited); removing a current source requires that its terminals be
opened (I=0 amper, open circuit). Any internal resistance or conductance associated with the
displaced sources is not eliminated but must still be considered.
The total current through any portion of the network is equal to the algebraic sum of
the currents produced independently by each source. That is, for a two-source network, if the
current produced by one source is in one direction, while that produced by the other is in the
opposite direction through the same resistor, the resulting current is the difference of the two
and has the direction of the larger. If the individual currents are in the same direction, the
resulting current is the sum of two in the direction of either current. This rule holds true for
the voltage across a portion of a network as determined by polarities, and it can be extended
to networks with any number of sources. Therefore, the voltage polarities and current
directions must be carefully indicated in each step.
3-) EXPERIMETAL PROCEDURE:
3.1-) Set up the circuit as shown in Figure 8.1.
49
1k
E=0 30 V
b
b
a
a
IS=10
mA
100
250
500
500
250
E1=12
V
c
E2=8
V
Figure 8.1
a-) Replace E2 by a short circuit and IS by an open circuit, then measure the voltage V1 and
current through 500
(between the points (a) and (c)) generated by the source E1.
Important Note: Be careful about the polarities of the measured voltages and currents.
b-) Replace E1 by a short circuit and IS by an open circuit, then measure the voltage V2 and
the current I2 through 500
generated by the source E2.
c-) Replace E1 and E2 by short circuits then measure the voltage V3 and I3 through 500
generated by the IS.
d-) Connect all of the sources, then measure voltage VT and current IT through 500
.
e-) Check whether the superposition theorem is satisfied, VT=V1+V2+V3, IT =I1+I2+I3 .
4-) DISCUSSION and CONCLUSIONS
4.1-) Using Superposition theorem, also calculate all voltages and currents associated with
each element in the circuit of Fig. 8.1. Indicate the actual direction of current flow
through each component as well as the polarity of voltage drops.
4.2-) Compare measured and calculated values, then calculate the percentage differences of
voltages and currents between calculated and measured values on 500
resistive
elements in Figure 8.1.
4.3-) What is the effect of internal resistance of voltage and current sources when they
became short and open in superposition theorem?
4.4-) What is meant by an open circuit and short circuit?
4.5-) Using superposition theorem, determine the magnitude and direction of the current in
the 100
for Fig.8.2.
50
+
IS=10 mA
100
100
250
E1=8 V
250
250
500
+
E2=6 V
Figure 8.2.
4.6-) Which technique has greater advantage than others, say mesh, nodal or superposition.
51
52
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-9
THEVENIN’S AND NORTON’S THEOREM
1-) PURPOSE:
The purpose of this experiment is to verify experimentally the important network
theorems: Thevenin's and Norton's.
2-) THEORY:
2.1-) Thevenin's Theorem:
Thevenin’s theorem is one of the most important theorems in network analysis. This
theorem states the following:
“Any dc network can be replaced by an equivalent circuit consisting of a voltage
source and a series resistor as shown in Figure 9.1”
RTh
a
+
ETh
b
Figure 9.1
Now we present the steps leading to the proper value of RTh and ETh:
1) Remove that portion of the network across which the Thevenin equivalent circuit is to be
found. This means that the load resistor RL between the points a and b must be removed
from the network.
2) Mark the terminals of the remaining two-terminal network. (The importance of this step
becomes obvious as we progress though some complex networks.)
3) Calculate RTh by first setting all sources to zero (voltage sources are replaced by short
circuits and current sources by open circuits) and then finding the resultant resistance
between the two marked terminals. (If the internal resistance of the voltage and/or
current sources is included in the original network, it must remain when the sources are
set to zero.)
4) Calculate ETh by first replacing the voltage and current sources and then finding the
open-circuit voltage between the marked terminals. (This step is invariably the one that
53
will lead to the most confusion and errors. In all cases, keep in mind that it is the open
circuit potential between the two terminals marked in step 2 above.)
5) Draw the Thevenin equivalent circuit with the portion of circuit previously removed,
replaced between the terminals of the equivalent circuit. This step is indicated by the
placement of the load resistor RL between the terminals of the Thevenin equivalent
circuit as shown in Figure 9.2.
RTh
ETh
I
RL
a
+
V+
b
Figure 9.2
2.2-) Norton's Theorem
This theorem is very similar to Thevenin’s theorem and it states the following:
“Any dc network can be replaced by an equivalent circuit consisting of a current
sources and a parallel resistor as shown in Figure 9.3”
a
IN
+
RN
b
Figure 9.3
The steps leading to the proper values of IN and RN are now listed:
1) Removed that portion of the network across which the Norton equivalent circuit is
found.
2) Mark the terminals of the remaining two-terminal network.
3) Calculate RN by first setting all sources to zero (voltage sources are replaced by short
circuits and current sources by open circuits) and then finding the resultant resistance
between the two marked terminals. (If the internal resistance of the voltage and/or
current sources is included in the original network, it must remain when the sources are
set to zero.)
54
4) Calculate IN by first replacing the voltage and current sources and then finding the shortcircuit current between the marked terminals.
5) Draw the Norton equivalent circuit with the portion of the circuit previously removed,
replaced between the terminals of the equivalent circuit.
I
IN
RN
RL
a
+
V +
b
Figure 9.4
3-) EXPERIMETAL PROCEDURE:
3.1-) Set up the circuit shown in Figure 9.5.
a
100
100
250
RL=500
250
+
E1=12 V
E2=8 V
b
Figure 9.5.
a-) Record the values of the voltage V and the current I through RL=500
b-) Remove 500
.
resistor RL. Find the values of the Thevenin’s voltage and resistance by
using a voltmeter and an ohmmeter, respectively.
Important Note: Don’t forget that during the measurement of Thevenin’s resistance, all of
the voltage and current sources in the network must be setted to short and open circuit,
respectively.
3.3-) Find the Norton's equivalent circuit of the 2-terminal network considered in steps 3.1.
experimentally.
4-) DISCUSSION AND CONCLUSION
4.1-) Calculate the voltage and current values through 500
by using Superposition,
Thevenin's, and Norton's method. Then compare your measured and calculated values.
4.2-) If a dc network contains dependent sources, is it possible to measure its Thevenin's
resistance by using an ohmmeter only, why?
55
4.3-) Can you describe a method to find the Thevenin's equivalent circuit of a resistance
network by using a voltmeter and a variable resistor only?
4.4-) Write down briefly the statements of the Thevenin's and Norton's theorems that you
verified experimentally. Do the experiment results more or less fit to the theory? What
can you suggest for the practical use of these theorems?
4.5-) How do you find the Thevenin's or Norton's resistance without using an ohmmeter?
4.6-) Do these theorems applicable to non-planar circuit?
4.7-) Compare the Network Analysis Methods (mesh, nodal, superposition, Norton’s and
Thevenin’s) with each other and give your comments which of them are more easily
applicable than the others?
56
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-10
RECIPROCITY; MILLMAN'S and MAXIMUM POWER THEOREMS
1-) PURPOSE:
The purpose of this experiment is to verify experimentally Reciprocity; Millman's and
Maximum Power Theorems.
2-) THEORY:
2.1-) Maximum Power Transfer Theorem:
This theorem states the following:
“A load will receive maximum power from a linear bilateral dc network when its total
resistive value is exactly equal to the Thevenin resistance of the network as seen by the load”
In the network of Figure 10.1, maximum power will be delivered to the load when
(10.1)
RL = RTh
The Thevenin equivalent circuit can be found across any element or group of
elements in a linear bilateral dc network. Therefore, if we consider the case of the Thevenin
equivalent circuit with respect to the maximum power transfer theorem , we are, in essence,
considering the total effects of any network across a resistor RL, such as in Fig. 10.1.
Rth
Eth
+
-
I
a
a
I
RL+
IN
RL+
RN
b
b
Figure 10.1
Figure 10.2
For the Norton equivalent circuit of Figure 10.2, maximum power will be delivered to
the load when
RL = RN
(10.2)
This result [eq.(10.2)] will be employed to its fullest advantage in the analysis of
transistor networks where the most frequently applied transistor circuit model employs a
current source rather than a voltage source.
For the network of Fig.10.1,
57
I=
ETh
RTh + R L
(10.3)
and
2
PL = I R L = (
ETh
2
) RL
RTh + R L
(10.4)
so that
2
PL =
ETh R L
( RTh + R L )2
(10.5)
i.e; for ETh = 4 V and RTh = 5 W, the powers to RL for different values of RL are tabulated in
Table 10.1.
Table 10.1
RL
(Ohms)
PL
1
2
3
4
5
6
7
8
9
10
16R L
(5 R L ) 2
(Watts)
0.444
0.653
0.750
0.790
0.800
0.793
0.778
0.757
0.735
0.711
A plot of the above data (Fig.10.3) clearly indicates that maximum power is delivered
to RL when it is exactly equal to RTh.
For maximum power transfer conditions, the efficiency is now determined:
P0
V I
x100% = L L x100%
Pi
ETh I L
1
E /2
= Th x100% = x100% = 50%
2
ETh
%=
It will always be 50% for maximum power transfer conditions.
A plot of the efficiency of the system versus load resistance appears in Fig.10.4,
Since this efficiency level is relatively low, this theorem is seldom applied in the field of
power transmission, where 50% losses of energy could not be tolerated.
58
PL (W)
0,9
Maximu
m
0,8
0,7
0,6
0,5
0,4
0,3
RTh=RL
0,2
0,1
0
0 1
2 3 4
5 6 7
RL( )
8 9 10 11 12
Figure 10.3
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
=50%
RL=RTh
RL( )
1 2 3 4 5 6 7 8 9 10
Figure 10.4
A plot of load voltage versus RL appears in Fig 10.5, and of current versus RL in
Fig.10.6.
I (A)
VL(V)
3
E Th
2
2
1
0
RL=RTh
RL( )
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Imax
I max
2
RL=R
Th
RL( )
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
Figure 10.5
Figure 10.6
59
Note that the load voltage is one-half the Thevenin voltage at maximum power
conditions while the current is one-half the value obtained with RL=0
the condition, RL= 0
(short circuit). For
, and
I L = I max =
ETh
R Th
(10.6)
If PL, VL, and IL are plotted on a log scale, the variation in levels for the wide range of
resistor values becomes clear. Note that PL reaches only one maximum (at RL=RTh), that VL
increases with increasing values of RL as determined by the voltage divider rule, and that IL
drops with increasing levels of RL as controlled by Ohm's law. One obvious advantage of log
scales is that they permit a wide variation in the magnitude of a parameter (such as RL).
For any physical network, the value of RL= RTh can be determined by first measuring
the open-circuit voltage across the terminals as shown in Fig.10.7; Vaa'= ETh.
E Th
2
+
a
a
Rth
Rth I
+E
+
Open-circuit voltage
+
+
+Th
Eth
E
th
R
Vaa’=ETh
L
- 2
b
a’
Figure 10.7
Figure 10.8
Then complete the circuit with RL, and vary RL until the voltage appearing across the
load is one-half the open-circuit value, or VL=ETh/2 (Fig.10.8). When this condition is
established, the voltage across the Thevenin and the load resistance are the same. Since the
current through each is also the same, the resistance values of each are equal, and
RL =
E Th / 2 E open-circuit / 2 E oc
=
=
= R Th
I
I( R L = R Th)
2I
(10.7)
Both Eoc and I can be determined by instrument properly connected to the load
resistance branch.
The power delivered to RL under maximum power conditions (RL=RTh) is
I=
ETh
E
= Th
RTh + R L 2 RTh
2
2
PL = I R L = (
ETh 2
E R
) RTh = Th 2 Th
2 RTh
4 R Th
60
and
2
P L max =
E Th
4 R Th
(10.8)
For the Norton circuit of Fig.8.3,
2
PLmax =
IN RN
4
(10.9)
For loads connected directly to a dc voltage supply, maximum power will be
delivered to the load when the load resistance is equal to the internal resistance of the source;
that is, when
(10.10)
R L = Rinternal
2.2-) Millman's Theorem:
Through the application of Millman's theorem, any number of parallel-connected
voltage sources can be reduced into a single voltage source. For example, in Fig.(10.9), the
three voltage sources can be reduced to one. This would permit finding the current through or
voltage across RL without having to apply a method such as mesh analysis, nodal analysis,
superposition, and so on. There are basically three steps included in its application.
a
R1
E1
R3
R2
+
-
E2
a
+
-
+
-
E
+3
Req
RL
Eeq
b
+
-
RL
b
Figure 10.9
Step 1: Convert all voltage sources into their equivalent current source models, which are
easily added up because of their parallel connection. This is performed in Fig.10.10 for the
network of Fig.10.9.
a
I1
E1G1 G1
(
E1
)
R1
I2
+
E2G2 G2
(
E2
)
R2
I3
E3G3 G3
+ E
3
(
Figure 10.10
61
R3
)
R
+ L
b
Step 2: Combine parallel current sources by adding them into one source. The resulting
network is shown in Fig.10.11, where
IT = I1 + I2 + I3
GT = G1 + G2 + G3
a
Req
IT
+
RL
+
G
Eeq
T
b
1
GT
a
RL
+ IT
- GT
b
Figure 10.11
Figure 10.12
Step 3: Convert the resulting current source into its equivalent voltage source, and the desired
single-source network obtained as shown in Fig.10.12
In general, Millman's theorem states that for any number of parallel voltage sources,
+_
Eeq =
E1
E
E
E
+ _ 2 + _ 3 + _... + _ N
R1
R2
R3
RN
1
1
1
1
+
+
+ ... +
R1 R 2 R 3
RN
(10.11)
and
Req =
1
R1
+
1
R2
+
1
1
R3
+...+
1
(10.12)
RN
2.3-) Reciprocity Theorem:
The reciprocity theorem is applicable only to single-source networks. It is, therefore,
not a theorem employed in the analysis of multisource networks described thus far.
The theorem states the following:
The current I in any branch of a network, due to a single voltage E anywhere else in
the network, will equal the current through the branch in which the source was originally
located if the source is placed in the branch in which the current I was originally measured.
In other words, the location of voltage source and the resulting current may be
interchanged without a change in current. The theorem requires that the polarity of the
voltage source have the same correspondence with the direction of the branch current in each
position.
62
In the representative network of Fig.10.13(a), the current I due to the voltage source
E was determined. If the position of each is interchanged as shown in Fig.10.13(b), the
current I will be the same value as indicated.
a
a
+
-
E
I
c
I
b
+
db
Figure 10.13(a)
c
E
d
Figure 10.13(b)
3-) EXPERIMENTAL PROCEDURE:
3.1) Replace 500
resistor RL in Fig.10.14 by a variable resistor (Decade Box). For at least
10 different values of RL such as RL=10, 40, 70, 90, 100, 105, 110, 130, 170, and 250
,
record the voltage and current for each case.
a
100
250
RL=500
+
250
E1=12 V
100
E2=8 V
b
Figure 10.14
3.2) Set up the circuit shown in Fig.10.15 (a) and measure the voltage VL and current IL
through 250
. Set up also the circuit of in Fig.10.15 (b) and measure the voltage VL and
current IL through 250
R1
.
a
100
R2
500
RL=250
E1
4V
+2
E
8V
IL
+
VL
-
b
Req
85
a
RL=250
Eeq
IL
+
VL
-
4.7 V
b
Figure 10.15(a)
Figure 10.15(b)
3.3) Set up the circuit shown in Fig.10.16 (a) and measure I. Set up also the circuit of in
Fig.10.16(b) and measure I.
63
E=15 V 250
250
I
100
250
E=15 V
100
100
100
100
I
100
250
500
500
Figure 10.16(a)
Figure 10.16(b)
3.4-) Set up the circuit shown in Fig.10.17(a) and measure V. Set up the circuit in
Fig.10.17(b) and measure V.
100
I=10 mA
100
I=10 mA
A
A
250
E
0-30 V
100
100
100
V
V
250
100
500
E
0-30 V
500
Figure 10.17(a)
Figure 10.17(b)
4-) DISCUSSION and CONCLUSIONS
4.1-) When 500
resistor in Fig.10.14 is replaced by a variable resistor, for what value of RL
the maximum power is transferred to the load?
4.2-) Compare the result obtained in 4.1 with the corresponding ones obtained in the
experimental work. States the possible reasons for the differences.
4.3-) Calculate the voltage VL and IL in the network of Fig.10.15 (a) and the voltage VL and IL
in the network Fig.10.15 (b).
4.4-) Compare the voltage (VL) and currents (IL) measured in step 3.2.
4.5-) Calculate the current I in the network of Fig.10.16 (a) and Fig.10.16(b). Compare the
results in connection with the reciprocity theorem.
4.6-) Compare the currents measured in step 3.3. Comment on the results in view of the
reciprocity theorem.
64
4.7-) Calculate the currents I in the network of Fig.10.17 (a) and Fig.10.17(b). Compare the
results in connection with the reciprocity theorem.
4.8-) Repeat 4.7 for the voltages V measured in step 3.4.
4.9-) Why is the logarithmic paper used to show maximum power in circuits?
4.10-) When would the circuit efficiency be equal to 100%? Explain your answer.
65
66
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-11
SERIES AND PARALLEL CAPACITORS
1-) PURPOSE:
The purpose of this experiment is to verify total capacitance in series and parallel
capacitor connections.
2-) THEORY:
2.1-) Types of Capacitors:
All capacitor like resistor which can be included under either of two general headings:
fixed or variable. These symbols are used for a fixed capacitor ╫ and for a variable capacitor
╫.
Many types of fixed capacitors are available today. Some of the most common are the
mica, ceramic, electrolytic, tantalum, and polyester film capacitors.
See for detail information about the types of capacitors to the Appendix C in this
book.
2.2-) Capacitors in Series and Parallel
Capacitors can be placed in series and in parallel. Increasing levels of capacitance can
be obtained by placing capacitors in parallel, while decreasing levels can be obtained by
placing capacitors in series. For capacitors in series, the charge is the same on each capacitor
(see Fig.11.1):
QT
E
Q1
Q2
Q3
+ V1
+ V2
+ V3
+
-
Figure 11.1.
Q T Q1 Q 2 Q 3
Applying Kirchhoff’s voltage law around the closed loop gives
E V1 V2 V3
Combining eq.(11.1) and eq.(11.2) yields
Q T Q1 Q 2 Q 3
C T C1 C 2 C 3
Dividing both sides by QT, the total capacitance of three capacitors in series is
67
(11.1)
(11.2)
(11.3)
1
1
1
1
(11.4)
C T C1 C 2 C 3
For the capacitors in parallel (see Fig.11.2.), the voltage is the same across each
capacitor, and the total charge is the sum of that on each capacitor:
E
V1
QT
V2
Q1
Q2
Q3
(11.5)
(11.6)
C 3 V3
(11.7)
C3
(11.8)
V3
Therefore,
CT E
C1V1
C 2 V2
So the total capacitance,
CT
C1
C2
QT
E
+
-
+ Q1
- V1
+ Q1
- V1
+ Q1
- V1
Figure 11.2.
3-) EXPERIMENTAL PROCEDURE:
3.1-) Digital Capacitance Meter (Model CM200) : The CM200 is a 4½ digit liquid crystal
display meter which measures capacitance between 1 pF and 2500 F with a basic
accuracy of 0.2%. The CM200 is manual ranging with a reading rate of 3 per second
and virtually instantaneous setting which allows the value of unknown capacitor to be
determined very rapidly. Special input sockets provide for the direct connection of a
wide variety of capacitors or standard test leads. In addition to measuring capacitors the
CM200 will also capacitance in cables, switches etc. The CM200 can be operated
either from an AC line adaptor or from internal batteries. The CM200 has a
measurement accuracy of (0.2% of reading + 1 digit + ½ pF) except for the highest
range which is (0.8% of reading + 4 digits). This measurement accuracy applies to an
ideal capacitor only, i.e. a capacitor whose value is not affected by measurements
frequency, current, or voltage. In practise the value of many types of capacitor,
particularly HiK ceramics, electrolytics and tantalums, are highly dependant on
measurement frequency. The equivalent measurement frequency used by the CM200
depends upon the reading and varies from about 100 Hz at 20.000 counts through 1
kHz at 2.000 counts up to 10 kHz at 200 counts. Consequently frequency dependant
68
capacitors will show different values on different ranges, and the range should be
chosen to give the most appropriate equivalent frequency. The long scale length of the
CM200 gives a maximum resolution in excess of 0.005%. Although this figure is far
beyond the absolute measurement accuracy of the instrument, it can be very useful
when matching capacitors or measuring the stability of capacitors. When making high
resolution measurements on the lower ranges some care may be necessary to minimise
the pick-up of noise and thus achieve a stable reading. Firstly the capacitor and any
connecting leads may need to be screened. Secondly the instruments measurement
ground (black input socket) should be connected to the ground of the test bench.
Thirdly, where possible operation should be from internal batteries rather than an AC
line adaptor.
3.1a-) The CM200 is supplied with the zero control factory set for use without test leads.
When using test leads of any form, the capacitance of the test leads (up to 25 pF) can be
removed using the zero control. To correctly set the zero with or without test leads
connected, disconnect any capacitors, select the 20.000 nF range and set the zero
control for a reading of 1 digit, then rotate the control slightly anticlockwise so that the
display just goes to 00. Alternatively connect a small capacitor of known value between
1 pF and 5 pF and adjust the zero control until reads the correct value.
3.1b-) The CM200 has two 4 mm sockets on 19 mm (0.75”) spacing for the connection of
standard test leads or thick lead capacitors, and four 1 mm sockets for the direct
connection of capacitors with thin or medium gauge leads. A measurement may be
taken between any red and any black socket, and standard spacing of 0.3”, 0.4”, 0.6”,
and 1” are provided for.
3.1c-) The CM200 applies a 4 Volt Peak-to-Peak waveform with an average DC levels of up
to 1 volt to the capacitor under test. Polarized capacitors should be connected with their
positive terminal to a red socket. Capacitors which might be charged should be
discharged before connection.
3.1d-) The CM200 has six ranges labelled from 20.000 nF up to 2000.0 F. When the value
of capacitor being measured exceeds the maximum of the range, the display will read
00 with the last zero flashing on and off. A higher range should then be selected until
an inscale reading is achieved.
69
3.1e-)The decimal point is automatically positioned to give a direct reading in nF or F.
Leading zero blanking is provided for the three most significant digits and consequently
a zero reading is shown as 0.0 or .00 or . 00 depending on range. In the latter case it
should be noted that for readings of 99 or less there is a blanked zero to the right of the
decimal point. Thus 0. 47 nF should be interpreted as 0.047 nF and not as 0.47 nF.
3.2-) Firstly set up the part between (c) and (d) of circuit shown in Fig.11.3, and measure the
capacitance between ends (c) and (d), then complete the circuit and measure total
capacitance between the ends (a) and (b).
+ -
+ -
a
c
+
C4=50 F
-
C1=20 F C2=10 F
+
C3=30 F -
CT
b
+
-
C5=60 F
d
Figure 11.3
3-3-) Set up the circuit shown in Figure 11.4, and measure the total capacitance between the
C4=50 F
ends (a) and (b).
a
+
C2=10 F
+
C1=20 F
CT
+
C3=30 F
b
Figure 11.4.
3.4-) Peel and then break one of the capacitor in your set and decide what type of capacitor is
it?
4-) DISCUSSION and CONCLUSIONS
4.1-) Calculate the total capacitance between the given terminals in Fig.11.3 and 11.4, and
compare measured and calculated values, then calculate the percentage differences
between them.
4.2-) Compare the order of the leakage current and resistance of the different types of
capacitors.
70
4.3-) Briefly, identify the properties of each type of capacitors.
4.4-) Give some common applications of capacitors in most electronic circuits.
4.5-) What are the effects of temperature on the capacitance and breakdown voltage values of
a capacitor?
4.6-) Is there any relationship between the sizes and capacitance value and also used dielectric
materials between the plates?
4.7-) How can you determine the value of capacitance of a capacitor without uses a
capacitance meter? Explain in detail?
4.8-) Why do capacitors have same charge in series circuit?
4.9-) When a capacitor discharges, why is its discharge current in the opposite direction from
the charging current.
4.10-)All the capacitance values are 1 F for the network shown in below Fig.11.5, determine
the equivalent capacitance between the terminals (a) and (b).
a
b
Figure 11.5.
71
72
EP 212
CIRCUIT ANALYSIS
EXPERIMENT-12
TRANSIENT PHASES OF RC-CIRCUITS
1-) PURPOSE:
The purpose of this experiment is to study transient phases of a R-C circuit network.
2-) THEORY:
There are transient phases in a R-C circuit: charging and discharging. Figure 12.1 was
designed both charge and discharge of the capacitor.
+ VR-
S
1
R
2
3
+
E
+
VC
-
Figure 12.1
At the initial case (t=0) there is no charge on the capacitor. During the charging phase
(at time t=0) the switch is closed (switch position 1) and a DC voltages of E is applied across
the RC circuit network. Then from the Kirchhoff's voltage divider rule;
E = VR + VC
(12.1)
where VR=iR, then substituting this equation into Equation (12.1)
iR + Vc = E
(12.2)
The current of the capacitor to the voltage across the capacitor can be found that:
Q = C.V
dQ
i=
dt
(12.3)
(12.4)
from these two equations (12.3) and (12.4)
ic = C
dVc
dt
(12.5)
Then since the current i is the same for the resistor and capacitor (iR=iC), then from Equation
(12.2);
C
dVc
R + Vc = E
dt
73
(12.6)
The voltage Vc from equation 12.6 can be solved using the methods of calculus:
Vc (t) = E(1- e
-t / RC
(12.7)
)charging
In this equation RC product is called time constant and its unit is seconds and is shown by
simply .
(12.8)
= RC
The current in the charging phase is given as;
ic (t) =
E -t /
e
R
(12.9)
charging
The voltage across the resistor is determined by ohm's law:
VR (t) = E e-t /
(12.10)
charging
If the switch is moved to position 2, (Figure 12.2), the capacitor will retain its charge
for a period of time determined by its leakage current. For capacitor such as the mica and
ceramic, the leakage current is very small, so that the capacitor will retain its charge, and
hence the potential difference across its plate, for a long period of time.
VR=0
1 S
1
i=0
R
S
2
2
3
3
+
+
VC
E
E
-
- VR +
iC
R
+
+
VC=E
-
Figure 12.2
If the switch is then moved to position 3, the capacitor will discharge through the
resistor R. The mathematical expression for the current ic and potential Vc and VR can again
be found by using calculus for discharging phase. The functions are:
Vc (t) = E e-t / discharging
E
ic (t) = e-t / discharging
R
VR (t) = E e-t / discharging
(12.11)
(12.12)
(12.13)
If the switch of Figure 12.1 is moved between the various position every five time
constant (5 ), the wave shapes will be as shown in Figure (12.3) for the current ic and
voltages Vc and VR.
74
Charging
E
Storage Discharging
etc.
Vc
Pos.3
Pos.2
Pos.1
E ic
R
E
R
Pos.2
Pos.1
Pos.2
Pos.1
Pos.2
Pos.1
t
Pos.3
Pos.2
Pos.1
t
E
R
E VR
Pos.3
Pos.2
Pos.1
-E
5
10
15
20
t
25
Figure 12.3
3-) EXPERIMENTAL PROCEDURE:
3-1-) Set up the circuit shown in Figure 12.4.
S
R2=55 k
1
2
E=15 V
A
3
+
a
R1=100 k
Figure 12.4
C=220 F V
b
i-)Charging Phase: Record Vc(t) and ic(t) in appropriate time intervals such as t=0, 5, 10, 15,
20, 30, 40, 50, 60, 80, 100 sec as switch is on position 1.
ii-)Discharging Phase: Record Vc(t) and ic(t) in appropriate same time intervals of below
steps i as the switch is on position 2.
3-2-) Set up the circuit shown in Figure 12.5.
75
S
R2=10 k
1
2
A
3
E=15 V
+
a
R1=47 k
C=220 F V
R3=22 k
b
Figure 12.5
a-) Measure the time variation of Vc(t) and ic(t) at appropriate time intervals such as t = 0, 5,
15, 20, 30, 40, 55, 75, 100, 120 sec for both charging and discharging phases.
b-) Measure also the RTh and VTh across the terminals a and b by first removing capacitor C
from the circuit.
Important Note: Remember that all of the voltage sources must be set to short-circuit during
the measurement of RTh.
c-) Then construct the equivalent circuit of Figure 12.5 and measure the Vc(t) and ic(t) at
appropriate time intervals.
4-) DISCUSSION and CONCLUSIONS
4.1-) Find the expression for Vc(t) and ic(t) during the charging phase (switch position 1) and
discharging phase (switch position 3) for Figure 12.4. Sketch voltage and current variations
on two separate graphs and compare these graphs by your experimentally measured graphs.
4.2-) Repeat part 4.1 for Figure 12.5.
4.3-) Calculate the energy stored on the capacitor shown in Figure 12.4 and Figure 12.5
during charging and discharging phases over the time intervals (0, ).
4.4-) If a current source is connected across an uncharged capacitor, the capacitor charges
rapidly at the instant of connection and the current diminishes. Why? Explain this situation in
detail.
4.5-) What is meant by the term “time constant” for RC circuits?
4.6-) Derive the charging and discharging equations for Fig.12.1 using the methods of
calculus.
76
EP 212
DC CIRCUIT ANALYSES
EXPERIMENT-13
THE CATHODE-RAY OSCILLOSCOPE
1-) PURPOSE:
To familiarize the student with the basic usage of the cathode-ray oscilloscope (CRO)
operation and calibration of the oscilloscope. Also with the use of the oscilloscope as a device
to measure voltages (AC and DC), frequency, phase shift, the relation of peak-to-peak,
average, and rms values of a sine wave are studied.
2-) THEORY:
The oscilloscope (scope) is probably the most widely used instrument in the
electronic laboratory. Its complex of controls and adjustment may confuse the unskilled
operator. Most oscilloscopes will have the same basic controls, but they may be referred to by
different names. However, the names are so closely related it should not be difficult to locate
the controls on any scope.
The operator should be quite familiar with the operation of a voltmeter and it should
be kept in mind that the scope is really no more than an instrument to measure voltage. The
scope displays a vertical and horizontal graphics representation of the voltage under test. The
horizontal axis displays time and the vertical axis displays amplitude. Since the scope gives
us an X and Y-axis representation, it can be used to measure voltages of different frequency
and pulses of irregular shapes, which are not possible to measure with an ordinary voltmeter.
A waveform is a graphical picture of how voltage changes over a period of time.
Since this voltage is changing amplitude, it is necessary to interpret this graph into other
useful values for circuit calculations. The oscilloscope may be used to view sinusoidal as well
as complex waveforms. The calibration procedure for the oscilloscope to be used in this
experiment should be consulted before performing the experiment.
2.1-) OSCILLOSCOPE SPECIFICATIONS
Controls and Indicators
FRONT PANEL OF CS-1022
The Front Panel representation of a CS-1022 type oscilloscope is shown in Figure
13.1.
77
Figure 13.1: The Front Panel representation of a CS-1022 type oscilloscope
78
1-) POSITION
Rotation adjusts vertical position of channel 1 trace. In X-Y operation, rotation adjusts
vertical position of display.
2-) VOLTS/DIV
Vertical attenuator for channel 1; provides step adjustment of vertical sensitivity. When
VARIABLE control  is set to CAL, vertical sensitivity is calibrated in 12 steps from 5
V/div to 1 mV/div. For X-Y operation, this control provides step adjustment of vertical
sensitivity.
3-) VARIABLE Control
Rotation provides fine control of channel 1 vertical sensitivity. In the fully clockwise (CAL)
position, the vertical attenuator is calibrated. For X-Y operation, this control serves as the Y
axis attenuation fine adjustment.
4-) AC-GND-DC
Three-position lever switch which operates as follows:
AC: Blocks dc component of channel 1 input signal.
GND: Opens signal path and grounds input to vertical amplifier. This provides a zero-signal
base line, the position of which can be used as a reference when performing dc
measurements.
DC: Direct input of ac and dc component of channel 1 input signal
5-) INPUT Jack
Vertical input for channel 1 trace. Vertical input for X-Y operation.
6-) VOLTS/DIV
Vertical attenuator for channel 2; provides step adjustment of vertical sensitivity. When
VARIABLE control  is set to CAL, vertical sensitivity is calibrated in 12 steps from 5
V/div to 1 mV/div. In X-Y operation, this control provides step adjustment of horizontal
sensitivity.
7-) VARIABLE Control
Rotation provides fine control of channel 2 vertical sensitivity. In the fully clockwise (CAL)
position, the vertical attenuator is calibrated. In X-Y operation, this control becomes the fine
horizontal gain control.
8-) AC-GND-DC
Three-position lever switch which operates as follows:
AC:
Blocks dc component of channel 2 input signal.
GND: Opens signal path and grounds input to vertical amplifier. This provides a zero-signal
base line, the position of which can be used as a reference when performing dc
measurements.
DC:
Direct input of ac and dc component of channel 2 input signal.
9-) INPUT Jack
Vertical input for channel 2 trace in normal sweep operation. External horizontal input in XY operation.
10-) CH2 INV
In the NORM position (button released), the channel 2 signal is non-inverted. In the INV
position (button engaged), the channel 2 signal is inverted.
11-) POSITION; X-Y
Rotation adjusts vertical position of channel 2 trace. In X-Y operation adjusts horizontal
position of display.
12-) MODE
Five-position push switch; selects the basic operating modes of the oscilloscope.
CH1: Only the input signal to channel 1 is displayed as a single trace.
CH2: Only the input signal to channel 2 is displayed as a single trace.
ADD: When both CH1 and CH2 buttons are engaged the waveforms from channel 1 and
channel 2 inputs are added and the sum is displayed as a single trace. When the CH2
INV  button is engaged, the waveform from channel 2 subtracted from the channel
1 waveform and the difference is displayed as a single trace.
ALT: Alternate sweep is selected regardless of sweep time.
CHOP: Chop sweep is selected regardless of sweep time at approximately 250 kHz.
13-) POWER, SCALE ILLUM
Fully counterclockwise rotation of this control (OFF position) turns off oscilloscope.
Clockwise rotation turns on oscilloscope. Further clockwise rotation of the control increases
the illumination level of the scale.
14-) PILOT Lamp
Lamp Lights when oscilloscope is turned on.
15-) GND terminal/binding post.
Earth and chassis ground.
80
16-) PROBE ADJ.
Provides approximately 1 kHz, 0.5 Volt peak-to-peak square wave signal. This is useful for
probe compensation adjustment.
17-) TRACE ROTATION
Electrically rotates trace to horizontal position. Strong magnetic fields may cause the trace to
be tilted. The degree of tilt may vary as the scope is moved from one location to another. In
these cases, adjust this control.
18-) FOCUS
Adjust the trace for optimum focus.
19-) INTENSITY
Clockwise rotation of this control increases the brightness of the trace.
20-) ASTIG
Astigmatism adjustment provides optimum spot roundness when used in conjunction with
FOCUS and INTENSITY controls. Very little readjustment of this control is required after
initial adjustment.
21-) EXT TRIG INPUT Jack
Input terminal for external trigger signal. When SOURCE switch is selected in EXT position,
the input signal at the EXT TRIG INPUT jack becomes the trigger.
22-) LEVEL/PULL SLOPE (-)
LEVEL: Trigger level adjustment determines point on waveform where sweep starts. When
COUPLING switch is selected in VIDEO-FRAME or LINE, the trigger level
adjustment has no effect.
SLOPE: + equals most positive point of triggering and - equals most negative point of
triggering. Push-pull switch selects positive or negative slope. Sweep is triggered
on negative-going slope of sync waveform with switch pulled out.
23-) COUPLING
Three-position lever switch; selects coupling for sync trigger signal.
AC:
Trigger is ac coupled. Blocks dc component of input signal; most commonly used
position.
VIDEO
FRAME: Vertical sync pulses of a composite video signal are selected for triggering.
81
VIDEO
LINE: Horizontal sync pulses of a composite video signal are selected for triggering. The
LINE position is also used for all non-video waveforms.
24-) SOURCE
Five-position lever switch; select triggering source for the sweep, with following positions;
V.MODE: The trigger source is determined by vertical MODE selection.
CH1: Channel 1 signal is used as a trigger source.
CH2: Channel 2 signal is used as a trigger source.
ADD: The algebraic sum of channel 1 and channel 2 signal is the trigger
source. (If CH2 INV engaged, the difference becomes the trigger
source.)
CHOP: The display cannot be synchronized with the input signal since the
chopping signal becomes the trigger source.
CH1: Sweep is triggered by channel 1 signal regardless of vertical MODE selection.
CH2: Sweep is triggered by channel 2 signal regardless of vertical MODE selection.
LINE: Sweep is triggered by line voltage (50/60 Hz).
EXT: Sweep is triggered by signal applied to EXT TRIG INPUT jack21 .
25-) TRIG MODE
Three-position lever switch; selects triggering mode.
AUTO: Triggered sweep operation when trigger signal is present, automatically generates
sweep (free runs) in absence of trigger signal.
NORM: Normal triggered sweep operation. No trace is presented when a proper trigger
signal is not applied.
X-Y:
X-Y operation. Channel 1 input signal produces vertical deflection (Y axis). Channel
2 input signal produces horizontal deflection (x axis). This operates regardless
vertical MODE selection.
26-) VARIABLE Control
Fine sweep time adjustment. In the fully clockwise (CAL) position, the sweep time is
calibrated.
27-) SWEEP TIME/DIV
82
Horizontal coarse sweep time selector. Selects calibrated sweep times of 0.2 s/div to 0.5
s/div in 20 steps when sweep time VARIABLE26 control
is set to CAL position (fully
clockwise).
28-)
POSITION, PULL x 10 MAG
Rotation adjusts horizontal position of trace. Push-pull switch selects x 10 magnification
(PULL x 10 MAG) when pulled out; normal when pushed in.
REAR PANEL
Figure 13.2: The Rear Panel picture of a CS-1022 type oscilloscope.
29-) Z AXIS INPUT
External intensity modulation input; TTL compatible. Positive voltage increases brightness,
negative voltage decreases brightness.
30-) CH1 OUTPUT
CH1 vertical output signal connector. AC coupled output connector. This connector is used
to measure the frequency by connecting the frequency counter. For stable operation, do not
connect CH1 OUTPUT to channel 2 input as operation.
31-) Fuse Holder
Contains the line fuse. Verify that the proper fuse is installed when replacing the line fuse.
100 V, 120 V...........0.8 A
220 V, 240 V...........0.5 A
83
OPERATION
Preliminary Operation
When operating this oscilloscope, refer to panel controls and their functions. When starting
this oscilloscope initially set the operating controls as follows and the set may be turned on
safely.
Operating Procedures
Normal Sweep Display Operation
1-) Turn the POWER control 13 clockwise - the power supply will be turned on and the
pilot lamp will light. Set these modes as follows;
MODE
12 :
CH1
TRIG MODE
25 :
AUTO
2-) The trace will appear in the center of the CRT display and can be adjusted by the CH1
POSITION 1 and
POSITION 28 controls. Next, adjust the INTENSITY 19 and, if
necessary, the FOCUS 18 for ease of observation.
3-) Vertical Modes
With vertical MODE 12 set to CH1, apply an input signal to the CH1 INPUT 5 jack and
adjust the VOLTS/DIV 2 control for a suitable size display of the waveform. If the
waveform does not appear in the display, adjust the VOLTS/DIV and
POSITION
controls to bring the waveform into the center portion of the CRT display. Operation
with a signal applied to the CH2 INPUT 9 jack and the vertical MODE set to CH2 is
similar to the above procedure.
In the ADD mode, the algebraic sum of CH1+CH2 is displayed. If the CH2 INV 10
switch has engaged, the algebraic difference of the two waveforms, CH1-CH2 is
displayed. If both channels are set to the same VOLTS/DIV, the sum or difference can be
read directly in VOLTS/DIV from the CRT. In the ALT mode, one sweep displays the
channel 1 signal and the next sweep displays the channel 2 signal in alternating
sequence.
In the CHOP mode, the sweep is chopped at an approximate 250 kHz rate and switched
between CH1 and CH2. Note that in the CHOP mode of operation with the source
switch set to V.MODE, the trigger source becomes the chopping signal itself, making
waveform observation impossible. Use ALT mode instead in such cases, or select a
trigger SOURCE of CH1 or CH2.
84
If no trace is obtainable, refer to the following TRIGGERING procedures.
4-) After setting the SOURCE switch, adjust the SLOPE control.
The display on the screen will probably be unsynchronised. Refer to TRIGGERING
procedure below for adjusting synchronization and sweep speed to obtain a stable display
showing the desired number of waveform.
TRIGGERING
The input signal must be properly triggered for stable waveform observation.
TRIGGERING is possible the input signal INTernally to create a trigger or with an
EXTernally provided signal of timing relationship to the observed signal, applying such a
signal to the EXT TRIG INPUT jack. The SOURCE switch selects the input signal that is
to be used to trigger the sweep, with INT sync possibilities (V.MODE, CH1, CH2, LINE)
and EXT sync possibility.
Internal Sync
When the SOURCE selection is in INT (V.MODE, CH1, CH2, LINE), the input signal
is connected to the internal trigger circuit. In this position, a part of the input signal fed to
the INPUT  or  jack is applied from the vertical amplifier to the trigger circuit to cause
the trigger signal triggered with the input signal to drive the sweep.
When the V.MODE position is selected, the trigger source is dependent upon the
vertical MODE selection.
When the vertical MODE selection is in ALT, the ALT position is very convenient for
measuring the time duration of the waveform. However, for phase or timing comparisons
between the channel 1 and channel 2 waveforms, both traces must be triggered by the same
sync signal.
When the SOURCE selection is in CH1, the input signal at the channel 1 INPUT 
jack becomes trigger regardless of the position of vertical MODE. When the SOURCE
selection is in CH2, the input signal at the channel 2 INPUT  jack becomes trigger
regardless of the position of vertical MODE. When the SOURCE selection in LINE, the ac
line voltage powering the oscilloscope is used as sync triggering.
85
External Sync
When the SOURCE selection is in EXT, the input signal at the EXT TRIG INPUT 21
jack becomes the trigger. This signal must have a time or frequency relationship to the
signal being observed to synchronize the display. External sync is preferred for waveform
observation in many applications. For example, Fig.13.3 shows that the sweep circuit is
driven by gate signal when the gate signal in the burst signal is applied to the EXT TRIG
INPUT jack. Fig.8 also shows the input/output signals, where the burst signal generated
from the signal is applied to the instrument under test. Thus, accurate triggering can be
achieved without regard to the input signal fed to the INPUT  or  jack so that no
further triggering is required even when the input signal is varied.
Figure 13.3
Triggering Level
Trigger point on waveform is adjusted by the LEVEL/PULL SLOPE 22 control.
Fig.13.4 shows the relationship between the SLOPE and LEVEL of the trigger point.
Triggering level can be adjusted as necessary.
Figure 13.4
Auto Trigger
When the TRIG MODE 25 selection is in AUTO, the sweep circuit becomes freerunning as long as there is no trigger signal, permitting a check of GND level. When a
86
trigger signal is present, the trigger point can be determined by the LEVEL control for
observation as in the normal trigger signal. When the trigger level exceeds the limit, the
trigger circuit also becomes free-running where the waveform starts running. When the
LEVEL control is pushed in and/or, when the trigger signal is absent or the triggering level
exceeds the limit, there is no sweep.
MAGNIFIED SWEEP OPERATION
Since merely shortening the sweep time to magnify a portion of an observed waveform
can result in the desired portion disappearing off the screen, such magnified display should be
performed using the MAGNIFIED SWEEP.
Using the
POSITION control, adjust the desired portion of waveform to the CRT.
Pull out the PULL x 10 MAG control to magnify the display 10 times. For this type of display
the sweep time is the SWEEP TIME/DIV setting divided by 10.
X-Y OPERATION
For some measurements, an external horizontal deflection signal is required. This is also
referred to as an X-Y measurement, where the Y input provides vertical deflection and X
input provides horizontal deflection.
X-Y operation permits the oscilloscope to perform many types of measurements not
possible with conventional sweep operation. The CRT display becomes an electronic graph
of two instantaneous voltages. The display may be a direct comparison of two voltages such
as during phase measurement, frequency measurement with Lissajous waveforms.
To use an external horizontal input, use the following procedure;
1.
Set the TRIG MODE switch to X-Y the position.
2.
Use the channel 1 probe for the vertical input and the channel 2 probe for the
horizontal input.
3.
Adjust the amount of horizontal deflection with the CH2 VOLT/DIV and
VARIABLE controls.
4.
The CH2 (vertical) POSITION 11 control now serves as the horizontal position
control, and the
POSITION control is disabled.
5. All sync controls are disconnected and have no effect.
87
VIDEO SIGNAL OBSERVATION
The VIDEO FRAME/LINE switch permits selection of vertical or horizontal sync
pulse for sweep triggering when viewing composite video waveforms. In the LINE
position, horizontal sync pulses are selected as triggers to permit viewing of horizontal line
of video. This is also the position used for viewing all non-video waveforms. In the
FRAME position, vertical sync pulses are selected as triggers to permit viewing of vertical
fields and frames of video. When observing the video waveforms, stable display is
obtained on the screen regardless the TRIG LEVEL 22 control.
At most points of measurement, a composite video signal is of the polarity, that is, the
sync pulses are negative and the video is positive. In this case, use “–“ SLOPE.
If the waveform is taken at a circuit point where the video waveform is inverted, the
sync pulses are positive and the video is negative. In this case, use “+” SLOPE.
APPLICATIONS
1-) PROBE COMPENSATION
If accurate measurements are to be made, the effect of the probe being used must be
properly adjusted output of the measurement system using the internal calibration signal or
some other squarewave source.
1.
Connect probe to INPUT jack. Connect ground clip of probe of oscilloscope ground
terminal and touch tip of probe to PROBE ADJ terminal.
2.
Select single trace operation of channel 1, then channel 2, for step 3 and 4. Set the
probe for 10:1 attenuation (10 x position) and VOLTS/DIV to 10 mV/div.
3.
Set oscilloscope controls to display 3 and 4 cycles of PROBE ADJ square wave at 5
or 6 divisions amplitude.
4.
Adjust compensation trimmer on probe for optimum square waveshape (minimum
overshoot, rounding off, and tilt).
88
Figure 13.5
TRACE ROTATION COMPENSTAION
Rotation from a horizontal trace position can be the cause of measurement errors.
Adjust the controls for a single display. Set the AC-GND-DC switch to GND and
TRIG MODE to AUTO. Adjust the
POSITION control such that the trace is over the
center horizontal graticule line. If the trace appears to be rotated from horizontal, align it
with the center graticule line using the TRACE ROTATION control located on the front
panel.
DC VOLTAGE MEASUREMENTS
This procedure describes the measurement procedure for DC waveforms.
Procedure:
1. Connect the signal to be measured to the INPUT jack. Set the vertical MODE to the
channel to be used. Set the VOLTS/DIV and SWEEP TIME/DIV switch to obtain a
normal display of the waveform to be measured. Set the VARIABLE control to the
CAL position.
2. Set the TRIG MODE to AUTO and AC-GND-DC to the GND position, which
established the zero volt reference. Using the
POSITION control, adjust the trace
position to the desired reference level position, making sure not to disturb this setting
once made.
3. Set the AC-GND-DC switch to the DC position to observe the input waveform,
including its DC component. If an appropriate reference level or VOLTS/DIV setting
was not made, the waveform may not be visible on the CRT screen at this point. If
so, reset VOLTS/DIV and/or the
4. Use the
POSITION control.
POSITION control to bring the portion of the waveform to be measured to
the center vertical graduation line of the CRT screen.
89
5. Measure the vertical distance from the reference level to the point to be measured,
(the reference level can be rechecked by setting the AC-GND-DC switch again to
GND).
Multiply the distance measured above by the VOLTS/DIV setting and the probe
attenuation ratio as well. Voltages above and below the reference level are positive and
negative values respectively.
Using the formula:
DC level = Vertical distance in divisions x (VOLTS/DIV setting) x (probe attenuation ratio).
Example: The point being measured is 3.8 divisions from the reference level (ground
potential). If the VOLTS/DIV was set to 0.2 V and a 10:1 was used. (See Fig.13.6)
Substituting the given values:
DC level = 3.8 (div) x 0.2 (V) x 10 = 7.6 V
MEASREMENT OF THE VOLTAGE
BETWEEN
TWO POINTS ON A
Figure
13.6
WAVEFORM
This technique can be used to measure peak-to-peak voltages.
Procedure:
1. Apply the signal to be measured to the INPUT jack. Set the vertical MODE to the
channel to be used. Set the AC-GND-DC to AC, adjusting VOLTS/DIV and SWEEP
TIME/DIV for a normal display. Set the VARIABLE to CAL.
2. Using the
POSITION control, adjust the waveform position such that one of the two
points falls on a CRT graduation line and that the other is visible on the display
screen.
3. Using the
POSITION control, adjust the second point to coincide with the center
vertical graduation line.
90
4. Measure the vertical distance between the two points and multiply this by the setting
of the VOLTS/DIV control. If a probe is used, further multiply this the attenuation
ratio.
Using the formula: Volts Peak-to-peak = Vertical distance (div) x (VOLTS/DIV setting)
x (probe attenuation ratio)
Example: The two points are separated by 4.4 divisions vertically. Set the VOLTS/DIV
setting be 0.2 V/div and the probe attenuation be 10:1. (See Fig.13.7)
Substituting the given value:
Voltage between two points = 4.4 (div) X 0.2 (V) X 10 = 8.8 Volt.
Figure 13.7
ELIMINATION OF UNDESIRED SIGNAL COMPONENTS
The ADD feature can be conveniently used to cancel out the effect of an undesired
signal component which superimposed on the signal you wish to observe. Procedure:
1.
Apply the signal containing an undesired component to the CH1 INPUT jack and
the undesired signal itself alone to the CH2 INPUT jack.
2.
Set the vertical MODE to CHOP and source to CH2. Verify that CH2 represents
the unwanted signal in reverse polarity. If necessary reverse polarity by setting
CH2 to INV.
3.
Set the vertical MODE to ADD, SOURCE to V.MODE and CH2 VOLTS/DIV
and VARIABLE so that the undesired signal component is cancelled as much as
possible. The remaining signal should be the signal you wish to observe alone and
free of the unwanted signal.
91
TIME
Figure 13.8
MEASUREMENTS
This is the procedure for making time measurements between two points on a waveform.
The combination of the SWEEP TIME/DIV and the horizontal distance in divisions between
the two points is used in the calculation.
Procedure:
1. Apply the signal to be measured to the INPUT jack. Set the vertical MODE to the
channel to be used. Adjust the VOLTS/DIV and SWEEP TIME/DIV for a normal
display.
2. Using the
POSITION control, set one of the points to be used as a reference to
coincide with the horizontal centerline. Use the
point at the intersection of any vertical graduation line.
92
POSITION control to set this
3. Measure the horizontal distance between the two points.
Multiply this by the setting of the SWEEP TIME/DIV control to obtain the time
between the two points. If horizontal "x 10 MAG" is used, multiply this further by 1/10.
Using the formula:
Time=Horizontal distance (div) x (SWEEP TIME/DIV setting) x "x 10 MAG" value-1
(1/10).
Example: The horizontal distance between the two points is 5.4 divisions. If the
SWEEP TIME/DIV is 0.2 ms/div, we calculate. (see Fig.13.9).
Substituting the given value:
Time=5.4 (div) x 0.2 (ms)= 1.08 ms
Figure 13.9
FREQUENCY MEASUREMENTS
Frequency measurements are made by measuring the period of one cycle of waveform
and taking the reciprocal of this time value as the frequency. Procedure:
1. Set the oscilloscope up to display one cycle of waveform (one period).
2. The frequency is the reciprocal of the period measured.
Using the formula:
Freq=1/period
Example: A period of 40 ms is observed and measured (See Fig.13.10).
Substituting the given value:
Freq=1/[40x10-6]=2.5x104=25 kHz.
93
Figure 13.10
While the above method relies on the measurement directly of the period of one cycle, the
frequency may also be measured by counting the number of cycles present in a given time
period.
1. Apply the signal to the INPUT jack. Set the vertical MODE to the channel to be used
and adjusting the various controls for a normal display. Set the VARIABLE to CAL.
2. Count the number of cycles of waveform between a chosen set of vertical graduation
lines.
Using the horizontal distance between the vertical lines used above and the SWEET
TIME/DIV, the time span may be calculated. Multiply the reciprocal of this value by
the number of cycles present in the given time span. If "x 10 MAG" is used multiply
this further by 10. Note that errors will occur for displays having only a few cycles.
Using the formula:
94
Figure 13.11
Freq =
number of cycles x " x 10 MAG" value
Horizontal dist . (div) x SWEEP TIME/DIVse t .
Example: Within 7 division there are 10 cycles. The SWEEP TIME/DIV is 5 ms. (See
Fig.13.11). Substituting the given value:
Freq=10/[7 (div) x 5 ( s)]=285.7 kHz
PULSE WIDTH MEASUREMENTS
Procedure:
1. Apply the pulse signal to the INPUT jack. Set the vertical MODE to the channel to be
used.
2. Use the VOLTS/DIV, VARIABLE and
POSITION to adjust the waveform such that
the pulse is easily observed and that the center pulse width coincides with the center
horizontal line on the CRT screen.
3. Measure the distance between the intersection of the pulse waveform and the center
horizontal line in divisions. Be sure that the VARIABLE is in the CAL. Multiply this
distance by the set SWEET TIME/DIV and by 1/10 is "x 10 MAG" mode is being used.
Using the formula:
Pulse width=Horizontal distance (div)x(SWEEP TIME/DIV setting) x "x MAG 10" value-1
(1/10)
Example: For the example, the distance (width) at the center horizontal line is 4.6
divisions and the SWEEP TIME/DIV is ms. (See Fig.13.12). Substituting the given value:
Pulse width=4.6 (div) x 0.2 ms=0.92 ms
95
Figure 13.12
PULSE RISETIME and FALLTIME MEASUREMENTS
For risetime and falltime measurements, the 10% and 90% amplitude points are used
as starting and ending reference points.
Procedure:
1. Apply a signal to the INPUT jack. Set the vertical MODE to the channel to be
used. Use the VOLTS/DIV and VARIABLE to adjust the waveform peak-to-peak
height to six divisions.
2. Using the
POSITION control and the other controls, adjust the display such that
the waveform is centered vertically in the display. Set the SWEEP TIM/DIV to as
fast a setting as possible consistent with observation of both the 10% and 90%
points. Set the VARIABLE to CAL.
3. Use the
POSITION control to adjust the 10% point to coincide with a vertical
graduation line and measure the distance in divisions between the 10% and 90%
points on the waveform. Multiply this by the SWEEP TIME/DIV and also by 1/10,
if “x 10 MAG” mode was used.
Note : Be sure that the correct 10% and 90% lines are used. For such measurements
the 0, 10, 90, and 100% points are marked on the CRT screen.
Using the formula:
Risetime=Horizontal distance (div) x (SWEEP TIME/DIV setting) x “x 10 MAG”
value-1 (1/10)
Example: The horizontal distance is 4.0 divisions. The SWEEP TIME/DIV is 2 s
(see Figure 13.13). Substituting the given value:
Risetime = 4.0 (div) x 2 ( s ) = 8 s
Risetime and falltime can be measured by making use of the alternate step 3 as
described below as well.
4. Use the
POSITION control to set the 10% point to coincide with the center
vertical graduation line and measure the horizontal distance to the point of the
96
intersection of the waveform with the center horizontal line. Let this distance be D1.
Next adjust the waveform position such that the 90% point coincides with the
vertical centreline and measure the distance from that line to the intersection of the
waveform with the horizontal centreline. This distance is D2 and the total horizontal
distance is then D1 and D2 for use in the above relationship in calculating the
risetime or falltime.
Using the formula :
Risetime = (D1+D2)(div) x (SWEEP TIME/DIV setting) x “x 10 MAG” value1(1/10)
Figure 13.13
Example: For the example, the measured D1 is 1.8 division while D2 is 2.2
division. If SWEEP TIME/DIV is 2
s we use the following relationship (see
Fig.13.14). Substituting the given value:
Risetime = (1.8+2.2) (div) x 2 ( s) = 8 s
97
Figure 13.14
TIME DIFFERENCE MEASUREMENTS
This procedure is useful in measurement of time differences between two signals that
are synchronized to one another but skewed in time.
Procedure:
1. Apply the two signals to CH1 and CH2 INPUT jacks. Set the vertical MODE to
either ALT or CHOP mode. Generally for low frequency signals CHOP is chosen
with ALT used for high frequency signals.
2. Select the faster of the two signals as the SOURCE and use the VOLTS/DIV and
SWEEP TIME/DIV to obtain an easily observed display.
Set the VARIABLE to CAL.
3. Using the
and use the
POSITION control set the waveforms to the center of the CRT display
POSITION control to set the reference signal to be coincident with a
vertical graduation line.
4. Measure the horizontal distance between the two signals and multiply this distance
in divisions by the SWEEP TIME/DIV setting.
If “x 10 MAG” is being used multiply this again by 1/10.
Using the formula:
Time = Horizontal distance (div) x (SWEEP TIME/ DIV setting) x “ x 10 MAG “
value-1 (1/10)
Example : For the example, the horizontal distance measured is 4.4 divisions. The
SWEEP TIME/DIV is 0.2 ms (see Fig.13.15).
98
Substituting the given value:
Time = 4.4 (div) x 0.2 (ms) = 0.88 ms
Figure 13.15
PHASE DIFFERENCE MEASUREMENTS
This procedure is useful in measuring the phase difference of signals of the same
frequency.
Procedure :
1. Apply the two signals to the CH1 and CH2 INPUT jacks, setting the vertical
MODE to either CHOP or ALT mode.
2. Set the SOURCE to the signal which is leading in phase and use the VOLTS/DIV
to adjust the signals such that they are equal in amplitude. Adjust the other controls
for a normal display.
3. Use the SWEEP TIME/DIV and VARIABLE to adjust the display such that one
cycle of signals occupies 8 divisions of horizontal display.
Use the
POSITION to bring the signals in the center of the screen.
Having set up the display as above, one division now represents 450 in phase.
4. Measure the horizontal distance between corresponding points on the two
waveforms.
Using the formula:
Phase difference = Horizontal distance (div) x 450/div
99
Example: For the example, the horizontal distance is 1.7 divisions (see Fig.13.16)
Substituting the given value:
The phase difference = 1.7 (div) x 45 0/div = 76.50
Figure 13.16
The above setup allows 450 per division but if more accuracy is required the SWEEP
TIME/DIV may be changed and magnified without touching the VARIABLE control and if
necessary the trigger level can be readjusted.
For this type of operation, the relationship of one division to 450 no longer holds.
Phase difference is defined by the formula as follows.
Phase difference = Horizontal distance of new sweep range (div) x 450/div
x
New SWEEP TIME / DIV setting
Original SWEEP TIME / DIV setting
Another simple method of obtaining more accuracy quickly is to simply use x 10 MAG for
a scale of 4.50/div.
RELATIVE MEASUREMENT
If the frequency and amplitude of some reference signal are known, an unknown signal
may be measured for level and frequency without use of the VOLTS/DIV or SWEEP
TIME/DIV for calibration.
Vertical Sensitivity
Setting the relative vertical sensitivity using a reference signal.
Procedure:
100
1. Apply the reference signal to the INPUT jack and adjust the display for a normal
waveform display.
Adjust the VOLTS/DIV and VARIABLE so that the signal coincides with the CRT
face’s graduation lines. After adjusting, be sure not to disturb the setting of the
VARIABLE control.
2. The vertical calibration coefficient is now the reference signal’s amplitude (in
volts) divided by the product of the vertical amplitude set in step 1 and the
VOLTS/DIV setting.
Figure 13.17
Using the formula:
Vertical coefficient =
Voltage of the reference signal ( V )
Vertical amplitude ( div ) x VOLTS / DIV setting
3. Remove the reference signal and apply the unknown signal to the INPUT jack,
using the VOLTS/DIV control to adjust the display for easy observation. Measure
the amplitude of displayed waveform and use the following relationship to calculate
the actual amplitude of the unknown waveform.
Using the formula:
Amplitude of the unknown signal (V) = Vertical distance (div) x Vertical coefficient
x VOLTS/DIV setting
Example: The VOLTS/DIV is 1V. The reference signal is 2 Vrms. Using the
VARIABLE, adjust so that the amplitude of the reference signal is 4 divisions (see
Fig.13.18)
Substituting the given value:
101
Vertical coefficient =
2 Vrms
4 ( div ) x1 ( V )
0 .5
Then measure the unknown signal and VOLTS/DIV is 5V and vertical amplitude is
3 division.
Substituting the given value:
Effective value of unknown signal = 3 (div) x 0.5 x 5 (V) = 7.5 V
Figure 13.18
Period
Setting the relative sweep coefficient with respect to a reference frequency signal.
Procedure:
1. Apply the reference signal to the INPUT jack, using the VOLTS/DIV and
VARIABLE to obtain an easily observed waveform display.
Using the SWEEP TIME/DIV and VARIABLE adjust one cycle of the reference
signal to occupy a fixed number of scale divisions accurately. After this is done be
sure not to disturb the setting of the VARIABLE control
2. The Sweep (horizontal) calibration coefficient is then the period of the reference
signal divided by the product of the number of divisions used in step 1 for setup of
the reference and the setting of the SWEEP TIME/DIV control.
Using the formula:
Sweep coefficient =
Period of the reference signal (sec)
horizontal width ( div ) x SWEEP TIME / DIV setting
102
3. Remove the reference signal and input the unknown signal, adjusting the SWEEP
TIME/DIV control for easy observation.
Measure the width of one cycle in divisions and use the following relationship to
calculate the actual period.
Using the formula:
Period of unknown signal=Width of 1 cycle (div) x sweep coefficient x SWEEP
TIME/DIV setting
Example: SWEEP TIME/DIV is 0.1 ms and apply 1.75 kHZ reference signal. Adjust
the VARIABLE so that the distance of one cycle is 5 divisions.
Figure 13.19
Substituting the given value:
1.175( kHz ) 1
Horizontal coefficient =
5 x0.1( ms )
1.142
Then, SWEEP TIME/DIV is 0.2 ms and horizontal amplitude is 7 divisions (see
Fig.13.19)
Substituting the given value:
Pulse width = 7 (div) x 1.142 x 0.2 (ms)
1.6 ms
PHASE SHIFT MEASUREMENT
103
A method of phase measurement requires calculations based on the Lissajous patterns
obtained using X-Y operations. Distortion due to non-linear amplification also can be
displayed.
A sine wave input is applied to the audio circuit being tested. The same sine wave input
is applied to the vertical input of the oscilloscope, and the output of the tested circuit is
applied to the horizontal input of the oscilloscope. The amount of phase difference between
the two signals can be calculated from the resulting waveform.
To make phase measurements, use the following procedure.
1. Using an audio signal generator with a pure sinusoidal signal, apply a sine wave test
signal at the desired test frequency to the audio network being tested.
2. Set the signal generator output for the normal operating level of the circuit being
tested. If desired, the circuit’s output may be observed on the oscilloscope. If the test
circuit is overdriven, the sine wave display on the oscilloscope is clipped and the
signal level must be reduced.
3. Connect the channel 2 probe to the output of the test circuit.
4. Select X-Y operation by placing the TRIG MODE switch in the X-Y position.
5. Connect the channel 1 probe to the input of the test circuit. (The input and output
test connections to the vertical and horizontal oscilloscope inputs may be reversed.)
6. Adjust the channel 1 and 2 gain controls for a suitable viewing size.
7. Some typical results are shown in Fig.13.21.
If the two signals are in phase, oscilloscope trace is a straight diagonal line. If the
vertical and horizontal gain are properly adjusted, this line is at a 450 angle. A 900
phase shift produces a circular oscilloscope pattern. Phase shift of less (or more)
than 900 produces an elliptical oscilloscope pattern. The amount of phase shift can
be calculated from the oscilloscope trace as shown in Fig.13.20.
Figure 13.20: Phase Shift Calculation
104
Figure 13.21: Typical phase measurement oscilloscope display
FREQUENCY MEASUREMENT
1. Connect the sine wave of known frequency to the channel 2 INPUT jack of the
oscilloscope and select X-Y operation. This provides external horizontal input.
2. Connect the vertical input probe (CH1 INPUT) to the unknown frequency.
3. Adjust the channel 1 and 2 size controls for convenient, easy-to-read size display.
4. The resulting pattern, called a Lissajous pattern, shows the ratio between the two
frequencies.
Figure 13.21: Lissajous waveforms used for frequency measurement
105
4-) DISCUSSION and CONCLUSION
4.1-) In Fig.13.23(a),
(a) find the frequency of the waveform if the time base is set to 0.5 s/div.
(b) find the rms amplitude of the waveform if the vertical attenuator is set to 2 V/div.
(b)
(a)
(c)
Figure 13.23: Waveforms for Problems 4.1, 4.2 and 4.3
4.2-) In Fig.13.23(b),
(a) find the period of the waveform if the time base is 10 ms/div.
(b) Find the amplitude if the vertical attenuator is set to 1 V/div.
(c) Find the slope of the leading edge of the waveform.
4.3-) In Fig.13.23(c ),
(a) find the frequency if the time base is set to 2 s/div.
(b) Find the amplitude if the vertical attenuator is set to 5 V/div.
4.4-) A 1 kHz sine wave exactly fits onto a 10 cm-wide CRT graticule. What is the setting
of the time base knob in time/div units?
4.5-) In Fig.13.24(a) the Lissajous pattern, what is the phase difference between vertical
and horizontal signals?
4.6-) What is the phase angle of the signals in Fig.13.24(b)?
106
(b)
(a)
Figure 13.24: Signals for problems 4.5 and 4.6.
4.7-) The Lissajous pattern in Fig.13.25 is produced when a 41 kHz signal is applied to the
vertical channel and a signal of unknown frequency is applied to the horizontal input.
Find the frequency of the unknown signal.
Figure 13.25: Lissajous pattern for problem 4.7
4.8-) Find the bandwidth in Hertz required of an oscilloscope vertical amplifier if the rise
time of the input pulse is 26 ns.
107
REFERENCES
1-) Robert L.Reid and Thomas S. Kubala, “Experiments in Direct Current Circuits”,
Prentice-Hall, (1968).
2-) Robert L.Boylestad, “Introductory Circuit Analysis”, Prentice-Hall, (1997).
3-) Joseph J.Carr, “Elements of Electronic Instrumentation and Measurements”, PrenticeHall, (1996).
4-) Paul B.Zbar, “Electricity-Electronics Fundamentals: A Text-Lab Manual”, McGrawHill, (1969).
5-) Muhammet Köksal, ġ.Çetin Bayram, Salih MamiĢ, Murat Aksoy and Hakan Selçuk,
“Circuit Analysis Laboratory Manual”, Gaziantep University, (1992).
6-) Celal KoraĢlı, “AC and DC Circuit Laboratory Manual”, Gaziantep University, (1987).
7-) S.A.Boctor, “Electric Circuit Analysis”, Prentice-Hall, (1987).
8-) William H.Hayt, Jack E.Kemmerly, “Engineering Circuit Analysis” McGraw-Hill,
(1971).
9-) Phillip Cutlor, “DC Circuit Analysis with Illustrative Problems”, McGraw-Hill,
(1974).
10-) Thomas C.Power, “DC-AC Laboratory Mannual”, Prentice-Hall, (1969).
11-) Thurlby CM200 type Digital Capacitance Meter Operating Manual.
12-) PS2335B type DC Güç Kaynağı Kullanma Talimatı.
13-) CS-1022 type Dual Trace Oscilloscope Instruction Manual.
14-) Escort EDM-2347 type Digital Multimeter Operator’s Manual.
15-) FT-303TR type Avometer Instruction Manual.
16-) Thurbly 1503 type DMM Operating Manual.
108
109
APPENDIX A
LETTER SYMBOLS
Table A1 summarizes the letter symbols used as abbreviations for the electrical
characteristics and their basic units. All the metric prefix for multiple and fractional values
are listed in Table A2. In addition, Table A3 shows electronic symbols from the Greek
alphabet and Table A4 shows universal physical constant.
Table A.1: Electrical Characteristics
Qunatity
Current
Charge
Power
Voltage
Resistance
Conductanc
e
Capacitance
Frequency
Period
Symbol
I or I
Q or q
P
V or v
R
G
C
f or f
T
Basic Unit
Ampere (A)
Coulomb (C )
Watt (W)
Volt (V)
Ohm ( )
Siemens (S) or
mhos
Farad (F)
Hertz (Hz)
Second (s or sec)
Table A.2: Multiples and Submultiples of Units
Prefix
Tera
giga
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
pico
femto
atto
Value
1012
109
106
103
102
101
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
110
Symbol
T
G
M
k
h
da
d
c
m
n
p
f
a
Table A.3 : Greek Letter Symbols
Letter
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
Eta
Theta
Iota
Kappa
Lambda
Mu
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
Chi
Psi
Omega
Capita
l
A
B
E
Z
H
I
K
M
N
Small
Uses
Area, angles, coefficients, transistor characteristics
Angles, coefficients, flux density, transistor
characteristics
Specific gravity, conductivity
Density, variation
Permittivity, base of natural logarithm
Coefficients, coordinates, impedance
Efficiency, hysteresis coefficient
Phase angle, temperature
Dielectric constant, susceptibility
Wavelength
Amplification factor, micro, permeability, mobility
Reluctivity, frequency
O
P
T
Y
3.1416
Resistivity, density
Summation, conductivity
Time constant
Angles, magnetic flux
X
Dielectric constant, phase difference
Ohms, angular velocity
Table A.4: Universal Physical Constant
Constant
Boltzmann’s constant
Electric Charge (-e)
Electron (volt)
Electron (mass)
Permeability of free space
Permitivity of free space
Planck’s constant
Velocity of light
Pi
111
Value
Symbol
-23
1.38x10 j/K
K
-19
1.6x10 C
Q
1.6x10-19 J
eV
9.12x10-31 kg
m
-7
U
4 x10 H/m
0
8.85x10-12 F/m
0
6.626x10-34 J-sec
h
3x108 m/sec
c
3.141592654
APPENDIX B
DETERMINANTS
Determinants are employed to find the mathematical solutions for the variables in two
or more simultaneous equations. Once the procedure is properly understood, solutions can be
obtained with a minimum of time and effort and usually with a fewer errors than when using
other methods. Consider the following three simultaneous equations where x, y and z are the
unknown variables and a1, a2, a3, b1, b2, b3, c1, c2, and c3 are constants:
a 1x
b 1 y c1 z
d1
a 2x
b2 y c2z
d2
a 3x
b3 y c3z
d3
(B.1)
Using determinants to solve for x, obtain the determinant in the numerator by
replacing the first column by the elements on the right of the equal sign, and the denominator
is the determinant of the coefficients of the variables (the same approach applies to y and z).
The denominator;
D
a1
b1
c1
a2
b2
c2
a3
b3
c3
d1
b1
c1
d2
b2
c2
d3
b3
D
c3
a1
d1
c1
a2
d2
c2
a3
d3
c3
(B.2)
Then;
x
y
z
D
a1
b1
d1
a2
b2
d2
a3
b3
d3
D
112
(B.3)
(B.4)
(B.5)
There is more than one expanded format for the third-order determinant. Each, however, will
give the same result. One expansion of the determinant (D) is the following:
D
a1
b1
c1
a2
b2
c2
a3
b3
c3
a1
b2
c2
b3
c3
b1
a2
c2
a3
c3
c1
a2
b2
a3
b3
(B.6)
This expansion was obtained by multiplying the elements of the first row of D by
their corresponding cofactors. It is not a requirement that the first row be used as the
multiplying factors. In fact, any row or column (not diagonals) may be used to expand a thirdorder determinant. The sign of each cofactor is dictated by the position of the multiplying
factors (a1, b1, and c1 in this case) as in the following format:
Note that the proper sign for each element can be obtained by simply assigned the upper
left element a positive sign and then changing sign as you move horizontally or vertically
to the neighboring position. Expanding the entire expression for x, y and z, we have the
following solutions:
x
d1 (b 2 c 3 b 3 c 2 ) b1 (d 2 c 3
a 1 ( b 2 c 3 b 3 c 2 ) b1 ( a 2 c 3
d 3 c 2 ) c1 (d 2 b 3 d 3 b 2 )
a 3 c 2 ) c1 (a 2 b 3 a 3 b 2 )
(B.7)
y
a 1 (d 2 c 3
a 1 (b 2 c 3
a 3 c 2 ) c1 (a 2 d 3
a 3 c 2 ) c1 (a 2 b 3
(B.8)
z
a 1 (b 2 d 3 b 3 d 2 ) b1 (a 2 d 3 a 3 d 2 ) d1 (a 2 b 3 a 3 b 2 )
a 1 (b 2 c 3 b 3 c 2 ) b1 (a 2 c 3 a 3 c 2 ) c1 (a 2 b 3 a 3 b 2 )
d 3 c 2 ) d 1 (a 2 c 3
b 3 c 2 ) b1 (a 2 c 3
a 3d 2 )
a 3b 2 )
(B.9)
Finally please note that this method of expansion is good only for third-order
determinants. It can’t be applied to fourth- and higher-order system.
113
APPENDIX C
CAPACITORS
A capacitor consists of an insulator between two conductors. Capacitors are
manufactured for specific values of capacitance. The commercial capacitors are generally
classified according to the dielectric material used between electrodes. Most common
capacitors are air, paper, mica, ceramic, tantalum, polyester and electrolytic capacitors. The
most famous of them, electrolytic capacitors use a molecular-thin oxide film as the dielectric
material, resulting in large capacitance values in little space. The types of capacitors are
compared in Table C.1.
Table C.1: Types of Capacitors
Dielectric
Air
Ceramic
Electrolytic
Mica
Paper or plastic film
Construction
Meshed
Plates
Tubular
Disk
Aluminium
Tantalum
Stacked
sheets
Rolled foil
Capacitance
10-400 pF
Breakdown Voltage
400 (0.02 in. air gap)
0.5-1600 pF
0.002-0.1 F
5-1000 F
0.01-300 F
10-5000 pF
500-20.000
0.001-1 F
200-1.600
10-450
6-50
500-20.000
There is no required polarity, since either side can be the more positive plate, except
for electrolytic capacitors. These are marked to indicate which side must be positive to
maintain the internal electrolytic action that produces the dielectric required to form the
capacitance. It should be noted that it is the polarity of the charging source that determines
the polarity of the capacitor voltage.
Mica capacitors are often used for small capacitance values of 50 to 500 pF; their
length is ¾ in. or less with about ⅛-in. thickness. Thin mica sheets are stacked between
tinfoil sections for the conducting plates to provide the required capacitance. Alternate strips
of tinfoil are connected together and brought out as one terminal for one set of plates. The
entire unit is generally in a molded Bakelite case.
Paper capacitors are often used for medium capacitance values of 0.001 to 1.0 F,
approximately. The physical size for 0.05 F is typically 1 in. long with ⅜-in. diameter. For
this type of capacitors, two rolls of tinfoil conductor separated by a tissue-paper insulator are
114
rolled into a compact cylinder. Each outside lead connects to its roll of tinfoil as a plate. The
entire cylinder is generally placed in a cardboard container coated with wax or encased in
plastic. A black band at one end of a paper capacitor indicates the lead connected to the
outside foil. This lead should be used for the ground or low-potential side of the circuit to
take advantage of shielding by the outside foil. There is no required polarity, however, since
the capacitance is the same no matter which side is grounded. It should also be noted that in
the schematic symbol for C the curved line usually indicates the low-potential side of the
capacitor.
The ceramic type capacitors are made in many shapes and sizes. A ceramic dielectric
material is coated on two sides with metal, such as copper or silver, to act as the plates. The
leads are then attached through electrodes to the plates. The ceramic dielectric materials are
made from earth under extreme heat. These types of capacitors are obtained with high
dielectric constant materials. In the disk form, silver is fired onto both sides of the ceramic, to
form the conductor plates. The disk types of ceramic capacitors have capacitance values up to
0.01 F in much less space than a paper capacitor. For tabular type ceramic capacitors, the
hollow ceramic tube has silver coating on the inside and outside surfaces between the values
1 and 500 pF. These types of capacitors are generally smaller than mica type capacitors but
have the same application as them.
Electrolytic type capacitors are designed primarily for use in networks where only dc
voltage will be applied across the capacitor and these types capacitors are commonly used for
capacitance values from 5 to 2.000 F. Because of the extremely thin dielectric film, very
large capacitance values can be obtained. This capacitor consists of a roll of aluminium foil
coated on one side with an aluminium oxide, the aluminium being the positive plate and the
oxide the dielectric. A layer of paper or gauze saturated with an electrolyte is placed over the
aluminium oxide on the positive plate. In most cases the negative plate is connected directly
to the aluminium container, which then serves as the negative terminal for external
connections. The area is increased by using long strips of aluminium foil and gauze, which
are rolled into a compact cylinder with very high capacitance. For example, an electrolytic
capacitor may have 1.000 F or more even if it is same size with a 0.1 F paper capacitor, but
rated at 10 V breakdown. These types of capacitors are also used in circuits that have a
combination of dc voltage and ac voltage.
115
If these types of capacitors are connected in opposite polarity, the reversed
electrolysis forms gas in the capacitor. Then it becomes hot and may explode. This is a
possibility only with electrolytic capacitors.
The one of the most important disadvantage of electrolytic type capacitors is their
high leakage current. When a voltage is applied across the plates of a capacitor, a current due
to the free electrons flows from one plate to the other and this current is known as leakage
current. This current is usually so small, however it can be important for electrolytic type
capacitors.
Another type of electrolytic type capacitor uses tantalum (Ta) instead of aluminium.
Typical tantalum capacitors have large capacitance values in a smaller size, less leakage
current and longer shelf life. However, one of the important disadvantages of this capacitor is
the its cost. This type of capacitor is more expensive than the aluminium type capacitor.
The disk type ceramic capacitors have a tolerance 20% but paper type capacitors
have 10%. On the other hand, mica and tabular type ceramic capacitors have tolerance
between 2 and 20%. The silver plated mica type capacitors have minimum tolerance on the
order of 1%, but electrolytic type capacitors have a large tolerance that lies up to 50%.
The voltage rating (VR) of capacitors specifies the maximum potential difference that
can be applied across the plates without explosion of capacitor. Usually the voltage rating is
for temperatures up to about 60 0C. Higher temperatures result in a lower voltage rating. The
breakdown VR is lower than for ac voltage because of the internal heat produced by
continuous charge and discharge. The VR of some common capacitors are given in Tab C.1.
Mica and tabular ceramic types capacitors are color-coded to indicate their
capacitance value. Since coding is necessary only for very small sizes, the color-coded
capacitance value is always in pF units. The colors used are the same as for resistor coding,
from black for 0 up to white for 9. The capacitance, voltage rating value and polarities are
printed on the electrolytic type capacitors.
In the construction of variable type capacitors, the fixed metal plates connected
together form the stator. The movable plates connected together on the shaft form the rotor.
Capacitance is varied by rotating the shaft to make the rotor plates mesh with the stator
plates. They do not touch, however, since air is the dielectric. Full mesh is maximum
capacitance. Moving the rotor completely out of mesh provides minimum capacitance.
116
APPENDIX-D
Thurly 1503 High Resolution Digital Multimeters
The 1503 is a 4¾ digit (± 32.768 count) manual ranging bench/portable multimeter
and its front panel picture si shown in Fig.E.1. It provides high accuracy readings of DC
and AC voltage, DC and AC current, resistance, frequency and diode test. Operation is
either from AAC line power or internally-fitted batteries and the rugged case with tilt
stand/handle makes it suitable for bench of field use.
Figure E.1: The Front Panel Picture of Thurbly 1503 type DMM.
1. Operation : The basic sequence of operation for any measurement is as follows:
a-) Turn on power by depressing the red button
b-) Select the function either V,
or A (depress both buttons together to select A).
c-) Depress the AC button if AC voltage or AC current measurement is required.
Ensure it is released if a DC or Resistance measurement is required.
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d-) Select a range whose maximum reading is higher than the input you wish to
measure.
e-) Connect the source to the input terminals and take the measurement.
2. Overrange Indication: Where the input exceeds the maximum reading of the
range, display will indicate overrange by showing two zeros with the last zero
flashing on and off approximately once per second. Note that resistance ranges will
of course always show overrange with no input connected.
3. Negative Indication: On DC voltage and current ranges, a negative symbol will
automatically appear on the left hand side of the display if the red input socket it
taken negative with respect to black (ground) socket.
4. Decimal Point Position: The decimal point is automatically positioned to give a
direct reading in mV, V, A, mA, A,
,k
or M
as shown by the range and
function buttons. Leading zero blanking is provided for the three most significant
digits, consequently a zero reading is shown as 0.0 or .00 or . 00 depending on
range. In the latter case it should be noted that for readings of 99 or less there is a
blanked zero to the right of the decimal point. For example, . 83 (V) should be
interpreted as .083 volts and not as.83 volts.
5. DC Voltage Measurement: The 1503 reads DC voltage between 10 V and 1200
V. Maximum displayed reading is 32767 except on the highest range. Voltage
measurement is selected by depressing the button marked V. Ensure that the button
marked AC is released for DC measurement. The input is applied between the red
socket marked V- -A, and the black (ground) socket next to it. The input
impedance of all five ranges is 10 M .
6. AC Voltage Measurement: The 1503 reads AC voltage between 100 A and 750
V. Maximum displayed reading is 16.383 except on the highest range. Voltage
measurement is selected by depressing the button marked V. The button marked
AC should also be depressed. The input is applied between the red socket marked
V- -A, and the black (ground) socket next to it.
7. Resistance Measurement: The 1503 reads resistance between 10 m
and 32 M .
Maximum displayed reading is 32.767. Resistance measurement is selected by
depressing the button marked
. Ensure that the button marked AC is released.
118
The input is applied between the red socket marked V- -A, and the black (ground)
socket next to it.
8. DC or AC Current Measurements: The 1503 reads DC or AC current from 10
nA up to 10 amps (25 amp short term), Maximum displayed reading is
8191
except on the 10 amp range. Current measurement is selected by depressing
together the buttons marked V and
. For AC measurements, the button marked
AC should be depressed, for DC measurements it should be released. Inputs up to
800 mA should be applied between the red socket marked V- -A, and the black
(ground) socket next to it. Currents in excess of 1 amp DC or AC rms will cause the
fuse located on the back panel to rupture. Inputs 10 A continuous (or 25 amps for
less than 10 seconds) should be connected between the red socket marked 10 A and
the black (ground) socket on its right. Depress the range button marked 10 A to
position the decimal point for a direct reading in amps. An additional range with 1
nA resolution can be obtained by selecting voltage and depressing the 320 and 32
M buttons together. Note that; the standard test leads provided are not suitable for
currents in excess of 6 amps.
9. Diode Test Measurements: The 3200
resistance range can be used to measure
the forward voltage drop of diodes and transistors at a current of 1 mA with a direct
reading in millivolts. The anode should be connected to the red socket marked V-A, and the cathode to the black (ground) socket.
10. Frequency Measurement: The 1503 can measure frequency from 0.1 kHz up to
3999.9 kHz. Frequency measurement is obtained by plugging a 3.5 mm jack plug
into the socket marked kHz. This automatically switches the meter from multimeter
mode to frequency meter mode regardless of the position of the function button.
The range switch marked kHz should be depressed in order to position the decimal
point for a direct reading in kHz.
11. Fuse Replacement. The protection fuse for the current ranges is mounted on the
back panel. If blown, it should be replaced with a 20 mm quick blow 1 amp H.R.C.
fuse.
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APPENDIX E
SOURCE CONVERSION
There are two types of power sources: 1-) Voltage and 2-) Current Sources. The
current and voltage sources are often referred to as the dual of each other. In general, both
of the sources can be considered as ideal and non-ideal sources. In ideal voltage source, the
internal resistance of source is taken to be equal to zero (RS=0
source, the internal resistance is taken as infinity (RS=
) but for an ideal current
).However, all sources, whether
they be voltage or current, have some internal resistance but the internal resistance in
voltage source series with load resistor (RL) is so small that it can be ignored, then we have
assumed that ideal voltage source and the internal resistance parallel with load resistor (RL)
in current source is large enough that can be ignored, then we have assumed that ideal
current source.
RS
ES
IL
RL
IL
+
IS
RS
RL
+
(b)
(a)
Figure E.1: (a) A non-ideal voltage source (b) A non-ideal current source.
The non-ideal voltage and current sources can be converted to each other using the
following procedure: The current of the current source or the voltage of the voltage source is
determined using Ohm’s law and the parameters of the other configuration.
i-) From Voltage to Current Source Conversion:
IS=ES/(RS+RL)
RS
RS
ES
+
ii-) From Current to Voltage Source Conversion:
RS
IS RS
ES=IS(RS+RL)
120
+
APPENDIX F
GLOSSARY TERMS
Angular Velocity (w): The velocity with which a radius vector projecting a sinusoidal
function rotates about its center.
Ammeter: An instrument designed to read the current through the circuit elements in series
with the meter.
Amper (A): The SI unit of measure applied to the flow of charge through a conductor.
Branch: The portion of a circuit consisting of one or more elements in series.
Branch-Current Method: A technique for determining the branch currents of a multiloop
network.
Capacitive: A measure of a capacitor’s ability to store charge; measured in farads (F).
Capacitive Time Constant ( ): The product of resistance and capacitance that establishes
the required time for the charging and discharging phases of a capacitive transient.
Capacitive Transient: The waveforms for the voltage and current of a capacitor that result
during the charging and discharging phases.
Capacitor: A fundamental electrical element having two conducting surfaces separated by an
insulating material and having the capacity to store charge on its plates.
Circuit: A combination of a number of elements joined at terminal points providing at least
one closed path through which charge can flow.
Closed Loop: Any continuous connection of branches that allows tracing of a path that
leaves a point in one direction and returns to that same point from another direction without
leaving the circuit.
Color Coding: A technique employing bands of color to indicate the resistance levels and
tolerance or resistors.
Conductance (G): An indication of the relative ease with which current can be established in
a material. It is measured in siemens (S).
Conductors: Materials that permit a generous flow of electrons with very little voltage
applied.
Conventional Current Flow: A defined direction for the flow of charge in an electrical
system that is opposite to that of the motion of electrons.
Coulomb (C ): The fundamental SI unit of measure for charge. It is equal to the charge by
6.242x1018 electrons.
Current Divider Rule: A method by which the current through parallel elements can be
determined without first finding the voltage across those parallel elements.
Cycle: A portion of a waveform contained in one period of time.
DC current source: A source that will provide a fixed current level even though the load to
which it is applied may cause its terminal voltage to change.
DC generator: A source of dc voltage available through the turning of the shaft of the device
by some external means.
Decibel (dB): A unit of measurement used to compare power-levels.
Determinants Method: A mathematical technique for finding the unknown variables of two
or more simultaneous linear equations.
Dielectric: The insulating material between the plates of a capacitor that can have a
pronounced effect on the charge stored on the plates of a capacitor.
Dielectric Strength: An indication of the voltage required for unit length to establish
conduction in a dielectric.
121
Diode: A semiconductor device whose behaviour is much like that of a simple switch; that is,
it will pass current ideally in only one direction when operating within specified limits.
Direct Current: Current having a single (unidirectional) and a fixed magnitude over time.
Efficiency ( ): A ratio of output to input power that provides immediate information about
the energy-converting characteristics of a system.
Electron Flow: The flow of charge in an electrical system having the same direction as the
motion of electrons.
Energy (W): A quantity whose change in state is determined by the product of the rate of
conversion (P) and the period involved (t). It is measured in joules (J) or wattseconds (Ws).
Frequency (f): The number of cyles of a periodic waveform that occur in one second.
Frequency Counter: An instrument that will provide a digital display of the frequency or
period of a periodic time-varying signal.
Fuse: A two-terminal device whose sole purpose is to ensure that current levels in a circuit
do not exceed safe levels.
Hay Bridge: A bridge configuration for measuring the resistance and inductance of coils in
those cases where the resistance is a small fraction of the reactance of the coil.
Insulators: Materials in which a very high voltage must be applied to produce any
measurable current flow.
Internal Resistance: The inherent resistance found internal to any source of energy.
Inductor: A fundamental element of electrical systems constructed of numerous turns of
wire around a ferromagnetic or air core.
Kirchhoff’s Voltage Law: The algebraic sum of the potential rises and drops around a
closed loop (or path) is zero.
Kirchhoff’s Current Law: The algebraic sum of currents entering and leaving a node is
zero.
Leakage Current: The current that will result in the total discharge of a capacitor if the
capacitor is disconnected from the charging network for a sufficient length of time.
Maximum Power Transfer Theorem: A theorem used to determine the load resistance
necessary to ensure maximum power transfer to the load.
Maxwell Bridge: A bridge configuration used for inductance measurements when the
resistance of coil is large enough not to require Hay bridge.
Mesh Analysis: A technique for determining the mesh (loop) currents of a network that
results in a reduced set of equations compared to the branch-current method.
Millman’s Theorem: A method employing source conversions that will permit the
determination of unknown variables in a multiloop network.
Nodal Analysis: A technique for determining the node voltages of a network.
Node: A junction of two or more branches.
Norton’s Theorem: A theorem that permits the reduction of any two-terminal linear dc
network to having a single current source and parallel resistor.
Ohm ( ): The unit of measurement applied to resistance.
Ohm’s Law: An equation that establishes a relationship among the current, voltage, and
resistance of an electrical system.
Ohmmeter: An instrument for measuring resistance levels.
Ohm/Volt Rating: A rating used to determine both the current sensitivity of the movement
and the internal resistance of the meter.
Open Circuit: The absence of a direct connection between two points in a network.
122
Oscilloscope: An instrument that will display, through the use of a cathode-ray tube, the
characteristics of a time-varying signal.
Parallel Circuit: A circuit configuration in which the elements have two points in common.
Period (T): The time interval between successive repetitions of a periodic waveform.
Potential Difference: The algebraic difference in potential (or voltage) between two points
in an electric system.
Potentiometer: A three-terminal device through which potential levels can be varied in a
linear or nonlinear manner.
Power (P): An indication of how much work can be done in a specified amount of time; a
rate of doing work. It is measured in joules/second (J(s) or watts (W).
Reciprocity Theorem: A theorem that states for single source networks; the current in any
branch of a network, due to a single voltage source in the network, will equal the current
through the branch in which the source was originally located if the source is placed in branch
in which the current was originally measured.
Resistance (R ): A measure of the opposition to the flow of charge through a material.
Rheostat: An element whose terminal resistance can be varied in a linear or nonlinear
manner.
Semiconductor: A material having a conductance value between that of an insulator and that
of a conductor.
Series Circuit: A circuit configuration in which the elements have only one point in common
and each terminal is not connected to a third, current-carrying elements.
Short Circuit: A direct connection of low resistive value that can significantly alter the
behaviour of an element or system.
Substitution Theorem: A theorem states that if the voltage across and current through any
branch of a dc bilateral network are known, the branch can be replaced by any combination of
elements that will maintain the same voltage across and current through the chosen branch.
Superposition Theorem: A network theorem that permits considering the effects of each
source independently. The resulting current and /or voltages is the algebraic sum of the
currents and/or voltages developed by each source independently.
Thermistor: A two-terminal semiconductor device whose resistance is temperature
dependent.
Thévenin’s Theorem: A theorem that permits the reduction of any two-terminal linear dc
network to one having a single voltage source and series resistor.
Varistor: A voltage-dependent, nonlinear resistor used to suppress high-voltage transients.
Volt (V): The unit of measurement applied to the difference in potential between two points.
If one joule of energy is required to move one coulomb of charge between two points, the
difference in potential is said to be one volt.
Voltage Divider Rule: A method by which a voltage in a series circuit can be determined
without first calculating the current in the circuit.
Voltmeter: An instrument designed to read the voltage across an element or between any two
points in a network.
Wattmeter: An instrument capable of measuring the power delivered to an element by
sensing both the voltage across the element and the current through the element.
VOM: A Multimeter with the capability to measure resistance and both ac and dc levels of
current and voltage.
Working Voltage: The voltage that can be applied across a capacitor for long periods of time
without concern for dielectric breakdown.
123
Appendix-G
An Example for the First Page of Laboratory Report
124
Appendix-H
Data Sheets
125