University of California at San Diego
LABORATORY MANUAL for
PHYSICS 2CL
Electricity and Magnetism
Waves and Optics
Section I: Introduction to Course
This course is intended to provide some basic familiarity with experimental techniques as applied
to electromagnetism, optics, and waves.
In the first phase, a series of four experiments are used to show how simple circuits are designed,
constructed and tested using items of standard laboratory equipment such as the oscilloscope
and signal generator, and procedures for measuring time dependent voltages are developed.
This type of experience gives insight into the methods of research used in many labs and is
essential to the development of good experimental practice. It also has a practical reward in that
it should provide some background of understanding for connecting up or debugging other
commonly used items of electronic equipment such as stereo systems.
The second phase involves experiments with wave phenomenon, such as demonstrations of
refraction, diffraction, and interference effects using microwaves and lasers light. Techniques for
measuring magnetic fields are explored in another experiment. An experiment using lenses and
the human eye demonstrates with simple equipment how lenses form images and how the human
eye functions. Finally, the relationship between mechanical energy and heat can be also studied.
Experimental physics requires careful measurements of a variety of phenomena, and in all
measurements there is some limitation on the precision, or accuracy of the quantity being
determined. No physical measurement whose result is in the form of a quoted number is
complete without an understanding and analysis of the uncertainties associated with the
measurement. A statement of the result of an experiment is incomplete without a statement of its
precision or accuracy. This course therefore emphasizes error analysis. In many experiments
several error analysis techniques are possible and the judgment of the experimenter is required to
determine which is appropriate for the particular result.
This course assumes a previous or current lecture course in which the foundations of
electromagnetism, optics and waves are developed in a cohesive manner. Because of the nature
of this laboratory, and its conduct (including limited sets of apparatus), it is not possible to "key"
the experiments of a lecture course. While some of the background for the experiments is
developed in each description, outside reading or review in a calculus-level introductory physics
text may be needed, first to understand the role of the experiment or measurement in the context
of electromagnetism or optics, and second for the "theory" relevant to the particular experiment.
Throughout this course we will use the metric (MKS or SI) system, the basic units being length
(meter), mass (kilogram), and time (second). Familiarity with the metric system is assumed. On
occasion, however, we will make measurements, or express results, in terms of the related cgs
system, which is also used extensively in the scientific literature. Here the units are length
(centimeters), mass (grams), and time (seconds). Engineering in this country is increasingly
being done in MKS units; eventually the rest of the society will follow. We may occasionally use
an English unit such as the inch or lb in the discussion of an experiment; however all work and
calculation are of course to be accomplished in the metric system.
The mechanical, electromagnetic, and thermodynamic quantities are related through the
definitions of current (Amperes) and temperature (Kelvin or centigrade) in the SI system. The
derived electromagnetic quantities, Potential (Volts), Charge (Coulombs), and Magnetic Field
(Tesla), are assumed to be familiar as they are used in all scientific, engineering, and practical
work.
The goals of this course are therefore to:
1)
Perform certain experiments that illustrate the foundations of electromagnetism and optics.
2)
Develop the experimental approach as a method of inquiry, upon which all physical science
is based.
3)
Illustrate the use of modern techniques to improve measurements.
4)
Understand, quantitatively if possible, the uncertainties or errors in the measured physical
quantities as determined by limitations of technique.
There are a number of methodologies that are needed in order to succeed in these experiments.
The following sections describe some of these, including data taking and notebook technique,
errors and error analysis, graphing and presentation of data, electrical circuit conventions, and
electronic test and measuring equipment.
Important Note: A separate syllabus for the course is handed out in class and contains a schedule,
course requirements and information on other features of the course. If there are conflicts between that
syllabus and this manual, the syllabus is the final word.
Section II: Laboratory Notebooks and Reports
Results obtained in research must be documented. Most researchers keep a notebook in which
results are entered as they are obtained. The object of research is to communicate new
information to other research workers and to society as a whole; this requires the writing of
complete and understandable reports.
An important part of the laboratory course is to learn to adopt these procedures and make them a
permanent part of your own way of working. To help you with this, you are required to:
1)
Maintain laboratory notebooks for use during the performance of each experiment.
2)
Write a brief report in your laboratory notebook for most experiments and a full formal report
on one or two of the experiments.
The instructor will announce at the beginning of the quarter for which experiments a formal report
is required.
The formats of a laboratory notebook and a formal report are very different. We discuss each of
these below.
1.
Laboratory Notebook and Brief Reports
The laboratory notebook is a log of all activities during the performance of an experiment and the
analysis of the data. You want to be able to reconstruct a few days or weeks later what happened
during the performance of the experiment. This is especially important if you find some problem
in the analysis stage of your experiment. The hard thing to learn is to make sure that all
necessary information is entered.
The notebook is by no means neat and will normally contain crossed out words, sentences,
sections or pages. Some people find this hard to accept and choose to either write their initial
data on separate sheets for later transfer to the notebook or they enter the data in pencil in the
notebook so that it can be erased if necessary. Both procedures are wrong. The data taken is a
permanent part of the record of performing an experiment, especially if an error was made that
was later corrected. Therefore, all information is entered in the notebook in ink. You want to
avoid making an error and not realize it. It is clear that it is very suspicious when a notebook
looks particularly clean and neat.
It is obviously necessary that the text in the notebook is readable. You can achieve this by writing
on alternate pages during the performance of the experiment. The blank space can then be used
later for annotations, graphs, or more calculations.
Here are some guidelines for the laboratory notebook:
n
Leave the first two pages of the notebook for a table of contents.
n
Begin the text in the notebook for each experiment with its title and number, the date, and the
name of your lab partner, if any.
n
State briefly the objective of the experiment. Five sentences or less are usually sufficient.
n
Enter all data in your notebook in ink, using a kind that is not prone to smudge. A number
alone is meaningless, without a description, appropriate units, and an associated estimate of
uncertainty. Label each column in data tables and give units.
n
Make clear diagrams of the overall experimental setup and all relevant circuits. Note the
geometry, dimensions, settings of the apparatus, and conditions under which the results were
obtained.
n
Use graphs to display experimental results, including labeled axes and plot points.
2.
n
Justify the choice of plot. A sentence like “We expect the voltage V to decay exponentially
with time so plot logV (voltage) vs. t (time) to obtain a straight line”is all you need;
n
Give the graph a title;
n
Label your axes and put the units (e.g. sec) in parentheses next to the axis name;
n
Put error bars on the experimental points;
n
If you are fitting (comparing) some mathematical expression (the fitting function) to
experimental points, then include the fitting function on the graph. Also include any fitting
parameters with their uncertainties (errors). Finally, graph the fitting function through your
experimental points and include in your report a succinct comment on the agreement between
fitting function and experimental data, i.e. goodness of the fit.
n
Show how you converted the measurements into the final derived quantities. Do an error
analysis on the results by using the rules for propagation of errors. A single example of each
type of calculation is sufficient. If feasible, the results of calculations and accompanying
errors should be presented in the form of tables.
n
State results and comment on them including their (dis)agreement with accepted values. If
your report requires a comparison between an experimental result and some expectation,
then make a quantitative statement. Simply writing two results (numbers and their
uncertainties) next to each other and making a remark like “they ’
re almost the same”is not
sufficient
Formal Laboratory Reports
The formal report is meant to provide experience at communicating the results of an experiment.
The intended audience is your colleagues who have not done the experiment and have not read
about it. You should assume that they have had the same courses as you and are equally
familiar (or unfamiliar) with the theory. Reports are the primary method by which scientific
knowledge is disseminated; but writing a readable report requires considerable effort (as you will
notice) and practice (that’
s the idea here).
Clear and concise writing is an essential element in a useful report so that reports are limited in
length to no more than five pages of double-spaced typewritten text (not including figures and
tables). Handwritten reports are not acceptable. Note that Greek symbols and equations may be
added by hand, if you keep it neat. Graphs, diagrams, and data tables should be individually
labeled (e.g. Figure 1, Table 1); they may be on separate pages, and are not part of the 5-page
limit. Cut and paste procedures for tables and figures are acceptable. Reports that are shorter
than the 5-page limit, and convey all of the necessary information, will receive the highest grades.
The formal report should have the following elements:
n
Title Page. Include the experiment title, your name and institution, the date, and a succinct,
well-written abstract. (You might want to consult a research journal in the library to get an idea
about how to write an abstract.) In general, the abstract briefly states what you did,
summarizes the principal results, and mentions the work’
s significance, if any. Do not exceed
150 words.
n
Introduction. Write an overall description of the experiment and state briefly, in your own
words, the principal objectives.
n
Theory. Briefly review the theory behind the experiment and include the theory’
s numerical
predications. The measurement results will be compared to the predictions of the theory.
n
Experiment. Describe the experimental apparatus and the measurement procedure. Use
diagrams to make this section absolutely clear. Neatly hand-drawn diagrams are as
acceptable as computer-generated ones. The reader should be able to understand clearly
and quickly your procedure and the tools (apparatus) you assembled to accomplish your
objectives.
3.
n
Results. This section should be divided into two parts. Present the data in tabular form with
explanatory text. State units.
n
Present the raw data transferred from your laboratory notebook. Use tables, graphs, etc and
pay attention to organization and clarity. You have already mastered this in your brief reports,
so just keep up the good work;
n
Analysis of raw data. Here is the place to convert the raw data into final results. Do an error
analysis on the results. Example calculations of relevant error analyses are performed as
required. Use tables and graphs to maximize clarity and brevity.
n
Discussion and Conclusions. Summarize the results in a brief quantitative discussion of
their agreement (or disagreement) with the theoretically predicted values or other accepted
values. Avoid repeating what you may already have stated in the Results section.
Course Procedures
Please consult the syllabus for information not found below.
You are asked to include some information in the laboratory notebook that is not mentioned
above. This information is necessary to administer the class and would not normally be part of a
laboratory notebook.
All experiments will be documented in the two laboratory notebooks. Each notebook is a bound,
quadrille-ruled 7 7/8" x 10 1/8" record book. The course name and number, your name, section
ID, and lab assistant's name must be on the outside cover of each. Maintain an index on the first
page of each notebook giving the week number, experiment number and page number.
If the experiment is performed with a partner, make sure to share all aspects of doing the
experiment. For example, do not have one partner perform the measurements while the other
only writes in the notebook. At the end of the laboratory session, all data should be transferred
from one notebook to the other so that both contain a complete record. The notes in both
notebooks might be very similar at this stage. However, work added in the notebook outside the
classroom must be your own.
Prior to leaving the lab you should show your work to your TA, who will sign it if he or she
determines that you have completed all necessary work. In most cases, this should include
computer printouts of plots of your data and curves you have fit to it. After you leave the
laboratory you will perform any additional analysis that is needed to complete the work.
Most labs are to be reported in a “brief format”which includes only a description of your analysis
of the data and a statement of your conclusions about the results of the measurements. These
brief reports must be written in the lab book as described above. Do not exceed two handwritten
pages of text after the signature of the TA. The required brevity of the reports is an indication of
the limited time that we wish you to spend on the report and a requirement that you organize your
thoughts carefully so as to write concisely and accurately
After performing an experiment, the notebook that contains its data, analysis, and results must be
handed in to your TA a week later on the same day of the week. If a report is required on that
experiment, it is due at the same time as the notebook. The TA will grade your notebook and
short report and return the notebook to you a week after you handed it in, again on the same day
of the week. Because you will do another experiment in the interim, the second notebook must
be used for it. Thus you alternate between the two notebooks; one is with your TA for grading,
the other is in use by you.
You must carefully prepare yourself for each experiment by reading the laboratory manual and
reviewing the theory before coming to class. The need for advance preparation can not be
overstated. Unprepared students will have a negative learning experience, place a heavier
demand on the TA at the expense of the other students in the class and will usually have trouble
finishing the experiment on time. Therefore the TA may ask unprepared students to leave the
class.
The TA will initial the notebook when you leave the class at the end of the session. Outside class
you are to complete calculations, error analysis, and graphing. A page limit of two pages beyond
the TA's signature is enforced. This is to discourage you from spending excessive amounts of
time at home adding unnecessary material in hopes of obtaining a higher grade by turning the
laboratory notebook into a report. A formal report contains material that should not be part of a
laboratory notebook.
4.
Grading
Conduct in the laboratory and the contents of the laboratory notebooks and reports are the basis
of a major fraction of the grade in this course.
Other grading criteria may include the following:
1)
The care taken in making your measurements. The quality and completeness of the data
obtained.
2)
The analysis of the data (including errors), the interpretation of the results and comparison
with accepted values.
3)
Completeness of tables, quality of graphs.
4)
Your understanding of the experiment.
5)
Your adherence to the guidelines for laboratory notebooks (page limit beyond the TA's
signature) and reports.
As part of the preparation for each lab, you are required to answer the questions posed for the
experiment in your notebook before coming to the laboratory.
Section III: Errors in Physical Measurement
1.
Introduction and Overview
A real measurement of a physical quantity is never perfectly exact. This is in part due to the fact
that no real instrument is infinitely precise. Therefore, an integral part of any experimental result is
an estimate of its precision, or conversely- its uncertainty, and this estimate is referred to as the
measurement error. This section describes the methods that should be used to correctly handle
errors when analyzing experimental data.
It is instructive to classify error into two categories- systematic errors and random errors.
Systematic errors affect all measurements in a particular experiment in a similar fashion. The
sources of these errors can be as simple as an incorrectly calibrated instrument or the tendency
of an observer to consistently overestimate readings that fall between scale divisions, or real
physical effects that were not accounted for in the design of the experiment. Systematic errors
that stem from instrument calibration can usually be detected (by repeating the experiment with
different instruments) and avoided by careful calibration.
We classify errors that are not deterministic and that may affect each data point in the experiment
in a different way as random errors. These may result from finite instrument precision and from
intrinsic or external “noise”. Errors of this type may be reduced by optimizing the experimental
setup or averaging large number of repeated measurements, but can never be completely
eliminated.
Note that for the purpose of the discussion here, mistakes are not considered as errors- these can
and should be avoided.
Finally, for the purpose of the discussion that follows, it is important to understand the distinction
between accuracy and precision. Precision refers to the resolution or sensitivity of the
measurement apparatus. In instruments such as a ruler or a gauge, the precision may be taken to
be the smallest separation between two marked “ticks”. For example, the precision of a ruler with
marks every 1mm will be 1mm; the precision for reading a voltage off an oscilloscope set at 1V
per division, and that has 5 ticks per division will be 0.2 V. Accuracy defines how far the
measured value is from the “truth”. Note that one can have an instrument with high precision but
low accuracy- all measurements of a certain quantity done with this instrument would fall with a
very narrow spread around a particular value, but this value would turn out to be far off from the
actual quantity that we set to measure. An instrument can also have high accuracy and a low
precision so that the spread in readings would be wide, but their average would fall right on the
‘
true’value.
2.
Statistical Error Analysis
A.
Precision and Multiple Measurements
Earlier it was suggested that random errors lead to a limit in the precision of a measurement. It
was also mentioned that the effects of random errors may be reduced by repeating an experiment
many times and averaging the results. Understanding how this happens requires some discussion
of "Gaussian distribution of errors".
Figure 1 Multiple Measurements of a Physical Quantity
The distribution of results one would get by repeatedly measuring a single physical quantity will
be Gaussian, or bell-shaped curve, centered around the true value of that quantity. The more
measurements one makes the smoother this distribution gets, so if one performed an infinite
number of measurements, the mean of the results would coincide exactly with the true value of
the quantity that was measured. Since it is only possible to make a finite number of
measurements, the average of the results, noted as x , would only be an estimate of the true
value. Fig. 1 shows schematically how this distribution emerges for increasing number of
measurements.
The probability density function of the Gaussian distribution with mean x 0 and standard deviation
σ is given by:
G x0 ,σ( x) =
1
σ 2π
e
−( x − x 0 ) 2 / 2 σ 2
We use this distribution to determine probabilities that a new measurement will fall between two
values of x; the area under the curve (definite integral) between the two x values gives us the
probability. Since there is no useful closed form for the integral, we have to look up these areas
in a table of "Error Function Integrals" or some similarly named compilation. It is customary to
assign the error associated with a single measurement to be ± σ with a probability of 68%.
The Gaussian distribution usually arises because of many smaller effects coming together to form
one overall error distribution. The improvement in precision comes from the reduction in the
"error of the mean". It is a property of the Gaussian distribution that the mean value of several
samples will also have a Gaussian distribution and have a decreasing width as N increases. If
you make N measurements then you may say:
[Best estimate of x 0 ] = x [mean or average]
[Best estimate of σ] = s =
1 N
(x i − x )2
N − 1 i =1
∑
[Best estimate for error on x 0 ] =
s
[standard deviation]
[standard deviation of the mean]
N
In other words, the error in your final answer decreases as 1 / N ; taking the average of four
measurements should increase precision by a factor of two. What is the limit of this
improvement? A good rule of thumb is that a factor of ten is hard to achieve because the
assumption of many small random effects contributing to the uncertainty fails or systematic effects
dominate. Also, this implies 100 measurements! However, improvements of a factor of 2 or 3 are
usually possible with four or nine measurements.
There are additional benefits from doing several measurements. A single measurement may be
quite wrong or very different from the average of the others. Secondly, the spread of
measurements indicates the width of the initial distribution (which may tell us some important
things about the measurement technique), and defines the random error.
The whole procedure is the following:
a.
Make a set of N measurements of the quantity x. Call these xi , i = 1,L ,N .
b.
Find the mean (or average):
x=
c.
1
N
N
∑ xi
i =1
Find the standard deviation:
s=
1 N
( x i − x) 2
N − 1 i =1
∑
d.
We can equate s to σ which appears in the formula for the Gaussian distribution (which
allows us to calculate the probabilities for where to expect subsequent measurement
values).
e.
The statement of your result is that the parameter x has the best-estimate value:
x=x±
s
N
Note that a correct interpretation of errors is in terms of probability. If you did an experiment with
N measurements and found x = 15.5 ± 0.1, then there is only a 68% chance that doing it again
with N measurements will find x between 15.4 and 15.6.
Example: Free-Fall Experiment
During an experiment to determine the acceleration of gravity, ten trials (drops) were
made from a known height. The time was obtained in milliseconds (ms) to the nearest
ms, and reduced according to Table 1.
Trial
1
2
3
4
5
6
7
8
9
10
Sum
Free-fall deviation
d*d
time [ms]
d [ms]
[ms*ms]
645
0.0
0.0
640
-4.8
23.4
643
-1.8
3.1
649
4.3
18.1
644
-1.1
1.3
655
10.4
108.1
641
-4.3
18.6
648
2.7
7.0
649
4.6
20.9
635
-9.8
96.1
6449
0
297
Table 1 Analysis of Free-Fall Experiment
The mean or average value was
t=
1
N
N
∑ ti
=
i =1
6449
= 644 .9 ms
10
The sum of the algebraic differences between the mean t and each ti are of course
zero by definition of the mean. The standard deviation was
 1 N

SD = 
(t i −t )2 
 N − 1 i =1

∑
1/ 2
=
297
= 5 .74 ms
9
The final result can be expressed as
t best = t ±
SD
N
= 644 .9 ± 1 .8 ms
It is understood that the "true" value of the time, which could, in principle, be determined
by an infinite number of measurements, has 68% probability of lying between 643.4 ms.
and 646.6 ms.
3.
Propagation of errors
A.
Errors of derived quantities
Consider the following situation: one is interested in finding the frequency of some sinusoidal
signal. In order to find it, one views the signal on an oscilloscope, and measures its period (recall
that ω=2π/T) - T ± ∆T where ∆T is the measurement error. How would this error translate into the
error on the frequency, ∆ω?
Suppose the error on the period is ±0.1 ms. If the period measured is 1.0 ms, then the true value
of the period could be between 0.9 and 1.1 ms. This would translate to frequencies in the range
7.0 and 5.7 kHz so ∆ω=1.3 kHz. On the other hand, if a period of 10 ms is measured with the
same error, the frequency would be in the range 0.63 and 0.62 kHz so ∆ω=0.01 kHz ! Clearly, the
way the error on the period translates into an error in frequency depends on the period. More
accurately, it depends on the derivative of the relation between the variables. In general, the error
on a function f(x) where x is measured with an error ∆x is:
∆f ( x) =
∂f ( x)
∆x
∂x
∆ω =
2π
∆T
so if
ω = 2π / T
B.
Errors in several variables
then
T2
.
When several variables go into making a result, we write it as
f ( x1 , x 2 ,K, x n )
The result is a function of the n variables x i. The sensitivity of f to changes in x is characterized
∂f
by the value of ∂x1 , the partial derivative of f with respect to x1 .
If each of the variables has a Gaussian-like error distribution with σ = ∆x i (the "error" for xi ), then
the "total error", ∆f , is the root-mean-square of weighted errors
∂f
∂f
∆f = (
∆x1 ) 2 + (
∆x 2 ) 2 + ... =
∂x1
∂x2
 ∂f

∑  ∂x ∆xi 
i= 1 
i

N
2
(1)
The above relation also demonstrates another important property of Gaussian errors: the total
error σtotal resulting from the cumulative effect of several errors σ1 , σ2, ... is obtained by summing
the squares of the σi’
s (i = 1,2, ...) and then taking the square root of that sum. For example,
finding the total of 2 errors σ1 and σ2 is equivalent to finding the hypotenuse of a triangle with
edges σ1 and σ2 :
C.
σ total = σ12 + σ22 .
A simple case
The above expression (Eq. 1) can be simplified if a function f depends on its arguments in the
form:
f = A r B sC t L
df
df
= rAr −1 × B s C t ...
= Ar × sB s −1 × C t ...
The partial derivatives are dA
; dB
etc. We can now
df
f
df
f
=r
=s
pull f out of each term: dA
A ; dB
B and so on. If we now plug all this into Eq. (1) we
get:
2
2
2
2
 ∆A   ∆B 
 ∆A   ∆B 
∆f =  rf
 +  sf
 + ... = f ×  r
 + s
 + ...
A  
B 

 A  B 
or:
2
2
∆f
 ∆A 
 ∆B 
= r2 
 + s2
 + ...
f
 A 
 B 
The quantities
etc.
∆f f , ∆A A etc. are called “relative errors ”and can also be written as ε f , ε A
Example: Electrical Resonance
Here
ω=
1
1
2
2
= L−1 / 2C −1/ 2
εω =
εL + εC
LC
, so
2
.
Note that the fractional error in ω is typically smaller than the error in L or C.
Example: RC time constant
The decay time constant for an RC circuit is given by τ =RC . If R and C are measured
with errors ∆R and ∆ C then the calculated ∆τ will be:
2
 ∆R   ∆C 
∆τ = τ × 
 +

 R   C 
2
Example: Resistors in Series
If Rtotal = R 1 +R 2 , and the resistors are measured with errors ∆R 1 and ∆R 2 then the
calculated error for the equivalent resistor Rtot is:
∆Rtot =
4.
(∆R1 ) 2 + (∆R2 )2
Drawing Conclusions
It is often necessary to draw conclusions on an experiment with regards to its agreement or
disagreement with theory, specifications, or previously established results. The relevant question
is whether within measurement errors, the results of the experiment are consistent with the
expected value for the quantity measured.
A quantitative answer can be given by performing a statistical t-test. This test assumes again that
the errors are Gaussian, and measures how many standard deviations separate the measured
value and the expected (or given) value. Therefore, in order to compare the two values, one
calculates
t=
xmeasured − xexp ected
σtotal
(2)
where xmeasured is the experimental value, xexpected is the expected value, and σtotal is the total
error including the total error on the experimental value and the error on the expected value if it
has any.
Once we have a t-value, we can say how confident we are that the measured value agrees with
the expected value. We will have to use a table of the Gaussian distribution integrals to find out
what is the probability to obtain an result between xexpected and xmeasured if xexpected is the “true”
value to which we add random error. For example, for t = 2.0 this probability is ~95%. This means
that in only 5% of the time we would get an experimental result further away from the “true”value
than xmeasured. For t = 3.0 this probability is ~99.7% so it is quite unlikely (0.3% chance) that
x measured comes from a distribution around xexpected, so we can conclude that this particular
measurement is in disagreement with the expected value with 99.7% confidence.
For the purpose of this course, 95% confidence level is sufficient so results that yield a t-value of
less than 2 will be considered to agree with expectations, and those with t > 2 will be considered to
disagree.
Note that a low t-value does not mean that the experiment was “good” or “successful”, it just
means that the results are consistent with the supplied values. In addition, one must be careful
with low t-values as these can arise when a measurement has a large error (σ in the denominator
of Eq. 2). Therefore for a conclusion drawn based on t-values to be meaningful, the relative error
in the experiment should be kept small.
Section IV: Tektronix 2225 Oscilloscope
1.
Summary of Controls, Connectors, and Indicators
No.
Title
Function
Recommended Use
1
INTENSITY
Adjusts trace brightness.
2
BEAM FIND
3
4
5
6
FOCUS
TRACE
ROTATION
POWER
Power Indicator
Compresses display to within CRT
limits.
Adjusts for finest trace thickness.
Adjusts trace parallel to centerline.
Compensate for ambient lighting,
trace speed, trigger frequency.
Locate off -screen phenomena.
7, 9
POSITION
8
TRACE SEP
10
CH 1 - BOTH - CH
2
11
NORM- INVERT
Turns power on and off.
Illuminates when power is turned
on.
Moves trace up or down screen.
Moves the magnified trace
vertically with respect to the
unmagnified trace when
HORIZONTAL MODE is set to
ALT.
Selects signal inputs for display.
Inverts the Channel 2 signal
display.
Optimize display definition.
Compensate for earth's field.
Control power to the instrument.
Know power condition.
Position trace vertically and
compensate for dc component of
signal.
Position unmagnified and
horizontally magnified traces for
convenient viewing and
measurement.
View either channel
independently or both channels
simultaneously
Provide for differential (CH 1 - CH
2) or summed (CH 1 + CH 2)
signals when ADD is selected.
No.
Title
Function
Recommended Use
12
ADD-ALTCHOP
Display summed or individual
signals.
13
VOLTS/DIV
ADD shows algebraic sum of CH 1
and CH 2 signals. ALT displays
each channel alternately. CHOP
switches between CH 1 and CH 2
signals during the sweep at 500 kHz
rate.
Selects vertical sensitivity.
14
Variable (CAL)
15
AC -GND-DC
16
CH 1 OR X CH
2 OR Y
17
18
POSITION
COARSE
POSITION FINE
19
X1 -ALT- MAG
20
SEC/DIV
21
Variable (CAL)
22
MAG(X5 - X10 X50)
Provides
The CAL control
continuously
can be pulled
variable
out to vertically
deflection factors
magnify the
between
trace by a factor
calibrated
of 10. Limits
positions of the
bandwidth to 5
VOLTS/DIV
MHz.
switch. Reduces
gain by at least
25:1.
In AC, isolates dc component of
signal. In GND, gives reference
point and allows precharging of input
coupling capacitor. In DC, couples
all components of signal.
Provides for input signal
connections. CH 1 gives horizontal
deflection when SEC/DIV is in X -Y.
COARSE is convenient for moving
unmagnified traces
FINE is convenient for moving
magnified traces when either ALT or
MAG is selected.
X1 displays only normal (horizontally
unmagnified) waveform. ALT
displays normal and magnified
waveforms alternately. MAG
displays only the magnified
waveform.
Selects time-base speed.
Adjust vertical signal to suitable
size.
Match signals
Inspecting
for common
small signals.
mode readings.
Adjust height
of pulse for risetime
calculations.
Selects method of coupling input
signals to the vertical deflection
system.
Apply signals to the vertical
deflection system.
Control trace positioning in
horizontal direction.
Control trace positioning in
horizontal direction.
Select normal, comparative or
expanded waveforms.
Set horizontal speed most suited
to requirements.
Extend the slowest speed to at
least 1.25 s/div
24
PROBE
ADJUST
Provides continuously variable
uncalibrated sweep speeds to at
least 2.5 times the calibrated setting.
Selects degree of horizontal
magnification.
Provides safety earth and direct
connection to signal source.
Provides approximately 0.5-V,1-kHz
square wave.
No.
Title
Function
Recommended Use
25
SLOPE
Selects the slope of the signal that
triggers the sweep.
Provide ability to trigger from
positive-going or negative -going
signals.
23
Examine small phenomena in
detail.
Chassis ground connection.
Match probe capacitance to
individual circuit. This source may
be used to check the basic
functioning of vertical and
horizontal circuits but is not
intended to check their accuracy.
2.
26
LEVEL
27
TRIG'D
29
30
RESET
HOLDOFF
31
SOURCE
32
COUPLING
33
EXT INPUT
Selects trigger-signal amplitude
point.
Indicator lights when sweep is
triggered in P-P AUTO, NORM, or
TV FIELD.
Arms trigger circuit for SGL SWP.
Varies sweep holdoff time 10:1.
CH 1, CH 2, and EXT trigger
signals are selected directly. In
VERT MODE, trigger source is
determined by the VERTICAL
MODE switches as follows: CH 1:
trigger comes from Channel 1
signal. CH 2: trigger comes from
Channel 2 signal. BOTH-ADD and
BOTH CHOP: trigger is algebraic
sum of Channel 1 and Channel 2
signals. BOTH-ALT: trigger comes
from Channel 1 and Channel 2 on
alternate sweeps.
AC blocks dc components and
attenuates signals below 15 Hz. LF
REJ blocks dc components and
attenuates signals below about 30
kHz. HF REJ blocks dc components
and attenuates signals above about
30 kHz. DC couples all signal
components.
Connection for
Connection for
applying external
applying
signal that can
external signal
be used as a
that can be used
trigger.
for intensity
modulation.
Select actual point of trigger.
Indicate trigger state.
Improve ability to trigger from
aperiodic signals.
Select source of signal that is
coupled to the trigger circuit.
Select how the triggering signal is
coupled to the trigger circuit.
Trigger from a
source other
than vertical
signal. Also
used for singleshot
application.
Provide
reference blips
by intensity
modulation from
independent
source.
Learning the Controls
After turning the power on, let the oscilloscope warm up for a few minutes before starting this
procedure.
n
Set instrument controls as follows:
Display
INTENSITY
FOCUS
Vertical (both channels)
POSITION
MODE
VOLTS/DIV
VOLTS/DIV Variable
Input Coupling
Horizontal
COARSE POSITION
MODE
SEC/DIV
SEC/DIV Variable
Trigger
SLOPE
LEVEL
Midrange
Midrange
Midrange
CH 1
0.5 V (10X PROBE)
CAL detent (fully clockwise)
AC
Midrange
X1
0.2 ms
CAL detent (fully clockwise)
/
Midrange
MODE
HOLDOFF
SOURCE
COUPLING
P-P AUTO
MIN
CH 1
AC
n
Connect a probe to the input BNC connector for Channel 1 (labeled CH 1 OR X). Attach the
probe ground lead to the collar of the EXT INPUT connector and apply the probe tip to the
PROBE ADJUST terminal. If necessary, adjust the TRIGGER LEVEL control to get a stable
display.
n
Change the Channel 1 input coupling switch to GND and use the Channel 1 POSITION
control to align the baseline trace to the center horizontal graticule line. This sets the zero
reference for the display.
n
Switch input coupling back to AC. Notice that the square wave is centered vertically on the
screen. Now switch input coupling to DC and observe what happens to the waveform. The
zero reference is maintained at the center horizontal graticule line.
NOTE: More information about using the controls is contained at the end of this procedure. Refer to it as
often as needed while learning the front-panel controls.
n
Use the following controls and notice the effect each has on the displayed waveform as the
settings are changed.
Each POSITION control
CH 1 VOLTS/DIV
CH 1 VOLTS/DIV Variable (CAL)
SEC/DIV
SEC/DIV Variable (CAL)
HORIZONTAL MODE
HORIZONTAL MAG
TRACE SEP
TRIGGER SLOPE
n
At this point, connect the second probe to the CH 2 OR Y input connector. Set the
VERTICAL MODE switch to CH 2 and TRIGGER SOURCE to CH 2, then follow steps 2
through 5 again, using the channel 2 controls.
n
Now set the VERTICAL MODE switches to BOTH-NORM -ALT and return both VOLTS/DIV
switches to 0.5 V (10X PROBE). Rotate all variable controls clockwise to their CAL detents.
Set the TRIGGER SOURCE switch to VERT MODE. Then use the VERTICAL POSITION and
TRACE SEP controls to position the four traces to convenient locations on the screen.
n
While watching the Channel 2 waveforms, set the middle VERTICAL MODE switch to CH 2
INVERT and notice the effect. Then set the right MODE switch to ADD. What happens to the
waveforms? Finally, return the middle MODE switch to NORM. What waveform is displayed
now?
Congratulations! You now know how to use the 2225 front-panel controls to display signals and move
them about on the screen. The remainder of this section gives you more information about the controls
and offers suggestions for their use.
3.
Display Controls
Set the INTENSITY control for comfortable viewing, but no brighter than you need. Use highintensity settings to observe low-repetition-rate signals, narrow pulses in long time intervals, or
occasional variations in fast signals.
4.
Vertical Controls
When making voltage measurements, rotate the VOLTS/DIV CAL control fully clockwise (in
detent). Best accuracy can be achieved by setting the VOLTS/DIV control for the largest display
possible.
A.
Input Coupling
For most applications use DC input coupling. This mode is compatible with the standardaccessory, high-impedance probes and it displays logic levels and dc levels of static signals.
Use GND input coupling to show where the 0-volt level will be located when you shift to DC or
AC coupling.
Use AC coupling for the special cases where you need to see small signals on large dc
voltage levels.
B.
Channel Selection
With the three VERTICAL MODE buttons, you can display combinations of the two vertical
channels. When CH 1 is selected, the other two MODE switches are not active. When CH 2 is
selected, the middle MODE switch (NORM/CH 2 INVERT) becomes active. And when BOTH
channels are selected for display, all three MODE switches are active.
C.
ADD and INVERT
Select ADD mode to display the algebraic sum of the CH 1 and CH 2 signals. When you use
ADD, the CH 1 and CH 2 VOLTS/DIV settings should be equal.
Selecting CH 2 INVERT changes the sense of the CH 2 waveform. This allows you to see the
difference between the CH 1 and CH 2 signals on the ADD trace.
D.
CHOP or ALT?
When BOTH channels are selected, the display is time-shared. The CHOP mode displays
each channel for a short time and multiplexes during the sweep to give the appearance of
displaying both channels at once. This mode (CHOP) works better than ALT for sweep
speeds slower than 1 ms per division and for low-repetition-rate signals that make the display
flicker (up to 2 µ s/division).
The ALT mode displays each channel for the duration of a complete sweep. It gives a cleaner
display of multiple channels than CHOP does and is usually preferred at moderate to high
sweep speeds.
E.
Increasing the Sensitivity
Pulling the VOLTS/DIV CAL control out (towards you) magnifies the vertical axis by a factor of
10, increasing the sensitivity to 500 µV per division. This function is useful for investigating
small-amplitude signals (in general, less than 5 mV p-p) or small amplitude details on larger
signals.
5.
Horizontal Controls
A.
Sweep-Speed Selection
The unmagnified sweep (MODE set to X1) is the horizontal function needed for most
applications. Best measurement accuracy is achieved by setting the SEC/DIV control for the
fastest sweep that will display the interval of interest. The variable control (CAL) should be in
its detent (fully clockwise).
B.
Magnifying Waveform Details
Each of the two magnified modes — ALT or MAG— expands the unmagnified trace. When ALT
is chosen, both the unmagnified and the magnified waveforms appear together on the crt
screen. Vertical separation between them is adjusted with the TRACE SEP control. If MAG is
selected, only the magnified trace is displayed on screen. This is useful for eliminating
unwanted clutter from the crt when you are making accurate timing measurements or looking
at waveform details. Whenever ALT or MAG is set on the upper HORIZONTAL MODE switch,
the amount of waveform expansion is determined by the setting of the HORIZONTAL MAG
switch located beneath the SEC/DIV control. Three magnifications are available— 5X, 10X,
and 50X. Having the ability to select various combinations of waveform expansion and
SEC/DIV control setting lets you extend the time-base range out to a maximum of 5 ns per
division..
The marker that links the timing of the unmagnified and magnified traces with each other is
the center vertical graticule line. The intersections of that line with the unmagnified and the
magnified waveforms are the points of equal time duration from sweep start. With the center
vertical graticule as the reference line, the investigation of waveform details around any point
on the unmagnified trace, as well as the measurement of time with greater accuracy, then
become easy tasks.
6.
Trigger Controls
For most signals, the trigger-control settings that will yield hands off triggering are:
MODE
HOLDOFF
SOURCE
COUPLING
A.
P-P AUTO
MIN
VERT MODE
DC
Which Mode to Use
P-P AUTO/TV LINE — With this mode set, the range of the LEVEL control is confined to the
values between the triggering-signal peaks. For example, selecting P-P AUTO and rotating
the LEVEL control to the center half of its range establishes a trigger point that is about
midway between the peaks of the triggering signal.
In this mode, the absence of a triggering signal causes the sweep to free-run. And with
signals below 20 Hz, the P-P AUTO circuit may not find the correct level.
Whenever P-P AUTO is active and VERT MODE source selected, the triggering signal is
supplied by the channel that is being displayed— or by Channel 1 in a two-channel display.
The P-P AUTO mode is effective for monitoring logic signals and television lines having at
least a 20-Hz repetition rate. Selecting P-P AUTO at the instrument front panel also sets the
TV LINE triggering mode.
NORM — This mode produces a sweep only when the triggering signal meets the criteria set
by the LEVEL and SLOPE controls. With NORM mode selected, range of the LEVEL control
is sufficient to set any voltage threshold that can be displayed by the instrument. In the
absence of a triggering signal, there is no sweep.
Use the NORM mode for viewing infrequent events and erratic signals.
SGL SWP — When this mode is selected, the sweep is triggered only once. Press the RESET
button once to arm the trigger circuit and illuminate the READY indicator. When a trigger
event occurs, the sweep runs once and the READY light extinguishes.
Use the SGL SWP mode to display or photograph non-repetitive or unstable signals.
TV FIELD— This mode triggers the sweep at the beginning of a television field. To change the
TV field being displayed, you must interrupt the trigger signal by setting the input coupling
switch momentarily to GND then back to either DC or AC until the desired field is displayed.
To display Field 1 and Field 2 at the same time, connect the same television signal to both the
CH 1 and CH 2 inputs; set VERTICAL MODE to BOTH and ALT; set the SEC/DIV control to
0.5 ms or faster sweep speed.
If you magnify the vertical display beyond the graticule, the trigger may be degraded. To avoid
trigger overload, use either CH 1 or CH 2 for display and use the EXT INPUT channel with an
appropriate video signal as the trigger source. A composite sync signal can be used for the
trigger source as well as composite video.
B.
Source
Choose a single trigger source to correctly display the timing relationships between two
channels. Choose the channel with the lowest -frequency signal to avoid ambiguous displays.
With VERT MODE TRIGGER SOURCE and either P-P AUTO TRIGGER MODE or CHOP
VERTICAL MODE, the triggering signal is the algebraic sum of the Channel 1 and Channel 2
input signals.
Use a composite trigger source only to compare asynchronous signals. To generate a
composite trigger: select VERT MODE TRIGGER SOURCE, BOTH-ALT VERTICAL MODE,
and any TRIGGER MODE except P-P AUTO.
C.
Coupling
For signals with strongly interfering components, HF Reject and LF Reject coupling give
added selectivity. When AC coupling is selected, triggering continues as the dc level of the
signal changes.
D.
Slope
Use the SLOPE control to select either the rising (/ ) or the falling (\) edge of the signal to
trigger the sweep.
E.
Level
The LEVEL control gives you complete freedom to choose the most appropriate threshold
voltage on a signal to initiate sweeps whenever any trigger mode except P-P AUTO is
selected.
F.
Holdoff
With irregular signals such as bursts, the HOLDOFF setting can improve display stability.
Also, if the signal has a fixed pattern of variation from cycle to cycle, some modes of the
signal may be omitted from the display. Changing the HOLDOFF setting can force the
instrument to display all the modes of the signal. Normally, the HOLDOFF control should be
set at MIN.
7.
Calibration Summary
Calibrate the voltage (vertical) and time (horizontal) scales of the scope as follows:
1)
Connect a wire from the PROBE ADJUST to CH1 or CH2.
2)
Adjust the trace using the position controls until the square wave is located at a convenient
position on the screen.
3)
Measure the height of the square wave in volts. You should find that it is 0.5 Volts peak-to peak so that the 0.1 V/div scale is appropriate. Make certain that the Variable (CAL) knob is in
its calibrated (detent) position. If the square wave does not measure 0.5 V ask your TA for
help.
4)
Measure the period of the square wave in seconds. Use a time scale setting that displays
several cycles of the square wave. In order to obtain the best accuracy, measure the time for
several cycles and divide by the number of cycles. Again make certain that the Variable (Cal)
knob for the horizontal sweep (SEC/DIV) is in the calibrated (detent) position. The period
should be 10 -3 seconds.
Section V: Goldstar FG-2002C Function Generator
1. Summary of Controls, Connectors and Indicators
No.
Function
Usage
1
2
DISPLAY
COUNTER INPUT SWITCH
3
4
RANGE SWITCHES
FUNCTION SWITCHES
5
6
7
ATTENUATOR
OUTPUT IMPEDANCE
OVERFLOW INDICATOR
8
9
10
11, 12
FREQUENCY DIAL
GATE TIME INDICATOR
MULTIPLIER INDICATOR
NA
DISPLAYS INTERNAL OR EXTERNAL FREQUENCY.
PUSH IN : EXTERNAL FREQUENCY COUNTER.
PUSHOUT: INTERNAL FUNCTION GENERATOR
FREQUENCY COUNTER.
FREQUENCY RANGE SELECTOR.
SELECTS SINE, TRIANGLE OR SQUARE WAVE
OUTPUT.
CHANGES OUTPUT LEVEL BY-20dB
50 Ω,600 Ω
WHEN THE LIGHT ON, INCREASE THE FREQUENCY
RANGE.
COUNTER CANNOT DISPLAY FROM .02Hz to 2Hz
X10, X100:1SEC X1K, X10K, X100K, X1M:.5SEC
UNIT OF FREQUENCY
MANUFACTURER’
S ILLUSTRATOR COULDN’
T COUNT.
13
14
15
16
EXTERNAL INPUT
SWEEP RATE
SWEEP WIDTH
VCF INPUT
17
SYMMETRY CONTROL
18
19
20
21
TTL/CMOS CONTROL
TTL/CMOS OUTPUT
DC OFFSET CONTROL
OUTPUT
No.
Function
Usage
22
23
24
20
AMPLITUDE CONTROL
TILT STAND
POWER SWITCH
DC OFFSET CONTROL
ADJUST OUTPUT LEVEL.
PULL SIDES OUT TO ADJUST.
CONTROL MAIN UNIT POWER.
ADJUST DC LEVEL OF OUTPUT SIGNAL.
INPUT SIGNAL TO USE EXTERNAL COUNTER MODE.
ADJUST REPEAT RATE OF SWEEP.
ADJUST RANGE OF SWEEP.
VOLTAGE CONTROLLED FREQUENCY CONTROL.
SWEEP RATE SHOULD BE OFF WHEN IN USE.
ADJUST SYMMETRY OF OUTPUT WAVE FROM 1:1 TO
4:1 WITH SWITCH PULLED OUT.
PUSH: TTL; PULL:CMOS LEVEL OUTPUTS.
OUTPUT SIGNAL FROM CONTROL CONFIGURATION.
ADJUST DC LEVEL OF OUTPUT SIGNAL.
OUTPUT SIGNAL FROM GENERATOR
CONFIGURATION.
2.
Settings Summary
POWER
ON
SWEEP RATE
OFF (CCW)
SYMMETRY
OFF (push)
DC OFFSET
OFF (push)
ATTENUATOR
RELEASE (button out)
COUNTER INPUT
INT (button out)
IMPEDANCE
50 Ω (button out)
RANGE
any ONE button in
FUNCTION
any ONE button in
AMPLITUDE
midrange
NOTE: RANGE, FUNCTION and COUNTER INPUT must be set for proper operation!